Ultrahigh-resolution integrated calculation spectrometer based on single waveguide and implementation method

Abstract

The invention discloses an ultrahigh-resolution integrated calculation spectrometer based on a single waveguide and an implementation method, and belongs to the field of spectral measurement. The spectrometer comprises a cladding, an input end face coupler, a multi-stage reflection measurement waveguide, a phase modulator, an output end face coupler, a photoelectric detector and a microcontroller. The multi-stage reflection measurement waveguide comprises multiple stages of microstructure reflection units which are sequentially connected through waveguides in the propagation direction. The invention solves the problems of low resolution and insufficient bandwidth and expandability, has high resolution and large bandwidth performance, and realizes 0.9 pm-level double-peak distinguishable and 800nm effective bandwidth in the near-infrared band; due to the simple structure of the single straight waveguide, high independent channel density can be obtained without a long-chain cascade device; the waveguide loss can be maintained within 5 dB by limiting the reflectivity and the segment number of the micro-structure reflection units, and a good detection effect can also be achieved for low-intensity light to be detected; the method is applied to high-precision measurement of various complex spectrums.

Description

Technical Field

[0001] This invention belongs to the field of spectral measurement, specifically relating to an ultra-high resolution integrated computational spectrometer based on a single waveguide and its implementation method. Background Technology

[0002] With the widespread application of spectral analysis technology in environmental monitoring, industrial testing, and biomedical diagnostics, the trend towards miniaturization and integration of spectroscopic instruments is becoming increasingly significant. While traditional free-space spectrometers offer high-precision wavelength resolution, their large size and complex structure make them unsuitable for use in portable devices. Therefore, on-chip integrated spectrometers have emerged. Spectrometers based on photonic integration technology not only possess advantages such as small size, low power consumption, and ease of mass production, but also offer compatibility with optical communication and sensing circuits, providing fundamental support for future intelligent sensor networks, wearable medical systems, and integrated optical computing platforms.

[0003] Currently, common integrated spectrometer solutions are arrayed waveguide grating (AWG) type and Fourier transform type spectrometers. The resolution of these on-chip spectrometers is proportional to the device size, making it difficult to achieve high-precision spectral line resolution on tiny chip sizes. Computational spectrometers (RS) can significantly improve resolution, but still have the following main problems: 1. Limited resolution: Computational spectrometers are still only on the order of a few picometers or even tens of picometers, making it difficult to achieve sub-picometer resolution, which is insufficient to support applications such as gas molecule sensing; 2. Insufficient insertion loss and bandwidth: In order to improve resolution, computational spectrometers often need to use disordered media or cascade multiple filter units, which leads to increased insertion loss and limited bandwidth, restricting their feasibility in large-scale applications. 3. Insufficient scalability: Traditional structures are difficult to adapt to multiple bands on the same platform, which limits their application potential in multimodal spectral sensing. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention proposes an ultra-high resolution integrated computational spectrometer based on a single waveguide and its implementation method.

[0005] One objective of this invention is to propose an ultra-high resolution integrated computational spectrometer based on a single waveguide.

[0006] The present invention relates to an ultra-high resolution integrated computational spectrometer based on a single waveguide, comprising: a cladding, an input end-face coupler, a multi-stage reflection measurement waveguide, a phase modulator, an output end-face coupler, a photodetector, and a microcontroller; wherein, along the propagation direction, the input end-face coupler, the multi-stage reflection measurement waveguide, and the output end-face coupler are sequentially connected and disposed on the cladding; the output end-face coupler is connected to the photodetector; the multi-stage reflection measurement waveguide comprises multiple stages of microstructure reflection units sequentially connected along the propagation direction via the waveguide; each stage of the microstructure reflection unit is characterized by low insertion loss and weak reflection, i.e., partial reflection; a phase modulator is disposed on the waveguide connecting two adjacent stages of microstructure reflection units; the phase modulator is connected to the microcontroller; The light to be measured is input to the multi-stage reflection measurement waveguide through the input end-face coupler. The light is partially reflected when it encounters the microstructure reflection units at each stage. Reflected by microstructure reflection units located at different positions, different reflected light is formed with different optical path lengths. The light converges at the output end and interferes to form a wavelength-dependent amplitude response, which is output to the photodetector through the output end-face coupler. The microcontroller adjusts the voltage applied to the phase modulator, causing a corresponding phase change and forming different amplitude responses. Multiple different amplitude responses are obtained by combining the modulation states of various phase modulators. The spectrum of the light to be measured is obtained based on the multiple different amplitude responses.

