Terahertz vortex waves, as important carriers of orbital angular momentum (OAM), exhibit great potential in multichannel communications, high-dimensional information encoding, and super-resolution imaging. However, conventional coding metasurfaces based on metallic structures still suffer from limitations in dynamic switching of vortex wave modes, precise wide-angle beam steering, and reconfigurability. To overcome these drawbacks, this work proposes a graphene-based reconfigurable coding metasurface. By utilizing the excellent electrical tunability of graphene, flexible control over the phase response of individual coding metasurface elements is achieved. In addition, a genetic algorithm is introduced to intelligently optimize the coding sequences, thereby enabling precise radiation control of terahertz vortex waves over a wide angular range. Specifically, a reconfigurable coding metasurface element with a four-layer configuration is designed. By applying an external bias voltage to adjust the Fermi level of graphene, we achieve the dynamic modulation of the reflection phase via the continuously tunable surface conductivity of graphene. Full-wave simulations are performed in CST to obtain the reflection amplitude and phase responses of the coding metasurface elements under different Fermi levels. Furthermore, an FPGA is employed to independently apply bias voltages to individual elements across the metasurface, enabling real-time programmable switching of coding sequences. According to the phase distribution characteristics of vortex waves, single-mode coding sequences with topological charges of l = -1, 1, 2, and 3 are designed. Moreover, based on the principle of field superposition, multimode coding sequences corresponding to l = -1 and 1, as well as l = 1 and 2, are constructed. Finally, a genetic algorithm is introduced to iteratively optimize the coding sequences with the target radiation angle (0, j) as the optimization objective. Combined MATLAB-CST co-simulations are conducted to analyze the vortex wave modes and radiation angle characteristics. The simulation results demonstrate that the proposed coding metasurface elements achieve full 0-2p phase coverage at 1.1 THz, with a phase interval of approximately 45 degrees between adjacent coding metasurface elements, while the reflection amplitude remains above 0.8 over the entire operating band. The coding metasurface based on these coding elements can flexibly generate and dynamically switch among six vortex wave modes, including four single-mode states and two multimode states. With the assistance of the genetic algorithm, the coding metasurface enables precise control of the radiation angle over a wide angular range of 0 degrees <= 0 <= 60 degrees and 0 degrees <= j <= 360 degrees. In summary, the proposed graphene-based reconfigurable coding metasurface achieves dynamic generation and flexible switching of multimode vortex waves by tuning the Fermi level of graphene via bias voltage control, combined with FPGA-based programmable operation. Meanwhile, precise beam steering over a wide angular range is realized with the aid of a genetic algorithm. This work provides an effective approach and valuable design reference for programmable wavefront manipulation, OAM multiplexing, and high-capacity multichannel communication systems in the terahertz regime.

Objective Terahertz (THz) vortex beams are electromagnetic waves characterized by helical phase structures and frequencies ranging from 0.1 to 10 THz (wavelengths from 30 to 3000 mu m). These beams demonstrate significant potential in emerging applications, including broadband communication, military radar, high-resolution THz imaging, electron acceleration, and quantum state manipulation. While current research has achieved multimodal vortex beams, their elevation angles remain fixed. This paper introduces a 2-bit coding phase gradient metasurface designed to generate multimodal vortex beams with switchable elevation angles. The integration of two tunable materials enables dynamic switching of the elevation angle of multimodal vortex beams, presenting applications in radar detection, wireless communication, and stealth technology. Methods According to the Pancharatnam-Berry (PB) geometric phase principle, a phase gradient is introduced to design the coding elements, which are arranged following a specific coding sequence. Through the phase superposition principle, a multimodal vortex beams coding phase gradient metasurface is developed. The coding elements incorporate two tunable materials, photosensitive silicon and vanadium dioxide (VO2). By modifying the control methods, the top-layer structure of the metasurface unit undergoes adjustments, introducing different phase gradients and forming three distinct sets of coding elements. State A represents an unregulated condition, where neither material is affected. During this state, VO(2)maintains a dielectric state, and the photosensitive silicon exhibits dielectric properties. State B implements optical control, regulating the photosensitive silicon while leaving VO(2)unaffected. In this state, the photosensitive silicon displays metallic properties, while VO(2)remains dielectric. State C employs both thermal and optical controls, regulating both materials, resulting in metallic properties for both VO(2)and photosensitive silicon. Results and Discussions Under linearly polarized (LP) wave excitation, the co-polarized reflection amplitude and phase difference of the designed coding phase gradient metasurface unit (Fig. 1) satisfy the requirements of the PB geometric phase principle (Fig. 3). In different states, the top structure of the metasurface unit changes, leading to variations in the phase gradient and the size of the coding elements, thereby realizing the control of the elevation angle of the emitted beam. In state A, the central open circle is active; in state B, the small open ring is active; in state C, the large open ring is active (Fig. 2). Subsequently, three sets of coding elements with different phase gradients were formed in states A, B, and C, with sizes of 4x4, 6x6, and 9x9, respectively (Figs. 4-6). After arrangement, the far-field scattering of the coding phase gradient metasurface was simulated using CST Microwave Studio. The results indicate that without regulation, when a 1.2 THz LP wave is incident perpendicularly, the metasurface generates multimodal vortex beams with an elevation angle of 16 degrees (Fig. 7); with optical control alone, a 1.0 THz LP wave incident perpendicularly yields an elevation angle of 20 degrees (Fig. 8); and when both optical and thermal controls are applied, a 0.54 THz LP wave incident perpendicularly results in an elevation angle of 28 degrees (Fig. 9). The simulation results are basically consistent with the theoretical values calculated using the generalized Snell's law. Conclusions This research presents a coding phase gradient metasurface capable of simultaneously generating vortex beams with topological charges of l=-1 and l= +1 in the x-direction, and l= +2 and l=-2 in the y-direction. The elevation angles can be switched by modifying the control methods of two tunable materials to activate different coding elements on a single metasurface, thereby altering the phase gradient. This approach provides an efficient method for flexible control of terahertz beams, offering significant potential in wireless communication, radar detection, and high-resolution imaging applications. The capability to switch angles of multimodal vortex beams enhances adaptability across various applications, establishing this metasurface as a promising component for advanced terahertz technologies.

