A method for measuring coupling coefficient based on identical waveguide arrays

Abstract

This invention discloses a method for measuring the coupling coefficient based on an identical waveguide array, belonging to the field of measurement and testing of optical waveguide properties. The method includes: constructing a measurement system for the coupling coefficient of the waveguide array; testing the evolution results of the waveguide array; and recalculating the coupling coefficient through simulation experiments. Based on the consistency between the evolution process of photons in the waveguide array and continuous-time quantum walks, this invention uses an identical single-mode waveguide array, relies on the physical model of continuous-time quantum walks, and measures the output probability amplitude at different evolution lengths. The simulation and test results are evaluated using the least squares method to finally obtain the waveguide coupling coefficient. This method has low requirements for experimental equipment, low workload, and requires less sample width; it can accurately predict and analyze the evolution of light in the waveguide array.

Description

Technical Field

[0001] This invention belongs to the field of measurement and testing of optical waveguide properties, specifically relating to a method for measuring the coupling coefficient based on an identical waveguide array. Technical Background

[0002] As the most basic and important component in integrated photonic chips, optical waveguides guide light beams to propagate efficiently in a specific direction. They are not only the basic units constituting on-chip integrated components but also the link connecting various integrated components. The coupling coefficient describes the intensity of the interaction between the optical fields of adjacent waveguides in a waveguide array. By determining the coupling coefficient, the propagation path, mode distribution, and intensity variation of light in the waveguide array can be accurately predicted and analyzed, which is crucial for the design and optimization of waveguide array-based photonic devices. Currently, research groups mainly use far-field imaging techniques, Mach-Zehnder interferometers, and transmission spectrum measurements to determine the coupling coefficient of waveguide arrays. However, these methods suffer from problems such as poor measurement accuracy, high equipment cost, susceptibility to external interference leading to large errors, and low efficiency. Summary of the Invention

[0003] To address the shortcomings of existing technologies, this invention provides a novel method for measuring waveguide coupling coefficients based on identical waveguide arrays. This method is applicable to the measurement of coupling coefficients between waveguides and waveguide arrays. Based on the consistency between the evolution of photons in a waveguide array and continuous-time quantum walks, this invention employs identical single-mode waveguide arrays. According to the physical model of continuous-time quantum walks, the Hamiltonian H of the system is:

[0004]

[0005] Where κ is the coupling coefficient between adjacent waveguides, and a n This represents the annihilation operator for photons in the nth waveguide. Let βn represent the photon generation operator in the nth waveguide, and β0 be the propagation constant of a single waveguide. This is based on Heisenberg's equations of motion. We can obtain:

[0006]

[0007] in, Let z be the column vector consisting of all waveguide generation operators, and z be the propagation distance of the photon in the waveguide. Let be the form of the Hamiltonian of the system in matrix representation. The matrix form is:

[0008]

[0009] The solution to the above equation is:

[0010]

[0011] in, This represents the initial probability amplitude distribution. Due to the intrinsic propagation term... It contributes only a single phase factor, has no impact on the propagation result, and the Hamiltonian is only related to the coupling coefficient κ. The output probability amplitude is measured at different evolution lengths z. The simulation and test results were evaluated using the least squares method, and the waveguide coupling coefficient κ was finally obtained.

[0012] This invention is achieved through the following technical solution:

[0013] A method for measuring the coupling coefficient based on an identical waveguide array, the specific steps of which are as follows:

[0014] (1) Build a measurement system for the coupling coefficient of waveguide array;

[0015] The specific steps are as follows: The measurement system includes a light source, a polarizing beam splitter (PBS), a camera (CCD), a half-wave plate (HWP), mirrors M1 and M2, objectives OL1 and OL2, the waveguide array under test, a displacement stage, an illumination source (LED), a beam profiler, and a computer (PC). The light emitted from the light source can be adjusted to arbitrary linear polarization after passing through the PBS and HWP, and then collimated by M1 and M2 before entering objective OL1. The waveguide array under test is placed on the displacement stage. The height and rotation angle of the beam profiler are adjusted so that its center position is the same as the sample height and perpendicular to the direction of the sample's emission end. The CCD is used to observe the alignment between the light emitted from OL1 and the waveguide array.

