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On the Cover: 3D Coaxially Printing rGO Aerogel-Based Biocompatible Fiber for Peripheral Nerve Regeneration

In this study, we developed a hollow aerogel fiber out of reduced graphene oxide (rGO), with a hierarchically ordered microstructure through a three-dimensional coaxial printing methodology, that enabled a physicochemically cooperative construction process at multiscale.

Jul. 03, 2024Journal Slide
On the Cover: Pressure Regulated Printing of Semiliquid Metal on Electrospinning Film Enables Breathable and Waterproof Wearable Electronics

Application of liquid metals and electrospun nanofibers offer a promising solution to insufficient resilience and human comfort of wearable electronics. However, a sustainable manufacturing process is hindered by the low surface tension of liquid metal, and its poor attachment to the surface of the fabric. This research reveals that tuning the pressure can control the adhesion of semiliquid metal (SLM) on substrates with varying roughness to achieve selective adhesion. Furthermore, a simple and rapid (30 s) fabrication method based on selective adhesion and low mobility of SLM is presented for preparing a multilayered monitoring device capable of measuring human body temperature and ECG signals for 24 h. This device exhibits excellent air permeability of 311.1 g·m−2·h−1, water resistance (washing for 120 min). Our novel approach can inspire the development of methods for printing liquid metal circuits on roughness substrates and enable the practical use of waterproof and breathable wearable electronic devices in the future.

Jul. 03, 2024Journal Slide
On the Cover: A Review of Multifunctional Nanocomposite Fibers: Design, Preparation and Applications

Nanocomposite fibers are fibrous materials with specific properties and functionalities, which are prepared by introducing nanomaterials or nanostructures in the fibers. Polymeric nanocomposite fibers exhibit multiple functionalities, showing great application potential in healthcare, aerospace, mechanical engineering, and energy storage. Here, six functionalities of polymer nanocomposite fibers are reviewed: mechanical reinforcement, resistance to electromagnetic interference and flame, thermal and electrical conduction, generation of far-infrared ray, negative ion and electricity, energy storage, and sensing. For each functionality, the fiber component selection and preparation methods are summarized. The commonly used polymers comprise natural and synthetic polymers, and typical nanomaterials include carbon-based, polymer-based, metal-based, and metal oxide-based ones. Various compounding strategies and spinning approaches, such as wet-spinning, melt-spinning, and electrospinning, are introduced. Moreover, the functional properties of fibers fabricated from different constituents and by different strategies are compared, providing a reference for performance optimization. Finally, the prospective directions of research and application are discussed, and possible approaches are suggested to facilitate the development of advanced nanocomposite fibers.

Jul. 03, 2024Journal Slide
High Efficiency of Exciton-Polariton Lasing in a 2D Multilayer Structure

AbstractHigh Resolution ImageDownload MS PowerPoint SlideWe have placed a van der Waals homostructure, formed by stacking three two-dimensional layers of WS2 separated by insulating hBN, similar to a multiple-quantum well structure, inside a microcavity, which facilitates the formation of quasiparticles known as exciton-polaritons. The polaritons are a combination of light and matter, allowing laser emission to be enhanced by nonlinear scattering, as seen in prior polariton lasers. In the experiments reported here, we have observed laser emission with an ultralow threshold. The threshold was approximately 59 nW/μm2, with a lasing efficiency of 3.82%. These findings suggest a potential for efficient laser operations using such homostructures.IntroductionNanolasers that employ two-dimensional (2D) materials, particularly transition metal dichalcogenides (TMDs), are gaining significant interest in the field of photonic and optoelectronic devices. (1−4) The inherent properties of 2D TMDs, namely, direct bandgaps and large exciton binding energies, make them ideal for diverse optical applications. (5)Here, we report a polariton laser using multiple TMD monolayers, with an ultralow lasing threshold and a high efficiency, allowing light emission visible to the naked eye. Exciton-polaritons emerge from the interplay between photons and excitons in semiconductors, (6) with unique benefits. (7) Lasing based on exciton-polaritons can be viewed as a type of Bose–Einstein condensation, a phenomenon that can occur even in the upper branch of the polariton spectrum. (8) As discussed in previous works, (9,10) the nonlinear properties of polariton lasers lead to the enhancement of carrier scattering into lasing states. This gives rise to the possibility of achieving a significantly lower lasing threshold. The compact nature of these polariton lasers, combined with their short lifetime, could also potentially lead to faster response times. (11) Polariton lasers can be crafted from a variety of substances, such as CdTe, GaAs, ZnO, organics, perovskites, and metallic plasmons. (12−18) However, TMD semiconductors stand out for their strong light–matter interaction (19) and ease of integration into small-scale photonic systems. (20,21) TMDs have been used with high optical gain (22) and tunability (23−26) in compact lasing applications and in a range of optoelectronic devices such as photodetectors, LEDs, and solar cells. (27−29)Laser efficiency is pivotal as it significantly influences the device’s usability, economic feasibility, and application breadth. A recent study claimed an ultralow polariton condensation threshold for exciton-polariton lasers, (30) although a definite measurement of the lasing threshold and the lasing efficiency was not reported. In the work reported here, we have been able to directly measure an ultralow threshold and the lasing efficiency of a multilayer TMD structure. This laser utilizes three monolayers of WS2 as the gain medium. Between each monolayer, there is a thin-film layer of hBN that is approximately 6 nm thick. This set of layers is effectively the same as a multiple-quantum well (MQW) structure and is encapsulated within top and bottom hBN spacer layers and embedded in a microcavity. The benefits of multiple gain layers have been well established in studies with III–V semiconductor structures since 1995. (31) Increasing the number of gain layers N will both increase the oscillator strength, proportional to N, and raise the saturation density, which linearly scales with N. (9,32) In addition, the increase in the oscillator strength of 2D materials with an increasing number of layers has been measured experimentally. (33)Our structure has a vertical-cavity surface-emitting laser (VCSEL) geometry, which allows for easy access to the light emission and can eventually lead to the ability to control gain properties through external means such as electrostatic gating and current injection for electrically pumped operation. The laser operates in the visible regime and achieves continuous-wave single-mode operation, exhibiting an impressively bright emission with a modest optical pumping threshold of 59 nW/μm2 at 4 K, similar to quantum-dot lasers. (34) At higher temperatures (around 200 K), the laser becomes multimode.Device Design, Fabrication, and Characterization As shown in Figure 1a, the complete sample structure includes a bottom mirror made from a distributed Bragg reflector (DBR) consisting of 12 layers of SiO2/SiNx, which was fabricated by using the plasma-enhanced chemical vapor deposition (PECVD) method, plus a 66 nm SiO2 spacer layer. On this base, a superlattice of seven layers of WS2/hBN was transferred using a top-down dry transfer technique. (35) This distinctive homostructure contains three layers of monolayer WS2 and four 6 nm hBN spacer layers; the extra layers amplify the oscillator strength of the exciton coupling to the cavity photon mode.Figure 1Figure 1. (a) Illustration of the device. (b) Optical microscope image of the homostructure sample inside the cavity. The dashed lines circle each monolayer WS2, and the red area is the area of overlap of the three monolayers of WS2.High Resolution ImageDownload MS PowerPoint SlideFollowing this, a layer of poly(methyl methacrylate) (PMMA) with a thickness of 67 nm was evenly spin-coated onto the homostructure. This intermediate layer serves to align the cavity modes near the exciton energy with a designed cavity Q of 485. The microscopic image depicted in Figure 1b shows the monolayer WS2 and the overlapping area of the three WS2 layers, which is approximately 8 × 12 μm2 in size. The fabrication process was concluded by placing a 10-pair distributed Bragg reflector on top using plasma-enhanced chemical vapor deposition (PECVD). This method is commonly used in many similar studies, and PMMA will protect the monolayer from degradation. (30,36,37)We excited the sample by utilizing a 532 nm continuous diode laser with a laser spot radius of about 1.5 μm. We made measurements for the real-space photoluminescence (PL) within a monolayer domain, as depicted in Figure 2a, which presents typical PL for monolayer WS2 post-transfer on the bottom DBR. By applying a double Lorentzian fit analysis to the spectrum, we were able to ascertain the energies of the exciton and the trion to be approximately 2.0 and 1.94 eV, respectively, consistent with the findings from our earlier studies. We then performed Fourier-plane spectroscopy, which gives the in-plane momentum dependence. The angle of emission directly corresponds to the in-plane momentum (k∥) via the equation k∥=(ω/c) (sin θ), where c is the speed of light. Multiple cavity modes were observed in both the simulation and the PL spectrum of the bare cavity (Figure 2b). Although the PL in the bare cavity is very weak, it is nonzero due to emission from impurity states in the medium. The modes in the observed spectral range correspond to 2.02 and 1.83 eV at k∥ = 0.Figure 2Figure 2. (a) Typical low-temperature PL of WS2 from a monolayer region. (b) Left panel: angle-resolved PL spectrum of the bare cavity. The dashed line is the fitted energies of the uncoupled second cavity mode. Right panel: simulated reflectivity spectrum using the transfer matrix method. (c) Left panel: angle-resolved PL for the three-layer homostructure at a pump power below the threshold (19 nW/μm2). Right panel: simulated reflectivity spectrum using the transfer matrix method. (d) Integrated PL spectrum corresponding to the gray area in Figure 2c, fit to two Lorentzian peaks. The splitting deduced from the fits is 18 ± 10 meV. All measurements were performed at 4 K.High Resolution ImageDownload MS PowerPoint SlideWhen we moved the pump laser to the overlapping area of the three-layered WS2 region inside the cavity, we identified an anticrossing-like feature. From the data of Figure 2c,d, a splitting of 18 ± 10 meV is observable. Since the splitting is not large compared to the line width, the coupling is not technically in the strong coupling limit. This phenomenon of weakly coupled polaritons was observed extensively within the overlap area of the three WS2 layers. To further confirm this, we calculated the coupled harmonic oscillator model for the mixing of the bare cavity and exciton states. (38) The dashed white lines in the right panels of Figure 2b,c give the uncoupled cavity and exciton lines for the coupling used in the simulation. The gray area in Figure 2c includes the anticrossing regime. The spatial PL spectrum shown in Figure 2d results from the intensity integration over the gray area depicted in Figure 2c. Using the experimentally measured line widths for the exciton (?Γex = 30 meV), the cavity photon (?Γcav = 16 meV), and the Rabi splitting (?ΩRabi = 18 meV), we can deduce the light–matter interaction potential via ?ΩRabi=2??2−1/4[(?Γex−?Γcav]2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√?ΩRabi=2g2−1/4[(?Γex−?Γcav]2. The calculated value of g is about 11.4 meV at the point of anticrossing, which is consistent with the PL and reflectivity spectra. This results in g ? |?Γex + ?