A Terahertz Waveguide Design Method Based on Anderson Localization

Abstract

This invention proposes a novel terahertz waveguide design method based on Anderson localization, comprising the following steps: Step S1, setting the initial waveguide structure dimensions and substrate material, and dividing the waveguide into N regions along the transverse direction (perpendicular to the light propagation direction), such that the refractive index of the N regions fluctuates randomly within a desired range relative to the substrate refractive index, forming the initial structure of the Anderson localized waveguide; Step S2, setting the FOM function representing the quality factor of the waveguide transmission performance, and importing the initial waveguide structure into electromagnetic field simulation software for simulation to obtain the FOM value of the initial structure; Step S3, using a particle swarm optimization algorithm to iteratively optimize the refractive index fluctuation and distribution of the initial structure of the Anderson localized waveguide, thereby optimizing the FOM value of the waveguide, and finally obtaining the optimal design parameters for the refractive index fluctuation and distribution of the Anderson localized waveguide structure; This invention solves the problems of high manufacturing cost, large size, and high waveguide loss in existing terahertz waveguides.

Description

Technical Field

[0001] This invention relates to the field of THz devices and numerical optimization calculation technology, and in particular to a terahertz waveguide design method based on Anderson localization. Background Technology

[0002] Terahertz (THz) waves generally refer to electromagnetic waves in the frequency range of 0.1-10 THz, corresponding to wavelengths of 0.03-3 mm. They represent a region of the electromagnetic spectrum transitioning from millimeter waves to infrared light. Terahertz waves possess excellent penetrability, low energy, and wide bandwidth, making them promising candidates for applications in high-speed space communication, environmental monitoring, heterodyne detection, medical detection, non-destructive testing, and national defense.

[0003] The absorption loss of terahertz waves by water molecules in the air hinders their long-distance transmission in the atmosphere. Waveguide technology is particularly important for the development of terahertz technology. Traditional terahertz waveguides can be divided into parallel plate waveguides, metal wire waveguides, photonic crystal fibers, and metal surface plasmon waveguides. Parallel plate metal waveguides consist of two parallel metal plates, confining electromagnetic waves to propagate between them. However, parallel plate metal waveguides have high losses and relatively large geometric dimensions, making them unsuitable for long-distance terahertz wave transmission and miniaturized system integration. Metal wire waveguides utilize the Sommerfeld mode at the metal-air interface, achieving extremely low transmission dissipation. However, the coupling efficiency between terahertz waves and metal wire waveguides is very low; the fabrication process of terahertz band photonic crystal fibers is complex, with a high defect rate, resulting in high manufacturing costs. Metal surface plasmon waveguide technology has high losses and is not yet mature.

[0004] Anderson proposed in 1958 that electrons diffuse when propagating in an ordered, regular array (such as a solid crystal lattice). When a randomly fluctuating potential energy is introduced (such as in disordered impurity atoms), the moving electrons are localized to a specific region, causing the electron diffusion behavior to disappear. Photon localization is the optical analogue of Anderson's electron localization. Utilizing the Anderson photon localization effect, terahertz waves can be confined to a specific region for propagation. Waveguide structures can be designed and fabricated based on this principle. Summary of the Invention

[0005] This invention proposes a terahertz waveguide design method based on Anderson localization, which solves the problems of high manufacturing cost, large size, and high waveguide loss of existing terahertz waveguides.

[0006] The present invention adopts the following technical solution.

[0007] A terahertz waveguide design method based on Anderson localization, wherein the waveguide is a two-dimensional planar structure, including a periodic wire grid structure located on a substrate, wherein the periodic wire grid structure uses fluctuating refractive index to form an Anderson localization effect on terahertz waves, thereby realizing waveguide function;

[0008] The design method includes the following steps;

[0009] Step S1: Set the initial waveguide structure dimensions and substrate material, and divide the waveguide into N regions along the transverse direction, which is perpendicular to the light propagation direction. Make the refractive index of the N regions fluctuate randomly within the required range relative to the refractive index of the substrate to form the initial structure of the Anderson localized waveguide.