[0016] (2) Test the evolution results of the waveguide array;

[0017] The specific steps are as follows: First, turn on the light source and LED, and adjust the displacement stage with the assistance of the CCD to couple the light into the input end of the waveguide array; second, adjust the position of the beam profiler so that the output spot is located at the center of the beam profiler; then, adjust the output power of the light source to maximize the light intensity received by the beam profiler and save the data; next, change the waveguide array evolution length z, repeat the above measurement steps, and measure the light intensity at different evolution lengths z.

[0018] (3) Simulation experiments were used to deduce the coupling coefficient;

[0019] The specific steps are as follows: First, extract the centroid position of each spot in the array evolution result in step (2), and fit it with a Gaussian function to obtain the position, shape and intensity of each spot; then, combine the Hamiltonian and the evolution formula to simulate the evolution results of the waveguide array with different coupling coefficients κ in MATLAB, and evaluate it using the least squares method and the peak intensity information of the spot, with the coefficient of determination R in statistics. 2 As an indicator for evaluating effectiveness, R 2The κ value at its maximum is the coupling coefficient of the waveguide array.

[0020] Further, in step (1), the waveguide array under test is a 1×N type all-same-dimensional waveguide array with the output ends on the same side. The array has 1 input port and N output ports, such as 1×2, 1×5 or 1×7 type, etc. The sample width required for a single waveguide array is (N-1) times the coupling spacing.

[0021] Furthermore, the waveguide array evolution length in step (2) is 0.1-25mm, and the number of arrays is 2-8.

[0022] Furthermore, the change of waveguide array evolution length z in step (2) is achieved by processing multiple arrays with different evolution lengths z, or by using a diamond wire cutter to cut multiple times from the array output end to obtain arrays with different evolution lengths z, and the subsequent array width is calculated according to the former.

[0023] Furthermore, the extraction of the position, shape, and intensity of the light spot described in step (3) specifically includes the following:

[0024] First, the test results are read, and the influence of background noise on the spot energy is removed. Then, column summation is performed to reduce stray light influence while compressing the data into one dimension. The peak value and peak width of the spot are extracted using the `findpeaks` function in MATLAB, and the spot is classified according to its peak value. A one-dimensional Gaussian fitting is used for peak values ​​below 1500, while a two-dimensional Gaussian fitting is used for values ​​above 1500. The form of the one-dimensional Gaussian function is as follows:

[0025]

[0026] Where, the fitting parameter A is the peak intensity of the light spot, x0 is the center of the light spot, and σ x The width of the light spot;

[0027] The form of the two-dimensional Gaussian function is:

[0028]

[0029] Where, the fitting parameter A is the peak intensity of the light spot, (x0, y0) is the center of the light spot, and (σ x , σ y ) represents the beam width, thus obtaining the position, shape, and intensity of each beam.

[0030] Furthermore, in step (3), the evolution results of the simulated waveguide array show that the coupling coefficient κ in the Hamiltonian is calculated within the range of [0.2, 0.8] mm. -1 The calculation step size is limited to 0.0001, the evolution length is 5-25 mm, and R... 2 The calculation formula is:

[0031]

[0032] Where SSE is the sum of squares of the errors between corresponding points in the simulated data and the Gaussian fitted data, and SST is the sum of squares of the differences between the Gaussian fitted data and its mean.

[0033] Compared with the prior art, the present invention has the following advantages:

[0034] (1) Compared with the traditional waveguide array coupling coefficient measurement method, this method has lower requirements for experimental equipment, less workload, and requires less sample width;

[0035] (2) This method can accurately predict and analyze the evolution of light in waveguide arrays. Attached Figure Description

[0036] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn to scale.

[0037] Figure 1 A flowchart illustrating a coupling coefficient measurement method based on an identical waveguide array provided by this invention;

[0038] Figure 2 This is a schematic diagram of the measurement system of the present invention;

[0039] Among them, PBS represents polarization beam splitter, CCD represents camera, HWP represents half-wave plate, M1 and M2 represent mirrors, OL1 and OL2 represent objective lenses, LED represents illumination source, and PC represents computer.