Objective High birefringence terahertz fibers have a strong polarization preservation ability for linearly polarized light. They can be used for polarization-maintaining transmission of terahertz waves, polarization control, and modulation of terahertz signals. Currently, the most common high birefringence terahertz fibers include photonic crystal fibers and hollow core anti-resonant fibers (HC-ARFs). The former generally introduces structural asymmetry by arranging air holes or changing the core shape to achieve mode birefringence (B). However, their structures are relatively complex, leading to higher fabrication difficulties and significant effective material losses. The latter utilizes the anti-resonant reflection effect for light guidance, which results in low confinement loss and a simple structure. This not only simplifies the fabrication process but also minimizes effective material loss, which makes it a focal point of current research. However, most of the reported high birefringence terahertz HC-ARFs fail to achieve both high mode birefringence and low loss across a broad bandwidth. Based on this, a new structure is designed for high birefringence terahertz HC-ARF. This design combines the introduction of non-circular tubes and nested structures in the cladding. Additionally, four gap-compensated circular tubes are introduced, and high-resistivity silicon with low absorption loss is used as the fiber material to further reduce transmission loss (TL) and improve fiber performance. Methods Firstly, we present the design of the structure for a high birefringence terahertz HC-ARF. Nested structures are incorporated in both the x and y directions, and non-circular tubes are introduced within the cladding tubes to induce asymmetry in the fiber structure, thereby achieving high birefringence. Secondly, four gap compensated circular tubes are added to the interstitial spaces within the cladding tubes, with the aim of reducing confinement loss in the fiber. Furthermore, high resistivity silicon is selected as the fiber material to minimize the effective material loss within the fiber. Subsequently, the control variable method is used to optimize the fiber structure parameters, including the outer diameter of the circular tube in the y-direction (d(1)), the outer diameter of the nested circular tube in the y-direction (d(2)), the major axis of the outer elliptical tube in the x-direction (d(3)), the ellipticity eta, the major axis of the nested elliptical tube in the x-direction (d(4)), the outer diameter of the gap compensated circular tubes (d(5)), and tube thickness t. The objective is to achieve optimal values for both the TL and the B of the fiber. Finally, based on the optimal structural parameters of the fiber, within the frequency range of 0.7 to 1.4 THz, the properties of the fiber are analyzed such as TL, B, and dispersion. Results and Discussions Firstly, a high birefringence terahertz HC-ARF is designed in this paper. On one hand, high birefringence is achieved by incorporating non-circular tubes and nested structures within the cladding tubes. On the other hand, the introduction of four gap compensated circular tubes in the interstitial spaces of the cladding tubes reduces confinement loss. Additionally, the use of high resistivity silicon materials further decreases the effective material loss (Fig. 1). Secondly, at an operating frequency of 1 THz, the structural parameters of the fiber are optimized. The results show that the best TL and B are achieved with d(1)=3.0 mm, d(2)=1.0 mm, d(3)=3.1 mm, eta=0.525, d(4)=d(2)=1.0 mm, d(5)=1.2 mm, and t=0.035 mm. Next, we analyze the properties of the fiber, such as TL, B, and dispersion, within the frequency range of 0.7 to 1.4 THz. The results indicate that within the bandwidth ranging from 0.92 to 1.32 THz, B exceeds 1.09x10(-3) [Fig. 8(a)]. TL remains as low as 1 dB/m, with the minimum transmission loss of 0.09 dB/m occurring at a frequency of 1.18 THz. Finally, the dispersion performance of the fiber is simulated and analyzed. The results show that in the bandwidth of 0.92 to 1.32 THz, the designed high birefringence terahertz HC-ARF exhibits near-zero and flat waveguide dispersion, with a dispersion variation of (0.13513 +/- 0.22014) ps(-1)THz(-1)cm(-1) (Fig. 9). Meanwhile, the lowest polarization mode dispersion of 3.68x10(-12) s is achieved (Fig. 10). Conclusions In this paper, we design a high birefringence terahertz HC-ARF with both high B and low TL across a wide bandwidth. To accomplish this, we incorporate non-circular tubes into the cladding, introduce nested structures in both the x and y directions, and incorporate gap-compensated circular tubes within the cladding gaps. The results demonstrate that, within the bandwidth ranging from 0.92 to 1.32 THz, the high birefringence terahertz HC-ARF exhibits B greater than 10(-3) and TL as low as 1 dB/m. Notably, the lowest transmission loss is achieved at a frequency of 1.18 THz, where the TL for the x-polarization mode is 0.14 dB/m and the TL for the y-polarization mode is 0.09 dB/m. Additionally, it possesses excellent dispersion characteristics. This fiber has broad prospects in areas such as polarization-maintaining transmission of terahertz waves and polarization control of terahertz signals. It also provides a reference for the design of high birefringence terahertz fiber

Objective In practice, the environment and atmospheric conditions of free space influence the transmission of terahertz waves, leading to issues such as dispersion and large transmission loss (TL). Hollow core fibers emerge as promising for terahertz wave transmission because of their broad application potential. However, current hollow core photonic bandgap fibers (HC-PBGFs) for terahertz wave transmission have issues including poor mode purity, elevated surface scattering loss, and complex manufacturing processes. In contrast, hollow core anti-resonant fibers (HC-ARFs) have a simpler structure and are easier to fabricate, making them a research focus. Nevertheless, reported HC-ARFs still have room for improvement in TL and some fiber properties. To overcome these limitations, we have designed a novel terahertz HC-ARF structure. By carefully designing the geometric configuration of the nested structure in the cladding, increasing the number of nested layers, and using high-resistivity silicon with minimal absorption loss as the fiber material, we further reduce TL and dispersion and thus enhance the overall fiber performance. This fiber provides a valuable reference for the development of high-performance, low-loss terahertz wave transmission waveguides. Methods The anti-resonant reflection waveguide model combined with the suppression coupling theory comprehensively explains the guiding mechanism in HC-ARFs. These fibers mainly use the anti-resonant effect to confine energy within the fiber cores. First, we design the nested structure that constitutes the cladding of HC-ARF. Unlike typical fiber structures using circular nested tubes (fiber structure A), elliptical nested tubes (fiber structure B), and double-layer elliptical nested tubes (fiber structure C), the innovative nested configuration integrating ellipses, circles, and straight rods has superior performance in constructing the fiber cladding. In addition, the nine nested structures in the cladding are arranged without nodes, which avoids the resonance of nodes between nested structures affecting the fiber loss. High-resistivity silicon is selected as the fiber material, which helps reduce the effective material loss. Second, the control variable method is used to optimize the fiber structure parameters, including diameter D-c, elliptical major axis d(1), ellipticity eta, and tube thickness t. Within the frequency range of 0.5-1.6 THz, the TL of the fiber is optimized. Finally, based on the optimal structural parameters of the fiber, the properties of the fiber such as mode field distribution, dispersion, bending resistance, and effective mode field area are analyzed. Results and Discussions First, we propose a combination of increasing the number of nested layers and changing the geometric shape of the nested structure. A terahertz HC-ARF with nine uniformly distributed multilayer nested structures is designed (Fig. 1). On the one hand, the anti-resonant reflecting effect is used to guide light, reducing the confinement loss. On the other hand, the use of high-resistivity silicon in the cladding structure helps reduce the effective material loss. Next, the structural parameters of the fiber are optimized. The results show that the best TL is achieved with a diameter D-c=6 mm, an elliptical major axis d(1)=2.4 mm, an ellipticity eta=1.104, and a tube thickness t=0.030 mm. That is, the proposed HC-ARF achieves a TL of less than 10-1dB/m within the transmission window of 0.84-1.56 THz. Moreover, in the frequency range of 0.98-1. 44 THz, TL is as low as 10(-4) dB/m, and the lowest TL of 2.80x10(-4) dB/m is achieved at f=1.10 THz (Fig. 7). Finally, other performance parameters of the fiber are simulated. The results show that within 0.84-1.56 THz, near-zero and flat dispersion is achieved, with a dispersion variation of (0.02139 +/- 0.08824) psTHz(-1)cm(-1) (Fig. 9). A large effective mode field area is obtained, with values reaching the order of 10(7) mu m(2) (Fig. 11). Excellent bending resistance is demonstrated, with bending losses less than 10(-2)dB/m at smaller R-b (35 and 45 cm) (Fig. 10), which is beneficial for more stable and effective transmission of terahertz waves. This makes the fiber have broad application value in the fields of terahertz wave sensing, detection, and terahertz communication systems. Conclusions We design a terahertz HC-ARF with low TL and wide bandwidth, using high-resistivity silicon (HRS) as the fiber material. Its nested structure, consisting of a combination of ellipses, circles, and straight rods, is advantageous for forming the cladding of the fiber. The results indicate that the HC-ARF achieves a low TL bandwidth of 0.72 THz within the transmission window. The lowest TL of 2.80x10(-4) dB/m is obtained at 1.10 THz. The dispersion variation is (0.02139 +/- 0.08824) psTHz(-1)cm(-1). The effective mode field area remains above 10(7) mu m(2). The bending loss is less than 10(-2 )dB/m at the smaller R-b (35 and 45 cm). We achieve more stable and high-performance terahertz wave transmission. The fiber has potential application value in the fields of terahertz wave sensing, detection, and terahertz communication systems.

