Active broadband unidirectional focusing of terahertz surface plasmons based on a liquid-crystal-integrated on-chip metadevice

Yi-Ming Wang; Fei Fan; Hui-Jun Zhao; Jing Liu; Yun-Yun Ji; Jie-Rong Cheng; Sheng-Jiang Chang

doi:10.1364/PRJ.527697

1. INTRODUCTION

With the rapid development of terahertz (THz) technology, THz functional devices provide critical support in the fields of wireless communications, high-resolution imaging, and biochemical sensing [1,2]. In particular, metasurfaces provide wide applications for free-space beam steering [3 –5], but controlling on-chip propagation requires new mechanisms. Surface plasmons (SPs) are special electromagnetic modes propagating at the conductor-medium interface, showing great prospects in ultra-compact optical devices and integrated systems [6,7]. Unfortunately, in the THz regime, surface plasmonic waves (SPWs) at flat metal surfaces can hardly be highly confined. Structured metallic surfaces composed of subwavelength elements provide a way to construct on-chip metadevices, of which the resonance fields are capable of SP coupling and control [8,9]. In recent years, THz SPW-based devices have made great progress [10 –12], meeting the requirements of miniaturization, low energy consumption, high efficiency, and on-chip integration in future THz applications.

Previous studies have shown that the excitation and propagation of SPWs are controllable by precisely customizing the geometry and distribution of microstructural units [13 –15]. In 2013, Lin et al. utilized plasmonic hole array structures to realize the spin-dependent directional excitation of surface waves in the visible and near-infrared bands [16], which also provides a path for efficient generation and flexible wavefront control of SPWs in the THz band [17 –19]. For example, based on the Pancharatnam–Berry mechanism, Wang et al. proposed a gradient-phase on-chip metadevice that converts the circularly polarized (CP) beams into SPWs with focusing or defocusing, dictated by the chirality of the incidences [19]. However, the on-chip wavefront manipulation of SPW typically requires complex shapes or several phase elements. The SPW interference effect of subwavelength slits offers an alternative route to simplify the design process [20 –22]. In 2022, an SP metalens was constructed by two sets of slit pairs with different resonance responses as the basic unit, which can work for non-uniformly polarized incidence [20]. It is worth noting that, because of the strong dispersion of SPWs, broadband wavefront manipulations for THz SPWs have been rarely reported [23,24], which hinders the development of broadband communication and optical information processing, especially about on-chip achromatic wavefront modulation.

Moreover, on-chip active manipulation of THz SPWs has also faced challenges, due to the difficulties in the functional material integration on-chip and the active interaction with THz waves [25 –27]. The modulations of a unidirectional SPW launcher and propagator based on metadevices are almost passive, or simply by mechanically changing the incident polarization [28 –30]. To our knowledge, there are few experimental reports on active THz SPW on-chip transmission or wavefront modulation [26,27,31]. The strategy of introducing functional materials into microstructures, such as semiconductors, graphene, and vanadium dioxide, has been widely applied in active metasurfaces to manipulate the free-space THz waves [32 –34], which is of referential significance for the development of active THz SPW on-chip devices.

In particular, liquid crystal (LC) has broadband adjustable anisotropy in the THz regime, so remarkable phase shift and polarization conversion can be reversibly and continuously regulated by thermal, optical, electrical, and magnetic means [35 –37]. There have been some works on free-space wavefront modulation based on THz LC metadevices, such as LC active beam deflection and coded metasurfaces [38 –40]. Recently, Zhuang et al. demonstrated a metasurface with an LC elastomer as the substrate, enabling broadband wavefront steering by the control method of infrared light or heating [41]. Therefore, the combination with the LC configuration is considered a promising method to develop active THz devices, but it has been rarely applied in SPW-based metadevices.

In this work, we take the lead in demonstrating the broadband focusing and the active modulation of on-chip SPWs. To achieve this purpose, an on-chip metadevice based on the combination of arc-arrayed pair-slit resonators (APSRs) and LC configuration is proposed. In our scheme, multiple APSRs with mirror symmetry are adopted to achieve spin-selective unidirectional focusing of SPWs. More importantly, the broadband feature is realized by selecting several slit geometric sizes and further considering the corresponding arc radius to meet the phase-matching conditions. Moreover, the integration of LC introduces an approach for the polarization conversion enabling SPW intensity modulation and dynamic energy distribution between left and right focal spots.