Γcav|/2, which puts them in a weakly coupled polariton regime.Exciton-Polariton LasingARTICLE SECTIONSJump ToAbstractIntroductionDevice Design, Fabrication, and CharacterizationExciton-Polariton LasingConclusionsSupporting InformationAuthor InformationReferencesCited ByAn exceptionally bright emission becomes evident when the homostructure is excited by an adequately powerful pump, as depicted in Figure 3a. The laser signal was filtered out by using a long-pass filter. The emission from the homostructure was visible with the unaided eye.Figure 3Figure 3. (a) Real-space image of the emission from the homostructure area (highlighted in the red region). The laser spot size was approximately 1 μm in radius. (b) Typical interferogram for the real-space PL spectra from the homostructure area, taken at a pump power of 1.5 Pth, above the lasing threshold. (c,d) Angle-resolved PL of the exciton-polariton laser measured at bath temperatures of 4 and 200 K, respectively (the effective temperature of the low temperature data may be higher than that of the bath due to inefficient cooling).High Resolution ImageDownload MS PowerPoint SlideTo ascertain the characteristics of this emitted light, we measured the coherence using a Michelson interferometer. This setup included using a right-angle prism and a retro-mirror to flip one of the incoming images along one axis relative to the other, aligning it with the spectrometer’s slit direction, defined as the x-axis. Figure 3b shows a characteristic interferogram captured under threshold conditions without any temporal delay between the two beams. The interference is discernible across the beam’s dimension, ranging from −2.5 to 2.5 μm.Switching a lens allowed us to convert real-space imaging into k-space photoluminescence imaging. The k-space PL spectrum revealed a peak emission at 615 nm, at an angle of −30° where the exciton and the second photon cavity mode intersect. As the particle density was ramped up, polaritons reached a steady state, forming a nonequilibrium Bose–Einstein condensate (BEC) in the crossing region of the photon and the exciton, as shown in Figure 3c. The interference pattern displayed in Figure 3b shows the coherence of this nonequilibrium BEC state, consistent with the well-known property of polariton condensates of emitting coherent light. (39)Further examination of the k-space PL data revealed that the pronounced bright spot was displaced from the k∥ = 0 axis. This displacement is likely because the strongest light–matter coupling is at that point; that is, the exciton and photon energies are resonant there. Polaritons that decrease in energy will have a much less excitonic nature and, therefore, less gain due to particle interactions. This is a type of polariton bottleneck effect in which the polaritons cannot thermalize into lower energy states as they descend along the lower polariton branch (LPB). As the polaritons descend along their dispersion curve, this diminishes exciton–phonon scattering efficiency, as detailed in ref (40). Additionally, an asymmetric lasing mode was observed in the momentum space. The disparity in emission angles suggests the existence of competing lasing modes, likely due to two laser transitions engaging in competition mediated by an optical phonon transition. (41) The laser maintains functionality at temperatures as high as 200 K, as shown in Figure 3d. However, at this elevated temperature, the laser’s performance substantially degrades, devolving into a multimode emission.We measured the power dependence of the light output as we varied the pump power level. The absolute light output of the polariton laser was calibrated by first sending a laser source with known power through our optical system to measure the count rate per photon of the CCD (charge-coupled device) camera. This allowed us to convert the intensity measurements captured by the CCD camera into photon counts per second.Below the threshold for lasing, there is a direct linear relationship between the photon output and the pump power. Once the threshold power of 59 nW/μm2 is exceeded, there was a jump in the photon output, as shown in Figure 4a. Additionally, the PL line width narrowed at the same threshold power, as indicated in Figure 4b. Higher pumping of the sample revealed a return to a linear correlation between the photon count and the pump power. Continuing to increase the pump power led to the line width broadening again, which can be understood as a consequence of increased interactions among the particles. (42)Figure 4Figure 4. (a) Variation of photoluminescence (PL) photon emission with pump power. The two dashed lines show a linear relationship, and the red arrow denotes the Pth. (b) Relationship between polariton laser line width and pump power. (c) Efficiency of the polariton laser as a function of pump power. (d) Coherence time of the laser compared to the pump power. The dashed lines in (b–d) are guides to the eye. All measurements were performed with a bath temperature of 4 K.High Resolution ImageDownload MS PowerPoint SlideFigure 4c depicts the efficiency of emitted light, which is measured to be around 3.82% immediately beyond the pump threshold, and this efficiency level remains consistent thereafter. This efficiency is calculated as the total photon output per second measured by the CCD camera divided by the total photon input per second from the pump laser, having corrected for the reflectivity of the top mirror and accounting for unobserved transmission output through the bottom mirror, knowing its transmission at the emission wavelength (for more details about the calculation, refer to the Supporting Information). The lasing threshold of our structure is considerably lower than that of quantum-dot lasers, which usually exhibit a minimum threshold of approximately 500 nW/μm2, (43,44) and comparable to that of other polariton lasers, as discussed in the Introduction. A fit to the standard laser equation is given in the Supporting Information.To study the temporal coherence characteristic of polariton lasing, we varied the length of one of the arms of the Michelson interferometer and determined the coherence time as a function of the pump power. The experimental visibility data is quantified as the ratio between the difference in the intensity of the maximum and the minimum to their sum, formulated as (Imax – Imin)/(Imax + Imin). For each pump power, we fitted the collected visibility data with a Gaussian function to ascertain the coherence time. Figure 4d shows the coherence time versus pump power (note that the horizontal axis for power is a smaller range than in the other data of Figure 4). We observed that the coherence time increased from 100 to 211 fs when the pump power exceeded the lasing threshold.ConclusionsARTICLE SECTIONSJump ToAbstractIntroductionDevice Design, Fabrication, and CharacterizationExciton-Polariton LasingConclusionsSupporting InformationAuthor InformationReferencesCited ByAll of the power-dependent measurements are consistent with the interpretation that we have observed lasing with a pronounced emission at 615 nm. The power series analysis indicates that the lasing threshold was 59 nW/μm2 injected pump power (uncorrected for reflection from the top mirror), which corresponds to an injected carrier density of the order of 108 cm–2, assuming a cavity lifetime of 5 ps, based on the Q of the cavity and the cavity mode spacing. Remarkably, even with its extremely low threshold, the system maintained a high efficiency level, reaching around 3.82% of injected electron–hole pairs turning into photons in the laser output. The polariton effect is seen to be playing a role in that the emission occurs in the region of exciton-photon resonance, where the polariton effect is strongest. The lasing action maintains its intensity even at raised temperatures. However, at high temperatures, it becomes multimode. Despite this, the prospects are good for realizing a room-temperature, micrometer-sized, ultralow threshold and efficient lasing using two-dimensional materials.

Jun. 27, 2024Journal
A Low-Loss Hollow-Core Waveguide Bundle for Terahertz Imaging under a Cryogenic Environment

AbstractHigh Resolution ImageDownload MS PowerPoint SlideOptical fiber bundles have been widely used in microendoscopic biomedical imaging, Raman microscopy, and depth-resolved imaging due to their flexibility, long-distance transmission, and high spatial resolution. However, there are few reports on fiber bundles in the terahertz (THz) band, which significantly limits the applications in the biomedical field and nondestructive imaging. Although sapphire dielectric fiber-based bundles have shown promising applications in THz imaging, it is difficult to achieve long-distance and high-quality imaging due to the high absorption coefficient and uneven arrangements of fibers. Here, we propose a copper hollow-core waveguide bundle with a hexagonal arrangement, which is fabricated by a low-cost extrusion and stacking method. Simulation results demonstrate that transmission loss of the TE11 mode increases with the decrease of the inner radius of metallic waveguides, which is consistent with the experimental results. Moreover, under liquid nitrogen conditions, the metallic waveguide bundle exhibits higher output power under different biasing currents of THz quantum cascade lasers (QCLs). The effect of the inner radius of the waveguide on the bundle&rsquo;s spatial resolution has been thoroughly analyzed theoretically and experimentally with a maximum spatial resolution of &sim;400 &mu;m, indicating the accuracy of fabrication. In addition, different square tablets with four different mixed ratios of polytetrafluoroethylene powders and silver nanoparticles are well distinguished by the THz waveguide bundle-based transmission images. Moreover, the imaging performance of the THz waveguide bundle is simulated and such a bundle with a length of 6 cm is employed to experimentally demonstrate the remarkable terahertz imaging capabilities. The THz waveguide bundle in this work is well integrated with QCLs to enable long-distance submillimeter near-field terahertz imaging, especially in applications with cryogenic environments.1. Introduction Terahertz (THz) waves (0.1&ndash;10 THz) have stronger penetration compared to visible and infrared radiation, which have attracted widespread attention in various imaging applications ranging from industrial inspections to medical diagnosis. (1&minus;4) According to the operating mode of the THz source, THz imaging can be divided into continuous-wave imaging and pulsed imaging. The THz pulsed imaging (TPI) system is able to distinguish normal and diseased tissues, as well as the content and state of tissue water by analyzing the difference of absorption spectra and specific principal component information on frequency-domain signals. (5) Moreover, the TPI system provides a higher signal-to-noise ratio and dynamic ranges for measured samples due to a higher average power and insensitivity to the thermal background (6) while the continuous-wave THz imaging system is more simple and compact without any extra pump-and-probe elements, (7) which provides a favorable compromise between the sensitivity, acquisition rate, and cost efficiency for the development of THz imaging systems in biomedical applications. However, most THz imaging systems are bulky and complex since such a system relies on free-space transmission. Water vapor and other gas molecules could also lead to serious absorption during the transmission process of THz radiation. Therefore, research on an effective transmission medium is critically important for the development of THz imaging systems.The THz waveguide or fiber is an effective method to guide and deliver THz waves, which shows significant values in applications such as endoscopy and subwavelength resolution imaging. (8,9) Among all of the waveguide structures, hollow-core waveguides have proved to be significantly functional in imaging applications. For example, Lu et al. proposed a fiber-scanning THz imaging system based on a subwavelength plastic fiber. (10) Chiu et al. demonstrated an all-THz fiber-scanning near-field imaging system under room temperature with a 210 &mu;m spatial resolution. (11) You and Lu designed a continuous-wave THz imaging system by using an antiresonant reflecting Teflon pipe. (12) 3D printing technology has been widely applied in fabrication of THz waveguides since it could greatly improve the freedom of designing various waveguide structures according to different transmission mechanisms with low cost. (13) Liu et al. fabricated the Kagome THz waveguide by 3D-printed technology, which is low-cost and simple and achieves confocal transmission and reflection imaging. (14,15) Kucheryavenko et al. proposed an antiresonant hollow-core waveguide coupled with a sapphire solid immersion lens to achieve a resolution of &sim;0.2 &lambda; at the wavelength of 500 &mu;m. (16) However, antiresonant optical waveguides suffer from large cross-section dimensions, which limit their capabilities in a narrow and complex space. (17) In addition to the antiresonant reflecting mechanism, total internal reflection (TIR)-based waveguides have also been applied in THz imaging. The structures generally consist of a substrate tube and a highly reflective metallic coating layer, which exhibits low-loss transmission, single mode, excellent flexibility, (18) and temperature tolerance. (19) Yu et al. fabricated a hollow-core waveguide by 3D printing and metal-cladding technology, building a 0.1 THz confocal waveguide imaging system with &sim;0.5 &lambda; resolution. (20) To reduce imaging time, Wang et al. demonstrated a confocal hollow-core waveguide scanning method for THz reflective super-resolution and high-speed imaging based on the slider crank at 0.1 THz. (21) To further increase resolution, Li et al. fabricated a hollow-core meta-waveguide by the 3D printing method and presented a lens-free THz scanning imaging system at 0.1 THz with a resolution of 1/3 &lambda;. (22) He et al. proposed a gradually tapered waveguide, which realizes low-loss transmission and imaging under bent and unbent conditions at 0.3 THz. (23) Subsequently, they further designed a hollow elliptical core waveguide to achieve maintained-polarization, low-loss transmission, and imaging capability at 0.1 THz, which could improve the contrast of imaging. (24) To increase the reflectivity and reduce loss, Liu et al. fabricated ABS/Ag-coated hollow waveguides and established a far-field confocal waveguide-based THz imaging system with a resolution of 1.12 mm at 0.1 THz. (25)Furthermore, THz waveguides are able to serve as probes in near-field super-resolution imaging. Kaurav