[0010] Step S2: Set the FOM function to represent the quality factor of waveguide transmission performance, and import the initial waveguide structure into the electromagnetic field simulation software for simulation to obtain the FOM value of the initial structure.

[0011] Step S3: Use the particle swarm optimization algorithm to iteratively optimize the refractive index fluctuation and distribution of the initial structure of the Anderson localized waveguide, thereby optimizing the FOM value of the waveguide and finally obtaining the design parameters of the optimal refractive index fluctuation and distribution of the Anderson localized waveguide structure.

[0012] The electromagnetic field simulation software is FDTD Solutions; the quality factor is the Figure of Merit (FOM); and the particle swarm optimization algorithm is Particle Swarm Optimization (PSO).

[0013] Step S1 is the initialization stage, which is used to construct the initial structure of the terahertz waveguide. In this step, the waveguide is divided into N equal parts along the lateral direction, and the refractive index of the N regions is arranged regularly along the lateral direction, that is, the low refractive index region and the high refractive index region are distributed alternately.

[0014] Step S2 involves random fluctuation of the refractive index and calculation of the initial FOM. Assuming the substrate refractive index is n0, the refractive index of each region is randomly fluctuated relative to the substrate refractive index n0 within a preset range; the amount of refractive index fluctuation is... Formula 1;

[0015] in The larger the value of the periodic modulation index, the greater the refractive index fluctuation and the better the Anderson photon localization effect. It is a periodic function, with a value of 1 in the high refractive index region and 0 in the low refractive index region; C is the degree of disorder, the value of which determines the difference in refractive index between different regions; The function is a random function, uniformly distributed between 0 and 1 in the high refractive index region and 0 in the low refractive index region; the waveguide obtained in step S2 is the Anderson photonic localized waveguide, whose photonic localization effect follows a probability statistical distribution. Then, the initial structure is simulated in FDTD Solutions software to obtain the FOM value of the initial structure.

[0016] In step S2, the FOM function is set to the sum of the root mean square deviations of the actual electric field distribution values ​​and the ideal values ​​at each point on the output plane.

[0017] In step S1, the substrate material is erbium-doped bismuthate glass with a refractive index n0 = 1.46; the initial structure of the terahertz waveguide has a length L of 100 mm, a width W of 18 mm, and a thickness H of 2 mm. The refractive index of the low-refractive-index region in the initial structure is the substrate refractive index n0, and its width L... s =300um; the refractive index of the high refractive index region in the initial structure is n1, which deviates from the substrate refractive index Δn, and the width L w =300um;

[0018] In step S2, the periodic modulation index The value is 0.1.

[0019] Step S3 is the intelligent algorithm optimization stage. The PSO algorithm is used to further optimize the refractive index distribution of each region on the Anderson photonic localized waveguide prototype, that is, the initial structure of the waveguide. The FOM value change gradient obtained in each simulation is used as a guide to optimize the fluctuation and arrangement of the refractive index, and output the optimal refractive index distribution structure of the waveguide to improve the localization capability of Anderson photonics, thereby improving the transmission performance of the terahertz waveguide.

[0020] The refractive index of the optimal refractive index distribution structure fluctuates within a preset range in the transverse direction relative to the substrate material, and the refractive index fluctuation in each region is optimized to the optimal value after optimization by the PSO algorithm.

[0021] When performing electric field simulation on the optimal refractive index distribution structure of the terahertz waveguide, a Gaussian light source is input from the bottom of the waveguide with an input light source frequency of 1 terahertz and a beam waist diameter of 1500 μm. An electric field detector is placed on the waveguide cross section and the end face, respectively, to detect the electric field distribution of the terahertz wave propagating in the waveguide and the electric field distribution of the waveguide end face when the wave exits the waveguide.

[0022] The Anderson local waveguide is fabricated on an erbium-doped bismuthate glass substrate using ultrafast laser direct writing technology, and the transverse direction of the waveguide is perpendicular to the light transmission direction, with the refractive index in this direction fluctuating randomly within a preset range relative to the background refractive index.

[0023] When fabricating Anderson localized waveguides using ultrafast laser direct writing technology, the ablation time is controlled by controlling the laser scanning speed, thereby controlling the refractive index of each region of the waveguide.

