Performance testing and calibration method of photonic interconnect chips based on deep machine learning algorithm

Through the performance testing and calibration method of photon interconnection chip based on deep machine learning algorithms, the problem of unstable test results and large errors in the existing technologies have been solved, and precise evaluation and efficient calibration of chip performance have been achieved.

CN118884192BActive Publication Date: 2025-01-24JIANGXI GANTONG COMM CO LTD
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Patent Information

Application Number
CN202411380839.2
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-09-30
Publication Date
2025-01-24
Estimated Expiration
2044-09-30

AI Technical Summary

Technical Problem

The existing photonic interconnect chip performance testing and calibration methods are difficult to accurately measure and compensate for losses caused by connection and alignment errors, resulting in unstable test results and large errors, which are difficult to reflect the performance of the chip in actual applications.

Method used

Adopt the performance testing and calibration method of photon interconnection chip based on deep machine learning algorithms. By setting the wavelength and power of the light source, measured the output and reflection of the chip, analyzed spectrum response and phase response, calculated insertion loss and echo loss, and and the echo losses, and and the echo loss, and also, and the echo loss, and the echo loss, and the echo loss, and the echo loss, and the echo loss, and the echo loss, and the echo loss, and the echo loss, and the echo loss, and the echo loss. Establish a model of output power and temperature and wavelength changes to achieve precise assessment and efficient calibration.

Benefits of technology

It improves the measurement accuracy, accurately evaluates the insertion loss and return loss of the chip, and ensures the performance stability and accuracy of the chip under different working conditions.

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Abstract

The present invention relates to the field of chip performance testing technology, and specifically, to a performance testing and calibration method for a photonic interconnect chip based on a deep machine learning algorithm. It includes the following steps: calibrating the output of a light source, calculating the root mean square error of the light source power over time; considering the connection loss and alignment loss between the optical fiber and the chip, calculating the insertion loss and return loss; using a photonic chip deep learning analysis algorithm to analyze the spectral response and phase response of the chip, and calculating the spectral response width; measuring the output signal of the photonic interconnect chip to generate an eye diagram, calculating the signal-to-noise ratio and the bit error rate; placing the photonic interconnect chip in an environment with adjustable temperature, introducing the thermal expansion of the material to affect the calculation of the temperature coefficient, and establishing an optical output power model. This method effectively improves the accuracy and reliability of chip testing by compensating for connection loss and alignment error, and using a deep learning model to model transmission characteristics.
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Description

Technical Field

[0001] The present invention relates to the technical field of chip performance testing, and in particular to a performance testing and calibration method for a photonic interconnect chip based on a deep machine learning algorithm. Background Art

[0002] The performance testing and calibration method of photonic interconnect chips based on deep machine learning algorithms aims to improve test accuracy and optimize chip performance stability. By combining deep learning models to analyze the chip's spectral response and phase response, considering the compensation of connection losses and alignment errors, and integrating the effects of temperature and wavelength changes, the stability of test conditions and changes in environmental factors are controlled to achieve accurate evaluation and efficient calibration of photonic interconnect chips under different working conditions.

[0003] The existing performance testing and calibration methods of photonic interconnect chips are usually difficult to accurately measure and compensate for the loss caused by connection and alignment errors. In addition, due to temperature changes and fiber alignment errors during the test and errors caused by manual adjustments, the test results are unstable, with large errors, and it is difficult to accurately reflect the performance of the chip in actual applications. In view of the above problems, a performance testing and calibration method for photonic interconnect chips based on deep machine learning algorithms is provided. Summary of the invention

[0004] The purpose of the present invention is to provide a performance testing and calibration method for photonic interconnect chips based on a deep machine learning algorithm, so as to solve the problems raised in the above background technology that errors caused by temperature changes and optical fiber alignment errors, material thermal effects and wavelength drift during the test process will lead to unstable test results, large errors, and difficulty in accurately reflecting the performance of the chip in actual applications.

[0005] To achieve the above object, the present invention aims to provide a performance testing and calibration method for a photonic interconnect chip based on a deep machine learning algorithm, comprising the following steps:

[0006] S1. Set the wavelength and power of the light source, use an optical power meter to calibrate the output of the light source, record the output power and wavelength of the light source, and calculate the root mean square error of the light source power over time;

[0007] S2. Input the optical signal of the light source into the photonic interconnect chip, measure the chip output optical power and reflected optical power, consider the connection loss and alignment loss between the optical fiber and the chip, calculate the insertion loss and return loss, and analyze the efficiency and reflection characteristics of the chip in the process of transmitting optical signals;

[0008] S3. Use the photonic chip deep learning analysis algorithm to analyze the chip's spectrum response and phase response, generate the chip's transmission model at different wavelengths in real time, calculate the half-height full width of the spectrum bandwidth to evaluate the chip's spectrum response width, and analyze the chip's phase response at different wavelengths;

[0009] S4. Set different input signal conditions, measure the output signal of the photonic interconnect chip to generate an eye diagram, perform frequency scanning to obtain the frequency response characteristics of the chip, and calculate the signal-to-noise ratio and bit error rate to evaluate the signal and data transmission quality of the photonic interconnect chip;

[0010] S5. Place the photonic interconnect chip in an environment with adjustable temperature, collect temperature data in real time, introduce the influence of material thermal expansion to calculate the temperature coefficient, and establish an optical output power model of output power, temperature change and wavelength change, and analyze the optical output power change of the chip under different temperature conditions.