We propose an integrated device for polarization-independent electro-optic (EO) modulation and wavelength division multiplexing (WDM). The device is composed of a polarization splitter-rotator-combiner, a graphene EO modulator, and a photonic crystal wavelength division multiplexer. The TE0 and TM0 modes at wavelengths of 1550 nm and 1553.2 nm are combined after polarization rotation, then modulated by the modulator to achieve on-state and off-state. Finally, the two wavelengths of light are output as TE0 modes from the same port of the wavelength division multiplexer. The simulation results based on the three-dimensional finite-difference time-domain method show that the insertion loss of the integrated device is lower than 0.72 dB, the extinction ratio is greater than 21 dB, and the crosstalk is less than -37.5 dB. The integrated device can achieve polarization-independent EO modulation and WDM functionality.

【Objective】Terahertz vortex waves have a wide range of applications in the fields of broadband communications, military radar, biomedicine and detection, etc. However, the realization of beam modulation using traditional terahertz devices suffers from structural complexity, large size and poor tunability. To solve these problems, this paper proposes a terahertz coding metasurface that can modulate terahertz waves to achieve reversible beam switching. The design is based on the tunable conductivity of photosensitive silicon.【Methods】The metasurface has a three-layer structure. Its top layer is metal photosensitive silicon composite structure, middle layer is the silicon dioxide layer, and the bottom layer is the metal layer. The beamform generated by the coding metasurface is determined by the coding metasurface units and coding sequence. By changing the conductivity of the photosensitive silicon, the change in the unit properties can be realized, and then the opposite coding sequence on the same coded metasurface are presented. The modulation of the terahertz wave can realize vortex wave generation and reversible beam switching.【Results】Simulation results show that the same coded metasurface can produce vortex beams with higher reflection amplitude and opposite topological charges under two different coding sequences. A vortex beam with topological charge l=1 and a reversible beam with l=-1 are realized by adjusting the conductivity of the photosensitive silicon. By adjusting the conductivity of photosensitive silicon on the same coding metasurface, the reversible beamform switching is achieved.【Conclusion】This paper takes the generation of vortex beams with good application prospects as an example to design relevant coding sequences, achieving the generation of terahertz vortex beams and reversible beam switching, which improves the ability of the coding metasurface to manipulate terahertz waves to a certain extent. This is of great significance for terahertz vortex beam communication and information processing.

We propose an eight-channel integrated device for electro-optic modulation and dense wavelength division multiplexing based on photonic crystals. The device consists of eight photonic crystal AAH cavities and eight reflection cavity filters to contribute a modulation module and a dense wavelength division multiplexing module, respectively. First, the physical model of the eight-channel integrated device is established, and then modeling and analyzing the transmission performance of the single channel modulator according to the coupled mode theory. The parameters of the proposed device are calculated by two dimensional finite-difference time-domain method for verification. The numerical results shows that the minimum insertion loss, channel crosstalk in the "on" state are 0.24 dB and -17.8 dB, respectively, and the extinction ratio in the "off" state is higher than 19.3 dB. The designed eight-channel integrated device has the advantages of low loss, small size (114.81 x16 x0.22)mu m3 and easy cascading structure, which can realized "on" and "off" modulation with channel space of 0.8 nm, dense wavelength division multiplexing function in the operating wavelength range of 1552.8 nm-1558.4 nm and applied in data center and highly integrated optical communication system.

Objective Terahertz vortex beams are a type of optical beam with a helical optical phase structure and frequencies in the range of 0.1-10 THz. Meanwhile, they have potential applications in emerging fields such as high- resolution terahertz imaging, electron acceleration, and manipulation of quantum states. The terahertz coding phase gradient metasurface serves as an important device for modulating terahertz waves, featuring simple structure, small size, low cost, low loss, and high efficiency. By introducing phase gradients in the super- unit- cell, the coding elements are formed to enable more flexible control of electromagnetic waves by altering the coding elements and coding sequences. Currently, the generation of multibeam multi- modal terahertz vortex waves is generally achieved by adopting the coding metasurface. However, this approach requires a large number of coding metasurface units, resulting in high computational complexity and a complex design process with large dimensions. To generate multibeam multi- modal terahertz vortex waves more flexibly and simply, we propose a transmissive coding phase gradient metasurface. By utilizing Fourier convolution operations and the phase superposition principle, the generation of multibeam multi- modal terahertz vortex waves is realized. This technology holds potential application significance in fields such as wireless communication and high- resolution imaging. Methods First, we design the transmission metasurface units based on the Pancharatnam-Berry- Berry (PB) geometric phase principle. Next, the designed metasurface units are employed to form the 6x6 super- unit- cell, in which phase gradients are introduced to create coding elements. Then, three coding phase gradient metasurfaces are designed to produce double beams and generate single beams of l= - 1 and l= - 2 vortex waves. Additionally, Fourier convolution of the double beams coding sequences is performed with the vortex wave coding sequences of different modalities, with the coding phase gradient metasurface for generating single- mode double beams vortex waves acquired. The phase distribution of the coding phase gradient metasurface which generates double vortex beams with l= - 2 is matrix inversion and then combined with the phase distribution of the coding phase gradient metasurface which generates double vortex beams with l=-1 using the phase superposition principle, thus preventing the overlapping of spiral waves generating different modes. By arranging the coding elements, this process leads to the coding phase gradient metasurface capable of generating multibeam multi- modal terahertz vortex beams. Results and Discussions When 2.0 THz x-- and y- polarized waves are vertically incident on the metasurface units (Fig. 1), the amplitudes of the co- polarized transmission for both polarizations are approximately 0.9, and their co- polarized transmission phase differences are close to 180 degrees , which meets the requirements of the PB geometric phase principle (Fig. 2). Then, phase gradients are introduced in the super- unit- cell and 2- bit coding elements are designed (Fig. 4). Based on the Fourier convolution operation (Fig. 9) and phase superposition principle, the coding phase gradient metasurface is designed (Fig. 12). The far- field scattering of the coding phase gradient metasurface is simulated by CST Microwave Studio. The results show that under the vertical incidence of 2. 0 THz linear polarization (LP) waves, it is possible to simultaneously generate two vortex beams of l= - 1, two vortex beams of l= - 2, two vortex beams of l= +1, and two vortex beams of l= +2 [Fig. 13(a)]. Additionally, these eight vortex waves do not overlap and do not interfere with each other. The elevation angle theta and azimuth angle phi of each beam can also be obtained [Figs. 13(b) and (c)]. In the x- direction, there are two vortex beams of l= - 1 with an azimuth angle of 270 degrees and elevation angles of 58 degrees and 78 degrees respectively. In the +y direction, there are two vortex beams of l= +2 with azimuth angles of 25.5 degrees and 333.5 degrees and an elevation angle of 65 degrees . In the +x direction, there are two vortex beams of l= +1 with an azimuth angle of 90 degrees and elevation angles of 55 degrees and 80 degrees respectively. In the -y direction, there are two vortex beams of l=-2 with azimuth angles of 153 degrees and 207 degrees and an elevation angle of 46 degrees. Conclusions We propose a coding phase gradient metasurface working at a frequency of 2.0 THz based on the PB geometric phase principle, Fourier convolution operation, and phase superposition principle. Under the vertical incident of the LP wave, a newly coding phase gradient metasurface can generate eight vortex waves in total, with mode orders of l=+/- 1 and l=+/- 2 respectively. Compared to the reported metasurfaces for generating multibeam multi- modal terahertz vortex waves, this metasurface features small dimensions, relatively simple principles, few unit elements, easy material acquisition, and the ability to design different modes of vortex waves. This enables more flexible and diverse control of terahertz beam steering. Finally, potential applications are presented in wireless communication, radar, high- resolution imaging, energy transfer, and stealth technology.

