In a few-mode erbium-doped fiber (FM-EDF), which is a key section in a space-division multiplexing (SDM) communication system, linearly polarized (LP) and orbital angular momentum (OAM) modes, as two-mode bases with different phase profiles, can be transformed into each other. In principle, the LP and OAM modes have a different mode spatial intensity distribution and a gain difference for FM-EDF amplifiers. How to analyze and characterize the differential mode-bases gain (DMBG) is important, but still an issue. We build, for the first time to our knowledge, a local analysis model composed of discrete elements of the FM-EDF cross section in areas of mode spatial intensity distribution azimuthal variation. Using the model of the two mode bases, analysis of local particle number distribution and detailed description of the local gain difference are realized, and the overall gain difference between the two mode bases is obtained. By building an amplifier system based on mode phase profile controlling, the gain of two mode bases is characterized experimentally. The measured DMBG is ∼0.8 dB in the second-order mode, which is consistent with the simulation result. This result provides a potential way to reduce the mode gain difference in the FM-EDF, which is important in improving the performance of the SDM communication system.

This erratum notes a correction to a grant number listed in the Acknowledgments section of the originally published article.

Microresonator dispersion plays a crucial role in shaping the nonlinear dynamics of microcavity solitons. Here, we introduce and validate a method for dispersion engineering through modulating a portion of the inner edge of ring waveguides. We demonstrate that such partial modulation has a broadband effect on the dispersion profile, whereas modulation on the entire resonator’s inner circumference leads to mode splitting primarily affecting one optical mode. The impact of spatial modulation amplitude, period, and number of modulations on the mode splitting profile is also investigated. Through the integration of four modulated sections with different modulation amplitudes and periods, we achieve mode splitting across more than 50 modes over a spectral range exceeding 100 nm in silicon nitride resonators. These results highlight both the simplicity and efficacy of our method in achieving flatter dispersion profiles.

With the rapid development of the Internet of Things and big data, integrated optical switches are gaining prominence for applications in on-chip optical computing, optical memories, and optical communications. Here, we propose a novel approach for on-chip optical switches by utilizing the nonlinear optical Kerr effect induced spontaneous symmetry breaking (SSB), which leads to two distinct states of counterpropagating light in ring resonators. This technique is based on our first experimental observation of on-chip symmetry breaking in a high-Q (9.4×106) silicon nitride resonator with a measured SSB threshold power of approximately 3.9 mW. We further explore the influence of varying pump powers and frequency detunings on the performance of SSB-induced optical switches. Our work provides insights into the development of new types of photonic data processing devices and provides an innovative approach for the future implementation of on-chip optical memories.

The flexible and precise control of wavefronts of electromagnetic waves has always been a hot issue, and the emergence of metasurfaces has provided a platform to solve this problem, but their design and optimization remain challenging. Here, we demonstrate two design and optimization methods for metagrating-based metalenses based on the highest manipulation efficiency and highest diffraction efficiency. The metalens operating at 0.14 THz with numerical apertures of 0.434 is designed by these two methods for comparison. Then, the metalens is fabricated with photocuring 3D printing technology and an imaging system is built to characterize the distribution of focal spots. With the highest manipulation efficiency, the metalens shows a focal spot with the diameter of 0.93λ and depth of focus (DOF) of 22.7λ, and the manipulation and diffraction efficiencies reach 98.1% and 58.3%. With the highest diffraction efficiency, the metalens shows a focal spot with the diameter of 0.91λ and DOF of 24.6λ, and the manipulation and diffraction efficiencies reach 94.6% and 62.5%. The results show that the metalenses designed by both methods can perform a filamentous focal spot in the sub-wavelength scale with a long DOF; simultaneous high manipulation and diffraction efficiencies are obtained. A transmission imaging manner is used to verify the imaging capability of the metalenses, and the measurements are satisfactorily congruous with the anticipated results. The proposed methods can stably generate focal spots beyond the physical diffraction limit, which has a broad application in terahertz imaging, communications, etc.

Grating optics lie in the heart of X-ray spectroscopy instruments. The low efficiency and angular dispersion of conventional single-layer-coated gratings significantly limit the transmission and energy resolution of monochromators and spectrometers, particularly in the tender X-ray region (E=1-5 keV). Multilayer-coated blazed gratings (MLBGs) operating at high diffraction orders offer the advantage of achieving both high efficiency and high dispersion simultaneously. Tender X-ray monochromators and spectrometers using different high-order MLBGs have been designed, all demonstrating one to two orders of magnitude higher transmission compared to conventional systems. By employing a 2400 l/mm MLBG at the -4th or -8th diffraction order, the theoretical energy resolution of the instrument is improved by two to three times at 2.5 keV. Two MLBGs operating at the -2nd and -4th orders have been fabricated, showcasing remarkable efficiencies of 34%–12% at 2.5 keV, surpassing that of single-layer-coated gratings by an order of magnitude. Further optimization of manufacturing accuracy can yield even higher efficiencies. The measured angular dispersion agrees well with theoretical predictions, supporting the potential for high resolution. High-order MLBG optics pave the way for a new generation of tender X-ray monochromators/spectrometers that offer both high transmission and high resolution.