[0011] As a further improvement of the technical solution, in S1, the wavelength and power of the light source are set, the output of the light source is calibrated using an optical power meter, and the output power and wavelength of the light source are recorded, and the root mean square error of the light source power over time is calculated. The specific steps are as follows:

[0012] S1.1. Select the test light source and use the light source control device to set the wavelength and output power of the light source;

[0013] S1.2. Connect the light source to the optical power meter and adjust the control parameters of the light source device to match the light source output power with the light source output power setting value;

[0014] S1.3. Record the wavelength, output power, test date and environmental conditions of the light source;

[0015] S1.4. Continuously collect optical power meter data and calculate the root mean square error of the light source output power , as follows:

[0016] ;

[0017] in, For the The output power of the light source measured at this time; is the average output power of all measurements; is the number of measurements.

[0018] As a further improvement of the technical solution, in S2, the light source optical signal is input into the photonic interconnect chip, the chip output optical power and reflected optical power are measured, the connection loss and alignment loss between the optical fiber and the chip are considered, the insertion loss and return loss are calculated, and the efficiency and reflection characteristics of the chip in the process of transmitting the optical signal are analyzed. The specific steps are as follows:

[0019] S2.1. Use a high-precision fiber coupler to align the light source signal with the input end of the photonic interconnect chip, and record the input power of the light source signal. ;

[0020] S2.2. Connect an optical power meter to the output end of the chip to measure the output power of the optical signal passing through the chip , use an optical reflectometer at the input end of the photonic interconnect chip to measure the reflected optical signal power ;

[0021] S2.3. Calculate the insertion loss compensation value caused by angle deviation and the insertion loss compensation value caused by lateral offset , and finally calculate the insertion loss ;

[0022] S2.4. Calculate the return loss compensation value caused by end face reflection , and finally calculate the return loss ;

[0023] S2.5, Insertion loss It is the power ratio of the light source optical signal lost when passing through the photonic interconnect chip. The lower the insertion loss, the higher the transmission efficiency of the chip. Return loss Indicates the reflection characteristics inside the chip. The higher the return loss, the less reflection.

[0024] As a further improvement of the technical solution, in S2.3, the insertion loss compensation value caused by the angle deviation is calculated and the insertion loss compensation value caused by lateral offset , and finally calculate the insertion loss , the specific method is as follows:

[0025] ;

[0026] ;

[0027] Total insertion loss compensation value:

[0028] ;

[0029] Insertion loss:

[0030] ;

[0031] in, is the refractive index of the optical fiber; is the refractive index of the photonic interconnect chip material; is the angular deviation between the fiber axis and the normal line of the input end face of the photonic interconnect chip; is the lateral offset between the core of the fiber and the center of the input optical path of the chip; is the radius of the optical fiber emitting light beam, that is, the spot size of the light beam at the chip input end;

[0032] In S2.4, the return loss compensation value caused by the end face reflection is calculated. , and finally calculate the return loss , the specific method is as follows:

[0033] ;

[0034] Total insertion loss compensation value:

[0035] ;

[0036] Return loss:

[0037] ;

[0038] in, is the refractive index of the optical fiber; is the refractive index of the photonic interconnect chip material.

[0039] As a further improvement of the technical solution, in S3, the photonic chip deep learning analysis algorithm is an algorithm based on variational autoencoder and recurrent neural network, which is used to analyze the spectrum response and phase response of the photonic interconnect chip;

[0040] The photonic chip deep learning analysis algorithm is used to analyze the spectral response and phase response of the chip, generate the transmission model of the chip at different wavelengths in real time, calculate the half-height full width of the spectrum bandwidth to evaluate the spectral response width of the chip, and analyze the phase response of the chip at different wavelengths. The specific steps are as follows:

[0041] S3.1. Obtain spectrum response data and phase response one-dimensional array data from the photonic interconnect chip test, normalize the data so that the spectrum response data and phase response array data values ​​are between 0 and 1, and use 30% of the spectrum response data and phase response data as test set data, and the remaining 70% as training set data;

[0042] S3.2. Construct a variational autoencoder model and use the spectrum response data to train the variational autoencoder model. Use the trained variational autoencoder model to infer and reconstruct the new spectrum data to generate the spectrum response model of the chip at different wavelengths. ;

[0043] S3.3. Construct a recurrent neural network model and use the phase response data to train the recurrent neural network model. Use the trained recurrent neural network model to predict and analyze the phase response under new wavelength conditions and generate a phase response model. ;

[0044] S3.4. Based on the spectrum response model and the phase response model predicted by the recurrent neural network model, a comprehensive transmission model of the chip at different wavelengths is generated, and the full width at half maximum of the spectrum bandwidth is calculated;

[0045] S3.5. Use the comprehensive transmission model to calculate the average transmission efficiency of the chip within the target wavelength range to evaluate the performance of the photonic interconnect core.