Objective Terahertz waves refer to electromagnetic waves between microwave and infrared wave, which can be applied in different fields such as communication, sensing, radar, and imaging. Terahertz coding metasurface, as an important device for modulating terahertz waves, has the advantages of simple structure, small size, low cost, low loss, and high efficiency. The coding metasurface units are arranged according to a certain coding sequence, and by changing the phase difference between the units, the flexible modulation of terahertz waves can be achieved to generate various forms of beams. However, when the design of a general terahertz coding metasurface is completed, the function and operating frequency are relatively single. In order to fully utilize the coding metasurface, an anisotropic metasurface is proposed, which can regulate the incident orthogonal polarized waves separately. And a frequency independent coding metasurface has been proposed, which can separately regulate the incidence waves at different frequency points to generate different forms of beams. In addition, the phase change materials such as vanadium dioxide (VO2) were used to achieve the switching of transmission and reflection modes of terahertz waves, thereby achieving the goal of full spatial modulation of electromagnetic waves. The above methods improve the ability of the coding metasurface to regulate terahertz waves, but the integration level still needs to be improved. Therefore, we integrate these technologies to achieve multi-frequency and multi-beam tunable terahertz coding metasurface in full space, greatly improving its ability to regulate terahertz waves. Methods In this paper, a coding metasurface which can regulate the circular polarized waves and orthogonal polarized waves separately is proposed by combining the principle of PB geometrical phase as well as the frequency independence and anisotropy of double crosses. In addition, introducing the phase change material VO2, flexible switching of terahertz waves between transmission and reflection is achieved by changing its phase change state. The details are as follows. When VO2 is in an insulating state, the designed coding metasurface is a single-frequency-point 3-bit PB geometrical phase transmitting coding metasurface, which generates transmission-type vortex waves with topological charge number of 1. When VO2 is in a metallic state, the designed coding metasurface is a dual-frequency-point independently adjustable 1-bit anisotropic reflective coding metasurface, which generates four symmetric beams, of which two symmetric beams on the xoz plane with RCS reduction and two symmetric beams are on the yoz plane, respectively. Results and Discussions The designed coding metasurface units (Fig. 1) with identical metallic split-ring structures in the third, fifth, and seventh layers are rotated from 0 degrees to 157.5 degrees in a step of 22.5 degrees to obtain a total of eight coding metasurface units (Fig. 2). When VO2 is in an insulating state and a circularly polarized wave with f(1) = 0.6 THz is incident, the units maintain a high transmission amplitude and strictly satisfy a phase difference of 45 degrees. The design conditions for a 3-bit transmission type coding metasurface unit are met. Arranging them according to a certain coding sequence [Fig. 4(b)] can produce transmission-type vortex waves with topological charge number of 1 (Fig. 5). When VO2 is in a metallic state and the orthogonal polarized waves of f(2) = 0.5 THz and f(3) = 0.85 THz are incident, a dual-frequency and anisotropic 1-bit reflective-type coding metasurface unit (Fig. 3) is designed by using the two cross structures. After arranging them according to a certain coding sequence [Figs. 4 (c)-(f)], the perpendicular incidence of y-polarized wave with f(2)=0. 5 THz on the xoz plane produces two symmetric beams [Figs. 6(a) and 6(b)]. When a y-polarized wave with f(3)= 0. 85 THz is incident vertically, two symmetric beams are generated on the yoz plane [Figs. 6(c) and 6(d)]. When a x-polarized wave with f(2) = 0. 5 THz is incident vertically, four symmetrical beams are generated [Figs. 7(a) and 7(b)]. When a x-polarized wave with f(3)=0. 85 THz is incident vertically, a diffuse scattering beam can be generated [Figs. 8( a) and 8(b)], realizing RCS reduction. The results show that with the rational design of the coding metasurface combined with the phase transition state of VO2, the frequency of the incident wave source, and the polarization state, the full space regulation of terahertz wave's reflection and transmission can be realized and five beam forms on the same coding metasurface can be obtained. Conclusions In this paper, a coding metasurface with full space multi-frequency and multi-beam tunability is designed by changing the phase transition state of VO2, combining the principle of PB geometrical phase and the cross unit structure with dual-frequency anisotropy. A 3-bit transmission coding metasurface with an operating frequency of f(1) = 0. 6 THz is designed to produce a transmitted vortex beam. And a dual-frequency 1-bit anisotropic reflective coding metasurface with operating frequencies of f(2) = 0. 5 THz and f(3) = 0. 85 THz is designed to produce various forms of symmetric and scattered beams. This coding metasurface, which introduces phase change material and realizes full space multi-frequency multi-beam regulation by transmission and reflection, is important for designing multifunctional terahertz beam modulation devices.

Objective Terahertz waves are electromagnetic waves between microwave and infrared wave with the frequency of 0. 1-10 THz and feature strong penetration, large information capacity, high security, and strong maneuverability. Additionally, they have extensive applications in remote communication, security imaging, radar detection, and other fields. With the increasing number of application scenarios, there is an urgent need for functional devices that can regulate terahertz waves in multiple frequency bands. As an important device to regulate terahertz waves, the coding metasurface is characterized by the phase response properties of the coding metasurface units by binary digital code and arranges the coding metasurface units according to the coding sequence to achieve flexible wave regulation. Meanwhile, it can generate various beam forms such as vortex waves, deflection waves, and focused waves. However, once a traditional coding metasurface is designed, it can only generate a beam form at a single frequency point, limiting the working frequency range of the coding metasurface. As a kind of phase change material, vanadium dioxide (VO2) can change its temperature by electricity, heat, and light to achieve phase change function, and is widely applied to metasurface design. Some studies implement the function of generating different beam forms by different coding sequences, but the working frequency band is single and cannot be switched. Another study adopts the PB phase principle combined with VO2 to design a frequency switchable coding metasurface, which achieves vortex wave generation at different frequency points. However, it only yields good results at three frequency points, limiting the working frequency range. Therefore, it is significant to broaden the working frequency range of the coding metasurface and achieve frequency band switching. Methods First, a new type of coding metasurface unit is designed by combining the PB phase principle with the VO2 phase transition characteristics. By rotating the unit at a certain angle and changing the phase transition state of VO2, the reflection amplitude and phase in different working frequency ranges are studied. The conditions are as follows. When VO2 is in an insulated state and a metallic state, it works in different frequency bands respectively and meets the conditions of 3-bit coding metasurface unit in the corresponding frequency band. Then, by taking the terahertz metasurface which can generate high-capacity vortex waves and high RCS reduced scattering waves as an example, a coding sequence is designed. Finally, the wave forms generated by the coding metasurface are simulated at different frequencies to study whether the beam form corresponding to the coding sequence can be generated. By changing the phase transition state of VO2, switching of the operating frequency band can be achieved. Results and Discussions By rotating the designed metasurface units (Fig. 1) counterclockwise in a step of 22. 5 degrees from 0 degrees to 157. 5 degrees, eight metasurface units can be obtained (Table 1). The unit analysis based on the two phase transition states of VO2 shows that when VO2 is in an insulated state, the unit maintains a large reflection amplitude between 1. 17 THz and 1. 37 THz, and the phase difference of the eight units strictly meets a 45 degrees phase difference. When VO2 is in a metallic state, it maintains a large amplitude and a phase difference of 45 degrees in sequence at 0. 87-0. 92 THz and 1. 4-1. 6 THz. Therefore, at all three frequency bands, the metasurface unit meets the design conditions for a 3-bit coding metasurface unit. The coding metasurface units are arranged according to a certain coding sequence, the coding metasurface formed by them can flexibly regulate terahertz waves, and its mechanism of regulating terahertz waves is similar to traditional phased array antenna theory (Formula 1). Therefore, the designed coding metasurface units are arranged according to the coding sequence that generates vortex waves with topological charge number 1 (Fig. 4) and scattered waves that can reduce RCS (Fig. 6). The results show that VO2 can generate the same beams with the same coding sequence at different operating frequency bands under different phase transition states, and the operating frequency band can change with the phase transition state of VO2. Conclusions Based on the PB phase principle and phase change material VO2, we design the 3-bit coding metasurface units. A variety of coding metasurfaces are formed by different coding sequence arrangements, which can regulate terahertz waves to generate beam forms corresponding to the coding sequences. Under an insulated state, VO2 works in a single frequency band of 1. 17-1. 37 THz, and it works in dual bands of 0. 87-0. 92 THz and 1. 4-1. 6 THz in a metallic state. The designed VO2 based on coding metasurface can switch the frequency bands without changing the wave forms, and provide important ideas for frequency modulation of terahertz waves.