2. METHOD

A. Geometric Structure and Theoretical Analysis

Figure 1(a) schematically illustrates the principle of wideband excitation and unidirectional focusing of multi-APSRs for THz SPWs. This on-chip metadevice is a metallic thin film with a subwavelength pair-slit as its basic structure. Each APSR with the same central angle $ψ$ is composed of $ψ / θ$ pair-slits arrayed by the equal angular spacing $θ$ . As shown in the detailed diagram in Fig. 1(a), one pair-slit consists of two slits of the same geometric size, with an orientation angle of $ϕ_{1} = 135 °$ and $ϕ_{2} = 45 °$ . Their geometric centers with transverse and longitudinal relative distances $l$ are both at $λ_{SPW} / 4$ . The excited SPW field under the CP incidence can be expressed as follows [16,42]: $E_{τ, σ} = \frac{\tilde{C}}{\sqrt{2 l}} τ [e^{i \frac{π}{4} (σ + τ)} + e^{- i \frac{π}{4} (σ + τ)}],$ (1)where $τ = - 1$ and $+ 1$ respectively represent one-way excitation to the left and right sides of the pair-slit unit; $σ = - 1$ and $+ 1$ represent right-handed circular polarization (RCP) and left-handed circular polarization (LCP) incidences. $\tilde{C}$ is a complex coefficient determined by the response of SPWs on a single slit. It is indicated that the LCP/RCP incidence only excites the SPWs to the left/right along the unit orientation, which is called spin-dependent unidirectional excitation.

Figure 1.(a) Schematic diagram of the broadband SPW excitation in the multi-APSR. Left corners are the detailed diagrams of paired slits and one single APSR structure. (b) Functions of broadband APSR. (c) Simulated and experimental transmission spectra of slits with different geometric sizes. (d) Simulated $E_{z}$ near-field (real part) distribution and (e) phase maps of SPWs excited by each APSR at 0.35, 0.40, 0.50, and 0.60 THz.

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The wavefront shaping of SPWs can be realized by arranging the orientation of the pair-slits. As illustrated in Fig. 1(a), each arc-shaped structure is composed of pair-slits with the same geometry, which are arrayed in a radial orientation with an equal distance $r$ to the center. In one APSR, the SPWs excited from each pair-slit can propagate radially towards the arc center with the same efficiency, forming a focal spot with strong intensity due to the same initial phase and propagation phase. In contrast, when the SPWs propagate radially outwards, the intensity is much weaker owing to the divergent wavefront and can hardly be detected. The on-chip metadevice is further designed as two sets of multi-APSRs with mirror symmetry as shown in Fig. 1(b). Each side of the structure consists of five concentric arcs with $ψ = 120 °$ , which are numbered as $j = 1 - 5$ from the outermost to the innermost, with $+$ and $-$ representing the right side and left side, respectively. The APSR metadevice excites the SPWs unidirectionally focusing at the left/right center responding to LCP/RCP wave incidence.

As defined in Eq. (1), for a certain arc under the incident LCP (RCP) wave, the SPW will be excited unidirectionally toward the center with the initial SPW field obtained as $E_{1, - 1} = \frac{\tilde{C}}{\sqrt{l / 2}} (E_{- 1, 1} = - \frac{\tilde{C}}{\sqrt{l / 2}})$ . More importantly for the multi-APSRs, the overall SPW field is the interference between $E_{- 1, 1}$ from the different five arcs on the left side, while $E_{1, - 1}$ in the right-side field. The SPW fields $E_{F}$ at the left/right center are calculated by Eqs. (2) and (3): $E_{F, L} = \sum_{j} - \frac{{\tilde{C}}_{j}}{\sqrt{l_{j} / 2}} A_{LCP} e^{i [φ_{LCP} - k_{SPW} \cdot (- r_{j})]} = \sum_{j} - \frac{| C_{j} |}{\sqrt{l_{j} / 2}} A_{LCP} e^{i [ϕ_{LCP} + k_{SPW} \cdot r_{j} + ang (C_{j})]},$ (2) $E_{F, R} = \sum_{j} + \frac{{\tilde{C}}_{j}}{\sqrt{l_{j} / 2}} A_{RCP} e^{i (φ_{RCP} + k_{SPW} \cdot r_{j})} = \sum_{j} + \frac{| C_{j} |}{\sqrt{l_{j} / 2}} A_{RCP} e^{i [φ_{RCP} + k_{SPW} \cdot r_{j} + ang (C_{j})]} .$ (3)