et al. proposed a sub-THz-based waveguide iris probe for detecting tumor margins intraoperatively during lumpectomies with a frequency range of 0.11&ndash;0.17 THz. (26) Liu et al. proposed a stainless steel-based THz waveguide consisting of two halves of a conically tapered structure with a variable gap, which could achieve near-field imaging capabilities without cutoff using a broadband THz wave. (27) Lu and Argyros designed a flexible tube-lattice fiber as a probe and combined it with THz time-domain spectroscopy to demonstrate THz hyperspectral imaging with a resolution of &lambda;/0.75. (28) Liu et al. built a broadband low-loss near-field THz imaging system based on a tapered parallel-plate waveguide with a resolution of &sim;100 &mu;m. (29) Mitrofanov et al. demonstrated an HE11 mode as dominated linearly polarized mode transmitting in the dielectric-lined cylindrical metallic THz waveguide based on THz near-field microscopy. (30)In order to solve the time consumption problem for the fiber-based scanning imaging, Choi et al. proposed a single multimode fiber to realize scanner-free and wide-field imaging due to the possibility of direct image transmission via multiple spatial modes, which shows a potential application in endoscopy including medicine and industry. (31) Stellinga et al. demonstrated a near-video-rate 3D imaging based on multimode fibers by measuring the round-trip flight time of laser pulses, (32) whereas the measurement of the transmission matrix is a great challenge for a single multimode fibers, which requires precise optics, such as spatial light modulators, and image reconstruction is sensitive to the environmental variations and mechanical strains. Therefore, long distance, high resolution, and environmentally robust THz real-time imaging is crucial for biomedical imaging and nondestructive testing.The imaging technology based on fiber bundles has been widely applied in the visible and infrared spectral range, which involves one-photon confocal microscopy, multiphoton microscopy, and optical coherence tomography. (33,34) Research of the fiber bundle in the THz band is rarely explored due to the high THz absorption and complex fabrication technology. Yokota et al. designed a new THz fiber structure based on polymer tube bundles and simulated transmission loss and mode field distributions. (35) Recently, Skorobogatiy et al. fabricated high-refractive-index sapphire optical fiber bundles by the edge-defined film-fed growth technique to realize a subwavelength resolution at 0.5 THz. (36,37) However, the materials of dielectric waveguides, such as sapphire and polymer, have a strong absorption of THz wave, leading to the increase of transmission loss. Moreover, the guided mode of dielectric waveguide is generally dominated by HE11, which can lead to serious crosstalk issues in fiber bundle. (8)In addition to the dielectric fiber bundle, a wire medium has been widely applied in the super-resolution THz imaging due to the extreme optical anisotropy and strong spatial dispersion. (38,39) Evanescent waves in free space can be transformed into TEM wave transmission in the wire medium, enabling a given field distribution to be transmitted through such structure with a minimal loss of resolution. It is a significant group of uniaxial metamaterials, usually consisting of subwavelength periodic arrays of metal wires embedded within a dielectric host. (40) Awad et al. explored the potential applications of tapered Sommerfeld wire waveguides for THz near-field imaging. (41) Belov et al. proposed an original regime of near-field image transportation by using capacitively loaded wire media and experimentally fabricated a lens consisting of parallel conducting wires to achieve transmission images with a subwavelength of 1/15 &lambda;. (42,43) Subsequently, further theoretical work reveals that subwavelength transmission images can be achieved by controlling the lattice constant of the wire medium. (44) Furthermore, the super-resolution imaging capability of the wire medium slab was experimentally validated by illuminating a broadband light source. (45) At the wavelength range of infrared to THz band, Silveirinha et al. theoretically investigated the performance of an array of metallic nanorods for subwavelength near-field infrared imaging, showing low attenuation and a wide bandwidth. (46) To overcome the challenges on large-scale fabrication of a wire medium, Tuniz et al. proposed a drawn metamaterial composed of polymethyl-methacrylate and indium and investigated the corresponding optical properties in the THz band. (47) Subsequently, they designed wire array metamaterial fibers for near-field THz spectral imaging, which could focus down to 1/28 &lambda;. (48) Habib et al. numerically and experimentally investigated a wire medium prism as an imaging element at the THz band, combined with a filtering technique to achieve ultrabroad band THz imaging. (49) However, high transmission losses, crosstalk rates, and complexity of the fabrication process may limit the application of wire medium metamaterials in THz imaging. Thus, it is important to explore the THz fiber bundles with a simple fabrication process, low-loss transmission, and low interfiber crosstalk.THz quantum cascade lasers (THz QCLs) are the most powerful solid-state semiconductor-based THz sources so far, which are compact and able to cover the lasing frequency ranging from &sim;1 to 5 THz. THz QCLs with various schemes and designs have demonstrated high output power and a collimated beam pattern. (50) Thus, THz QCLs serve as the source of imaging in this work. In this article, we designed hexagonally arranged Cu hollow-core waveguide bundles by low-cost extrusion and stacking methods. The effect of the Cu waveguide inner radius on the transmission loss and spatial resolution of bundles was systematically investigated by numerical and experimental methods, exhibiting a preeminent consistency. For the Cu waveguide bundle with a length of 6 cm, more than three times longer than other dielectric fiber bundle, (36) the maximum experimental spatial resolution is &sim;3.8 &lambda; (&sim;400 &mu;m). In addition, the imaging sensitivity of the Cu waveguide bundle was investigated by a CW THz transmission imaging system for tablets with different mixed ratios of polytetrafluoroethylene (PTFE) and silver nanoparticles (Ag NPs). Lastly, we performed THz imaging of several samples based on the waveguide bundle using numerical and experimental methods, verifying the imaging capability of such a Cu waveguide bundle. To the best of our knowledge, this is the first time submillimeter near-field THz transmission imaging based on Cu waveguide bundles, which will achieve long-distance imaging in low-temperature applications.2. MethodsFabrication of Cu Hollow-Core Waveguide BundlesCopper is an excellent metallic material that has been widely applied for THz applications due to the low loss, preeminent ductility, and high electrical conductivity, which reduces skin depth and ohmic losses. Thus, Cu hollow-core metallic waveguides were prepared as the individual waveguide of bundles, as shown in Figure 1a, which were commercially extruded cylinders with three inner radii of 0.5, 0.35, and 0.25 mm, respectively. The wall thickness and length of the waveguide are 0.15 mm and 6 cm, respectively. Notably, THz radiation can travel through the individual waveguide in the bundle without crosstalk because the wall thickness of the Cu waveguide is much thicker than the skin depth at 2.85 THz, which is the lasing frequency of the THz quantum cascade laser in the imaging system. Then, the Cu waveguides were assembled into a bundle inside a 3D-printed polymer tube. Instead of a square array, Cu hollow-core metallic waveguide bundles were designed with hexagonal arrangement due to a higher limiting resolution. (51)Figure 1Figure 1. (a) Schematic of the Cu hollow-core THz waveguide bundle. There are three different inner radii in the designed waveguide bundle, which are 0.5 0.35, and 0.25 mm, respectively. (b) A continuous-wave THz imaging setup based on Cu hollow-core waveguide bundle and THz QCLs.High Resolution ImageDownload MS PowerPoint Slide Numerical SimulationsIn order to analyze the transmission loss and dispersion coefficient of the waveguide with different modes, COMSOL Multiphysics was performed to simulate the two-dimensional (2D) geometry along the cross section of the Cu hollow-core waveguide. The inner radii of the Cu waveguide are 0.5, 0.35, and 0.25 mm, respectively, and the wall thickness is 0.15 mm, which are the same as the experimental parameters. The refractive index of copper was calculated by the Drude model. The complex dielectric function can be defined as follows (52):??=??c+????i=(??+????)2&epsilon;=&epsilon;c+i&epsilon;i=(n+ik)2(1)According to Drude model:??=??&infin;&minus;??2p??2+????????&epsilon;=&epsilon;&infin;&minus;&omega;p2&omega;2+i&omega;&omega;&tau;(2)where &omega;p represents the plasma frequency of Cu, corresponding to &sim;6.38 &times; 104 cm&ndash;1, &omega;&tau; represents the damping frequency of Cu, corresponding to &sim;2.78 &times; 102 cm&ndash;1, &omega; represents the angular frequency (&omega; = 2&pi;f), and &epsilon;&infin; represents the high-frequency dielectric constant. &epsilon;c and &epsilon;i represent the real and imaginary parts of complex dielectric function, respectively, and &epsilon;&infin; is much less than &epsilon;c or &epsilon;i. (53) Thus, &epsilon;c and &epsilon;i can be described as follows:??c=&minus;??2p??2+??2??&epsilon;c=&minus;&omega;p2&omega;2+&omega;&tau;2(3)??i=??2p??????3+????2??&epsilon;i=&omega;p2&omega;&tau;&omega;3+&omega;&omega;&tau;2(4)The thickness of the perfectly matched layer was set as threefold of the inner radius, and a mesh was set as a quarter of operating wavelength. To analyze the near-field imaging capability of THz waveguide bundles, a finite-difference time-domain (FDTD) method (Lumerical Solutions) was used to analyze the electric field distribution at the output end (image plane) of the bundles. The inner radius and wall thickness of the waveguide are 0.35 and 0.15 mm, respectively. Considering the simulation time and limited computational resources, the length and waveguide number of the bundle were set as 5 mm and 234, respectively. A Gaussian light source is directly radiated toward the sample, and the square of the full width at half-maximum (FWHM) of the beam spot is larger than the targeting patterns area. The distance between the object sample (object plane) and the input end of the bundle is about 100 &mu;m, which is approximately close to the wavelength. The same distance was applied between the monitor and output end of the waveguide bundles. The mesh size of the simulated region is set as 30 &mu;m, and the light source, sample, waveguide bundle, and detector are all centered along the single optical axis. Experimental Characterization of THz Waveguide Bundles and Imaging ExperimentsAs shown in Figure 1b, a THz QCL serves as the continuous-wave source with a 2.85 THz central lasing frequency and the output power is &sim;2 mW, which is not corrected by windows mirror reflection, water absorption, and so on. (54) The THz beam emitted from the QCL is collected by two parabolic mirrors and modulated by a mechanical chopper with a frequency of 20 Hz. Then, the modulated THz beam is collimated by a TPX lens with a 50 mm focal length. The shape of the collimated THz beam is fixed by an aperture, and the fixed THz beam transmits the Cu hollow-core waveguide bundle. Finally, the transmitted THz beam is detected by a Golay cell and the detected signal is demodulated by a phase lock-in amplifier. A Golay cell serves as a detector of modulated THz beam intensity and features the sensitivity of 10&ndash;5 V/W and the time response of 30 ms. The output power of the waveguide bundles with different lengths is recorded to calculate the transmission loss. Imaging based on the Cu THz waveguide bundle was achieved by such continuous-wave THz system. A Golay cell with a &sim; 250 &mu;m-diameter scanning diaphragm was mounted on the 2D motorized moving stage to record the transmitted signal from the output end of the Cu waveguide bundle. The Golay cell is positioned approximately five times wavelengths away from the output end of the waveguide bundle for controlling any potential collisions between the detector and the output end of the waveguide bundle due to mechanical errors caused by the lead screw in the scanning plane.3. Results and Discussion3.1. Theoretical Analysis of the Cu Hollow-Core Waveguide BundleThe mode distribution of the waveguide plays a key role in THz imaging, which could influence the signal-noise-ratio (SNR). (55) For a Cu hollow-core waveguide with a 0.5 mm inner radius, the three theoretical low-order modes at 2.85 THz were calculated by finite element analysis simulations (COMSOL Multiphysics, see Section 2 for details), as shown in the inset of Figure 2a. TE01 shows the lowest transmission loss among the three modes (see Figure 2a), which can be calculated as follows (56):??theory=&minus;20ln(10)Im(??eff)(dB/m)&alpha;theory=&minus;20ln(10)Im(neff)(dB/m)(5)where Im(neff) represents the imaginary part of the effective refractive index. However, the doughnut-shaped TE01 mode is not expected to be the primary mode due to the fact that the QCL is linearly polarized. (57) The TE11 mode has been regarded as a fundamental mode due to a low loss (see Figure 2a) and a high coupling efficient with the linearly polarized source. (23) Moreover, the TE01 mode is easy to couple to the TE11 mode when the waveguide is under a bent or twist condition. In addition, the dispersion characteristics for the three low-order modes in the Cu hollow-core metallic waveguide are also investigated in Figure 2b. The dispersion coefficient D was calculated as follows (58):??