[0007] Light undergoes partial reflection at each stage of the microstructure reflection unit. The forward and backward reflection in each microstructure reflection unit has the same reflectivity, resulting in a symmetrical structure. Each stage of the multi-stage reflection measurement waveguide has the same microstructure reflection unit, which employs a Bragg grating or a geometry generated using a reverse design algorithm.

[0008] The length of the waveguide between each two adjacent microstructure reflection units can be obtained by using a particle swarm optimization algorithm or by using random numbers that are uniformly distributed within a set length range.

[0009] The invention also includes a substrate, a cladding disposed on the substrate, the substrate being made of silicon, glass or sapphire; the cladding being made of a low refractive index material, such as silicon dioxide or silicon oxynitride; and the input end coupler, waveguide and output end coupler being made of a high refractive index material, such as silicon, silicon nitride or lithium niobate.

[0010] It also includes one or more multi-branch couplers, where the light to be measured input from the input end face coupler is split into multiple branches by one or more multi-branch couplers, each branch is connected to a multi-stage reflection measurement waveguide, and each multi-stage reflection measurement waveguide is connected to the corresponding photodetector through the output end face coupler.

[0011] Each multi-stage reflection measurement waveguide has 7 to 12 microstructure reflection units; the reflectivity of the microstructure reflection units is (0 to 0.5], with an optimal value of 0.2, which ensures that the total transmitted power of the waveguide is >-5 dB. The width of the waveguide cross-section is 0.8 to 1.2 μm, and the thickness is 200 to 400 nm.

[0012] The number of phase modulators must be greater than 6, preferably 10; the number of modulation combination states of the phase modulators during spectrum scanning is 1024 channels, because it ensures accuracy while keeping the scanning time moderate; 4096 channels can be enabled when higher robustness is required.

[0013] Another objective of this invention is to propose a method for implementing an ultra-high resolution integrated computational spectrometer based on a single waveguide.

[0014] The implementation method of the ultra-high resolution integrated computational spectrometer based on a single waveguide of the present invention includes the following steps: 1) The light to be measured is input to the multi-stage reflection measurement waveguide through the input end face coupler; 2) When light encounters microstructure reflection units at various levels, it is partially reflected and reflected by microstructure reflection units located at different positions connected by waveguides, forming different reflected light with different optical paths. They converge at the output end and interfere to form a wavelength-dependent amplitude response, which is then output to the photodetector via the output end coupler. 3) The microcontroller adjusts the voltage state applied to each phase modulator, which changes the optical path through the waveguide, causing a corresponding phase change and forming different amplitude responses; 4) Different modulation combinations of phase modulators correspond to different amplitude responses, and multiple different amplitude responses can be obtained by using multiple modulation combinations of phase modulators; 5) Each modulation combination state corresponds to one channel. The amplitude response of all channels is scanned by the microcontroller, and the spectrum of the light to be measured is recovered by the least squares method.

[0015] In step 3), applying a voltage to a phase modulator has M voltage states: no voltage applied and M-1 voltages with different amplitudes, where M is a natural number ≥ 2.

[0016] In step 4), the multi-stage reflection measurement waveguide includes first to nth microstructure reflection units, which are connected by n-1 waveguides. n-1 phase modulators are correspondingly set, where n is the number of microstructure reflection units. Different voltage states are applied to each phase modulator, corresponding to different modulation combinations. The n-1 phase modulators have a total of M... n-1Modulation combination state; different modulation combination states of the phase modulator correspond to different modulation phases and thus different amplitude responses. Multiple modulation combination states are selected, and each modulation combination state corresponds to one channel. M is a natural number ≥2 and n is a natural number ≥7.

[0017] The microstructured reflective unit employs a Bragg grating, which consists of a series of parallel and equally spaced alternating high-refractive-index and low-refractive-index structures. The length of the high refractive index structure, For the length of the low-refractive-index structure, the period of the Bragg grating The Bragg interference condition should be satisfied: in, The target wavelength of the Bragg grating. and These represent the effective refractive indices of the high-refractive-index and low-refractive-index structures, respectively. The Bragg grating operates at the target wavelength by satisfying the Bragg interference condition. The reflectivity of the Bragg grating is set by adjusting the number of periods; more periods result in higher reflectivity. As a reflective element, the Bragg grating suffers significant losses and requires high lithographic precision.