[0024] Compared with the prior art, the present invention has the following advantages:

[0025] 1. The terahertz waveguide design method disclosed in this invention has higher reliability. The terahertz waveguide disclosed in this invention adopts a design scheme that combines theoretical design with intelligent algorithm optimization design. After obtaining the Anderson localized waveguide prototype with a random distribution of transverse refractive index, the intelligent algorithm is used to optimize the distribution of refractive index, which makes up for the deficiencies in the probabilistic statistical distribution of the Anderson photon localization capability of the initial waveguide structure, thereby significantly improving the reliability and performance of the waveguide.

[0026] 2. The terahertz waveguide based on localized Anderson localization disclosed in this invention has lower requirements for processing technology and lower manufacturing costs compared to traditional waveguides. This is because the waveguide design principle of this invention is based on the photon localization effect in Anderson localization, which requires the waveguide's transverse refractive index to fluctuate randomly. This refractive index fluctuation can be achieved using ultrafast laser direct writing technology, where the refractive index of different regions of the waveguide is controlled by adjusting the laser scanning speed. Ultrafast laser direct writing technology is now very mature and reliable, thus enabling the fabrication of terahertz waveguides at a relatively low cost.

[0027] 3. The design method disclosed in this invention has higher design efficiency. It only requires inputting structural dimension parameters and generating an Anderson localized oscillation prototype with randomly fluctuating transverse refractive index within a certain range. Then, intelligent algorithms can be used for automated optimization design. After the program optimization is complete, the required target device structure can be generated. The entire optimization direction is determined by the gradient information of the objective function change, enabling more targeted identification of structural adjustment directions. This is more efficient than traditional design methods that rely on theoretical design or random parameter adjustments. Attached Figure Description

[0028] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0029] Appendix Figure 1 This is a schematic diagram of each stage of the terahertz waveguide design method in the embodiments of the present invention;

[0030] Appendix Figure 2a This is a three-dimensional structural diagram of the terahertz waveguide in an embodiment of the method of the present invention;

[0031] Appendix Figure 2b This is a schematic diagram of the processing method in an embodiment of the present invention;

[0032] Appendix Figure 3This is a simulation diagram of the electric field of the terahertz waveguide in an embodiment of the method of the present invention. Detailed Implementation

[0033] As shown in the figure, a terahertz waveguide design method based on Anderson localization is presented. The waveguide is a two-dimensional planar structure, including a periodic wire grating structure located on a substrate. The periodic wire grating structure uses fluctuating refractive index to form an Anderson localization effect on the terahertz wave, thereby realizing the waveguide function.

[0034] The design method includes the following steps;

[0035] Step S1: Set the initial waveguide structure dimensions and substrate material, and divide the waveguide into N regions along the transverse direction, which is perpendicular to the light propagation direction. Make the refractive index of the N regions fluctuate randomly within the required range relative to the refractive index of the substrate to form the initial structure of the Anderson localized waveguide.

[0036] Step S2: Set the FOM function to represent the quality factor of waveguide transmission performance, and import the initial waveguide structure into the electromagnetic field simulation software for simulation to obtain the FOM value of the initial structure.

[0037] Step S3: Use the particle swarm optimization algorithm to iteratively optimize the refractive index fluctuation and distribution of the initial structure of the Anderson localized waveguide, thereby optimizing the FOM value of the waveguide and finally obtaining the design parameters of the optimal refractive index fluctuation and distribution of the Anderson localized waveguide structure.

[0038] The electromagnetic field simulation software is FDTD Solutions; the quality factor is the Figure of Merit (FOM); and the particle swarm optimization algorithm is Particle Swarm Optimization (PSO).

[0039] Step S1 is the initialization stage, which is used to construct the initial structure of the terahertz waveguide. In this step, the waveguide is divided into N equal parts along the lateral direction, and the refractive index of the N regions is arranged regularly along the lateral direction, that is, the low refractive index region and the high refractive index region are distributed alternately.