=&minus;????d2Re[??eff]d??2(ps/(nm&middot;km))D=&minus;&lambda;cd2Re[neff]d&lambda;2(ps/(nm&middot;km))(6)where Re(neff) represents the real part of the effective refractive index and &lambda; represents the operating wavelength. The numerical results show that the TE11 mode has the smallest dispersion effect among the three low-order modes, corresponding to <0.4 (ps/(nm&middot;km)) from 1 to 4 THz. Thus, the TE11 mode is usually discussed in the hollow-core metallic waveguide. However, there are varying group velocities and phase delays in different modes of hollow-core metallic waveguides, resulting in the dispersion effect. THz photonic crystal fibers with low dispersive propagations are more suitable for broadband pulsed THz radiation. (59) As shown in Figure 2c, the theoretical transmission loss of three Cu waveguides with 0.25, 0.35, and 0.5 mm inner radii, respectively, was analyzed as a function of frequency. The results show that transmission loss of the Cu waveguide increases with the decrease of frequency at the same inner radius. Moreover, transmission loss would decrease with the increase of the inner radius of the waveguide, which is beneficial for a longer distance transmission. (60) However, the inner radius of the Cu waveguide could also influence the spatial resolution of the waveguide bundle. In the absence of crosstalk issues in the waveguide bundle, the resolution &delta; along the X-axis can be defined analytically as &delta; = 2R/&lambda; = 2Rf/c, where R, &lambda;, f, and c refer to the inner radius of the Cu waveguide, operating wavelength, corresponding frequency, and light speed in vacuum, respectively, and the calculated results are shown in Figure 2d. In this work, the estimated resolution &delta; of waveguide bundles at the frequency of 2.85 THz are 4.8 &lambda;, 6.7 &lambda;, and 9.5 &lambda;, respectively, corresponding to the inner radii of 0.25, 0.35, and 0.5 mm for the Cu waveguide. Although the resolution of hollow-core metallic waveguides we proposed is lower than that of high-refractive-index optical fiber bundles, (36) it can be effectively improved by reducing the inner radius of the waveguide and increasing the operating wavelength. Moreover, we particularly focus on the transmission losses of waveguide bundles, aiming to achieve low-loss, long-distance propagation of THz waves and signals. In addition, the theoretical limit resolutions of the waveguide bundle are 0.585 &lambda;, 0.586 &lambda;, and 0.587 &lambda; corresponding to the inner radii of 0.25, 0.35, and 0.5 mm for the Cu waveguide at the cutoff frequency, respectively. To evaluate the imaging quality in the frequency domain, we analyzed the modulation transfer function (MTF) of metallic waveguide bundles with different inner radii of the Cu waveguide, as shown in Figure 2e,f. Considering the relative immobility between the waveguide bundle and the sample, the MTF in the X-axis and Y-axis can be calculated as follows (61):MTF??=[??1(2????????)????????]223[sin??(d????)+12sin??2(d????2)]MTFX=[J1(2&pi;fxR)&pi;fxR]223[sinc(dfx)+12sinc2(dfx2)](7)MTF??=[??1(2????????)????????]2sin??(d????23&oline;&radic;)sin??(3&oline;&radic;d????2)MTFY=[J1(2&pi;fyR)&pi;fyR]2sinc(dfy23)sinc(3dfy2)(8)where J1 is the first-order Bessel function, fX and fY represent the spatial frequencies along the X-axis and Y-axis, respectively, R is the inner radius of the waveguide, and d is the outer diameter of the waveguide (see the insets of Figure 2e,f). The theoretical results show that MTFX and MTFY would decrease when increasing the inner radius of the Cu waveguide. When the MTF decreases to 50% of its maximum value, the spatial frequency of the waveguide bundle along the Y-axis is higher than that along the X-axis due to a larger filling factor for the same inner radius. (51) Figure 2f shows that the spatial frequencies of the waveguide bundle corresponding to the inner radii of 0.25, 0.35, and 0.5 mm for the Cu waveguide are 0.66, 0.50, and 0.36 lp/mm, respectively.Figure 2Figure 2. (a) Theoretical transmission loss spectra for TE01, TE11, and TE21 modes of a Cu hollow-core waveguide from 1 to 4 THz. Insets show the corresponding simulated mode distribution at a frequency of 2.85 THz. (b) Dispersion coefficient of a Cu hollow-core waveguide. (c) Theoretical transmission loss as a function of frequency for different inner radii of waveguides. (d) Analytical estimates of the resolution parameter &delta; with different inner radii of waveguides. (e) Theoretical spatial resolution estimation of a Cu waveguide bundle in the X-axis direction and (f) the Y-axis direction.High Resolution ImageDownload MS PowerPoint SlideBased on the discussion above, a relatively large inner radius will reduce the transmission loss of the waveguide bundle and be greatly beneficial for a long propagation distance. A smaller inner radius waveguide results in a better spatial resolution. Therefore, an optimized waveguide inner radius and filling factor are crucial for long-distance and high-quality THz imaging. 3.2. Experimental Resolution and Transmission Properties of Cu Hollow-Core Waveguide BundlesTo verify the relationship between the inner radius of the Cu waveguide and spatial resolution of the bundle, we utilized metallic objects that lead to abrupt changes in the transmission properties and analyzed point spread function (PSF) of the waveguide bundle. The aluminum (Al) foil directly contacted with the input end of the waveguide bundle to avoid diffraction effects. The corner of a thick (? &lambda;) Al foil was illuminated by a THz QCL lasing at 2.85 THz, and its image was formed on the input end of the waveguide bundle, as shown in Figure 3a&ndash;c. Here, the input end of the waveguide bundle served as the object plane, and the output end of the waveguide bundle served as the image plane. Typical THz images of Al foil corner are clearly shown in Figure 3d&ndash;f. The scanning step is 500 &mu;m. Notably, there are features of distortions in the THz images caused by the variations of the THz radiation transmission over its aperture, as well as by the uneven intensity distribution of the source. (62) Meanwhile, the &sim;500 &mu;m gap between the image plane and the scanning plane of the Golay cell could introduce diffraction effects. In order to estimate the spatial resolution of the THz waveguide bundle along the X-axis and Y-axis accurately, an 8 &times; 8 mm region in the output images of the bundle (see the white dashed box in Figure 3d&ndash;f) was selected to conduct digital intensity sampling along the horizontal and vertical edges of the metallic corner, which could be fitted by the following formula to approximate the edge-spread function (ESF) (63):??(??)=??1+exp[&minus;??(??&minus;??c)]+??f(x)=a1+exp[&minus;k(x&minus;xc)]+d(9)where a, k, xc, and d are the parameters that can be found by fitting the formula to the experimental result. To increase the accuracy of resolution estimation, the digital intensity sampling was performed five times at different positions along the X-axis and Y-axis within the waveguide bundle, respectively. Then, intensity data were averaged to approximate ESFs, which contains abrupt change in intensity due to the Al foil corner, as shown in Figure 3g&ndash;i. The slope of the ESF increases obviously with the decrease in the Cu waveguide inner radius. Herein, statistics for the resolution estimation can be further improved by reducing the scanning step and increasing the sampling times along the vertical and horizontal edges of the Al foil corner. ESF represents the image intensity along the X-axis direction and the Y-axis direction, denoted as I(x) and I(y), respectively. I(x,y) is equal to the convolution of the object plane signal intensity S(x,y) with the PSF of the waveguide bundle. Therefore, the PSF can be regarded as dI(x)/dx or dI(y)/dy. The full width at half-maximum (FWHM) of the normalized function corresponds to the experimental spatial resolution of the waveguide bundle, (64) as shown in Figure 4a,b. The experimental spatial resolutions of the waveguide bundle along the X-axis direction are 6.1, 6.8, and 27.8 &lambda;, respectively, corresponding to the inner radii of 0.25, 0.35, and 0.5 mm for the Cu waveguide (see Figure 4a). Moreover, the experimental spatial resolutions of the waveguide bundle along the Y-axis direction are 3.8, 6.4, and 22.4 &lambda;, respectively, corresponding to the inner radii of 0.25, 0.35, and 0.5 mm for the Cu waveguide (see Figure 4b). The results show that experimental spatial resolutions are consistent with the estimated results for the bundles with waveguide inner radii of 0.35 and 0.25 mm. In the case of the bundle with a 0.5 mm inner radius of the waveguide, the experimental spatial resolutions in both X- and Y-directions are smaller than the theoretical results due to the nonuniform intensity distribution of the beam, as well as center misalignment between the waveguide bundle and the incident beam. (54) Moreover, the diffraction effect induced by the gap between the scanning plane of the Golay cell and the output end of the waveguide bundle could lower the measured spatial resolution. (65) The Cu hollow-core metallic waveguide bundle we proposed is able to achieve a submillimeter spatial resolution (maximum experimental value of &sim;400 &mu;m) and provide a more than three times longer transmission distance than other dielectric fiber bundles. (36)Figure 3Figure 3. (a&ndash;c) Optical images of the metallic barrier placed in contact with the input end of the THz waveguide bundles. (d&ndash;f) Corresponding THz images of the object formed at the output end of the THz waveguide bundle. (g&ndash;i) Evolution of the output intensity within the white dashed line box as shown in (d&ndash;f) in both X- and Y-axis directions.High Resolution ImageDownload MS PowerPoint SlideFigure 4Figure 4. Experimental spatial resolution of the Cu waveguide bundle with different inner radii in (a) the X-axis direction and (b) the Y-axis direction. (c) Experimental transmission loss of the Cu waveguide bundle with different inner radii under the different biasing currents of THz QCL. (d) Measured output power of waveguide bundles with 0.35 mm inner radius under room temperature and liquid N2 condition. The inset shows the transmission loss of the waveguide bundle under liquid N2 condition. (e) Optical images (top) and THz transmission images (bottom) of the square tables with different mixed ratios of PTFE and Ag nanoparticle powders.High Resolution ImageDownload MS PowerPoint SlideIn general, the numerical aperture of dielectric waveguide is higher than that of the hollow-core waveguide due to a higher refractive index of fiber core, which can be compensated by the lens integrated at the input end of the waveguide. Although the minimum resolution of the bundle can approach the free-space wavelength, the inner radius of an individual waveguide, the periodic arrangements of the waveguide, and the effective cross-sectional area of the waveguide bundle are crucial for the spatial resolution and transmission distance, which needs to be considered as trade-off.Transmission loss of the waveguide bundle was also investigated by the cutoff method as the following (66):??experiment=10??&times;log(??in??out)(dB/m)&alpha;experiment=10L&times;log(PinPout)(dB/m)(10)where Pin and Pout represent the input and output power of the 2 cm length (L) waveguide bundles, respectively. Figure 4c shows that transmission loss of the waveguide bundle decreases with the increase of the inner radius of the Cu waveguide, which is consistent with the theoretical results. The difference between simulated and experimental transmission loss can be attributed to the scattering loss introduced by the inner surface roughness of the hollow-core metallic waveguides. Furthermore, the effective cross-sectional area of the hollow-core metallic waveguide bundle is larger than the area summation of all individual Cu waveguides due to the existence of the wall thickness and the interstitial gaps among waveguides, leading to a higher transmission loss. In addition, the transmission loss of the bundle in cryogenic environments was also investigated, as shown in Figure 4d. The output power of the Cu waveguide bundle with an inner radius of 0.35 mm and a length of 6 cm is higher under low temperature conditions compared to that at room temperature, which can be ascribed to the condensation of water molecules and other gases in the air affecting THz absorption. The inset of Figure 4d indicates that low temperature could effectively reduce the transmission loss of the bundle, which shows promising applications of the Cu hollow-core waveguide bundles in a certain low-temperature environment. Considering the spatial frequency and transmission loss of the bundle, the waveguide with the inner radius of 0.35 mm was employed for further imaging experiments.As an effective medium of transmission imaging, it is necessary to verify whether there is a sufficient signal-to-noise ratio for the waveguide bundle to transmit the intensity difference of imaging objects. In this work, square tablets with a side length of 1.5 cm served as standard samples to evaluate the sensitivity for the sample&rsquo;s optical properties by the Cu waveguide bundle-based continuous-wave THz transmission imaging system.To further improve the spatial resolution of imaging, the scanning step is set as 300 &mu;m, which is less than the outer radius (0.5 mm) of the Cu waveguide and satisfies the Nyquist sampling criterion. (67) Various volume ratios of PTFE powders and Ag nanoparticles (NPs) are mixed and compressed into tablets due to the high transmission of PTFE and the high reflection of Ag NPs in the THz band, and the mixed ratios include 1:0, 4:1, 3:2, and 1:1. Figure 4e shows the visible and THz images of tablets with different mixing ratios, respectively. The scanning plane of the Golay cell is not perfectly parallel to the output end of the waveguide bundle due to the assembly errors of the 2D moving stage, resulting in distortion and aberrations of the THz images. The errors are expressed in the form of a translation between rows, whose distances are constant during scanning. Therefore, the comprehensive error of each row is in a linear relationship with the row number. In order to correct the linear drift, digital image processing techniques were employed to rectify the THz images. The linear relationship of translation of the ith row can be described below:{????