[0046] As a further improvement of the technical solution, the variational autoencoder model is constructed in S3.2, and the spectrum response data is used Train the variational autoencoder model, and use the trained variational autoencoder model to infer and reconstruct new spectrum data to generate the spectrum response model of the chip at different wavelengths. , the specific method is as follows:

[0047] S3.2.1. Construct the encoder network and decoder network in the variational autoencoder model;

[0048] Encoder Network:

[0049] ;

[0050] Decoder network:

[0051] ;

[0052] in, is the spectrum response data; is the hidden variable output from the encoder; and is the parameterized neural network output;

[0053] S3.2.2. Use the variational lower bound as the optimization objective to train the variational autoencoder model:

[0054] ;

[0055] in, for The divergence of are the encoder network parameters; is the approximate posterior distribution learned by the encoder network of the variational autoencoder model; are the decoder network parameters; Generate the conditional distribution of input data for the decoder network of the variational autoencoder model; is a hidden variable The prior distribution of To reconstruct the error term, we need to express it in the given latent variable Under the condition of Expected value of log probability; for Divergence term, used to measure the approximate posterior distribution of the encoder output With the prior distribution The difference between

[0056] S3.2.3. Use the trained variational autoencoder model to perform latent variable inference on the new spectrum data to generate reconstructed data of the spectrum response. , and generate a spectral response model ;

[0057] ;

[0058] ;

[0059] in, The decoder of the variational autoencoder model is transformed from the latent variable Reconstructed data; is the mean of the reconstructed data output by the decoder.

[0060] As a further improvement of the technical solution, in S3.3, a recurrent neural network model is constructed, and the recurrent neural network model is trained using the phase response data, and the trained recurrent neural network model is used to predict and analyze the phase response under new wavelength conditions, and a phase response model is generated. , the specific method is as follows:

[0061] S3.3.1. Build a recurrent neural network model, train the recurrent neural network model using phase response data, and optimize the loss function :

[0062] ;

[0063] ;

[0064] in, is at the time step The hidden state of is the phase response data; is at the time step The predicted value of is the weight matrix from hidden state to hidden state; is the weight matrix from phase response data to hidden state; is the weight matrix from hidden state to output; is the bias vector of the hidden state; is the bias vector of the output layer;

[0065] ;

[0066] in, is the number of time steps; For the time step The predicted value of For the time step The actual value of

[0067] S3.3.2. Use the trained recurrent neural network model to predict the phase response under new wavelength conditions and generate a phase response model :

[0068] ;

[0069] in, For the time step The predicted output is the phase response under the new wavelength condition; For the time step The input phase data at the new wavelength.

[0070] As a further improvement of the technical solution, in S3.4, based on the spectrum response model and the phase response model predicted by the recurrent neural network model , generate a comprehensive transmission model of the chip at different wavelengths , calculate the full width at half maximum of the spectrum bandwidth , the specific method is as follows:

[0071] ;

[0072] ;

[0073] in, For photonic interconnect chips at wavelengths Comprehensive transmission model under ; For the variational autoencoder in wavelength The spectral response model generated below; For recurrent neural networks in wavelength The phase response model predicted below; and They represent the two wavelength boundaries of the spectral response curve at half-maximum intensity; is the half-maximum full width of the spectral response, which represents the width between two wavelengths where the spectral intensity is half of the peak value;

[0074] S3.5 uses a comprehensive transmission model Calculate the average transmission efficiency of the chip within the target wavelength range , evaluate the performance of the photonic interconnect core, the specific method is as follows:

[0075] ;

[0076] in, is the average transmission efficiency of the photonic interconnect chip within the target wavelength range; is the number of wavelength points; The target wavelength range is wavelength points; For the wavelength The optical signal power input to the photonic interconnect chip; For the wavelength The optical signal power output from the photonic interconnect chip is shown below.