[0040] Figure 3 This is a schematic diagram of a 1×7 waveguide array in Embodiment 1 of the present invention;

[0041] The array contains 7 waveguides, with a coupling spacing d of 11 μm and a coupling length L of 5.2-7 mm.

[0042] Figure 4 This is a schematic diagram of the evolution test results of the 1×7 waveguide array of the present invention;

[0043] Among them, (a), (b), (c), and (d) are model field photographs with coupling lengths of 5.2, 5.8, 6.4, and 7 mm, respectively;

[0044] Figure 5 This is a schematic diagram of the simulation evolution results of the 1×7 waveguide array of the present invention;

[0045] Figure 6 This is a comparison chart of the Gaussian fitting results and simulation evolution results for the 1×7 waveguide array of the present invention. The array parameters are the same. Figure 4 ;

[0046] Figure 7 This is an evaluation diagram of the coupling coefficient of the 1×7 waveguide array of the present invention;

[0047] Figure 8 This is a schematic diagram of the evolution test results of the 1×5 waveguide array of the present invention;

[0048] Among them, (a) and (b) are model field photographs with coupling lengths of 1 and 1.5 mm, respectively;

[0049] Figure 9 This is a schematic diagram of the simulation evolution results of the 1×5 waveguide array of the present invention;

[0050] Figure 10 This is a comparison chart of the Gaussian fitting results and simulation evolution results for the 1×5 waveguide array of the present invention. The array parameters are the same. Figure 8 ;

[0051] Figure 11 This is an evaluation diagram of the coupling coefficient of the 1×5 waveguide array of the present invention. Detailed Implementation

[0052] To clearly and completely describe the technical solution and its specific working process of the present invention, the specific embodiments of the present invention are as follows, in conjunction with the accompanying drawings:

[0053] Example 1

[0054] This embodiment uses a 1×7 type identical waveguide array with a coupling spacing of 11μm as an example for illustration.

[0055] This embodiment provides a method for measuring the coupling coefficient based on an identical waveguide array, the flowchart of which is shown below. Figure 1 As shown, the measuring device used is as follows: Figure 2 As shown, combined with Figure 1 and Figure 2 The method of this embodiment is described in detail below:

[0056] (1) Measurement system setup;

[0057] like Figure 2The diagram shows the measurement system for the coupling coefficient of a waveguide array. The system includes a light source, a polarizing beam splitter (PBS), a camera (CCD), a half-wave plate (HWP), mirrors M1 and M2, objectives OL1 and OL2, the waveguide array under test, a displacement stage, an illumination source (LED), a beam profiler, and a computer (PC). The light emitted from the light source is adjusted to vertical V-polarization by the PBS and HWP, collimated by M1 and M2, and then focused by objective OL1 before entering the incident end of the waveguide array. The emitted light is focused by OL2 and received by the beam profiler.

[0058] (2) Test the waveguide array evolution results;

[0059] First, place the waveguide array under test on the displacement stage, turn on the light source and LED, and adjust the displacement stage with the assistance of the CCD to allow light coupling into the input end of the waveguide array. At this point, place an infrared fluorescent card behind OL2; a clear light spot can be observed on it, indicating that the coarse alignment of the light source and the waveguide has been completed. Second, fine-tune the position of the displacement stage to make the light spot as bright as possible under visual observation. Next, adjust the position of the beam profiler so that the light spot is centered on the beam profiler. Then, adjust the output power of the light source to maximize the light intensity received by the beam profiler and save the data. Subsequently, repeat the above steps several times. The final waveguide array evolution test results are as follows: Figure 4 As shown;

[0060] (3) Simulation experiments were used to deduce the coupling coefficient;