=??0+????=????{Pi=P0+ee=ik(11)where Pi is the position of the first tested point of the ith row, e is the mechanical error, and k is the constant distance of the translation between rows. The distinct color intensity (normalized to 1) of each tablet image in Figure 4e represents different THz-normalized transmission power, which shows that the transmission intensity of THz decreases with the increase in the mixed ratio of Ag. 3.3. Applications in THz Imaging by Cu Hollow-Core Waveguide BundlesIn order to characterize the imaging functionality of the Cu waveguide bundle, patterns with letters “T&Prime;, “H&Prime;, and “Z&Prime; were fabricated on thin sheets of stainless steel by laser cutting. The hollow width and thickness of patterns are 1 and 0.3 mm, respectively. To compare the size differences between the simulated images and actual patterns, the heights of all the three letters “T&Prime;, “H&Prime;, and “Z&Prime; are 9 mm, and in terms of width, “T&Prime; is 8 mm while “H&Prime; and “Z&Prime; are both 7 mm, as shown in Figure 5a. The FDTD simulations were performed to analyze the electric field distribution at the image plane of a Cu waveguide bundle-based transmission-mode continuous-wave imaging system (see Section 2 to further improve the ion for details). Figure 5b shows that Cu waveguide bundles generate clear patterns in the simulated results. The hollow portion of the samples (“T&Prime;, “H&Prime;, and “Z&Prime; patterns) allows the THz wave to pass through and reach the image plane via the waveguides. The height of all the three “T&Prime;, “H&Prime;, and “Z&Prime; images is &sim;8.5 mm. In the case of the width of simulated images, “T&Prime; is &sim;7 mm while “H&Prime; and “Z&Prime; are &sim;6 mm, which are smaller than the target size. This can be ascribed to the image distortions induced by the waveguide and THz-wave diffraction at the output of the Cu waveguide bundle. (65) Although the traditional fiber bundle could achieve the equal-size transmission of near-field images from the object plane to the image plane by discrete sampling, (37) the premise is that the image plane needs to align with the output end of the fiber bundle to ensure there are no diffraction phenomena. However, it is impossible for the image plane to align perfectly with the output end of the waveguide bundle due to the thickness of the tin foil membrane. As a result, the distance between the monitor and the output end of the waveguide bundle is set as 100 &mu;m in simulation, which is close to the operating wavelength. Moreover, the width of the “H&Prime; and “Z&Prime; patterns is &sim;6 mm while the width of the “T” pattern (&sim;7 mm) is larger than those of “H&Prime; and “Z&Prime;, which are consistent with the sizes of the actual patterns. In addition, wavelength also plays a key role in the spatial resolution of the waveguide bundle-based transmission imaging because the shorter wavelength has a smaller Fraunhofer diffraction limit, which could increase the spatial resolution. Figure 5c shows the THz images of “T&Prime;, “H&Prime;, and “Z&Prime; obtained by the Cu waveguide bundle-based continuous-wave THz transmission imaging system. With the same imaging parameters as in simulation, the height of the three patterns is &sim;8 mm. In terms of the width of the patterns, those of “H” and “Z&Prime; are consistent (&sim;8.2 mm) and smaller than that of the “T” pattern (&sim;9 mm). A gap between the Golay cell and the output end of the Cu waveguide bundle (image plane) could lead to the diffraction effect (see Section 2 for detail). Our work demonstrates that the Cu waveguide bundles could represent the size relationship of patterns both in simulations and in imaging experiments, which means that the nonrandom nature of image distortions induced by diffraction effects can be effectively addressed by resolving the integral equations of vector diffraction theory or machine learning methods. (68,69) At the same time, the Cu hollow-core waveguide bundle could be integrated with a THz array detector for real-time imaging when the imaging area of the detector is large enough. Further improvements in the quality of beam pattern and the stability of output power from THz QCL together with imaging processing techniques will help address the issue of nonuniform image intensity.Figure 5Figure 5. Cu waveguide bundle-based THz near-field transmission imaging. (a) Optical images of the designed sample with the letters “T”, “H”, and “Z”. (b) Simulated electric field distribution and (c) experimental results of terahertz imaging.High Resolution ImageDownload MS PowerPoint Slide4. ConclusionsIn this work, a hexagonally arranged Cu hollow-core waveguide bundle was fabricated by low-cost extrusion and stacking. The transmission losses of the Cu waveguide bundle increase as the inner radius of the Cu waveguide decreases, which is consistent with the simulation results. Furthermore, low temperature could lead to a higher output power of the Cu waveguide bundle when the bias of the THz QCL increases from threshold to peak. The effect of the Cu waveguide inner radius on the spatial resolution of the bundle was systematically investigated by theoretical and experimental methods, indicating a preeminent consistency with a maximum experimental spatial resolution of &sim;400 &mu;m. The results show that the proposed fabrication method of the Cu waveguide bundle can achieve excellent accuracy. Besides, the sensitivity of the Cu waveguide bundle-based terahertz imaging system was further investigated by the transmission THz imaging for tablets with different mixed ratios of PTFE and Ag NPs. Finally, we simulated and experimentally demonstrated the imaging capability of the Cu waveguide bundle by incorporating a Cu waveguide bundle with a 6 cm length and a continuous-wave terahertz transmission imaging system. This work shows that the Cu hollow-core waveguide bundles integrate well with THz QCLs and enable the long-distance and submillimeter resolution near-field terahertz imaging in a cryogenic environment. Further improvements may include the development of flexible, bendable, and stretchable THz waveguide-based bundles, as well as the reflective imaging enabled by the waveguide bundle.

Jun. 27, 2024Journal
Four-Channel Broadband Mode (De)multiplexer Based on Thin-Film Lithium Niobate Platform

Abstract The lithium-niobate-on-insulator (LNOI) platform has recently emerged as a promising candidate for advanced photonic functions due to its excellent electro-optic coefficient. However, there remain some challenges associated with the etching of LNOI, which typically results in a decreased performance of the fabricated devices. For instance, fabrication errors may reduce the bandwidth of the mode multiplexer and demultiplexer (MMUX/DEMMUX), thereby limiting the capacity of the communication transmission. In this study, a four-channel broadband MMUX/DEMMUX based on an LNOI strip waveguide is experimentally demonstrated by employing an asymmetrical directional coupler structure. To avoid phase mismatch caused by etching depth error, an LNOI strip waveguide was introduced instead of a ridge waveguide. Additionally, an auxiliary spiral loss line was introduced to consume the residual energy of incomplete coupling due to fabrication error and ensure the low crosstalk of the device. Experimental results show that the device achieves a bandwidth exceeding 130 nm with a crosstalk of less than &minus;10.6 dB, making it achieve the largest multiplexing bandwidth reported for LNOI-based platforms. Furthermore, a clear eye diagram at 64 Gbps demonstrates the capability for the high-speed communication offered by the fabricated device.This publication is licensed under the terms of your institutional subscription. Request reuse permissions.IntroductionThe rapid development of contemporary society has imposed higher demands on communication capacity and speed. (1) In this context, optical interconnect technology has emerged as a solution with enhanced transmission capacity, accelerated transmission speed, and reduced energy consumption. (2) Optical (de)multiplexer serves as the pivotal device of optical interconnects, with wavelength-division multiplexing currently being the most extensively employed technique. (3,4) However, increasing capacity through decreased channel spacing and expanding more channels present significant challenges, including increased complexities in integrated chip development, larger chip dimensions, more demanding laser sources, and increased system complexity and cost. To address these limitations, polarization-division multiplexing (PDM) has been proposed as a supplementary approach to enhance multiplexing channels. Nevertheless, PDM is restricted to only two multiplexing modes, which hinders the expansion of more modes. (5) At present, mode-division multiplexing (MDM) with higher scalability has gradually become a hot spot of attention. The implementation of on-chip MDM typically involves three structures: a multimode interferometer (MMI), (6) a Y-junction, (7&minus;9) and an asymmetrical directional coupler (ADC). (10&minus;13) MMI-based mode multiplexers and demultiplexers (MMUXs/DEMMUXs) have the advantages of large bandwidth and fabrication tolerance but suffer from poor scalability. Although Y-junction-based MMUXs/DEMMUXs have better channel scalability and a smaller footprint, the high requirement of etching accuracy makes it difficult to be widely used. ADC-based MMUXs/DEMMUXs have greatly attracted attention due to their high scalability, low loss, and low crosstalk. Thanks to the compatibility with mature complementary metal oxide semiconductor fabrication processes, several ADC-based structures have been proposed and experimentally verified on silicon-on-insulator platforms, including ultra-multi-channel (14) and ultra-compact (15) MMUXs/DEMMUXs. However, there are limited reports about MMUXs/DEMMUXs on the lithium-niobate-on-insulator (LNOI) platform so far. (16&minus;19)Lithium niobate (LN) has become a very attractive material for optical communication owing to its wind transparency window (0.4&ndash;5 &mu;m), strong electro-optical coefficient (r33 = 30.8 pm/V), and significant second-order optical nonlinearity (d33 = &minus;33 pm/V). (20) With the advancements in thin film technology and crystal ion slicing technology, LN waveguides on thin film insulators exhibit a large refractive index contrast (&Delta;n &sim; 0.7). This enables them to possess enhanced light confinement capabilities and reduced bending loss, thereby facilitating the development of large-scale and highly integrated LN photonic devices. (21) Currently, there are two main structures of LNOI photonic waveguides: one is made into a loaded strip waveguide by depositing another material (typically silicon nitride) onto the LNOI plate. Although this approach can avoid the loss issue associated with direct etching of LN, it increases costs due to additional material deposition processes and requirements for deposited materials. The other approach entails directly fabricating an LN strip or ridge waveguide through a dry etching process. However, precise control over the etching depth during ridge waveguide fabrication is challenging, leading to compromised device performance. Notably, the issues are not encountered with strip waveguides, which also offer a smaller extreme bending radius that facilitates improved device integration. To our knowledge, no reports have been published regarding the utilization of the strip waveguide structure in LNOI for achieving MMUX/DEMMUX.In this article, we implemented a four-channel broadband MMUX/DEMMUX using an ADC structure on an LNOI strip waveguide. The structure of the LNOI strip waveguide is utilized to significantly alleviate the sensitivity to phase-matching conditions in fabrication processes, thereby maintaining a well-functioning phase-matching mechanism in fabricated devices and greatly improving coupling efficiency for mode (de)multiplexing compared with traditional ADCs. Especially, spiral loss lines are connected at the end of the access waveguides, which have not been reported in previous works thus far. These spiral loss lines effectively dissipate