[0040] Step S2 involves random fluctuation of the refractive index and calculation of the initial FOM. Assuming the substrate refractive index is n0, the refractive index of each region is randomly fluctuated relative to the substrate refractive index n0 within a preset range; the amount of refractive index fluctuation is... Formula 1;

[0041] in The larger the value of the periodic modulation index, the greater the refractive index fluctuation and the better the Anderson photon localization effect. It is a periodic function, with a value of 1 in the high refractive index region and 0 in the low refractive index region; C is the degree of disorder, the value of which determines the difference in refractive index between different regions; The function is a random function, uniformly distributed between 0 and 1 in the high refractive index region and 0 in the low refractive index region; the waveguide obtained in step S2 is the Anderson photonic localized waveguide, whose photonic localization effect follows a probability statistical distribution. Then, the initial structure is simulated in FDTD Solutions software to obtain the FOM value of the initial structure.

[0042] In step S2, the FOM function is set to the sum of the root mean square deviations of the actual electric field distribution values ​​and the ideal values ​​at each point on the output plane.

[0043] In step S1, the substrate material is erbium-doped bismuthate glass with a refractive index n0 = 1.46; the initial structure of the terahertz waveguide has a length L of 100 mm, a width W of 18 mm, and a thickness H of 2 mm. The refractive index of the low-refractive-index region in the initial structure is the substrate refractive index n0, and its width L... s =300um; the refractive index of the high refractive index region in the initial structure is n1, which deviates from the substrate refractive index Δn, and the width L w =300um;

[0044] In step S2, the periodic modulation index The value is 0.1.

[0045] Step S3 is the intelligent algorithm optimization stage. The PSO algorithm is used to further optimize the refractive index distribution of each region on the Anderson photonic localized waveguide prototype, that is, the initial structure of the waveguide. The FOM value change gradient obtained in each simulation is used as a guide to optimize the fluctuation and arrangement of the refractive index, and output the optimal refractive index distribution structure of the waveguide to improve the localization capability of Anderson photonics, thereby improving the transmission performance of the terahertz waveguide.

[0046] The refractive index of the optimal refractive index distribution structure fluctuates within a preset range in the transverse direction relative to the substrate material, and the refractive index fluctuation in each region is optimized to the optimal value after optimization by the PSO algorithm.

[0047] When performing electric field simulation on the optimal refractive index distribution structure of the terahertz waveguide, a Gaussian light source is input from the bottom of the waveguide with an input light source frequency of 1 terahertz and a beam waist diameter of 1500 μm. An electric field detector is placed on the waveguide cross section and the end face, respectively, to detect the electric field distribution of the terahertz wave propagating in the waveguide and the electric field distribution of the waveguide end face when the wave exits the waveguide.

[0048] The Anderson local waveguide is fabricated on an erbium-doped bismuthate glass substrate using ultrafast laser direct writing technology, and the transverse direction of the waveguide is perpendicular to the light transmission direction, with the refractive index in this direction fluctuating randomly within a preset range relative to the background refractive index.

[0049] When fabricating Anderson localized waveguides using ultrafast laser direct writing technology, the ablation time is controlled by controlling the laser scanning speed, thereby controlling the refractive index of each region of the waveguide.

[0050] Example:

[0051] Figure 1 This diagram illustrates the various stages of the terahertz waveguide design method in this invention. Different shades of gray represent different refractive indices. S1 represents the initialization stage, where the initial structure of the terahertz waveguide is constructed, and the dimensions (length L = 100 mm, width W = 18 mm, thickness H = 2 mm) and substrate material are set. The substrate material used is erbium-doped bismuthate glass (refractive index n0 = 1.46). Subsequently, the initialized waveguide is divided into N equal parts laterally, and the refractive indices within the N intervals are arranged regularly along the lateral direction (the white area represents the low refractive index region, i.e., the substrate refractive index n0, with a width L). s =300um. The dark area is the high refractive index region n1, which deviates from the substrate refractive index Δn, with a width L. w =300um). S2 represents the initial FOM stage for random refractive index fluctuation, where the refractive index of each region fluctuates randomly within a certain range relative to the substrate refractive index n0. The amount of refractive index fluctuation is... ,in The periodic modulation index (0.1 in this design) is the largest value. The larger the value, the greater the refractive index fluctuation and the better the Anderson photon localization effect. It is a periodic function, with a value of 1 in the high refractive index region and 0 in the low refractive index region. C is the degree of disorder, and its value determines the difference in refractive index between different regions. The function is a random function, uniformly distributed between 0 and 1 in the high refractive index region and 0 in the low refractive index region. The waveguide obtained in this stage is the Anderson photonic localized waveguide, whose photonic localization effect follows a probabilistic statistical distribution. The initial structure is then simulated in FDTDSolutions software to obtain the FOM value of the initial structure. The FOM function is set as the sum of the root mean square errors of the actual and ideal electric field distribution values ​​at each point on the output plane. S3 is the intelligent algorithm optimization stage, which uses the PSO algorithm to further optimize the refractive index distribution in each region of the Anderson photonic localized waveguide prototype. Guided by the gradient of the FOM value change obtained in each simulation, the fluctuation and arrangement of the refractive index are purposefully optimized, ultimately outputting the optimal refractive index distribution structure of the waveguide. The refractive index of the finally obtained waveguide structure fluctuates within a certain range in the lateral direction relative to the substrate material, and the amount of refractive index fluctuation in each region is optimized by the PSO algorithm to the optimal value.

[0052] Figure 2 is a schematic diagram of the three-dimensional structure of the terahertz waveguide structure and the waveguide fabrication process in an embodiment of the method of the present invention. Figure a shows the three-dimensional structure of the waveguide; the white area represents the erbium-doped bismuthate glass substrate, whose refractive index... Other grayscale regions have different refractive indices n1 = n0 + Δn, and their refractive indices are relative to each other in the transverse direction of the waveguide. The refractive index fluctuates randomly within a certain range. Figure b is a schematic diagram of the fabrication of the Anderson localized waveguide using ultrafast laser direct writing technology. The refractive index of each region of the waveguide is controlled by controlling the laser scanning speed (i.e., the ablation time). Under the action of the laser, the chemical bonds between the molecules of the substrate material are broken, the internal structure of the glass substrate is changed, resulting in a change in polarizability, which ultimately leads to a change in refractive index.

[0053] Figure 3 This is a simulation diagram of the terahertz waveguide electric field in this embodiment. A Gaussian light source is input from the bottom of the waveguide (input light source frequency is 1 terahertz, beam waist diameter is 1500 μm). An electric field detector is placed on the waveguide cross-section and end face, respectively, to detect the electric field distribution of the terahertz wave propagating in the waveguide and the electric field distribution of the waveguide end face when the wave exits the waveguide. Figure a shows the electric field simulation diagram of the initial waveguide structure (i.e., substrate only); Figure b shows the cross-sectional electric field distribution diagram of the waveguide (waveguide prototype in stage S1) when the refractive index is regularly ordered in different regions. The electric field distribution of the waveguide with ordered refractive index distribution is similar to that of the initial structure waveguide, and the light propagates in the waveguide and diffuses to both sides. Figure c shows the electric field distribution diagram when the refractive index of each region of the waveguide is randomly fluctuating (disorder degree C=0.5); it can be seen that the light is localized to the middle region during propagation, and this new waveguide has a good Anderson photonic localization effect. d represents the electric field distribution curve at the waveguide end face; the dashed line and solid line represent the electric field intensity distribution curves at the end face under the conditions of the original waveguide substrate material and the refractive index distribution. The dotted line represents the electric field intensity distribution curve at the waveguide end face when the refractive index fluctuates randomly.

[0054] The above description is only a preferred embodiment of the present invention. All equivalent changes and modifications made within the scope of the claims of the present invention should be included in the scope of the present invention.