[0077] As a further improvement of the technical solution, in S4, different input signal conditions are set, the output signal of the photonic interconnect chip is measured to generate an eye diagram, and a frequency scan is performed to obtain the frequency response characteristics of the chip, and the signal-to-noise ratio and bit error rate are calculated to evaluate the signal and data transmission quality of the photonic interconnect chip. The specific steps are as follows:

[0078] S4.1. Set the output power and wavelength of the optical signal source, use a bit error rate tester to collect the output signal of the photonic interconnect chip at the receiving end, generate an eye diagram, and use the eye diagram data to calculate the signal-to-noise ratio and bit error rate;

[0079] S4.2. Set the scanning range and step size, use the spectrum analyzer to perform frequency scanning on the output of the photonic interconnect chip, and measure the output power and phase response of the chip;

[0080] In S4.1, the signal-to-noise ratio is calculated using the eye diagram data. And bit error rate , the specific method is as follows:

[0081] ;

[0082] ;

[0083] in, is the signal power, which is the average power of the ideal digital signal part represented in the eye diagram; is the noise power, which is the average power of the jitter and blur areas; is the number of error bits; is the total number of transmitted bits.

[0084] As a further improvement of the technical solution, in S5, the photonic interconnect chip is placed in an environment with adjustable temperature, temperature data is collected in real time, the influence factor of material thermal expansion is introduced and the temperature coefficient is calculated, and the output power change of the photonic interconnect chip under different temperature conditions is analyzed. The specific steps are as follows:

[0085] S5.1. Calculate the wavelength change of optical signals caused by thermal expansion of photonic interconnect chip materials :

[0086] The thermal expansion coefficient of the photonic interconnect chip material is , the initial length is , the initial wavelength is , the temperature changes to , then the length changes :

[0087] ;

[0088] Wavelength change :

[0089] ;

[0090] ;

[0091] in, is the initial length, the initial physical length of the photonic interconnect chip before temperature changes; is the temperature change; is the current temperature; is the reference temperature;

[0092] S5.2. Calculate the temperature coefficient of the output power considering the effect of wavelength change caused by thermal expansion :

[0093] ;

[0094] in:

[0095] ;

[0096] ;

[0097] The corrected temperature coefficient is :

[0098] ;

[0099] in, For temperature changes Changes in the output optical power of the photonic interconnect chip under different conditions; At the reference temperature Output optical power under At the initial wavelength When the photonic interconnect chip outputs optical power; is the output optical power after wavelength change;

[0100] S5.3. Establish output power and temperature variation and wavelength variation Optical output power model:

[0101] ;

[0102] It can also be expressed as:

[0103] ;

[0104] in, , represents the direct temperature variation coefficient of optical output power; , represents the temperature effect caused by the change of optical output power with wavelength;

[0105] S5.4. Based on the optical output power model The performance of the photonic interconnect chip under different temperature conditions is analyzed as follows:

[0106] S5.4.1 If is positive, indicating that the output power increases with increasing temperature; if is negative, indicating that the output power decreases with increasing temperature; by comparing ,Chips with large output power variations are sensitive to temperature changes;

[0107] S5.4.2 If , wavelength changes will enhance the effect of temperature on output power; if , wavelength changes will weaken the effect of temperature on output power.

[0108] Compared with the prior art, the present invention has the following beneficial effects:

[0109] 1. In the performance testing and calibration method of photonic interconnect chips based on deep machine learning algorithms, loss compensation based on connection loss and alignment error can accurately evaluate the insertion loss and return loss of photonic interconnect chips, improve measurement accuracy, and identify the efficiency and reflection characteristics of the chip during optical signal transmission.

[0110] 2. In the performance testing and calibration method of the photonic interconnect chip based on the deep machine learning algorithm, the chip spectrum response and phase response are modeled by a deep learning model, and a comprehensive transmission model combining temperature changes and wavelength changes is used to achieve accurate prediction and optimized evaluation of the chip transmission characteristics under different working conditions, ensuring the stable performance of the chip under various environmental changes. BRIEF DESCRIPTION OF THE DRAWINGS

[0111] Figure 1 The figure is a flow chart of the overall method of the present invention. DETAILED DESCRIPTION

[0112] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention. Example

[0113] See also Figure 1 As shown, this embodiment provides a performance testing and calibration method for a photonic interconnect chip based on a deep machine learning algorithm, comprising the following steps:

[0114] S1. Set the wavelength and power of the light source, use an optical power meter to calibrate the output of the light source, record the output power and wavelength of the light source, and calculate the root mean square error of the light source power over time;

[0115] In this embodiment S1, the wavelength and power of the light source are set, the output of the light source is calibrated using an optical power meter, the output power and wavelength of the light source are recorded, and the root mean square error of the light source power over time is calculated. The specific steps are as follows:

[0116] S1.1. Select the test light source and use the light source control device to set the wavelength and output power of the light source; the wavelength and output power of the light source are determined by the working band of the chip and the specific requirements of the test;

[0117] S1.2. Connect the light source to the optical power meter and adjust the control parameters of the light source device to match the light source output power with the light source output power setting value; the optical power meter is used to measure the actual power of the light source output optical signal for comparison with the setting value; the light source output power setting value is the output power required for the test;

[0118] S1.3. Record the wavelength, output power, test date and environmental conditions of the light source. When recording data, also pay attention to the operating current and temperature of the light source to ensure that these external conditions do not affect the output of the light source.