An integrated device for polarization-independent electro-optic (EO) modulation based on photonic crystal is proposed. It primarily consists of three components: a polarization splitter-rotator (PSR), a combiner, and a graphene EO modulator. In the PSR, the TE0 modes and TM0 modes achieve polarization splitting and mode conversion. Subsequently, the two TE0 modes pass through the combiner to merge into a single beam. Finally, the TE0 modes enter the modulator for EO modulation. The performance parameters of the integrated device are computed and analyzed using the three-dimensional finite-difference time-domain method. The results reveal that the integrated device achieves a polarization extinction ratio of 23 dB, an insertion loss of 0.3 dB, and an extinction ratio of 21.1 dB. The modulator has a driving voltage of 3.56 V and a modulation speed of 33 GHz. The integrated device is well-suited for application in large-capacity optical communication systems. (c) 2024 Optica Publishing Group. All rights, including for text and data mining (TDM), Artificial Intelligence (AI) training, and similar technologies, are reserved.

Terahertz (THz) wave has the advantages of low photon energy, high resolution, large communication bandwidth, etc. It has broad application prospects in security detection, high-resolution imaging, high-speed communication, and other fields. In recent years, as a new way to control THz wave, THz metasurface functional devices have attracted extensive attention of researchers. In this work, vanadium dioxide (VO2), a phase change material, is introduced into the coding metasurface. By regulating a circularly polarized wave and the orthogonal linearly polarized waves independently, a multi-function coding metasurface that can work at dual frequency points is obtained. It is composed of three layers. The top layer is a metal-VO2 composite structure. The middle is a polyimide dielectric layer. The bottom is a metal ground. Under certain conditions, the double split ring resonator (DSRR) and the cross structure in the top layer are relatively independent. Designing the coding sequences for them enable the coding metasurface to have multiple functions. The electromagnetic simulation software CST is used to establish model and conduct simulation, and the obtained results are as follows. When the VO2 is in an insulating state and a circularly polarized wave at 0.34 THz is incident vertically, the characteristics of coding metasurface elements are mainly affected by the DSRR. The DSRR is rotated to meet the requirements of 3-bit Pancharatnam-Berry phase coding. The coding sequence is designed to generate vortex beams with the topological charge l = ±1 at a specific angle. The VO2 state is changed into a metallic state, and the DSRR can be equivalent to a metal ring. When the orthogonal linearly polarized wave at 0.74 THz is incident vertically, the characteristics of coding metasurface elements are mainly affected by the cross structure. Because of its anisotropy, four different 2-bit coding metasurface elements can be obtained respectively by changing the length of the horizontal arm and the vertical arm. The design of appropriate coding sequences can reduce the radar cross section of the x-polarized wave and the beam splitting of the y-polarized wave, and the results have broadband characteristics. Multiple coding sequences can be designed by special characteristics of the coding metasurface, then various expected functions can be realized on the same metasurface. It solves the problem of single function of ordinary metasurface devices to a certain extent, and paves a novel way to the development of THz multi-function systems.

Objective Radar cross section (RCS) is an important physical quantity to measure the radar echo capability of the target. To reduce the RCS value of the target object is to achieve RCS reduction, which has important applications in the field of radar stealth. Terahertz (THz) waves refer to electromagnetic waves in the frequency range of 0. 1-10 THz, which have broad application space in high-speed broadband communication, precision military radar, high-resolution imaging, and other fields. With the increasing complexity of the international situation and the rapid development of science and technology, RCS reduction in the THz band and its application in radar stealth has become a new research direction. Currently, there are two most effective and commonly used methods for RCS reduction in the THz band. The first one is to use a perfect absorber, which can absorb the incident THz waves to the surface and convert them into internal energy. The other is to use a metasurface to reshape the THz wave waveform in the space domain. The former has the disadvantages of narrow bandwidth and easy discovery by far-infrared detectors. The latter has become a hot research topic because of its simple structure, small size, and wide operating frequency band. In this paper, a coding metasurface with more degrees of freedom than the traditional metasurface is adopted. By combining it with a phase gradient metasurface, this paper proposes a coding phase gradient metasurface. Compared with the normal coding metasurface without phase gradient, it has a better RCS reduction effect. Moreover, the coding phase gradient metasurface has a wider working band. This is due to the introduction of a double Omega-shaped symmetrical structure at the top of the metasurface element. The metasurface will generate magnetic dipole resonance and electric dipole resonance in its interior, and the multiple resonance modes are conducive to broadening its working frequency band. Methods First, according to the Pancharatnam-Berry (PB) geometric phase principle, a number of double Omega-shaped reflective metasurface elements with different phase responses are designed. The conditions they meet are as follows. For the vertically incident x- and y-polarized waves, the amplitudes of the co-polarized reflection are almost the same, and their co-polarized reflection phase difference is 180 degrees. Second, based on the designed metasurface elements, the coding elements are designed. The so-called coding element is the introduction of phase gradient on the basis of the supercell. Third, a genetic algorithm is written using Matlab to optimize the arrangement, so that the energy distribution of diffuse reflection is more uniform, and a better RCS reduction effect is obtained. Then, according to the optimized arrangement, the coding elements 0 and 1 are arranged to obtain the coding phase gradient metasurface. Finally, CST Microwave Studio is used to simulate the far-field scattering of the coding phase gradient metasurface at different frequencies. The RCS reduction value relative to a metal plate of the same size is calculated. In addition, the influence of x- and y-polarized incidence angles on the performance of the coding phase gradient metasurface is also analyzed. Results and Discussions When the x- and y-polarized waves are incident vertically to the metasurface element, the co-polarization amplitudes are larger than 0.8 in the frequency range from 1 THz to 1. 5 THz, and their phase differences are close to 180 degrees, which satisfy the PB geometric phase principle (Fig. 2). Then, the phase gradient is introduced on the basis of supercells, and 1 bit coding elements 0 and 1 are designed ( Fig. 4). The optimal arrangement M1 of the coding elements is achieved with the help of the genetic algorithm [Fig. 6(b)]. The coding phase gradient metasurface is obtained by arranging the coding elements according to M1. CST Microwave Studio is used to calculate the far-field scattering of the coding phase gradient metasurface at different frequency points under the normal incidence of x- and y-polarized waves. The result shows that the diffusely reflected scattering waves will be further reflected in the direction of the two symmetrical main lobes, and the far- field beams have both diffuse reflection and abnormal reflection characteristics ( Fig. 9). In addition, the results show that the designed 1 bit coding phase gradient metasurface can achieve RCS reduction of more than 10 dB (Fig. 10) in a wide frequency range (0.87-1.725 THz) with a relative bandwidth of 65.9%. The RCS reduction in the frequency range of 0.9-1.4 THz and 1.6-1. 7 THz both reaches over 15 dB with a maximum RCS reduction value of 31.26 dB. The RCS reduction effect of the coding phase gradient metasurface (composed of coding elements 0 and 1 arranged according to M1) is compared with that of the normal coding metasurface without phase gradient (composed of supercells 0 and 1 arranged according to M1), and it is found that the RCS reduction effect of the former is better. Finally, when the incident angles of x- and y-polarized waves are both gradually increased from 0 degrees to 30 degrees, the RCS reduction is more than 10 dB in the frequency bands of 0.9-1.5 THz and 0.9- 1. 7 THz (Fig. 11). It indicates that good RCS reduction effect can be achieved over a wide frequency range with a certain degree of angular stability. Conclusions In this paper, a coding phase gradient metasurface is proposed, which can reduce the RCS in the THz band. The results show that the designed 1 bit coding phase gradient metasurface can achieve RCS reduction of more than 10 dB in a wide frequency band from 0. 87 THz to 1. 725 THz, and the maximum reduction value reaches 31. 26 dB. Finally, the influence of the incident angles of the x- and the y-polarized waves on the performance of the coding phase gradient metasurface is analyzed. It was found that its performance is stable in the range of 0 degrees to 30 degrees. The above results show that this kind of metasurface has potential application value in radar stealth and other aspects.