[0018] A better approach is to use a reverse engineering algorithm to generate the geometry of the microstructured reflective unit, resulting in lower losses. A two-dimensional design region is divided into two-dimensional mesh elements. The dielectric constant of each mesh element is binarized to the dielectric constant of the waveguide or substrate material. The optical field is calculated using finite-time difference physics simulation, and the following formula is used as the design target for the microstructured reflective unit. FoM R : in, and These represent the target's transmittance and reflectance, respectively. R ( p )and T ( p The reflectivity and transmittance of the current structure are represented by , respectively, while constraints are placed on the reflection, transmission, and loss of the microstructure reflective unit; the geometry is iterated according to the design goals of the microstructure reflective unit to achieve the design goals of the microstructure reflective unit. FoM R The maximum result is obtained by using a reverse design algorithm to generate a geometry that satisfies the target reflectivity. The geometry generated by the reverse design algorithm performs better than that of the Bragg grating.

[0019] The lengths of each waveguide are obtained using either a particle swarm optimization algorithm or by using a uniformly distributed random number within a set length range. The set length range for the uniformly distributed random number is 300–500 μm. The particle swarm optimization algorithm is used to obtain the positional distribution of the microstructure reflecting units on the waveguides, i.e., the length of the waveguide between every two adjacent microstructure reflecting units: first, a set of arbitrary lengths from the first to the (n-1)th waveguides is set. L 1~ L n-1 As initial parameters, the autocorrelation function and correlation distance under the current parameters are then calculated using the transfer matrix method. Furthermore, the design objective of minimizing the waveguide's autocorrelation is calculated. FoM L According to the design target of length FoM L The lengths of the first to (n-1)th waveguides are obtained through optimization. L 1~ L n-1 ; Design goal for length FoM L : in, Dl The correlation distance of the waveguide spectral response. R ( l () is the autocorrelation function of the waveguide spectral response. β The normalization coefficient is... l λ is the wavelength.

[0020] Advantages of this invention: (1) High resolution + large bandwidth: The spectrometer of the present invention provides high resolution and large bandwidth performance, and achieves 0.9 pm-level double peak resolution and 800 nm effective bandwidth in the near-infrared band; (2) Simple structure: The simple structure of a single straight waveguide can achieve high independent channel density without the need for long chain cascaded devices; (3) High light flux: By limiting the reflectivity and number of segments of the microstructure reflective unit, the waveguide loss can be kept within 5dB, and it can also have a good detection effect for low intensity light to be measured. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of an embodiment of the ultra-high resolution integrated computational spectrometer based on a single waveguide according to the present invention; Figure 2 The image shows the spectrum of the light to be measured obtained in an embodiment of the implementation method of the ultra-high resolution integrated computational spectrometer based on a single waveguide according to the present invention, wherein (a) is the spectrum of each monochromatic light in the 1290~2000nm band, and (b) is the broadband spectrum. Detailed Implementation

[0022] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0023] like Figure 1 As shown, the ultra-high resolution integrated computational spectrometer based on a single waveguide in this embodiment includes: a cladding, an input end-face coupler, a multi-branch coupler, a multi-stage reflection measurement waveguide, a phase modulator, an output end-face coupler, a photodetector, and a microcontroller. Along the propagation direction, the input end-face coupler, multi-branch coupler, multi-stage reflection measurement waveguide, and output end-face coupler are sequentially connected and disposed on the cladding. The input end-face coupler is connected to the multi-branch coupler, which is a one-to-three branch coupler, dividing the waveguide into three branches. Each branch connects to a multi-stage reflection measurement waveguide, and each multi-stage reflection measurement waveguide is connected to a corresponding photodetector via the output end-face coupler. The multi-stage reflection measurement waveguide includes first to nth microstructure reflection units sequentially connected along the propagation direction via waveguides. Each microstructure reflection unit has low insertion loss and weak reflection, i.e., partial reflection. A phase modulator is disposed on the waveguide connecting adjacent microstructure reflection units. The phase modulator is connected to the microcontroller. The photodetector is connected to the microcontroller.

[0024] The cladding is disposed on the substrate, which is 725 μm thick silicon; the cladding is 2 μm thick silicon dioxide; the input end coupler, waveguide and output end coupler are made of a single layer of 300 nm thick silicon nitride.