[0119] S1.4. Continuously collect optical power meter data and calculate the root mean square error of the light source output power , as follows:

[0120] ;

[0121] in, For the The output power of the light source measured at this time; is the average output power of all measurements; is the number of measurements.

[0122] In this embodiment, according to the calculated The results evaluate the stability of the light source if If the value is high, it means that the light source output is unstable and the light source equipment needs to be further adjusted or replaced; if The smaller the value, the better the stability of the light source output;

[0123] S2. Input the optical signal of the light source into the photonic interconnect chip, measure the chip output optical power and reflected optical power, consider the connection loss and alignment loss between the optical fiber and the chip, calculate the insertion loss and return loss, and analyze the efficiency and reflection characteristics of the chip in the process of transmitting optical signals;

[0124] In this embodiment S2, the light source optical signal is input into the photonic interconnect chip, the chip output optical power and reflected optical power are measured, the connection loss and alignment loss between the optical fiber and the chip are considered, the insertion loss and return loss are calculated, and the efficiency and reflection characteristics of the chip in the process of transmitting the optical signal are analyzed. The specific steps are as follows:

[0125] S2.1. Use a high-precision fiber coupler to align the light source signal with the input end of the photonic interconnect chip, and record the input power of the light source signal. ;

[0126] S2.2. Connect an optical power meter to the output end of the chip to measure the output power of the optical signal passing through the chip , use an optical reflectometer at the input end of the photonic interconnect chip to measure the reflected optical signal power ;

[0127] S2.3. Calculate the insertion loss compensation value caused by angle deviation and the insertion loss compensation value caused by lateral offset , and finally calculate the insertion loss ;

[0128] S2.4. Calculate the return loss compensation value caused by end face reflection , and finally calculate the return loss ;

[0129] S2.5, Insertion loss It is the power ratio of the light source optical signal lost when passing through the photonic interconnect chip. The lower the insertion loss, the higher the transmission efficiency of the chip. Return loss Indicates the reflection characteristics inside the chip. The higher the return loss, the less reflection.

[0130] The transmission efficiency of the optical signal in the chip is evaluated by calculating the insertion loss. It can be expressed as insertion loss:

[0131] ;

[0132] By analyzing the insertion loss, the main source of loss can be identified; high insertion loss may be caused by alignment errors between the fiber and the chip, material absorption, waveguide defects, or scattering losses. Through experiments and simulations, the specific cause of the loss can be further located; if the insertion loss is measured at different wavelengths, the spectral response of the chip can be analyzed to understand whether the loss varies with wavelength;

[0133] The reflection characteristics of the chip are evaluated by calculating the return loss. It can be expressed as return loss:

[0134] ;

[0135] By analyzing the return loss, the main source of reflection can be identified. Lower return loss may indicate end face reflection, interface mismatch or surface roughness problems. Through experiments and simulations, the cause of reflection can be further analyzed. If the return loss is measured at different wavelengths, it can be analyzed whether the reflection characteristics change with wavelength.

[0136] In this embodiment S2.3, the insertion loss compensation value caused by the angle deviation is calculated and the insertion loss compensation value caused by lateral offset , and finally calculate the insertion loss , the specific method is as follows:

[0137] ;

[0138] ;

[0139] Total insertion loss compensation value:

[0140] ;

[0141] Insertion loss:

[0142] ;

[0143] in, is the refractive index of the optical fiber; is the refractive index of the photonic interconnect chip material; is the angular deviation between the fiber axis and the normal line of the input end face of the photonic interconnect chip; is the lateral offset between the core of the fiber and the center of the input optical path of the chip; is the radius of the optical fiber emitting light beam, that is, the spot size of the light beam at the chip input end;

[0144] In this embodiment S2.4, the return loss compensation value caused by the end face reflection is calculated , and finally calculate the return loss , the specific method is as follows:

[0145] ;

[0146] Total insertion loss compensation value:

[0147] ;

[0148] Return loss:

[0149] ;

[0150] in, is the refractive index of the optical fiber; is the refractive index of the photonic interconnect chip material.