Terahertz (THz) wave has the advantages of high resolution, large information capacity, easy beam focusing, etc, and can be used in the fields of communication, radar, detection and others. Firstly, as a two-dimensional artificial electromagnetic metamaterial, the coding metasurface is proposed in the microwave band. It uses the digital coding of the electromagnetic wave phase to adjust electromagnetic waves. Subsequently, as an important way to regulate THz, the metasurface extends to terahertz frequency band and becomes a research hotspot. In this paper, we design a coding metasurface based on vanadium dioxide (VO2) with anisotropic characteristics. It is composed of three layers, with a metal cross structure embedded in VO2 at the top, polyimide in the middle, and pure metal at the bottom. The design of the cross shaped structure makes the coding metasurface unit anisotropic, which can provide complete and independent control of the orthogonally linearly polarized incident waves. The pure metal structure at the bottom can provide higher reflection amplitude for the incident wave. And VO2 is introduced into the coding metasurface. As a phase change material, VO2 can switch its properties between the insulating state and the metallic state, which further increases the flexibility of coding metasurface to regulate THz wave. Eight different coding metasurface units are designed in this work. They can be arranged according to a reasonable coding sequence to form a coding metasurface, which consisits of 20×20 metasurface units with an overall size of 2.4 mm × 2.4 mm. Its coding sequence will be changed with the phase of VO2, thus forming a corresponding 1 bit or 2 bit coding metasurface, and the generated beam form changes accordingly. The finite-difference time domain method is used for modeling and implementing simulation, and the results are as follows. The 1-THz orthogonal linearly polarized wave is vertically incident on the coding metasurface. When VO2 is in the insulating state, the designed metasurface can be regarded as an anisotropic 2 bit coding metasurface to generate dual-polarization orbital angular momentum (OAM) vortex beams. The x-polarized vortex wave has an OAM mode number of 2, and the y-polarized vortex wave possesses an OAM mode number of 1. When VO2 is in the metallic state, the designed metasurface can be regarded as an anisotropic 1 bit coding metasurface to generate dual-polarization symmetrical beams. Four reflected waves are generated by incident x-polarized waves, and two reflected waves are created by incident y-polarized waves. The proposed method of combining anisotropy material and phase change material realizes the function of generating multiple THz beams in different forms on the same metasurface. The present results provide a reference for the implementation of multi-functional coding metasurface that can be flexibly applied to multiple scenes.

Objective With the development of optical interconnection and high-speed optical communication, electro-optic modulators have become a research hotspot. Silicon insulator materials have the advantages of compatibility with the complementary metal oxide semiconductor process, high integration, low power consumption, and high temperature resistance. There are several electro- optic modulators based on silicon materials. Electro-optic modulators with high modulation rate, compact size, and easy integration have been investigated previously, and the study on electro- optic modulators is crucial. Therefore, we design an electro-optic modulator with a reflective wall based on a one-dimensional photonic crystal nanowire cavity (PCNC). The modulator exhibits a high extinction ratio, large modulation bandwidth, and high modulation rate. Furthermore, it has a compact and simple structure and can easily to cascade other silicon photonic devices. With the development of integrated photonics in communication systems, the cascade of silicon photonic devices has a wider application prospect. Methods This study proposes a download-type electro-optic modulator with a reflective wall based on a silicon-on-insulator (SOI) one-dimensional PCNC. The main line waveguide, one-dimensional PCNC and download- type waveguide are used to form a download-type structure with a reflective wall. The duty cycle of the nanowire cavity decreases linearly from the center of the waveguide to the two ends, and doping is introduced at both sides of the modulator to form PN junctions. The finite difference time domain (FDTD) model in the optical simulation software Lumerical is used for simulation analysis. According to the free carrier dispersion effect in the silicon material, when the modulation voltage applied at both ends of the electro- optic modulator changes, the dielectric constant of the nanowire cavity material also changes. The refractive index change in the nanowire cavity produces a slight difference; hence, the resonant frequency of the cavity changes, i. e., the central wavelength of the electro-optic modulator shifts. Specifically, corresponding to the wavelength of 1550. 01 nm, the addition or non-addition of the modulation voltage is equivalent to the" off"or" on"state of the modulator. Results and Discussions An electro-optic modulator with a reflective wall based on the SOI PCNC is proposed. The incident light is coupled into the one-dimensional PCNC after passing through the main line waveguide, and then coupled again to output through the download- type waveguide. The adjustments of the position and number of reflective circular holes in the main line waveguide and download- type waveguide are beneficial to improve the overall transmittance of the device. The nanowire cavity uses a gradual circular hole to confine the beam in the cavity. PN junction is generated by doping on both sides of the nanowire cavity, and a low bias voltage is applied to adjust the resonant wavelength of the nanowire cavity, to realize the"on"and" off"modulation of the optical signal at the working wavelength. 3D-FDTD is used to analyze the optical characteristics and electrical performance of the modulator. The results indicate that the electro-optic modulator can modulate the optical signal with the wavelength of 1550. 01 nm, and the transmittances under the" off"and" on"states are 0. 0037 and 96. 34%, respectively (Fig. 14). The modulation voltage is only 1. 2 V, the insertion loss is 0. 2 dB, the extinction ratio is 24 dB, and the size is only 54 mu m(2). The modulation frequency is 8. 7 GHz, and the modulation bandwidth can reach 122 GHz, which implies that the proposed device has applications in optical communication and integrated photonics. In addition, after comparing the performances of the photonic crystal electro- optic modulators (Table 1), it is inferred that the proposed device exhibits excellent performance. Conclusions This study proposes a download- type electro- optic modulator with a reflective wall based on SOI one-dimensional PCNC. The downloadable structure of the reflection wall comprises a main line waveguide, one-dimensional PCNC, and downloadable waveguide. The doping method is introduced to form PN junctions at both sides of the modulator. Under the action of the modulation voltage, the refractive index of the silicon in the nanowire cavity changes, which triggers the migration of defect modes in the nanowire cavity; in addition, the" on"and" off"state modulations of the electro-optic modulator are realized. The electrooptical modulation is simulated and analyzed via the 3D-FDTD model in the Lumerical commercial simulation software. The simulation results demonstrate that compared with other electro-optical modulators based on nanowire cavity, the proposed electrooptical modulator has a higher extinction ratio, higher modulation bandwidth, higher modulation rate, compact and simple structure, and can easily be cascaded to other silicon photonic devices. The proposed electro-optic modulator exhibits a significant development and application value in the integrated photonics of optical communication.