[0061] First, import the waveguide array test results from step (2) into MATLAB. Using the HDF5 standard, read the original data with a threshold lower limit intensity of 1% to remove the interference of background noise on the spot energy test, and perform column summation to reduce the influence of stray light while compressing it into one-dimensional data. Next, use the findpeaks function to extract the peak value and peak width of the spot, and classify them according to the peak value. If the peak value is lower than 1500, use one-dimensional Gaussian fitting, otherwise use two-dimensional Gaussian fitting. Then, combined with the physical model of Hamiltonian evolution, set the calculation interval of coupling coefficient κ to [0.2, 0.4] mm. -1 With a calculation step size of 0.0001 and an evolution length of 8.5 mm, the evolution results of the simulated waveguide array are as follows. Figure 5 As shown, with the increase of the evolution length, the incident light energy is gradually coupled from the input end into the remaining waveguides of the array; next, the Gaussian fitting results and simulation results are evaluated using the least squares method, R 2 The κ value corresponding to the maximum value is the coupling coefficient of the waveguide array, as shown in the following figure. Figure 6-7 As shown, the Gaussian fitting results and the simulation results show that the spot position and peak intensity are basically consistent. In a 1×7 waveguide array with a coupling spacing of 11 μm, the coupling coefficient of the waveguide array is 0.2928 mm. -1.

[0062] In this embodiment, the laser light source used is 808nm, but other wavelength light sources can also be used.

[0063] In this embodiment, the light source used is vertically V-polarized light, but other polarized light can also be used.

[0064] In this embodiment, the fabrication process for the 1×7 type identical waveguide array is femtosecond laser direct writing technology, but other processes can also be used.

[0065] Example 2

[0066] This embodiment uses a 1×5 type identical waveguide array with a coupling spacing of 9μm as an example for illustration. The specific steps are as follows:

[0067] (1) Measurement system setup: Same as in Example 1;

[0068] (2) Test waveguide array evolution results: Same as in Example 1;

[0069] (3) Simulation experiment to deduce the coupling coefficient: Same as in Example 1, except that the calculation interval for the coupling coefficient κ is set to [0.5, 0.7] mm. -1 With a calculation step size of 0.0001 and an evolution length of 5 mm, the evolution results of the simulated waveguide array are as follows. Figure 9 As shown; then, the Gaussian fitting results and simulation results are evaluated using the least squares method, R 2 The κ value corresponding to the maximum value is the coupling coefficient of the waveguide array, as shown in the following figure. Figure 10-11 As shown, the Gaussian fitting results and the simulation results show that the spot position and peak intensity are basically consistent. In a 1×5 waveguide array with a coupling spacing of 9μm, the coupling coefficient of the waveguide array is 0.621mm. -1 .

[0070] In this embodiment, the sample width used by a single waveguide array is only 36 μm. However, methods using directional couplers with different coupling lengths to measure the splitting ratio of DCs typically require testing five DCs. Due to the large turning radius in their structure, the sample width consumed by a single DC can reach 127 μm. To achieve crosstalk-free operation between different devices, the same spacing is required. In this example, a 60 μm device spacing ensures no crosstalk. The sample width used in this embodiment is 132 μm, while the latter method consumes 875 μm of sample width. This method effectively reduces workload and significantly reduces the footprint, which is beneficial for improving the integration density of photonic chips.

[0071] The preferred embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the specific details of the above embodiments. Within the scope of the technical concept of the present invention, various simple modifications can be made to the technical solution of the present invention, and these simple modifications all fall within the protection scope of the present invention.

[0072] It should also be noted that the various specific technical features described in the above specific embodiments can be combined in any suitable manner without contradiction. In order to avoid unnecessary repetition, the present invention will not describe the various possible combinations separately.

[0073] Furthermore, various different embodiments of the present invention can be combined in any way, as long as they do not violate the spirit of the present invention, they should also be regarded as the content disclosed by the present invention.