[0151] S3. Use the photonic chip deep learning analysis algorithm to analyze the chip's spectrum response and phase response, generate the chip's transmission model at different wavelengths in real time, calculate the half-height full width of the spectrum bandwidth to evaluate the chip's spectrum response width, and analyze the chip's phase response at different wavelengths;

[0152] In this embodiment S3, the photonic chip deep learning analysis algorithm is an algorithm based on variational autoencoders and recurrent neural networks, which is used to analyze the spectrum response and phase response of the photonic interconnect chip;

[0153] The photonic chip deep learning analysis algorithm is used to analyze the spectral response and phase response of the chip, generate the transmission model of the chip at different wavelengths in real time, calculate the half-height full width of the spectrum bandwidth to evaluate the spectral response width of the chip, and analyze the phase response of the chip at different wavelengths. The specific steps are as follows:

[0154] S3.1. Obtain spectrum response data and phase response one-dimensional array data from the photonic interconnect chip test, normalize the data so that the spectrum response data and phase response array data values ​​are between 0 and 1, and use 30% of the spectrum response data and phase response data as test set data, and the remaining 70% as training set data;

[0155] The spectrum response data includes the power intensity at different wavelengths, usually expressed as a spectrum curve, and the phase response data is a curve showing the phase angle changing with wavelength;

[0156] S3.2. Construct a variational autoencoder model and use the spectrum response data to train the variational autoencoder model. Use the trained variational autoencoder model to infer and reconstruct the new spectrum data to generate the spectrum response model of the chip at different wavelengths. ; The variational autoencoder model is used to reduce the dimension and extract features of the spectrum response data; the variational autoencoder model can learn the potential distribution of the spectrum response data and generate a low-dimensional latent variable representation, which is suitable for capturing complex spectrum characteristics. The variational autoencoder model is trained using the preprocessed spectrum response data, so that it can effectively extract the key features in the spectrum response and generate reconstructed spectrum data; the low-dimensional representation output by the variational autoencoder model can provide reliable feature data for further spectrum bandwidth analysis;

[0157] S3.3. Construct a recurrent neural network model and use the phase response data to train the recurrent neural network model. Use the trained recurrent neural network model to predict and analyze the phase response under new wavelength conditions and generate a phase response model. ;

[0158] The recurrent neural network model is used to perform sequence prediction and analysis on phase response data. The recurrent neural network model is good at processing time series data and can capture the dynamic characteristics of phase response changing with wavelength. The predicted data output by the recurrent neural network model is used to analyze the phase response characteristics of the chip at different wavelengths.

[0159] S3.4. Based on the spectrum response model and the phase response model predicted by the recurrent neural network model, a comprehensive transmission model of the chip at different wavelengths is generated, and the full width at half maximum of the spectrum bandwidth is calculated;

[0160] The comprehensive transmission model takes into account the impact of spectrum response and phase response on the transmission characteristics of the photonic chip; the full width at half maximum of the spectrum bandwidth is the frequency or wavelength width when the spectrum response intensity is half of the maximum value, reflecting the signal transmission capability of the chip within a specific wavelength range;

[0161] S3.5. Use the comprehensive transmission model to calculate the average transmission efficiency of the chip within the target wavelength range to evaluate the performance of the photonic interconnect core.

[0162] In this embodiment S3.2, a variational autoencoder model is constructed and the spectrum response data is used Train the variational autoencoder model, and use the trained variational autoencoder model to infer and reconstruct new spectrum data to generate the spectrum response model of the chip at different wavelengths. , the specific method is as follows:

[0163] S3.2.1. Construct the encoder network and decoder network in the variational autoencoder model;

[0164] Encoder Network:

[0165] ;

[0166] Decoder network:

[0167] ;

[0168] in, is the spectrum response data; is the hidden variable output from the encoder; and is the parameterized neural network output;

[0169] The encoder is used to convert the input spectrum response data Mapping to latent variation The decoder is derived from the latent variable Reconstruct spectrum data ;

[0170] S3.2.2. Use the variational lower bound as the optimization objective to train the variational autoencoder model:

[0171] ;

[0172] in, for The divergence of are the encoder network parameters; is the approximate posterior distribution learned by the encoder network of the variational autoencoder model; are the decoder network parameters; Generate the conditional distribution of input data for the decoder network of the variational autoencoder model; is a hidden variable The prior distribution of To reconstruct the error term, we need to express it in the given latent variable Under the condition of Expected value of log probability; for Divergence term, used to measure the approximate posterior distribution of the encoder output With prior distribution The difference between

[0173] Optimizing model parameters via stochastic gradient descent and ;

[0174] S3.2.3. Use the trained variational autoencoder model to perform latent variable inference on the new spectrum data to generate reconstructed data of the spectrum response. , and generate a spectral response model ;

[0175] ;

[0176] ;

[0177] in, The decoder of the variational autoencoder model is transformed from the latent variable Reconstructed data; is the mean of the reconstructed data output by the decoder.