Neglecting the loss of divergent propagation from the other side, they can be uniformly described as Eq. (4): $E_{F} = \sum_{j} τ A_{σ} \frac{| C_{j} |}{\sqrt{l_{j} / 2}} e^{i [φ_{σ} + k_{SPW} \cdot r_{j} + ang (C_{j})]},$ (4)where $r_{j}$ represents the distance from the slit position to a certain on-chip point.

To ensure the SPW focuses from the different arcs simultaneously, constructive interference is desired to happen at the left/right center, of which conditions can be described as follows: $| C_{j + 1} | / | C_{j} | = \sqrt{l_{j + 1} / l_{j}} = \sqrt{λ_{SPW, j + 1} / λ_{SPW, j}},$ (5) $k_{SPW} (r_{j + 1} - r_{j}) + ang (C_{j + 1} / C_{j}) = 2 n π,$ (6)where $n$ is an integer, and $k_{SPW} = 2 π / λ_{SPW}$ is the wave vector with the SPW wavelength $λ_{SPW}$ . In this case, Eq. (4) can be expressed in a form of satisfying the constructive interference condition: $E_{F} = τ A_{σ} \frac{| C_{1} |}{\sqrt{l_{1} / 2}} e^{i [φ_{σ} + k_{SPW} \cdot r_{1} + ang (C_{1})]} \cdot {1 + \sum_{2}^{j} \frac{| C_{j} | / | C_{1} |}{\sqrt{l_{j} / l_{1}}} e^{i [k_{SPW} \cdot (r_{j} - r_{1}) + ang (C_{j} / C_{1})]}} = j τ A_{σ} \frac{| C_{1} |}{\sqrt{l_{1} / 2}} e^{i [φ_{σ} + k_{SPW} \cdot r_{1} + ang (C_{1})]},$ (7)where the first arc $j = 1$ is set as a reference. When the geometries of the different arcs satisfy Eq. (7), a good focusing can be obtained at a certain frequency.

As illustrated in Eq. (5), the geometry of slits in the different arcs related to $C_{j}$ determines its operating band, which stems from the resonance-determined local controlling ability of slits over the phase, amplitude, and dispersion of the SPW field. For a certain geometry of slit arrays, the operating band is very narrow. Figure 1(c) shows the simulated and experimental transmission spectra of slits with four geometry sizes [as illustrated in Appendix A, Fig. 7(a)] for the polarization direction perpendicular to the slit long-axis (i.e., ${| E_{y} |}^{2}$ spectra). The numerical simulation methods can be found in Appendix B. The results show the typical extraordinary optical transmission (EOT) peaks of THz subwavelength metallic hole arrays, which are closely related to SP excitation. The central excitation frequency of SPW is always located slightly higher than the peak frequency of EOT. The dashed line marks the four different SPW excitation frequencies from 0.38 to 0.61 THz with different slit geometries.

When we design these four kinds of slits in different arcs, each arc excites the SPWs at the corresponding frequency and contributes to broadening the frequency band, so the broadband APSR is designed as shown in Fig. 1(b). In particular, the radius $r_{j}$ of multi-APSRs should be tailored according to the different dispersion characteristics of slits based on Eq. (6). As a comparison, the narrowband APSR including only one kind of slit is also designed, where $Δ r = n λ_{SPW}$ for $Δ C_{j} = 0$ . The detailed geometric parameters can be found in Appendix A. In the broadband APSR, the near-field $E_{z}$ distributions of SPWs excited by each APSR at four different frequencies are simulated as shown in Fig. 1(d), where the temporal and spatial dispersion characteristics among the different APSRs can be seen clearly. The arc radii $r_{j}$ ( $j = \pm 5, \pm 4, \pm 3$ , both $\pm 2$ and $\pm 1$ ) of broadband APSR are precisely designed: (i) for a certain arc, the focusing intensity of SPWs at the frequency matching its slit size is enhanced; (ii) at a certain frequency, the total phase difference of SPWs excited by multiple APSRs at the focal spot is close to 0 rad, which satisfies the phase matching condition. Furthermore, Fig. 1(e) gives a more comprehensive view of phase distribution, which further proves the theoretical analysis that phase matching at the focal spot has been achieved. Thus, the broadband APSR focuses the SPWs with spin-selectivity to the left and right arc centers over a wider frequency band.