Claims

1. A terahertz waveguide design method based on Anderson localization, characterized in that: The waveguide is a two-dimensional planar structure, including a periodic wire grating structure on a substrate. The periodic wire grating structure uses a fluctuating refractive index to form an Anderson localization effect on terahertz waves, thereby realizing the waveguide function. The design method includes the following steps; Step S1: Set the initial waveguide structure dimensions and substrate material, and divide the waveguide into N regions along the transverse direction, which is perpendicular to the light propagation direction. Make the refractive index of the N regions fluctuate randomly within the required range relative to the refractive index of the substrate to form the initial structure of the Anderson localized waveguide. Step S2: Set the FOM function representing the quality factor of waveguide transmission performance, and import the initial waveguide structure into electromagnetic field simulation software for simulation to obtain the FOM value of the initial waveguide structure; the electromagnetic field simulation software used is FDTDSolutions; Step S3: Use the particle swarm optimization algorithm to iteratively optimize the refractive index fluctuation and distribution of the initial structure of the Anderson localized waveguide, thereby optimizing the FOM value of the waveguide and finally obtaining the design parameters of the optimal refractive index fluctuation and distribution of the Anderson localized waveguide structure. In step S2, the refractive index of the substrate is set to n0, and the refractive index of each region is randomly fluctuated relative to the substrate refractive index n0 within a preset range; the amount of refractive index fluctuation is... Formula 1; in The larger the value of the periodic modulation index, the greater the refractive index fluctuation and the better the Anderson photon localization effect. It is a periodic function, with a value of 1 in the high refractive index region and 0 in the low refractive index region; C is the degree of disorder, the value of which determines the difference in refractive index between different regions; The function is a random function, uniformly distributed between 0 and 1 in the high refractive index region and 0 in the low refractive index region; the photon localization effect of the initial waveguide structure follows a probability statistical distribution, and the initial waveguide structure is simulated using FDTD Solutions software to obtain the FOM value of the initial waveguide structure. Step S3 is the intelligent algorithm optimization stage. The particle swarm optimization algorithm is used to further optimize the refractive index distribution of each region on the initial structure of the Anderson photonic localized waveguide. The gradient of the FOM value change obtained in each simulation is used as a guide to optimize the fluctuation and arrangement of the refractive index, and output the optimal refractive index distribution structure of the waveguide to improve the localization capability of Anderson photonics, thereby improving the transmission performance of the terahertz waveguide. The refractive index of the optimal refractive index distribution structure fluctuates within a preset range in the transverse direction relative to the substrate material. The amount of refractive index fluctuation in each region is optimized by the particle swarm optimization algorithm to obtain the optimal value.

2. The terahertz waveguide design method based on Anderson localization according to claim 1, characterized in that: Step S1 is the initialization stage, which is used to construct the initial structure of the Anderson localized terahertz waveguide. In this step, the waveguide is divided into N equal parts along the lateral direction, and the refractive index of the N regions is arranged regularly along the lateral direction, that is, the low refractive index region and the high refractive index region are distributed alternately.

3. The terahertz waveguide design method based on Anderson localization according to claim 2, characterized in that: In step S2, the FOM function is set to the sum of the root mean square deviations of the actual electric field distribution values ​​and the ideal values ​​at each point on the output plane.

4. The terahertz waveguide design method based on Anderson localization according to claim 3, characterized in that: In step S1, the substrate material is erbium-doped bismuthate glass with a refractive index n0 = 1.46; the initial structure of the Anderson localized terahertz waveguide has a length L of 100 mm, a width W of 18 mm, and a thickness H of 2 mm. The refractive index of the low-refractive-index region in the initial waveguide structure is the substrate refractive index n0, and its width L... s =300um; the refractive index of the high refractive index region in the initial waveguide structure is n1, which deviates from the substrate refractive index Δn, and the width L w =300um; In step S2, the periodic modulation index is... The value is 0.

1.

5. The terahertz waveguide design method based on Anderson localization according to claim 1, characterized in that: The Anderson localized waveguide is fabricated on an erbium-doped bismuthate glass substrate using ultrafast laser direct writing technology, and the transverse direction of the waveguide is perpendicular to the light transmission direction, with the refractive index in this direction fluctuating randomly within a preset range relative to the background refractive index.

6. The terahertz waveguide design method based on Anderson localization according to claim 5, characterized in that: When fabricating Anderson localized waveguides using ultrafast laser direct writing technology, the ablation time is controlled by controlling the laser scanning speed, thereby controlling the refractive index of each region of the waveguide.

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