[0178] For each hidden variable , the decoder neural network will output a predicted reconstructed data mean. The output layer of the decoder is usually a linear layer or an activation function layer. Calculated, the specific value depends on the structure and parameter settings of the decoder network, and is obtained through optimization learning during model training;

[0179] In this embodiment S3.3, a recurrent neural network model is constructed, and the phase response data is used to train the recurrent neural network model. The trained recurrent neural network model is used to predict and analyze the phase response under the new wavelength condition, and a phase response model is generated. , the specific method is as follows:

[0180] S3.3.1. Build a recurrent neural network model, train the recurrent neural network model using phase response data, and optimize the loss function :

[0181] ;

[0182] ;

[0183] in, is at the time step The hidden state of is the phase response data; is at the time step The predicted value of is the weight matrix from hidden state to hidden state; is the weight matrix from phase response data to hidden state; is the weight matrix from hidden state to output; is the bias vector of the hidden state; is the bias vector of the output layer;

[0184] ;

[0185] in, is the number of time steps; For the time step The predicted value of For the time step The actual value of

[0186] S3.3.2. Use the trained recurrent neural network model to predict the phase response under new wavelength conditions and generate a phase response model :

[0187] ;

[0188] in, For the time step The predicted output is the phase response under the new wavelength condition; For the time step The input phase data at the new wavelength.

[0189] In this embodiment S3.4, based on the spectrum response model and the phase response model predicted by the recurrent neural network model , generate a comprehensive transmission model of the chip at different wavelengths , calculate the full width at half maximum of the spectrum bandwidth , the specific method is as follows:

[0190] ;

[0191] ;

[0192] in, For photonic interconnect chips at wavelengths Comprehensive transmission model under ; For the variational autoencoder in wavelength The spectral response model generated below; For recurrent neural networks in wavelength The phase response model predicted below; and They represent the two wavelength boundaries of the spectral response curve at half-maximum intensity; is the half-maximum full width of the spectral response, which represents the width between two wavelengths where the spectral intensity is half of the peak value;

[0193] In this embodiment S3.5, the comprehensive transmission model is used Calculate the average transmission efficiency of the chip within the target wavelength range , evaluate the performance of the photonic interconnect core, the specific method is as follows:

[0194] ;

[0195] in, is the average transmission efficiency of the photonic interconnect chip within the target wavelength range; is the number of wavelength points; The target wavelength range is wavelength points; For the wavelength The optical signal power input to the photonic interconnect chip; For the wavelength The optical signal power output from the photonic interconnect chip is shown below.

[0196] Average transmission efficiency of photonic interconnect chips within the target wavelength range When it is close to 100%, it means that the photonic interconnect chip has efficient optical signal transmission capability within the target wavelength range. Most of the input optical signals can be transmitted through the chip, and only a small amount of optical signals are lost. This situation indicates that the chip has low insertion loss and high transmission efficiency, which are the characteristics of high-performance photonic chips.

[0197] Average transmission efficiency of photonic interconnect chips within the target wavelength range When it is close to 0%, it means that the chip has significant loss when transmitting optical signals. The lower average transmission efficiency may be due to high insertion loss, reflection loss, scattering loss or other loss mechanisms. Such performance is usually not ideal and may limit the application of the chip in high-performance optical communication systems.

[0198] Has a higher The performance of photonic interconnect chips is better.

[0199] S4. Set different input signal conditions, measure the output signal of the photonic interconnect chip to generate an eye diagram, perform frequency scanning to obtain the frequency response characteristics of the chip, and calculate the signal-to-noise ratio and bit error rate to evaluate the signal and data transmission quality of the photonic interconnect chip;

[0200] In this embodiment S4, different input signal conditions are set, the output signal of the photonic interconnect chip is measured to generate an eye diagram, and a frequency scan is performed to obtain the frequency response characteristics of the chip, and the signal-to-noise ratio and bit error rate are calculated to evaluate the signal and data transmission quality of the photonic interconnect chip. The specific steps are as follows:

[0201] S4.1. Set the output power and wavelength of the optical signal source, use a bit error rate tester to collect the output signal of the photonic interconnect chip at the receiving end, generate an eye diagram, and use the eye diagram data to calculate the signal-to-noise ratio and bit error rate;

[0202] Measure the opening width and height of the eye diagram. The larger the opening, the lower the signal bit error rate and the better the signal quality. Check the closure of the eye diagram. The smaller the closure, the lower the signal jitter and noise.

[0203] S4.2. Set the scanning range and step size, use the spectrum analyzer to perform frequency scanning on the output of the photonic interconnect chip, and measure the output power and phase response of the chip;

[0204] Evaluate the flatness of the frequency response within the bandwidth. The better the flatness, the more stable the frequency characteristics of the chip.

[0205] In this embodiment S4.1, the signal-to-noise ratio is calculated using the eye diagram data And bit error rate , the specific method is as follows:

[0206] ;

[0207] ;

[0208] in, is the signal power, which is the average power of the ideal digital signal part represented in the eye diagram; is the noise power, which is the average power of the jitter and blur areas; is the number of error bits; Is the total number of transmitted bits. A low BER indicates higher reliability and accuracy of signal transmission.

[0209] S5. Place the photonic interconnect chip in an environment with adjustable temperature, collect temperature data in real time, introduce the influence of material thermal expansion to calculate the temperature coefficient, and establish an optical output power model of output power, temperature change and wavelength change, and analyze the optical output power change of the chip under different temperature conditions.