Claims

1. A method for measuring the coupling coefficient based on an identical waveguide array, characterized in that, The specific steps are as follows: (1) Build a measurement system for the coupling coefficient of waveguide array; The specific steps are as follows: The measurement system includes a light source, a polarizing beam splitter (PBS), a camera (CCD), a half-wave plate (HWP), mirrors M1 and M2, objectives OL1 and OL2, the waveguide array under test, a displacement stage, an illumination source (LED), a beam profiler, and a computer (PC). The light emitted from the light source can be adjusted to arbitrary linear polarization after passing through the PBS and HWP, and then collimated by M1 and M2 before entering objective OL1. The waveguide array under test is placed on the displacement stage. The height and rotation angle of the beam profiler are adjusted so that its center position is the same as the sample height and perpendicular to the direction of the sample's emission end. The CCD is used to observe the alignment between the light emitted from OL1 and the waveguide array. (2) Test the evolution results of the waveguide array; The specific steps are as follows: First, turn on the light source and LED, and adjust the displacement stage with the assistance of CCD to make the light couple into the input end of the waveguide array; second, adjust the position of the beam profiler so that the output spot is located at the center of the beam profiler; then, adjust the output power of the light source so that the light intensity received by the beam profiler is maximized and save the data; next, change the evolution length z of the waveguide array, repeat the test steps of the above steps (2), and measure the light intensity under different evolution lengths z. (3) Simulation experiments were used to deduce the coupling coefficient; The specific steps are as follows: First, extract the centroid position of each spot in the array evolution result in step (2), and fit it with a Gaussian function to obtain the position, shape and intensity of each spot; then, combine the Hamiltonian and the evolution formula to simulate the evolution results of the waveguide array with different coupling coefficients κ in MATLAB, and evaluate it using the least squares method and the peak intensity information of the spot, with the coefficient of determination R in statistics. 2 As an indicator for evaluating effectiveness, R 2 The κ value at its maximum is the coupling coefficient of the waveguide array.

2. The coupling coefficient measurement method based on an identical waveguide array as described in claim 1, characterized in that, In step (1), the waveguide array under test is a 1×N type all-same-dimensional waveguide array with the output ends on the same side. The array has 1 input port and N output ports. The sample width required for a single waveguide array is (N-1) times the coupling spacing.

3. The coupling coefficient measurement method based on an identical waveguide array as described in claim 1, characterized in that, The waveguide array evolution length in step (2) is 0.1-25mm, and the number of arrays is 2-8.

4. The coupling coefficient measurement method based on an identical waveguide array as described in claim 1, characterized in that, The change of waveguide array evolution length z in step (2) is achieved by processing multiple arrays with different evolution lengths z, or by using a diamond wire cutter to cut multiple times from the array output end to obtain arrays with different evolution lengths z, and the subsequent array width is calculated according to the former.

5. The coupling coefficient measurement method based on an identical waveguide array as described in claim 1, characterized in that, In step (3), the centroid position of each spot in the array evolution result of step (2) is extracted, and a Gaussian function is used for fitting to obtain the position, shape and intensity of each spot, specifically including the following: First, the test results are read, and the influence of background noise on the spot energy is removed. Then, column summation is performed to reduce stray light influence while compressing the data into one dimension. The peak value and peak width of the spot are extracted using the `findpeaks` function in MATLAB, and the spot is classified according to its peak value. A one-dimensional Gaussian fitting is used for peak values ​​below 1500, while a two-dimensional Gaussian fitting is used for values ​​above 1500. The form of the one-dimensional Gaussian function is as follows: Where, the fitting parameter A is the peak intensity of the light spot, x0 is the center of the light spot, and σ x The width of the light spot; The form of the two-dimensional Gaussian function is: Where, the fitting parameter A is the peak intensity of the light spot, (x0, y0) is the center of the light spot, and (σ x ,σ y ) represents the beam width, thus obtaining the position, shape, and intensity of each beam.

6. The coupling coefficient measurement method based on an identical waveguide array as described in claim 1, characterized in that, In step (3), the evolution results of the simulated waveguide array are used, and the coupling coefficient K in the Hamiltonian is calculated in the range of [0.2, 0.8] mm. -1 The calculation step size is limited to 0.0001, the evolution length is 5-25 mm, and R... 2 The calculation formula is: Where SSE is the sum of squares of the errors between corresponding points in the simulated data and the Gaussian fitted data, and SST is the sum of squares of the differences between the Gaussian fitted data and its mean.

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