Terahertz (THz) wave has the advantages of high resolution, large information capacity, easy beam focusing, etc, which can be used in communication, radar, detection and other fields. As a two-dimensional artificial electromagnetic metamaterial, the coding metasurface is first proposed in the microwave band. It uses the digital coding of the electromagnetic wave phase to adjust electromagnetic waves. Subsequently, as an important way to regulate THz, the metasurface extends to terahertz frequency band and becomes a research hotspot of scholars. In this paper, a coding metasurface based on vanadium dioxide (VO2) with anisotropic characteristics is designed. It is composed of three layers, with a metalcross structure embedded in VO2 at the top, polyimide in the middle, and pure metal at the bottom. The design of the cross shaped structure makes the coding metasurface unit anisotropic, which can provide complete and independent control of the orthogonally linearly polarized incident waves. The pure metal structure at the bottom can provide higher reflection amplitude for the incident wave. And VO2 is introduced into the coding metasurface. As a phase change material, VO2 can switch its properties between the insulating state and the metallic state, which further increases the flexibility of coding metasurface to regulate THz wave. In the paper, eight different coding metasurface units are designed firstly. They can be arranged according to a reasonable coding sequence to form a coding metasurface, which consisits of 20×20 metasurface units with an overall size of 2.4mm × 2.4mm. Its coding sequence will be changed with the phase change of VO2, thus forming the corresponding 1-bit or 2-bit coding metasurface, and the generated beam form changes accordingly. The finite-difference time domain method is used for modeling and simulation, and the results are as follow. In the paper, the 1 THz orthogonal linear polarized wave vertically incident on the coding metasurface. When VO2 is in the insulating state, the designed metasurface can be regarded as an anisotropic 2-bit coding metasurface to generate dual-polarization OAM vortex beams. The x-polarized vortex wave has the OAM mode number of 2, and the y-polarized vortex wave has the OAM mode number of 1.When VO2 is in the metallic state, the designed metasurface can be regarded as an anisotropic 1-bit coding metasurface to generate dual-polarization symmetrical beams. Four reflected waves generated by incident x-polarized wave, and two reflected waves generated by incident y-polarized wave. The proposed method of combining anisotropy and phase change materials realizes the function of generating multiple THz beams of different forms on the same metasurface. It provides a reference for the implementation of multi-functional coding metasurface that can be flexibly applied to multiple scenes.

unique band gap effect enables optical devices based on this structure to have the advantages of low loss and small size. In recent years, silicon-based PhC devices such as beam splitters, electro-optic modulators, optical switches, mode multiplexers, and optical add-drop multiplexers (OADMs) have received widespread attention from scholars in various countries due to their small size and easy cascading performance in the highly integrated optical communication system. Of various PhC-based devices, OADM, a key device in wavelength division multiplexing (WDM) systems, has attracted more and more attention from researchers. To meet the requirement of the highly integrated optical communication system, OADM design faces three possible challenges that cannot be ignored, namely, low insertion loss, compact size, and easy cascading performance. Moreover, with the advent of 5G, dense wavelength division multiplexing (DWDM) has become a key technology for increasing transmission capacity in optical fiber communication systems. As DWDM devices occupy an important position in optical communication systems, more requirements are posed for OADM design in channel spacing and crosstalk. In this study, we propose an OADM for DWDM systems based on PhCs. The device has low insertion loss, channel crosstalk, small size, and compact structure and can expand channels through cascading to achieve DWDM with channel spacing of 0. 8 nm, which has great application potential in highly integrated large- capacity communication systems. Methods This paper designs an OADM on the basis of a two-dimensional (2D) PhC triangular lattice plate of air holes in silicon. In the designed PhC plate in silicon, the circular air holes are arranged in a triangular lattice and periodically distributed along the 2D X- Y planes. The designed structure contains two different Aubry- Andre- Harper (AAH) bichromatic potential cavities, i. e., the resonant cavity and the reflection cavity. The resonant cavity couples the light intensity at the working wavelength, and the reflection cavity reflects the light intensity at the working wavelength. First, we design a PhC AAH cavity, which is the key component of the proposed OADM device. It is composed of onedimensional PhCs arranged according to different lattice constants based on the design principles of the AAH cavity model. Then, we model the basic structure of the designed OADM according to the coupled mode theory. Theoretical transmission spectra are derived to determine the optimal parameters of the OADM structure. After that, we calculate the parameters of the proposed device by the three-dimensional finite-difference time-domain (3D-FDTD) method for verification. In addition, we design a tapered structure for further optimization of the PhC OADM device on the basis of the modified step theory. Results and Discussions First, the theoretical spectra of the adding-dropping process based on Eqs. (12)-(17) present a clear trend that the transmission can reach resonant cavity 1 as. is close to.0. The following four rules must be satisfied to achieve this ideal condition of the theoretical model: 1) two resonant cavities have the same resonant frequency omega(0); 2) the amplitude coupling attenuation coefficients of the two resonant cavities to the bus waveguide are equal, which is gamma(2) = gamma(3) = gamma(4) = gamma(5) = gamma(wav); 3) the phase delay of the light wave from one cavity to another is phi 1 = ( n + 1/ 2) p (n is a non- negative integer); 4) the amplitude coupling attenuation coefficient of resonant cavity 1 to the input waveguide and the bus waveguide is gamma(1) = 4 gamma(wav). Second, when the above four rules are met, the parameters of the design device are calculated by the 3D-FDTD method. The numerical results show that the proposed device can add/ drop light intensity at the operation wavelength of 1556. 2 nm and 1555. 4 nm. The PhC AAH reflection cavity and tapered structure are designed to reduce the leakage of the light wave at the working wavelength on the bus waveguide and the mode mismatch loss at each port, which make the insertion loss and crosstalk lower than 0. 51 dB and - 29. 54 dB, respectively. The line width is 0. 2 nm due to the high Q value of the AAH cavity. However, the comparison of the theoretical and numerical spectra [Fig. 5 ( b) and Fig. 6 (c)] demonstrates that the two transmission spectra overlap, but the highest transmittance obtained by the simulation is lower than the theoretical transmittance. This is because the simulation algorithm based on the 3D- FDTD method is more comprehensive than the coupled mode equation in the calculation of such loss as the coupling loss between waveguide and resonant cavity and that between silicon waveguide and PhC waveguide, the vertical direction loss of the resonant cavity, and the transmission loss of the PhC waveguide. In addition, the spectra of ports 1, 2, and 3 obtained by simulation are consistent with the spectral trend derived from the theoretical equations in Section 2.1. Conclusions An OADM based on PhCs for DWDM is proposed. The theoretical model of the three-port filter is built, and the transmission spectrum is derived on the basis of the coupled mode theory. The 3D-FDTD method is used to calculate transmission performance to verify theoretical results. The device has low insertion loss, channel crosstalk, and small size (19. 35 mu mx13. 33 mu m) and can expand channels through cascading to achieve DWDM with channel spacing of 0. 8 nm, which has great application potential in highly integrated large- capacity communication systems.