B. Device Fabrication

LC is introduced into the broadband APSR to construct an active on-chip SP metadevice, as shown in Fig. 2(a). The integration of the LC provides an effective strategy for active modulation of the focusing SPWs. The thickness of the LC layer is designed to get an anisotropic phase difference of $π / 2$ rad at the central frequency of 0.475 THz, which enables the polarization conversion as a quarter-wave plate (QWP). As shown in Fig. 2(b), when the polarization direction of the incident linearly polarized (LP) wave is along $+ 45 °$ , the THz wave transmitting through the LC will be converted into an RCP or LCP state in the condition of $α = 0 °$ or 90°, respectively, where $α$ represents the angle between the orientation of LC molecules and the $x$ -axis [43]. It is noted that the ratio of LCP and RCP components can be tuned by the rotation of LC molecules. More importantly, the focusing SPW energy distribution of broadband APSR is relevant to the LC orientation, which concentrates at the left or right focal spot when $α = 0 °$ or 90°. Therefore, the active modulation of the focusing SPWs can be realized with the rotation of LC molecules driven by the electric field.

Figure 2.(a) Structure of THz LC-integrated APSR on-chip metadevices. The photo of practical broadband APSR and its micrographs are shown in the right dotted frame. (b) Schematic diagram of the working principle of LC-integrated SP metadevices. (c) Near-field scanning with THz microprobe. The details of two microprobe types for transversal and longitudinal near-field detection are shown on the right. The antenna gap directions in probe spikes are along the $y$ direction and the $z$ direction. (d) Near-field scanning-terahertz time-domain spectroscopy (NFS-THz-TDS) system.

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The structure of the LC-integrated on-chip metadevice is listed as follows: (i) Broadband APSR, which is fabricated by a laser direct writing process on gold film with ion sputtering thickness $h_{1} = 100 nm$ . (ii) The front glass layer, which is the substrate of the broadband APSR. (iii) The LC layer, with its thickness $h_{3}$ of 525 μm. LC is filled in the cell between two glass substrates encapsulated by the ultraviolet glue. The LC used in this work is a kind of high-birefringence nematic LC (HTD028200) from Jiangsu Hecheng Technology Co., Ltd., of which $n_{e}$ and $n_{o}$ are 1.89 and 1.61 in the THz regime, respectively, that is, its birefringence $Δ n = 0.28$ . It has good thermal stability in the nematic state, and the transition temperatures from solid to nematic state and from nematic state to isotropic state are $T_{SN} = - 30 ° C$ and $T_{SI} = 103 ° C$ . The measured THz optical responses of the LC layer are shown in Appendix C. (iv) The back glass substrate, which is a pre-oriented anchor layer in the $y$ direction, so that LC molecules are initially oriented along the $y$ -axis. The thickness of these two JGS1 glass substrates is the same of $h_{2} = h_{4} = 300 μm$ . (v) Two custom copper wires with a diameter of 525 μm, serving as a spacer to ensure the thickness of the LC layer, and also as the electrodes, supporting a biased electric field along the $x$ direction. As the bias electric field increases from 0 to 12 V/mm, the orientation of LC molecules rotates from the $y$ -axis to the $x$ -axis.