[0025] The outputs converge and interfere to form a wavelength-dependent amplitude response. Where N is the total number of optical paths, A 0 represents the amplitude of a single optical path. For the first k Phase and amplitude response of the optical path I It is angular frequency The function is . Applying a voltage to a phase modulator has three voltage states: no voltage (0V), a low voltage of 3.5V, and a high voltage of 5V. In this embodiment, the multi-stage reflection measurement waveguide includes 11 microstructure reflection units, i.e., n=11. The 11 microstructure reflection units are connected by 10 waveguides, and each waveguide has a phase modulator, for a total of 10 phase modulators. The 10 phase modulators have a total of 3 10=59049 modulation combination states; different modulation combination states of the phase modulator correspond to different modulation phases and thus different amplitude responses. Each modulation combination state corresponds to one channel. The microcontroller provides on-chip phase drive time-division addressing, and the spectrum of the light under test is recovered by scanning the amplitude response of all channels. In this implementation, 1024 modulation combination channels are used to ensure accuracy and moderate scanning time. For higher robustness requirements, 4096 channels can be enabled, with a total sampling time of 1.024 s. The scanning follows the principle of minimum power variation between adjacent channels to reduce temperature drift and improve system robustness.

[0026] Light undergoes partial reflection at each level of the microstructure reflective unit. The forward and backward reflection rates of the microstructure reflective unit are the same, exhibiting a symmetrical structure with a reflectivity of 20%. The microstructure reflective unit utilizes a geometric structure generated by a reverse design algorithm, dividing a 14μm × 2.5μm two-dimensional design region into 25nm × 25nm two-dimensional grid units. The dielectric constant of each grid unit is binarized to the dielectric constant of the waveguide material or substrate material. The optical field is calculated using finite-time difference physics simulation with the target wavelength, and the following formula is used as the design target for the microstructure reflective unit. FoM R : in, and These represent the target's transmittance and reflectance, respectively. R ( p )and T ( p The reflectivity and transmittance of the current structure are represented by , respectively. Simultaneously, constraints are imposed on the reflection, transmission, and loss of the microstructure reflective unit. The designed geometry of the microstructure reflective unit outperforms the Bragg grating. The geometry is iterated according to the design goals of the microstructure reflective unit, thus achieving the desired design objectives. FoM R The maximum result is obtained by using a reverse design algorithm to generate a geometry that satisfies the target reflectivity. The geometry generated by the reverse design algorithm performs better than that of the Bragg grating.

[0027] The particle swarm optimization algorithm is used to obtain the positional distribution of the microstructure reflection units on the waveguide, that is, the length of the waveguide between each two adjacent microstructure reflection units. First, a set of arbitrary lengths of the first to tenth waveguides is set. L 1~ L 10 As initial parameters, the autocorrelation function and correlation distance under the current parameters are then calculated using the transfer matrix method. Furthermore, the design objective of minimizing the waveguide's autocorrelation is calculated. FoM LAccording to the design target of length FoM L Optimize the lengths of the first to tenth waveguides L 1~ L 10 To obtain the optimal parameters; the design target for length. FoM L : in, Dl The correlation distance of the waveguide spectral response. R ( l () is the autocorrelation function of the waveguide spectral response. β The normalization coefficient is... l λ is the wavelength.

[0028] Example 1 Instead of using multi-branch couplers, only a single multi-stage reflection measurement waveguide is employed. The unit utilizes a chirped grating structure reflector obtained through reverse engineering. The lengths of the multi-stage reflection measurement waveguide are obtained using a particle swarm optimization algorithm. The lengths of the ten waveguide segments are 411.247 μm, 337.016 μm, 404.835 μm, 441.815 μm, 424.331 μm, 475.962 μm, 382.091 μm, 424.613 μm, 394.606 μm, and 305.939 μm, respectively. The waveguide cross-section has a width of 1 μm and a thickness of 300 nm. The total length of the input end-face coupler, the multi-stage reflection measurement waveguide, and the output end-face coupler, located on the substrate and cladding, is 4.5 mm.