residual energy and reduce reflection and crosstalk within the device, further ensuring efficient mode coupling based on a phase-matched physical mechanism. This new approach significantly enhances fabrication tolerance and addresses limitations in bandwidth observed in traditionally designed ADCs due to strict phase-matching requirements. This design presents a new solution for achieving large bandwidth mode multiplexing and hybrid multiplexing on LNOI.Principle and DesignThe 3D schematic diagram of the designed MMUXs/DEMMUXs based on the ADC structure is shown in Figure 1. The structure consists of two sections: MDM and mode-division demultiplexing areas. As depicted in the top view of Figure 2a, the MDM section consists of a cascade of three ADCs. The TE0 mode light is injected from the I0 port of the bus waveguide and subsequently transmitted along the crystal Y direction. If the TE0 mode light is input from ports I1, I2, or I3 of the input waveguide, it will be coupled into corresponding TE1, TE2, and TE3 modes when satisfying phase-matching conditions at their respective coupling regions within the device&rsquo;s structure. Due to optical path reversibility, the right half represents the mode-division demultiplexing area where the TE0 mode light in the bus waveguide exits through the O0 port. Similarly, TE1, TE2, and TE3 modes in the bus waveguide are guided toward their respective coupling regions for subsequent transformation into TE0 modes before being outputted through ports O1, O2, and O3, respectively, when phase-matching conditions are met accordingly. It completes both the processes of MDM and demultiplexing. An enlarged view of an individual ADC structure is presented in Figure 2b, where W1_TEi, W2_TEi, W3_TEi, and W4_TEi (i = 1,2,3) represent the waveguide widths of the TE0-TEi (i = 1,2,3). L_TEi (i = 1,2,3) are the corresponding coupling lengths. The spiral loss lines at the end of the input waveguides are utilized for filtering out residual energy caused by incomplete coupling due to fabrication error. Simultaneously, to avoid the transmission performance degradation caused by etching depth error, a strip waveguide is employed in the device, as shown in Figure 2c. The width of the marked waveguide corresponds to the bottom width of the waveguide, owing to the sidewall angle during etching. The coupling gap g denotes the distance between adjacent waveguides within the coupling region.Figure 1Figure 1. Schematic diagram of the three-dimensional structure of the MMUXs/DEMMUXs.High Resolution ImageDownload MS PowerPoint SlideFigure 2Figure 2. (a) Top view of the MMUXs/DEMMUXs, (b) enlarged view of the ADC structure, and (c) waveguide cross-section.High Resolution ImageDownload MS PowerPoint SlideIn this work, we employed an X-cut LNOI platform to achieve enhanced electro-optic coefficients and second-order nonlinear effects in the LN thin film plane, enabling seamless integration with other LNOI devices, such as high-speed electro-optic modulators, (22&minus;24) second-harmonic generators (25&minus;27) and optical frequency combs. (28,29) The X-cut LNOI wafer consisted of a 300-nm thick LN layer on a 2-&mu;m thick SiO2 substrate. Based on previous fabrication experience, the sidewall angle of the strip waveguide was set at approximately 71&deg;. The designed MMUX/DEMMUX is based on an ADC structure. In accordance with coupled-mode theory, the structure must satisfy the phase matching condition, where the effective mode index of the fundamental mode in the input waveguide matches that of its corresponding higher-order mode in the bus waveguide. As shown in Figure 3a, we simulate the variation of the effective refractive index for each order mode when the light propagates along the Y direction of the crystal at 1550 nm. Limited by the etching technology, LN waveguides inherently possess a sidewall angle that breaks vertical symmetry and readily excites the TM mode light. In the proposed device, mode hybridization between the excited TM mode light and TE mode light may occur, resulting in degradation of signal transmission quality. Therefore, it is crucial to select a large effective refractive index to avoid regions where such mode hybridization occurs, as illustrated in Figure 3b. Initially, we chose an effective refractive index of 1.6977. Under this condition, the width of an input waveguide is 1.3 &mu;m, and the corresponding bus waveguide widths in the coupling region are 2.72, 4.14, and 5.54 &mu;m, respectively.Figure 3Figure 3. (a) Mode effective refractive indices as a function of waveguide widths. (b) Mode hybrid region.High Resolution ImageDownload MS PowerPoint SlideTo ensure the successful fabrication of the coupling region, a sufficiently large coupling gap of g = 0.24 &mu;m is set. The input waveguide width is set as W1_TEi = 1.3 &mu;m (i = 1,2,3), and other parameters are defined as follows: W2_TEi < W1_TEi (i = 1,2,3), W3_TE1 < 2.72 &mu;m < W4_TE1, W3_TE2 < 4.14 &mu;m < W4_TE2, W3_TE3 < 5.54 &mu;m < W4_TE3. Subsequently, the coupling length (30,31) is estimated according to the coupled-mode theory, and the formula is as follows: L = &lambda;/[2(n1 &ndash; n2)], where n1 and n2 are the effective refractive indices of the symmetric and antisymmetric modes of the two eigenmodes in the coupled waveguides. At an operating wavelength &lambda; = 1.55 &mu;m, it can be approximated that for each order TE mode: L_TE1 &asymp; 97.58 &mu;m, L_TE2 &asymp; 118.99 &mu;m, L_TE3 &asymp; 134.27 &mu;m. Finally, the structural parameters of MMUXs/DEMMUXs are optimized using the three-dimensional finite-difference time-domain method.The optimized parameters of the designed MMUXs/DEMMUXs are summarized in Table 1. Lengths of four linear tapers are set at 200 &mu;m to ensure high transmission efficiency, resulting in a device length of 1664.4 &mu;m. The simulated transmission spectra of mode conversion in the wide spectral range of 1480&ndash;1640 nm are shown in Figure 4a&ndash;c. All channels exhibit excess losses below 1 dB, and the corresponding crosstalk levels are less than &minus;20 dB. Notably, channel TE0-TE1 demonstrates superior performance with an excess loss of 0.25 dB and a corresponding crosstalk of &minus;25.3 dB. Figure 5a&ndash;h shows the top view and cross-section of the electric field during transmission at 1550 nm. The designed device exhibits a broad bandwidth exceeding 150 nm, low crosstalk below &minus;20 dB, and improved fabrication tolerance due to its strip waveguide architecture and the addition of spiral loss lines at the end of the input waveguide. Furthermore, we analyzed the impact of fabrication errors on waveguide width and coupling gap. The simulation results in Figure 6a&ndash;f indicate that when the waveguide width error is within &plusmn;20 nm, all channels maintain excess losses below 2.1 dB and crosstalk levels are under &minus;19.25 dB within the wavelength range of 1480&ndash;1640 nm. Similarly, when the coupling gap error is within &plusmn;40 nm, all channels exhibit excess losses below 1.36 dB and the crosstalk levels are less than &minus;17.89 dB. Consequently, these analyses confirm that the designed device possesses excellent fabrication tolerance.Table 1. Parameters of the Designed MMUXs/DEMMUXsparameters (&mu;m)W1_TEiW2_TEiW3_TEiW4_TEiL_TEigTE0-TE11.31.052.462.47123.30.24TE0-TE21.31.13.843.85156.60.24TE0-TE31.31.125.175.27152.30.24Figure 4Figure 4. Simulated transmission spectrum of MMUXs/DEMMUXs (a) TE0-TE1, (b) TE0-TE2, and (c)TE0-TE3.High Resolution ImageDownload MS PowerPoint SlideFigure 5Figure 5. Simulated top view and cross-section of the transmission electric field of MMUXs/DEMMUXs at 1550 nm (a, b) TE0-TE0, (c, d) TE0-TE1, (e, f) TE0-TE2, and (g, h) TE0-TE3.High Resolution ImageDownload MS PowerPoint SlideFigure 6Figure 6. Error analysis of the designed MMUXs/DEMMUXs for TE0-TE1, TE0-TE2, and TE0-TE3 (a&ndash;c) waveguide width &Delta;W (d&ndash;f) coupling gap &Delta;g.High Resolution ImageDownload MS PowerPoint SlideFabrication and Experimental Results We prepared the designed MMUXs/DEMMUXs based on a commercial X-cut LNOI wafer from NANOLN. The designed pattern was exposed using electron beam lithography, and then the pattern was transferred into a 300-nm deep LN film using Ar+ reactive ion etching. A 2-&mu;m-thick SiO2 top cladding layer was deposited via plasma-enhanced chemical vapor deposition followed by cutting the chip edges and polishing the end faces with the chemical&ndash;mechanical polishing method. Figure 7a displays a magnified view of the fabricated MMUXs/DEMMUXs, while Figure 7b&ndash;d shows scanning electron microscope (SEM) images of TE0-TE1, TE0-TE2, and TE0-TE3 coupling regions, respectively.Figure 7Figure 7. (a) Enlarged view of the fabricated MMUXs/DEMMUXs, SEM image of the waveguide in the coupling region, (b) TE0-TE1, (c) TE0-TE2, and (d) TE0-TE3.High Resolution ImageDownload MS PowerPoint SlideWe conducted static and dynamic tests on the device, with the experimental setups depicted in Figure 8. The static experimental setups comprised a tunable laser (Santec TSL-710), a polarization controller (PC), and an optical power meter (OPM, Santec MPM-210). In the experiment, the laser output was adjusted by the PC, while the input and output of the optical fiber array were coupled from the chip&rsquo;s end faces. Subsequently, the spectral response was detected by the OPM. The dynamic test demonstrated the data transmission capability of the device: The laser output of the TL was adjusted by the PC and transmitted to an LN optical modulator (OM, iXblue MX-LN-40). A DC voltage source (DVS, KEYSIGHT E36312A) with a 5 V DC voltage was applied to the modulator to operate it at the static operating point. Then, a pseudorandom binary sequence with a rate of 64 Gbps was generated by an arbitrary waveform generator (AWG, KEYSIGHT M8199A) for modulation. The modulated signal was coupled to the chip&rsquo;s input and output through a fiber array, amplified by an erbium-doped fiber amplifier (EDFA, Amonics AEDFA-23-B-FA), and then filtered using an optically tunable filter (OTF, EXFO XTM-50). Finally, real-time reception of the signal and display of the eye image was achieved by using an oscilloscope (OSC, KEYSIGHT N1000A).Figure 8Figure 8. Schematic diagram of the experimental setup for static and dynamic testing (TL, tunable laser; PC, polarization controller; OM, optical modulator; DUT, device under test; OPM, optical power meter; EDFA, erbium-doped fiber amplifier; OTF, optical tunable filter; OSC, oscilloscope; AWG, arbitrary waveform generator; DVS, Dc voltage source).High Resolution ImageDownload MS PowerPoint SlideThe static test results of the device are presented in Figure 9. In the ultra-large bandwidth range of 1480&ndash;1610 nm, the excess losses for TE0, TE1, TE2, and TE3 channels are below 2.38, 2.06, 4.69, and 3.34 dB, respectively. Additionally, the intermodal crosstalk levels are lower than &minus;15.8, &minus;11.8, &minus;10.6, and &minus;13.7 dB, respectively. The reason that the excess loss is larger than the design value is estimated to be due to fabrication errors in waveguide width and coupling gap, which disrupt the strict phase matching and result in incomplete coupling. However, since all channels exhibit crosstalk below &minus;10 dB, this has a negligible effect on dynamic testing. As shown in Figure 10, the eye image of the device at 1550 nm under 64 Gbps of OOK modulation demonstrated clear eye images for all channels with an extinction ratio exceeding 5.6 dB. Experimental results indicate excellent data communication capability of the device. Furthermore, a summary of the previously reported MDM devices on LNOI is shown in Table 2. It can be observed that this work achieves the largest bandwidth. Although the excess loss is slightly high at present, it can be further reduced through process improvement.Figure 9Figure 9. Measured transmission spectra of four output ports of MMUX/DEMMUX at different input ports (a) I0, (b) I1, (c) I2, and (d) I3.High Resolution ImageDownload MS PowerPoint SlideFigure 10Figure 10. Measured eye diagrams.High Resolution ImageDownload MS PowerPoint SlideTable 2. Summary of MMUX/DEMMUX on LNOIreferenceexperimentmodeswaveguideEL (dB)CT (dB)bandwidth (nm)(16)yes4polymer-loaded4.0&ndash;9.570(17)yes4SIN-loaded1.6&ndash;16100(18)yes4SIN-loaded1.49&ndash;13.0340(19)yes4LN ridge0.2&ndash;2080this workyes4LN strip4.69&ndash;10.6>130Conclusions In this work, we investigate the MDM technology based on X-cut LNOI, utilizing a 300-nm fully etched LN strip waveguide combined with a spiral loss line to enhance phase matching and improve fabrication tolerance. This enables efficient mode multiplexing and demultiplexing functions for TE0-TE0, TE0-TE1, TE0-TE2, and TE0-TE3 with low crosstalk and large bandwidth. Experimental measurements of the transmission spectra demonstrate the crosstalk below &minus;10.6 dB over a large bandwidth exceeding 130 nm while maintaining excess loss below 4.69 dB for each channel tested. Moreover, we have also demonstrated a clear eye image when transmitting 64 Gbps data at 1550 nm, and the experimental results show that the designed device has excellent data communication capability. The device is by far the MDM device with the largest bandwidth on the LNOI platform. This work provides a new solution for achieving large bandwidth mode multiplexing as well as hybrid multiplexing on the LNOI platform while paving the way for future advancements in high-speed and large-capacity optical interconnection technology.