C. Experimental Setup

We conduct our experiments by using a near-field scanning THz time-domain spectroscopy (NFS-THz-TDS) system in Figs. 2(c) and 2(d). The excitation source is a femtosecond laser with 780 nm wavelength (CFL-10RFF, from Carmel Laser Company). It works with a repetition rate of 80 MHz, a pulse width of 86 fs, and a maximum average output power of 1.0 W. All experiments were carried out at room temperature (20°C) and relative humidity $< 30 %$ . The laser beam is divided into two optical paths; one is used to generate the THz wave by a GaAs photoconductive antenna, and the other is coupled into an optical fiber and then guides the output beam to the photoconductive near-field probe for THz detection. The sample is placed slightly away from the lens focus so that a parallel THz beam with a diameter of 2 cm is incident on the device from its substrate. The microprobe is fixed on the two-dimensional translation platform to allow mapping of the near-field distribution. In particular, as shown in Fig. 2(c), two types of microprobes, the transversal field microprobe and longitudinal field microprobe (TeraSpike TD-800-X and TD-800-Z, from Protemics Company, Aachen, Germany), are capable of detecting near-field components of $E_{y}$ and $E_{z}$ , respectively. The microprobe is 100 μm away from the device surface. The scanning area is $[- 6, + 6]$ mm in the $x$ direction and $[- 4, + 4]$ mm in the $y$ direction with the scanning step of both 1 mm. The mapping pixels after the interpolation algorithm are $61 \times 41$ . The time sampling interval is 0.2 ps, and the whole time of each time-domain signal is 40 ps in experiments. Fourier transform is performed with the rectangular window function after padding 0 to 400 ps to obtain the spectrum at each spatial point.

3. RESULTS AND DISCUSSION

A. Broadband SP and Spin-Selective Unidirectional Focusing

To characterize broadband and actively tunable SPWs focusing on devices, both the transversal near field and the longitudinal near field are detected. The transversal component $E_{y}$ reflects the localized field signal directly through the slits at the SPW excitation position, and the longitudinal component $E_{z}$ just reflects the SPW propagation on the metallic surface. First, the normalized transmittance spectra of near-field $E_{y}$ at several key scanning points labeled $P_{1} - P_{8}$ on the broadband APSR are obtained, as shown in Fig. 3(a). We notice that there is an EOT peak appearing at about 0.6 THz, 0.5 THz, 0.4 THz, and 0.35 THz, as the corresponding detected positions spatially move from $P_{1}$ to $P_{4}$ and mirrors from $P_{8}$ to $P_{5}$ . The experimental results indicate that the central frequency to excite SPWs of each arc in APSR is different, on account of the corresponding slits being different in size. The peak frequency of the near field on the whole APSR structure is in good agreement with that of far-field results in Fig. 1(c). Meanwhile, Figs. 3(b) and 3(c) illustrate that near-field $E_{y}$ hot spots are mainly concentrated on slits among the arcs numbered [ $\pm 5, \pm 4$ ], [ $\pm 3, \pm 2$ ], and [ $\pm 1$ ], respectively, at 0.35, 0.475, and 0.60 THz, while being weak at the remaining part of the structure due to total metal reflection. It is preliminarily indicated that the SPWs of different frequencies are excited by the arc of different radii in the broadband APSR as predicted in the theoretical design in Section 2.

Figure 3.Transversal near-field detection on the broadband APSR. (a) Normalized transmittance spectra of $E_{y}$ components in the near field of broadband APSR at the scanning points from $P_{1}$ to $P_{8}$ . (b) Experimental and (c) simulated near-field $E_{y}$ component intensity distributions.

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Next, we investigate the longitudinal near-field $E_{z}$ component to directly demonstrate the broadband SPW focusing characteristics of the broadband APSR. The LCP and RCP waves are normally incident on the chip surface to obtain the two different output states since the focusing of the SPWs on each side is spin-dependent. A THz QWP is applied in the experiment to convert the LP wave into the CP waves in the NFS-THz-TDS experiment, of which details can be found in Appendix D.

Figure 4(a) shows the near-field $E_{z}$ transmission spectra at the focal spot for the focusing and defocusing states on the broadband and the narrowband APSR, respectively. Since the mirror-symmetric pattern of APSR makes the unidirectional focusing, that is, when a strong focusing of the SPW occurs around the center of one side, the SPWs defocus on the other side with the maximum extinction ratio of 25 dB for the broadband APSR and 20 dB for the narrowband APSR. As the 5 dB bandwidth is considered as an index, it shows that the operating bandwidth of the broadband APSR is 270 GHz in the range of $0.33 - 0.60 THz$ , which is significantly broader by 2.45 times than the narrowband APSR within 110 GHz, from 0.45 to 0.56 THz. Figures 4(b) and 4(c) illustrate the simulated and experimental near-field SPW intensity ( ${| E_{z} |}^{2}$ ) distributions under LCP incidence. Obviously, at 0.475 THz, the SPWs excited on both the broadband and narrowband APSR propagate unidirectionally to the left and focus at the left center. The difference is that the focusing state still maintains at 0.35 THz and 0.60 THz in the broadband APSR, but not in the narrowband APSR. Similarly, the SPWs focus unidirectionally on the right center under RCP incidence, as additionally shown in Fig. 9(c) (Appendix D).