[0029] The implementation method of the ultra-high resolution integrated computational spectrometer based on a single waveguide in this embodiment includes the following steps: 1) The light to be measured is input to the multi-stage reflection measurement waveguide through the input end face coupler; 2) When light encounters microstructure reflection units at various levels, it is partially reflected and reflected by microstructure reflection units located at different positions connected by waveguides. Different reflected light forms optical paths with different optical paths, converges at the output end and interferes to form a wavelength-dependent amplitude response, which is output to the photodetector through the output end coupler. The photodetector obtains the amplitude response and transmits it to the microcontroller. 3) The microcontroller adjusts the voltage state applied to each phase modulator, which changes the optical path through the waveguide, causing a corresponding phase change and forming different amplitude responses; 4) Different modulation combinations of phase modulators correspond to different amplitude responses, and multiple different amplitude responses can be obtained by using multiple modulation combinations of phase modulators; 5) Each modulation combination state corresponds to one channel. The amplitude response of all channels is scanned by the microcontroller. The microcontroller uses the least squares method with L1 (Lasso) regularization and L2 (Ridge) regularization terms to recover the spectrum of the light to be measured.

[0030] Experimental data: Dual-peak recovery was achieved in the 1530–1580 nm band: the peaks could still be reliably distinguished with a spacing of 0.9 pm, indicating a resolution < 0.9 pm; broadband optical recovery was achieved: the error ε < 0.1 was achieved for three different light shapes; the waveguide loss was 6.1 dB. Energy consumption and speed: channel switching time < 0.5 ms, single measurement time 0.5 s, and power consumption approximately 49 mW.

[0031] The recovered spectrum is as follows Figure 2 As shown, Figure 2 (a) shows the spectra of various monochromatic lights in the 1290~2000nm wavelength range. Figure 2 (b) in the image is a broadband spectrum. (From...) Figure 2 It can be seen that the recovered spectrum obtained by the method of the present invention is in good agreement with the reference spectrum, proving that the method of the present invention is effective.

[0032] Example 2 The multi-branch coupler includes a two-stage 1-to-2 multi-branch coupler. The first-stage 1-to-2 multi-branch coupler divides the optical path into two branches. A second-stage 1-to-2 multi-branch coupler is installed on each branch, splitting the input light into four branches. Each branch connects to a multi-stage reflection measurement waveguide, corresponding to the center bands of 780 nm, 1310 nm, 1550 nm, and 2000 nm, respectively. The output is output through the four multi-stage reflection measurement waveguides, otherwise the same as in Example 1. Experimental data: After calibration, the spontaneous emission amplification (ASE) light source achieved a total detection coverage of approximately 800 nm; single-peak reconstruction was performed in the 1290–2000 nm range with errors ε < 0.05; the losses of the four channels were in the range of 11–16 dB (including more than 6 dB of splitting loss). Energy consumption and speed: The total power consumption was approximately 245 mW, about four times that of Example 1.

[0033] Finally, it should be noted that the purpose of disclosing the embodiments is to help further understand the present invention. However, those skilled in the art will understand that various substitutions and modifications are possible without departing from the spirit and scope of the present invention and the appended claims. Therefore, the present invention should not be limited to the content disclosed in the embodiments, and the scope of protection of the present invention is defined by the claims.

Claims

1. A single waveguide based ultra-high resolution integrated computational spectrometer, comprising: The spectrometer comprises a cladding, an input end face coupler, a multi-stage reflection measurement waveguide, a phase modulator, an output end face coupler, a photodetector and a microcontroller; wherein, along the propagation direction, the input end face coupler, the multi-stage reflection measurement waveguide and the output end face coupler are sequentially connected and arranged on the cladding; the output end face coupler is connected to the photodetector; the multi-stage reflection measurement waveguide comprises a plurality of microstructure reflection units which are sequentially connected along the propagation direction through the waveguide; each microstructure reflection unit is partially reflective; the phase modulator is arranged on the waveguide between the adjacent two microstructure reflection units; the phase modulator is connected to the microcontroller; The light to be measured is input into the multi-stage reflection measurement waveguide through the input end face coupler, and the light is partially reflected when encountering each microstructure reflection unit; the light is reflected by the microstructure reflection units at different positions to form different reflected lights with different optical paths, which are converged together at the output end and interfere to form a wavelength-dependent amplitude response, and then output to the photodetector through the output end face coupler; the microcontroller adjusts the voltage applied to the phase modulator to cause corresponding phase changes and form different amplitude responses; a plurality of different amplitude responses corresponding to a plurality of modulation combination states of the phase modulators are obtained; and the spectrum of the light to be measured is obtained according to the plurality of different amplitude responses.