Jun. 27, 2024Journal
Electrically Reconfigurable Mode Chirality in Integrated Microring Resonators

AbstractChirality, one of the universal phenomena in physics, forms the playground for fascinating phenomena in modern electromagnetism and industrial applications. Within the rapidly advancing technologies of integrated optoelectronic and all-optical devices, controlling the light flow on a chip using optical chiral modes emerges as a crucial topic, which implies numerous counterintuitive chiroptical effects such as unidirectional emission, magnetic-free non-reciprocity, chiral switching, and enhanced sensitivity. Here strong yet reconfigurable mode chirality is demonstrated in integrated silicon-based spiral microring resonators. Leveraging the adjustable azimuthal positions of two spiral edges as asymmetric local scatterers, the inter-modal coupling can be manipulated, which bypasses the requirement of external off-chip components in conventional schemes. Besides, an integrated phase shifter enables electrical reconfiguration of the non-Hermiticity toward or away from exceptional points. Experimental results reveal post-fabrication reconfiguration with a sign-reversible chirality and chirality-induced suppression of backscattering down to &minus;24 dB. By virtue of demonstrations using standard silicon photonics foundry services, the findings provide a new design framework of microresonators as a building block for integrated chiral photonics in both classical and quantum regimes.1 IntroductionChirality naturally exists in the molecular or material structures that possess handedness or asymmetry. In addition, its importance has been long intriguing in modern physics, especially topological states,[1] spintronics,[2] and emerging chiral quantum photonics.[3] Akin to chiral edge states in topological insulators, in optics, secured optical chirality suggests a forbidden propagation of photons in the opposite direction, which leads to fascinating phenomena such as photonic Aharonov&ndash;Bohm effect,[4] magnetic-free nonreciprocity,[5] unidirectional emission,[6] chiral light-matter interaction,[6, 7] asymmetric mode switching,[8] and so on. In recent years, whispering gallery mode (WGM) microresonators have been widely investigated as an open physical system for studying chiral photonics and non-Hermitian photonics.[9-12] In the sense of transverse spin angular momentum carried by lightwaves circulating in a WGM cavity, propagations in the clockwise (CW) and the counterclockwise (CCW) directions carry distinct chirality.[13] Harnessing the broken chiral symmetry, exotic properties of optical resonant fields open up new possibilities with even counterintuitive features, such as unidirectional emission,[9, 14, 15] reconfigurable symmetry-broken lasers,[16, 17] generation of tunable orbital angular momentum,[18, 19] enhanced sensing,[5, 20, 21] and chiral perfect absorption.[7, 22]The chirality of optical WGMs can be mediated simply via inter-modal coupling between two naturally existing near-degenerate resonant modes, in which adjusting the optical gain/loss condition is no longer a prerequisite. The mode chirality reaches its maximum at an exceptional point (EP), where two (or multiple) eigenvalues and the associated eigenstates coalesce.[23-25] Apart from the reported reconfigurable chirality in lasing,[16, 17] steering of non-Hermitian spectral degeneracies, and effective mode chirality, has been pioneered using the “two-scatterers” strategy,[24, 26-29] in which the relative positions of two external nano scatterers are judiciously controlled around the cavity for perturbing the evanescent field and maneuvering the induced inter-modal coupling. Despite the high accuracy of this well-established scheme, precision off-chip equipment (mainly nanotips and nanopositioners) cannot be avoided,[28, 30, 31] which significantly plagued the technology transfer into prospective applications especially in the burgeoning industry of integrated photonics. For on-chip densely integrated planar microresonators, mode chirality can be controlled by generating highly unbalanced backscattering strength between CW and CCW lightwaves using two approaches. The first one is to introduce lithographically patterned scatterers (e.g., nanonotches[32] and nanoparticles[33]) with deliberately controlled shapes, sizes, and locations. The second one is to employ extra on-chip (e.g., Taiji resonators,[34, 35] infinite-loop resonators,[36] and resonators with integrated reflectors[37-39]) or off-chip (e.g., optical isolators[21] and fiber loop mirror[7]) components facilitating mode conversion. However, in both approaches, the resulted chirality is fixed to a deterministic value, and the post-fabrication reconfigurability remains elusive. For on-chip waveguide-coupled microring resonators as an extensively exploited building block on various fronts, realizing reconfigurable mode chirality will unleash the potential of chiral devices in both classical and quantum regimes.In this article, we experimentally demonstrated a, hitherto lacking, framework of integrated optical microresonators with electrically reconfigurable mode chirality. In particular, the scheme has been successfully realized solely by on-chip integrated elements based on silicon photonics foundry processes, which is in contrast with previously demonstrated chirality tuning schemes leveraging off-chip components.[26, 30] In the proposed spiral ring system, the azimuthal spacing between two spiral edges serves as a generic knob to manipulate the mode chirality between the CCW/CW-dominated regimes. Strong mode chirality up to&asymp;0.86 was experimentally demonstrated, which counterbalances the intrinsic Rayleigh scattering in regular microrings with weak chirality, and results in coherent suppression of backscattering down to&asymp;&minus;24 dB. Besides, localized thermo-optic tuning enables a post-fabrication approach to steer around a chiral state toward or away from EPs. The observed sign-reversible chirality verifies the reconfigurability. The proof-of-concept demonstration using silicon nitride microring resonators in the submicrometer wavelengths is of great significance to their emerging applications,[40, 41] from sensing,[42] to data centers, to neural networks, to Lidar,[40] and to quantum photonics.2 Results2.1 Working PrinciplesFor analyses of perturbed modes in microrings, usually, an effective Hamiltonian as a 2 &times; 2 matrix is introduced,[43, 44](1)The diagonal elements describe original modes in the traveling-wave basis, including the energy (real part) and the decay rate (imaginary part), while the off-diagonal elements describe the coherent backscattering of light from CW to CCW (A) and from CCW to CW (B) direction. To generate backscattering inside a microring, a simple and intuitive way is to introduce a “protruded” segment along the radial direction (spanning an azimuthal angle &theta;, see the left panel of Figure 1a). A mismatch in the lateral dimension in a waveguiding system leads to nonconservative coupling of counter-propagating waves, impacting both A and B. Due to the preserved structural symmetry, the contributions of A and B are balanced. Tuning &theta; may effectively steer the system to break the mode degeneracy (see the left panel of Figure 1b). However, the mode chirality remains to be weak.Figure 1Open in figure viewerPowerPointSchematic showing the non-Hermiticity in a spiral microring resonator. a) Schematics of a regular ring perturbed by a protruded segment with preserved mirror-symmetry showing almost zero mode chirality (left) and a spiral ring with broken mirror-symmetry showing tunable mode chirality (right). b) Numerically calculated eigenvalues showing the resonant wavelength detuning between two non-degenerate modes in a segment-tailored ring (left) and spiral ring (right). In two systems, the azimuthal angle &theta; of the widened segment is the common tuning parameter. In the spiral ring, the asymmetric factor &chi; is an additional tuning parameter. The dashed lines represent the case where |&chi;| equals 1. c) Schematic of the waveguide-coupled spiral-ring-based add-drop filter with an integrated phase tuner. Inset: zoom-in view of (c) around the inner spiral edge where nonconservative coupling happens. W is the width of the ring and T is the radial offset.A simple yet efficient way to break the mirror symmetry in a ring is to utilize the spiral shape, which can be viewed as curving one waveguide into a loop. Two spiral edges feature a radial offset T and an adjustable relative azimuthal position (i.e., angle &theta;) describing the overlapping segment of this chopped spiral waveguide with a width of W + T (See the right panel of Figure 1a). Considering the mode delocalization due to bending curvature, the perturbation effects introduced by inner and outer edges might be highly unbalanced. This effect can be quantified using a complex “asymmetric factor” &chi; = , in which V and U are the complex mode shifts for positive- and negative-parity modes, respectively, and the subscript labels the corresponding spiral edges (for details, see Section S1, Supporting Information). Under this circumstance, the Hamiltonian matrix becomes non-Hermitian. Hence, the eigenvectors become in general not orthogonal. By adjusting the non-Hermicity using &theta; and &chi;, two EPs, namely EP+ (B = 0) and EP- (A = 0), can be approached (see the right panel of Figure 1b).In the following studies, the peculiar optical response using an integrated and waveguide-coupled spiral ring was investigated, in which the non-Hermiticity and associated mode chirality can be controlled by either adjusting &theta; at the pre-fabrication stage or local phase tuning at the post-fabrication stage. Leveraging the maturing silicon photonics technology, optically passive waveguide-coupled spiral microring resonators with well-defined geometries can be readily obtained from foundry services (see Figure 1c). Notably, the system is compatible with the standard complementary metal oxide semiconductor (CMOS) process for mass production. The smallest feature size here, namely T, can be realized using standard deep ultraviolet (DUV) lithography, which is in contrast with previous demonstrations adopting direct-writing nanolithography for discrete nanostructures (i.e., nanonotches[32] and nanocylinders[33]). Without loss of generality, in our proof-of-concept demonstrations, T was chosen as&asymp;166 nm (one-third of the waveguide width W of 500 nm) and the varying &theta; were chosen &asymp;120.00&deg;. Here a thermo-optic phase shifter was employed and placed on top of the ring segment between two spiral edges.2.2 Optical Responses of Spiral Ring-Based Filters in the Vicinity of An EPHere the mode chirality &alpha; was defined as &alpha; = according to the two-mode approximation. In addition to an absolute strength, the sign &alpha; indicates the dominance of propagation direction in real space. According to our Hamiltonian model, the strongest chirality of 1 and &minus;1, can be approached at EP + and EP- respectively, via engineering both &chi; and &theta; (see Figure 2a). Optical responses can be studied by forming waveguide-based spiral ring resonators as an add-drop filter. Here temporal coupled mode theory (TCMT)[45] was employed to study the spectral responses for injection from two opposite sides of the bus waveguide (i.e., ports 1 and 2, see Section S2, Supporting Information). Figure 2b illustrates the two excitation conditions, where Ijk denotes the intensity measured at the kth port for excitation at the jth port. In addition to TCMT, numerical simulations based on the finite-element method were carried out (see Experimental Section) to visualize the excited supermodes in both spectral and spatial domains.Figure 2Open in figure viewerPowerPointTheoretical studies visualizing the asymmetric backscattering in spiral rings. a) Numerically calculated surface of chirality in a |&chi;|- &theta; parameter space. b) Schematics showing light coupling from port 1 exciting in the CW direction (left) and port 2 exciting in the CCW direction (right). c) Simulated optical responses for the spiral ring with &theta; = 119.20&deg;, showing the backscattering for excitation in the CW direction (I14) is&asymp;6-fold stronger than that for excitation in the CCW direction (I23). d) Optical responses for the spiral ring with &theta; = 119.60&deg;, showing the backscattering for excitation in the CCW direction (I23) is&asymp;3.5-fold stronger than that for excitation in the CW direction (I14). Insets: simulated mode field intensity distributions at resonance wavelengths&asymp;780 nm, for (i) a regular ring excited at port 1, and (ii-iii) a spiral ring with &theta; = 119.20&deg; excited at port 1 (ii) and port 2 (iii). e) Summarized backscattering ratio &eta;BS as a function of &theta;. f) Extracted chirality &alpha; as a function of &theta;.Figure 2c,d presents the resonant spectra upon excitation at two ports for &theta; = 119.20&deg; and 119.60&deg;. Transmission spectra at the throughput port (i.e., I12 and I21) verify the preserved Lorentz reciprocity (see Section S3, Supporting Information). In contrast to previously reported microcavity systems perturbed by nano scatterers,[26, 32, 46, 47] no mode splitting is observed here. This is attributed to the limited coupling strength and consequently a very low “splitting quality factor” Qsp&asymp;0.8 (defined as 4 g/&Gamma;sum,[48] where g is the splitting width determined by the real part of , and &Gamma;sum is half of the sum of linewidths for two modes).For an ideal microring with negligible surface roughness-induced backscattering, the intensity at the add port (i.e., I14 here) is zero and the cavity field presents a clear traveling-wave pattern (inset i). As to spiral rings, although the signal intensities at the drop port (i.e., I13 and I24) are comparable regardless of the excitation in the CW or CCW direction, one can discern that I14 and I23 at the same resonant wavelength differ significantly from each other (Figure 2c). Such an asymmetry of backscattering is attributed to the chiral modes with highly unbalanced weights of CCW and CW components. For a spiral ring (&theta; = 119.20&deg;), one can discern a standing-wave feature due to the interference of copropagating CW and CCW components (insets ii-iii). Excitation at port 1 leads to a more pronounced interference pattern (inset ii) than that of excitation at port 2 (inset iii), which is attributed to the reinforced backscattering in a chiral mode with the dominant contribution of the CCW component. Therefore, the corresponding backscattering I14 is enhanced while its counterpart, I23, is diminished.Notably, an opposite effect (i.e., I14 < I23) can be obtained by changing &theta; from 119.20&deg; to 119.60&deg; (Figure 2d), which indicates the sign of mode chirality