Figure 4.Longitudinal near-field detection of the APSR. (a) Near-field $E_{z}$ spectra of broadband and narrowband APSR in focusing and defocusing cases. (b) The simulated near-field $E_{z}$ intensity distributions of the broadband and narrowband APSR under the LCP incidence. (c) The corresponding experimental results. (d) The simulated near-field $E_{z}$ intensity distributions of the longitudinal focusing along the $x$ direction and the transverse focusing along the $y$ direction on the focal spot at 0.475 THz. (e) The corresponding experimental results.

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To evaluate the focusing performance, the resolution of the focal spot is defined as $R = S_{FWHM} / λ_{0},$ (8)where $S_{FWHM}$ represents the spot diameter with half of the focusing peak, and $λ_{0}$ is the wavelength in free space. We choose the central frequency of 0.475 THz to discuss the SPW focusing resolution and its free-space wavelength $λ_{0} = 631 μm$ ( $λ_{SPW} < λ_{0}$ ). In the simulation, as shown in Figs. 4(d) and 4(e), the focusing resolutions of the broadband and narrowband APSRs are approximately the same, which indicates that the broadband design eliminates the spatial dispersion well and does not cause deterioration of the focusing resolution. The transverse resolution is $0.32 λ_{0}$ , higher than the longitudinal resolution of $1.42 λ_{0}$ in the simulation. The experimental results are lower than those in simulations. This is caused by the limitation of the probe scanning precision and the increase of the distance between the probe and the metallic surface in the experiment to limit the scanning time and prevent probe damage. Therefore, a broadband spin-dependent unidirectional SPW transmission is achieved in the broadband APSR, of which the mirror-symmetric structure makes it selectively focus to one side according to the incident spin state.

B. Active Unidirectional Focusing of the SPW

In this part, we demonstrate the LC-integrated APSR on-chip metadevice by the near-field $E_{z}$ intensity distributions. As shown in Fig. 5(a), the LC orientation can be controlled dynamically with the external electric bias in the $x - y$ plane. When there is no external electric field, the LC molecules are pre-oriented along the $y$ -axis and most of the SPW is concentrated around the left focal spot. With the increase of the external electric field, the LC gradually rotates towards the $x$ -axis, and the SPW energy is distributed in a certain proportion between both sides. Once the external electric field reaches 12 V/mm, the LC molecules are completely oriented along the $x$ -axis, so that the SPWs focus on the right center. Figures 5(b) and 5(c) show the SPWs focus on the left at 0 V/mm and then turn to the right at 12 V/mm at 0.35, 0.45, and 0.55 THz, and the simulated results are consistent with the experimental measurements.

Figure 5.(a) Diagram of active energy distribution in the LC-integrated broadband APSR on-chip metadevice. (b) Simulated and (c) experimental near-field $E_{z}$ intensity distributions for active unidirectional focusing of SPWs when the LC is orientated along the $y$ -axis (0 V/mm) and $x$ -axis (12 V/mm). (d) Measured time-domain signals at the left focal spot under the electric field of 0 V/mm and 12 V/mm. (e) Experimental near-field $E_{z}$ spectra of LC-integrated broadband metadevice in focusing and defocusing cases. $x$ -cutting line through the focal spots when the LC orientation is along (f) the $y$ -axis and (g) the $x$ -axis.

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A measured time-domain signal at the left focal spot is displayed in Fig. 5(d) in focusing and defocusing cases, and the corresponding frequency-domain spectra are obtained in Fig. 5(e) after data processing. It is indicated that active unidirectional on-chip focusing is achieved in the range of $0.33 - 0.60 THz$ , with an extinction ratio up to 20 dB. Figures 5(f) and 5(g) present the near-field $E_{z}$ intensity distributions along the $x$ -cutting line through the focal spots to characterize the spatial dispersion of the SPW focusing in the broadband range. The relative offset rate $D$ of the one-side focal spot is defined to describe the achromatic focusing ability, and its calculation formula is as follows: $D = A / S_{FWHM},$ (9)where $A$ stands for the absolute offset distance of the focused spot, and $S_{FWHM}$ is the spot diameter at the central frequency of $f_{0}$ . Thus, $D_{horizontal} = 12 %$ with the condition of $A_{horizontal} = 125 μm$ and $f_{0} = 0.45 THz$ . These results show that the SPWs of different frequencies are focused on the same point, indicating the device design eliminates the spatial dispersion of wideband focusing.