In the Internet era, the demand for transmission speed and transmission capacity of optical communication systems has increased significantly. Etectro-optic modulators for optical communication systems are developing towards high speeds. Traditional silicon-based electro-optic modulators have a slow response speed. Graphene has excellent optical and electrical properties and is compatible with Complementary Metal Oxide Semiconductor (CMOS) processes. Combining graphene with silicon materials can improve the response speed of etectro-optic modulators. At the same time, wide bandwidth, high extinction ratio, low insertion toss, and tow energy consumption are the development trends of graphene etectro-optic modulators. On the other hand, to meet the needs of optical communication systems, multiplexing technologies such as mode division multiplexing are used to increase the communication capacity. The research on a single-function optical communication device has gradually matured, and the combination of different devices to form an integrated device has become a research hotspot in recent years. The combination of etectro-optic modulation and mode division multiplexing technology can improve the transmission speed and transmission capacity of optical communication systems. With the continuous advancement of science and technology, optical interconnection has attracted widespread attention due to its advantages of high speed, wide bandwidth and large capacity, and various integrated devices have emerged as the times require. Among them, the integrated device for etectro-optic modulation and mode division multiplexing has shortcomings such as small transmission capacity and low transmission speed. Meanwhile, different devices are difficult to integrate due to differences in materials and structures. A three-channel integrated device for graphene electro-optic modulation and mode division multiplexing is proposed, which consists of a one-dimensional photonic crystal nanobeam cavity etectro-optic modulation module covered by a single-layer graphene and nanowire waveguides mode division multiplexing module. The etectro-optic modulator is composed of a one-dimensional photonic crystal nanobeam cavity, a nanowire waveguide, and a silicon plate. Combining the curved waveguide with the straight waveguide improves the coupling efficiency of the one-dimensional photonic crystal nanobeam cavity and the nanowire waveguides. A layer of Al2O3 is covered on top of the silicon plate and the one-dimensional photonic crystal nanobeam cavity, and a single-layer graphene is added on top of the Al1O3. The electrodes on graphene serve as anodes, and the electrodes on silicon plates serve as cathodes. Applying a voltage changes the chemical potential of graphene, enabling modulation of specific wavelengths. According to the principle of mode matching, the mode division multiplexer adopts an asymmetric directional coupling nanowire waveguides structure. In the phase matching region, the fundamental modes in the single-mode waveguide are converted into the higher-order modes in the multi-mode waveguide, realizing the conversion of different modes. The TE0 modes are output from the same port in the form of TE0 modes, TE1, modes and TE2, modes through the graphene electro-optic modulator and mode division multiplexer, achieving the functions of etectro-optic modulation and mode division multiplexing. The performance parameters of the three-channel integrated device for graphene etectro-optic modulation and mode division multiplexing are analyzed using the three-dimensional finite-difference time-domain method. During the production and preparation of the devices, the influence of process errors on the performance of the devices needs to be considered. Therefore, important structural parameters of the graphene etectro-optic modulator and nanowire waveguides mode division multiplexer are selected for tolerance analysis, respectively. At the wavelength of 1 570 rim, when the voltage is 0 V, the incident tight is not coupled with the one-dimensional photonic crystal nanobeam cavity and can he transmitted along the waveguide. The modulator is in the on-state. When the voltage is 3.8 V, the chemical potential of graphene changes, resulting in a change in the equivalent refractive index of the material. Therefore, the resonance wavelength of the one-dimensional photonic crystal nanobeam cavity is shifted to match the target wavelength (1 570 rim), and the incident light is coupled into the microcavity, realizing the off-state of the modulator. The insertion toss is 0.07 dB, the extinction ratio is 22.5 dB, and the 3 dB bandwidth is about 100 GHz. The modulated incident light enters the mode division multiplexer. In the phase matching region, the effective index of the single-mode waveguide and the multi-mode waveguide is equal, and the TE modes are converted into TE, modes and TE, modes. The insertion loss is less than 0.1 dB, and the channel crosstalk is less than 26 dB. The TE0 modes input from the three ports are output from the same port in different modes. In conclusion, a three-channel integrated device for graphene electro-optic modulation and mode division multiplexing is proposed. The integrated device can realize modulation and mode division multiplexing of TE0 modes, TE1 modes and TE2 modes at the same time. The simulation results using the three-dimensional finite-difference time-domain method show that when the wavelength is 1 570 nm, the extinction ratio of the integrated device is greater than 28.3 dB, the insertion loss is less than 0.21 dB, the channel crosstalk is less than -28.6 dB, and the 3 dB bandwidth of the modulator reaches 100 GHz. The integrated device has excellent performance and has important application value in high-capacity optical communication systems.

We proposed an integrated device for electro-optic (EO) modulation and dense wavelength di-vision multiplexing (DWDM) based on photonic crystals (PhCs). The transmittance performance of the designed structure was modelled and analyzed according to the time-domain coupled mode theory (CMT), using three-dimensional finite-difference time-domain (3D-FDTD) method to calculate the parameters of the proposed device for verification. The numerical results show that the proposed integrated device can realize the functions of "on", "off" modulation and DWDM with a channel spacing of 0.8 nm at the operating wavelengths of 1555 nm and 1554.2 nm. The minimum insertion loss, channel crosstalk and modulation voltage are 0.7 dB, -29.04 dB and 0.88 V, respectively. The maximum extinction ratio and modulation speed are 21.51 dB and 29.4 GHz. The designed integrated device has the advantages of low loss, compact size (41.28 mu m x 11.18 mu m), narrow channel spacing, large extinction ratio, which can be easily expanded the number of channels and used in highly integrated large-capacity optical communication systems and data center.

Based on a sandwich structure and adiabatic coupler, a polarization-independent optical power splitter with a designable splitting ratio is designed to achieve power distribution for the 1550 nm wavelength optical signal with a designable splitting ratio. By adjusting the refractive index of the sandwiched middle layer material SiNx, the splitting ratios of the transverse electric (TE) and transverse magnetic (TM) polarization modes are made equal at the same wavelength, and a polarization-independence function is realized. Next, the designable splitting ratio function is obtained by varying the asymmetry of the waveguide gaps in the adiabatic coupler. The three-dimensional finite-difference time-domain method is used for modeling and simulations. The results reveal that the coupling length of the proposed device is only 7 mu m. The device can achieve designable splitting ratios ranging from 0. 50 to 0. 95 and simultaneously support the TE and TM polarization modes. The insertion loss value is lower than 0. 31 dB. A 100 nm bandwidth can be obtained when the tolerance of the splitting ratio is within +/- 0. 01. The proposed approach is potentially applicable to future photonic integrated circuit systems.