is flipped. As presented in Figure 2e, tuning &theta; results in a periodic modulation of the backscattering strength, in which the modulation period agrees with the theoretical model in Section S1 (Supporting Information). The ratio of backscattering &eta;BS for two excitation directions (i.e., I14/I13 or I23/I24) oscillates between&asymp;&minus;20 and &minus;12 dB with an opposite trend. According to TCMT theory, the chirality &alpha; can be extracted using the transmission intensities in this add-drop filter system[26](2)As the transition point, the chirality of zero implies symmetric backscattering (I14&asymp;I23, and |A|&asymp;|B|) and nearly orthogonal eigenstates (see Section S3, Supporting Information). By virtue of tuning &theta;, the chirality gets efficiently modulated between&asymp;&minus;0.3 and 0.4 (Figure 2f).Despite the efficiency in tuning &theta; , EPs with optimal chirality of &plusmn; 1 has yet to be reached. The modeled topology of non-Hermitian degeneracies in Figure 1b also discloses the difficulty of steering to the singularity points via a single parameter. To address this, local phase tuning was employed as another control knob in manipulating the non-Hermiticity. Localized tuning of the effective refractive index neff at the segment between two spiral edges offers an alternative way of adjusting the perturbation strengths V and U for two edges, and hence effectively changes &chi;. As revealed in the simulated eigenmodes in a &theta; -&Delta;neff parameter space (Figure 3a), an EP, the discernable branch point singularity can be reached by proper engineering of &theta; and &Delta;neff. Therefore, these two tuning knobs together form a complete basis for steering toward a maximal chirality at EPs. In the simulated mode field distributions at EP (Figure 3b), the traveling-wave pattern for excitation at port 1 is in sharp contrast with the standing-wave pattern for excitation at port 2. Owing to the extremely high mode chirality, the backscattering upon excitation in the CW direction is suppressed down to&asymp;&minus;35 dB.Figure 3Open in figure viewerPowerPointSteering to an EP in a spiral ring. a) The eigenvalue surfaces summarized in &theta; -&Delta;neff parameter space, including the wavelength detuning (top) and the linewidth detuning (bottom). b) Simulated mode field intensity distributions at EP for a spiral ring with &theta;&asymp;119.66&deg; excited at port 1 (top) and 2 (bottom). The extracted chirality reaches&asymp;&minus;0.95.2.3 Characterizations of Mode Chirality by Scattering ImagingFor experimental demonstrations, a set of spiral ring-based add-drop filters was designed upon a fixed radius of 20 &micro;m and a varying &theta; in the range of 118.50&deg; and 122.00&deg;and fabricated leveraging the multiple-project wafer (MPW) service (see Figure 4a and Experimental Section). Silicon nitride as the waveguiding material features a wide transparency window, enabling characterizations at &asymp;780 nm. Instead of collecting transmission intensity signal Ijk at the grating couplers using fibers, out-of-plane scattering signals at multiple ports can be simultaneously collected through an objective lens and imaged using a low-noise CMOS image sensor (see Section S4, Supporting Information).Figure 4Open in figure viewerPowerPointCharacterization of mode chirality in fabricated spiral rings with varying &theta;. a) Optical microscope image of a spiral ring-based add-drop filter. b-c) Measured transmission spectra of I12 and I21 (top), I24 and I23 (middle), and I14 and I23 (bottom), for spiral rings with &theta; = 120.00&deg; (b), and &theta; = 119.00&deg; (c). d) Summarized relationship between the extracted chirality and &theta;.Figure 4b shows the measured transmission spectra for &theta; = 120.00&deg;. The consistency between I12 and I21 verifies Lorentz reciprocity. The moderate quality (Q) factor is attributed to the induced scattering loss at the spiral edges and potential radiation loss due to the mismatch of waveguide modes between different segments of the ring. The absence of mode splitting here agrees with the simulated results in Figure 2c,d. Due to edge-induced backscattering, &eta;BS upon excitation in the CCW direction is&asymp;&minus;7 dB. The&asymp;2&minus;fold higher value of I23 compared to I14 indicates a moderate asymmetry in backscattering. Besides, the extracted &alpha; of&asymp;&minus;0.16 exemplifies the co-existence of counterpropagating components. By changing &theta; to 119.00&deg; (Figure 4c), one can clearly discern that &eta;BS can be optimized by&asymp;&minus;17 dB. The backscattering gets significantly mitigated while the two eigenvectors become almost collinear in the case of strong mode chirality. The contrast between I14 and I23 implies a highly asymmetric backscattering and again examines the dominant contribution of the CCW component in this chiral mode (&alpha;&asymp;0.8).Figure 4d summarizes the measurement results of 15 samples (&theta; ranging from 118.50&deg; to 122.00&deg;) fabricated on a single block, showing a large dynamic range of &alpha; between&asymp;&minus;0.7 and&asymp;0.8. The characterized backscattering conditions of spiral rings were compared with those of regular rings in which the intrinsic surface roughness dominates the effect (see Section S5, Supporting Information). The characterized mode chirality of regular rings is typically very weak (|&alpha;| < 0.1). Notably, the intrinsic roughness-induced Rayleigh scattering may exhibit variations across different rings, leading to high yet probabilistic &eta;BS ranging between&asymp;&minus;9 and &minus;2 dB. Such an uncertainty of Rayleigh scattering also accounts for the complexity of the modulation depicted in Figure 4d. By introducing the spiral geometry and edge-induced backscattering, the effect of intrinsic Rayleigh scattering can be compensated, leading to an optimized &eta;BS down to&asymp;&minus;24 dB.2.4 Electrically Reconfiguring the Mode ChiralityConsidering inevitable fabrication errors, the mode chirality in a spiral ring might not be deterministically close to a desirable value due to uncertainties in structural parameters, especially T. Under this circumstance, an efficient post-fabrication reconfiguration of mode chirality is highly desirable. In particular, the tuning of &Delta;neff can be realized by an integrated thermal tuner module on top of the segment between two spiral edges. Upon electrical injection up to 60 mW, the tracked transmission spectra in Figure 5a reveal a spectral redshift &Delta;&lambda;res up to&asymp;0.42 nm (corresponding to &Delta;neff of&asymp;0.0031 RIU). For spectra with reversed excitation directions, the evolution of asymmetry in backscattering upon an increased injection power can be explicitly revealed, corresponding to reconfigured chirality from&asymp;&minus;0.2 to 0.6 (Figure 5b). Simulation results in Figure 5c present that the chirality continuously increases from&asymp;&minus;0.1 to 0.5 upon &Delta;neff of&asymp;0.004 RIU.Figure 5Open in figure viewerPowerPointCharacterization of electrically reconfigurable mode chirality. a) Lorentzian fits of resonant spectra upon an increased injection power for I14 (top) and I23 (bottom) in a spiral ring with &theta; = 120.00&deg;. b) Extracted chirality as a function of the injection power. c) Extracted chirality as a function of &Delta;neff. d) Extracted &eta;BS as a function of the injection power. e) Extracted &eta;BS as a function of &Delta;neff.Given the augmented chirality, experimentally characterized &eta;BS for excitation in the CCW direction was optimized from &minus;7 to &minus;18 dB (Figure 5d), while the simulated results suggest the optimized value from&asymp;&minus;14 to &minus;20 dB (Figure 5e). During this reconfiguration process, the extracted Q factor at strong chirality (power of 60 mW) gets improved by 15% compared to that at a weak chirality (power of 30 mW), which further ascertains the suppression of mode splitting width g (see Section S6, Supporting Information). Notably, electrical reconfiguration enables not only sign-reversing of chirality but also reinforced chirality approaching an EP (see Section S6, Supporting Information for a characterized maximal chirality of&asymp;0.86).In view of the deviation between experimental and simulation results in Figures 2, 3 and 5, one should note that numerical simulations cannot serve as a direct prediction of the performance of experimentally realized devices due to the uncertainties of geometry in actual fabrications. In our tolerance analysis (see Section S7, Supporting Information), the effect on the variance of T in actual fabrications was carefully studied. Considering &Delta;T = &plusmn; 20 nm at the very least, the mode chirality can be efficiently manipulated using &theta;. Therefore, there are no challenges arising from the constraints of dimensions, which is advantageous compared with the required precision in the dimensions of nanostructures and potential susceptibility in the reported “two-scatterers” approach for WGM microcavities.[28, 32],3 ConclusionIn this work, we proposed and demonstrated strong yet reconfigurable mode chirality in spiral microring resonators. Through benchmarking with previous experimental studies on chiral modes in microrings and other WGM microcavities (see Supporting Information Section 8), we report to our knowledge the first demonstration of reconfigurable mode chirality in integrated optical microresonators. Besides, the full process was implemented using solely on-chip integrated modules leveraging mature foundry services. The non-Hermiticity in the spiral microring system can be manipulated by tuning the relative spacing between two spiral edges, leading to the experimental observation of strong chirality up to&asymp;0.86. Compared with regular microrings with probabilistic non-Hermicity due to fabrication imperfections, the originally Rayleigh scattering-dominated backscattering can be suppressed with &eta;BS down to&asymp;&minus;24 dB. Besides, an integrated phase tuner was pivoted as a control knob to steer toward or away from EPs and the correlated maximal chirality. Electrical re-configuration of the chirality has been corroborated by both experimental and simulation results.All in all, we envision that the formulated insights in spiral ring resonators will serve as a bridge that connects peculiar behaviors in non-Hermitian photonics with various functional devices in optoelectronic integrated circuits. Such integrated microring resonators with electrically reconfigurable mode chirality have great potential as generic optically passive and active building blocks, shaping the light flow and emission on a chip for optical signal processing in both classical[49] and quantum[6, 50, 51] regimes. This finding may further spark a surge of chiral EP-enabled functionalities, such as enhanced sensing,[28] unidirectional and reconfigurable emissions,[16, 17, 52] non-reciprocity,[5] and chiral perfect absorption.[53]4 Experimental SectionNumerical SimulationNumerical simulations were performed based on the finite-element method (COMSOL Multiphysics, wave-optics module). Limited by the computation power, 2D modeling was adopted. The device geometry in the simulation follows exactly with the fabricated ones (W = 500 nm, T = 166 nm, and R = 20 &micro;m). The effective refractive index neff was set as&asymp;1.7 + 3 10&minus;7i, in which the real part takes into account the confinement in the vertical dimension through boundary mode analysis, and the imaginary part was introduced considering the waveguide propagation loss (&asymp;0.2 dB cm&minus;1). While the input port was excited using transverse electric (TE) -polarized light, transmission spectra at the other three ports can be collected by wavelength sweeping (step of 2 pm). Fine meshing condition was applied to the waveguide and microring region (grid size of&asymp;20 nm). Besides, for understanding the inter-modal coupling and non-Hermicity, a pair of eigenvalues and eigenstates was calculated using the eigenmode solver.Device FabricationWaveguide-coupled microring resonators were fabricated on a silicon-nitride-on-silica platform in a single block of&asymp;10 5 mm by an MPW service (AN150, LIGENTEC). The layout was prepared using a photonic integrated circuit design software (IPKISS, Luceda) leveraging the foundry PDK. For single-mode propagation at&asymp;780 nm, the waveguiding SiN layer thickness was chosen as 150 nm, and the waveguide width was chosen as 500 nm. The aluminum-based phase shifter was integrated on the segment between the two spiral edges, which offers a phase tuning up to&asymp;0.54 due to the thermo-optic effect.Device CharacterizationThe wavelength-tunable laser light (TLB-6712, Newport) at&asymp;780 nm was coupled into a single-mode fiber using free-space optics. The polarization was adjusted by a fiber-based polarization controller. The waveguide-coupled microring resonators were probed by grating couplers, and characterized by two fibers with the assistance of a high-precision aligning system with a feedback loop (AP-SSAS-SIP-SAXYZ, Apico). Transmission signals were measured using an optical power meter (PM100D, Thorlabs). For imaging of out-of-plane scattered light, a long-working-distance microscope objective lens (10&times; Mitutoyo Plan Apo, NA = 0.28) and a monochrome sCMOS camera (CS2100M-USB, Thorlabs) with 1080 &times; 1920 pixels (pixel size of 5.04 &times; 5.04 &micro;m) were employed. The optical power being scattered at the drop port was estimated to be&asymp;10 pW or less. The exposure time was adjusted between 1 and 200 ms to avoid signal saturation. For electrical reconfiguration of chirality, bias voltage was applied via two probes using a source meter (S100, Precise). The calibrated tuning efficiency was&asymp;5.2 &times; 10&minus;5 RIU mW&minus;1.AcknowledgementsJ.W. acknowledges the support from the National Natural Science Foundation of China (NSFC) under Grants U22A2093, 62105080 and 62211530431, the Guangdong Basic and Applied Basic Research Foundation Regional Joint Fund under Grants 2020B1515130006, 2021B515120056 and 2023A1515011944, the Science and Technology Innovation Commission of Shenzhen under Grants JCYJ20220531095604009 and RCYX20221008092907027.Conflict of InterestThe authors declare no conflict of interest.Author ContributionsY.C. and J.L. contributed equally to this work. J.W. and X.C.X. conceived the idea. J.L.,S.B., and R.F. performed the theoretical analysis and numerical modeling; Y.C., K.X., X.W., and J.D. designed the devices and conducted the experiments; Y.C. and J.L. performed the data analysis with the assistance of C.H.; J.W., L.P., and X.C.X. supervised the project; J.W. and J.L. wrote the manuscript; All authors discussed the results and contributed to the manuscript.

Jun. 27, 2024Journal
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