Finally, the active modulation and energy distribution processes of the THz SPWs are demonstrated. As shown in Figs. 6(a) and 6(b), the LC orientation angle $α$ is set varying from 90° to 0° to model the process of applying electric bias in the experiment. As the bias electric field intensity increases from 0 V/mm to 12 V/mm, the focusing SPWs’ intensity on the left center gradually decreases from the “on” to “off” state, and the modulation process on the right side is opposite. To characterize the performance of active modulation, the modulation depth $M$ is defined as follows: $M = (I_{\max} - I_{\min}) / I_{\max}$ , where $I_{\max}$ and $I_{\min}$ are the SPW intensity corresponding to the focusing switch on and off, respectively. Figures 6(c) and 6(d) show the variation of transverse focal spot intensity during the electric modulation and reflect that the introduction of the LC layer does not change the spatial resolution of SPW focusing, compared with Figs. 4(d) and 4(e). The modulation depth in simulation can reach 97.3%, while that in the experiment is slightly lower, achieving 73% driven by the electric field. Therefore, the LC-integrated APSR on-chip metadevice exhibits a high sensitivity for the modulation of SPWs focused in opposite directions, with most energy transferring dynamically.

Figure 6.At 0.45 THz, the near-field $E_{z}$ intensity distribution with the dynamic modulation of SPWs at the left and right focal spots: (a) as the LC rotates from $y$ - to $x$ -axis in the simulation; (b) as the external electric field is enhanced in the experiment. (c) Simulated and (d) experimental near-field $E_{z}$ intensity distribution along the $y$ -cutting line through the focal spots on the left and right sides.

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4. CONCLUSION

In conclusion, we have demonstrated an LC-integrated APSR on-chip metadevice, combining the spin-selective unidirectional focusing of SPW in mirror-symmetric multi-APSR structure and the polarization conversion of LC. A strategy for broadband achromatic focusing is provided in which a variety of slit geometry parameters and corresponding arc radii are elaborately tailored to meet the phase matching. The final focal spot would not deviate from the desired position to achieve achromatic focusing since the excited SPWs arrive at that point in phase. The LC-integrated metadevice realizes the active energy distributions of SPWs between left and right focal spots by applying a biased electric field. Both the simulation and experimental characterization show that the operating bandwidth is 270 GHz of $0.33 - 0.60 THz$ , which is significantly widened by 2.45 times compared to that of the narrowband devices. In terms of the on-chip focal spots, the transverse resolution is $0.32 λ_{0}$ , and the horizontal relative offset is only 12%. In addition, the experimental modulation depth of the SPW focusing can reach up to 73%. With new mechanisms and versatility including the wide operating bandwidth, and directional SPWs’ excitation, focusing, and active modulation in a single metadevice, this work paves the way for many exciting possibilities of realistic integrated THz SP on-chip applications.

Category: Surface Optics and Plasmonics

Received: Apr. 16, 2024

Accepted: Jul. 16, 2024

Published Online: Sep. 9, 2024

The Author Email: Fei Fan (fanfei@nankai.edu.cn)

DOI:10.1364/PRJ.527697

	$j = \pm 1$	$\pm 2$	$\pm 3$	$\pm 4$	$\pm 5$
$a_{j}$ (μm)	200	200	180	160	140
$b_{j}$ (μm)	50	50	50	50	50
$l_{j}$ (μm)	200	200	184	150	120
$θ_{j}$ (°)	5	6	8	10	15
$r_{j}$ (μm)	4000	3200	2576	1500	960

	$j = \pm 1$	$\pm 2$	$\pm 3$	$\pm 4$	$\pm 5$
$a_{j}$ (μm)	160 for all
$b_{j}$ (μm)	50 for all
$l_{j}$ (μm)	150 for all
$θ_{j}$ (°)	5	6	8	10	15
$r_{j}$ (μm)	3300	2700	2100	1500	900