2. The optical spectrometer of claim 1, wherein, The microstructure reflection unit adopts a Bragg grating or a geometric structure generated by an inverse design algorithm.

3. The optical spectrometer of claim 1 or 2, wherein, The length of each waveguide is obtained by a particle swarm optimization algorithm or a random number uniformly distributed in a set length range.

4. The optical spectrometer of claim 1, wherein, The cladding is arranged on a substrate; the material of the substrate is silicon, glass or sapphire; the material of the cladding is silicon dioxide or silicon oxynitride; and the materials of the input end face coupler, the waveguide and the output end face coupler are silicon, silicon nitride or lithium niobate.

5. The optical spectrometer of claim 1, wherein, The spectrometer further comprises one or more multi-branch couplers; the light input from the input end face coupler is divided into a plurality of branches through the one or more multi-branch couplers, each branch is connected to a multi-stage reflection measurement waveguide, and each multi-stage reflection measurement waveguide is connected to a corresponding photodetector through an output end face coupler.

6. An implementation method of the single waveguide based ultrahigh-resolution integrated computational spectrometer according to claim 1, characterized in that, The implementation method comprises the following steps: 1) The light to be measured is input into the multi-stage reflection measurement waveguide through the input end face coupler; 2) The light is partially reflected when encountering each microstructure reflection unit, and the light is reflected by the microstructure reflection units at different positions to form different reflected lights with different optical paths, which are converged together at the output end and interfere to form a wavelength-dependent amplitude response, and then output to the photodetector through the output end face coupler; 3) The microcontroller adjusts the voltage state of the voltage applied to each phase modulator, the optical path of the light through the waveguide changes, causing corresponding phase changes and forming different amplitude responses; 4) Different modulation combination states of the phase modulator correspond to different amplitude responses, and a plurality of different amplitude responses corresponding to a plurality of modulation combination states of the phase modulators are obtained; 5) Each modulation combination state corresponds to a channel, and the microcontroller scans the amplitude responses of all channels to restore the spectrum of the light to be measured using the least square method.

7. The implementation method of claim 6, wherein, In step 3), a voltage with M voltage states is applied to a phase modulator: no voltage and M-1 voltages with different amplitudes, M being a natural number ≥ 2.

8. The implementation method of claim 7, wherein, In step 4), the multi-stage reflection measurement waveguide comprises first to nth microstructure reflection units, the first to nth microstructure reflection units are connected by n-1 waveguides, n-1 phase modulators are correspondingly arranged, n is the number of the microstructure reflection units; different voltage states are applied to each phase modulator, different modulation combination states of the corresponding phase modulators, M n-1 modulation combination states are shared by the n-1 phase modulators; different modulation combination states of the phase modulators correspond to different modulation phases, and n is a natural number greater than or equal to 7.

9. The implementation method of claim 6, wherein, The geometry generated by the inverse design algorithm is used as the microstructured reflective unit, The method comprises the following steps: dividing a two-dimensional design area into two-dimensional grid cells, binarizing the dielectric constant of each grid cell into the dielectric constant of waveguide material or substrate material, calculating an optical field by a finite time domain difference physical field simulation, and taking the following formula as a design target of the microstructure reflection unit FoM R : wherein, and respectively represent the target transmittance and reflectance, R ( p ) and T ( p ) are the reflectance and transmittance of the current structure, respectively, while the reflection and transmission of the microstructured reflective element and the losses are constrained; the geometric structure is iterated according to the design targets of the microstructured reflective element so that the design targets of the microstructured reflective element FoM R maximum, obtaining the geometric structure generated by the inverse design algorithm that satisfies the target reflectance.

10. The implementation method of claim 8, wherein, The particle swarm optimization algorithm is used to obtain the length of each waveguide, including the following steps: first, set a group of arbitrary lengths of the first to the n-1th waveguide L 1~ L n-1 As initial parameters, then the autocorrelation function and the correlation distance under the current parameters are calculated by the transfer matrix method, and the design target of the length of the waveguide for minimizing the autocorrelation of the waveguide is further calculated FoM L According to the design target of the length FoM L The lengths of the first to the n-1th waveguide are obtained by optimization L 1~ L n-1 The design target of the length FoM L : wherein, Δλ is a correlation distance of the waveguide spectral response, R λ is an autocorrelation function of the waveguide spectral response, β is a normalization coefficient, λ is a wavelength.​

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