Numerical Fresnel diffraction is broadly used in optics and holography in particular. So far, it has been implemented using convolutional approaches, spatial convolutions, or the fast Fourier transform. We propose a new way, to our knowledge, of computing Fresnel diffraction using Gabor frames and chirplets. Contrary to previous techniques, the algorithm has linear-time complexity, does not exhibit aliasing, does not need zero padding, has no constraints on changing shift/resolution/pixel pitch between source and destination planes, and works at any propagation distance. We provide theoretical and numerical analyses, detail the algorithm, and report simulation results with an accelerated GPU implementation. This algorithm may serve as a basis for more flexible, faster, and memory-efficient computer-generated holography methods.

Gyroscopes are crucial components of inertial navigation systems, with ongoing development emphasizing miniaturization and enhanced accuracy. The recent advances in chip-scale optical gyroscopes utilizing integrated optics have attracted considerable attention, demonstrating significant advantages in achieving tactical-grade accuracy. In this paper, a new, to our knowledge, integrated optical gyroscope scheme based on the multi-mode co-detection technology is proposed, which takes the high-Q microcavity as its core sensitive element and uses the multi-mode characteristics of the microcavity to achieve the measurement of rotational angular velocity. This detection scheme breaks the tradition of optical gyroscopes based on a single mode within the sensitive ring to detect the angular rotation rate, which not only greatly simplifies the optical and electrical system of the optical gyroscope, but also has a higher detection accuracy. The gyroscope based on this detection scheme has successfully detected the Earth’s rotation on a 9.2 mm diameter microcavity with a bias instability as low as 1 deg/h, which is the best performance among the chip-scale integrated optical gyroscopes known to us. Moreover, its high dynamic range and highly simplified and reciprocal system architecture greatly enhance the feasibility of practical applications. It is anticipated that these developments will have a profound impact on the field of inertial navigation.

Owing to the dynamic tunability and strong confinement, graphene plasmons (GPs) have emerged as an excellent candidate for the manipulation of light–matter interaction. Surface plasmons (SPs) have been admitted as another effective way allowing strong confinement of light at the nanoscale. The combination of GPs and SPs like localized surface plasmons (LSPs) and propagating surface plasmon polaritons (SPPs) will lead to a synergistic effect that could remarkably improve light–matter interactions, showing great potential for many applications for the improvement of solar cell efficiency, biosensor sensitivity, and the performance of photonic devices. In this study, the GPs were activated by placing graphene film onto a two-dimensional (2D) phase-changing crystalline Ge2Sb1.5Bi0.5Te5 (cGSBT) nanograting structure, which also acts as an original source generating LSPs. The SPPs originated by laying the above structure onto an Au mirror. The combined effects of GPs, LSPs, and SPPs are epitomized in such a simple Gr/2D cGSBT gratings/Au heterostructure, which allows easy realization of an ultrafast mode-locked laser quite stable working at 1550 nm range due to the strong nonlinear optical absorption capability. This approach overcomes the heat and energy loss in metallic gratings or a Gr-based heterostructure, exhibiting great potential for applications in the design and fabrication of photonic devices.

We present a differential laser absorption spectroscopy (DLAS) system operating at 1550 nm for rapid and sensitive gas concentration measurements. A dual-wavelength toggling mechanism is presented, which significantly reduces data processing, hence supporting a high update rate and data robustness against fast-changing environmental conditions. We showcase the ability to toggle between two wavelengths separated by 90 pm in 14 μs and with minimal chirp (∼1 pm), facilitating sensitive DLAS measurements at 8 kHz update rate. This performance is achieved by driving a 1550 nm diode laser with a modified square-wave current pulse, overcoming the thermal time constant limited wavelength-modulation response of the diode laser. A sensitive feedback mechanism ensures excellent long-term wavelength stability better than 1.4 pm peak-to-peak at 8 kHz toggling over 20 h. As a performance test, we measured the volumetric ratio (VMR) of hydrogen cyanide (HCN) gas in a fiber-coupled gas cell with less than 0.2% peak-to-peak variation over 20 h at 40 Hz. A best sensitivity in VMR of 8×10-6 was achieved at 25 ms integration time. The simplicity and high update rate of our system make it well-suited for gas monitoring in dynamic atmospheric and industrial environments. Further, it offers potential utility in applications requiring precise wavelength control, such as injection seeding of pulsed lasers. A simple analytical model is derived, which, in detail, supports the experimental results, hence offering a tool for future design optimization.