[0210] In this embodiment S5, the photonic interconnect chip is placed in an environment with adjustable temperature, temperature data is collected in real time, the influence factor of material thermal expansion is introduced and the temperature coefficient is calculated, and the output power change of the photonic interconnect chip under different temperature conditions is analyzed. The specific steps are as follows:

[0211] S5.1. Calculate the wavelength change of optical signals caused by thermal expansion of photonic interconnect chip materials :

[0212] The thermal expansion coefficient of the photonic interconnect chip material is , the initial length is , the initial wavelength is , the temperature changes to , then the length changes :

[0213] ;

[0214] Wavelength change :

[0215] ;

[0216] ;

[0217] in, is the initial length, the initial physical length of the photonic interconnect chip before temperature changes; is the temperature change; is the current temperature; is the reference temperature;

[0218] S5.2. Calculate the temperature coefficient of the output power considering the effect of wavelength change caused by thermal expansion :

[0219] ;

[0220] in:

[0221] ;

[0222] ;

[0223] The corrected temperature coefficient is :

[0224] ;

[0225] in, For temperature changes Changes in the output optical power of the photonic interconnect chip under different conditions; At the reference temperature Output optical power under At the initial wavelength When the photonic interconnect chip outputs optical power; is the output optical power after wavelength change;

[0226] S5.3. Establish output power and temperature variation and wavelength variation Optical output power model:

[0227] ;

[0228] It can also be expressed as:

[0229] ;

[0230] in, , represents the direct temperature variation coefficient of optical output power; , represents the temperature effect caused by the change of optical output power with wavelength;

[0231] S5.4. Based on the optical output power model The performance of the photonic interconnect chip under different temperature conditions is analyzed as follows:

[0232] S5.4.1 If is positive, indicating that the output power increases with increasing temperature; if is negative, indicating that the output power decreases with increasing temperature; by comparing ,Chips with large output power variations are sensitive to temperature changes;

[0233] S5.4.2 If , wavelength changes will enhance the effect of temperature on output power; if , wavelength changes will weaken the effect of temperature on output power. Wavelength changes caused by thermal expansion may cause the frequency response of the chip to change, further affecting the output power. By observing the changes in wavelength, we can determine to what extent the wavelength change affects the performance of the chip.

[0234] If the output power changes slightly, it means the chip is more robust to temperature changes. If the temperature change shows a nonlinear trend, it is necessary to analyze whether the nonlinearity is due to the change in material properties or the wavelength change caused by thermal expansion.

[0235] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments, and the above embodiments and descriptions are only preferred examples of the present invention, and are not intended to limit the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, and these changes and improvements all fall within the scope of the present invention to be protected.

Claims

1. A performance test and calibration method for a photonic interconnect chip based on a deep machine learning algorithm, characterized in that: The following steps are involved: S1. Set the wavelength and power of the light source, use an optical power meter to calibrate the output of the light source, record the output power and wavelength of the light source, and calculate the root mean square error of the light source power over time; S2. Input the optical signal of the light source into the photonic interconnect chip, measure the chip output optical power and reflected optical power, consider the connection loss and alignment loss between the optical fiber and the chip, calculate the insertion loss and return loss, and analyze the efficiency and reflection characteristics of the chip in the process of transmitting optical signals; S3. Use the photonic chip deep learning analysis algorithm to analyze the chip's spectrum response and phase response, generate the chip's transmission model at different wavelengths in real time, calculate the half-height full width of the spectrum bandwidth to evaluate the chip's spectrum response width, and analyze the chip's phase response at different wavelengths; S4. Set different input signal conditions, measure the output signal of the photonic interconnect chip to generate an eye diagram, perform frequency scanning to obtain the frequency response characteristics of the chip, and calculate the signal-to-noise ratio and bit error rate to evaluate the signal and data transmission quality of the photonic interconnect chip; S5. Place the photonic interconnect chip in an environment with adjustable temperature, collect temperature data in real time, introduce the influence of material thermal expansion to calculate the temperature coefficient, and establish an optical output power model of output power, temperature change and wavelength change, and analyze the optical output power change of the chip under different temperature conditions; In S3, the photonic chip deep learning analysis algorithm is an algorithm based on variational autoencoder and recurrent neural network, which is used to analyze the spectrum response and phase response of the photonic interconnect chip; The photonic chip deep learning analysis algorithm is used to analyze the spectral response and phase response of the chip, generate the transmission model of the chip at different wavelengths in real time, calculate the half-height full width of the spectrum bandwidth to evaluate the spectral response width of the chip, and analyze the phase response of the chip at different wavelengths. The specific steps are as follows: S3.

1. Obtain spectrum response data and phase response one-dimensional array data from the photonic interconnect chip test, normalize the data so that the spectrum response data and phase response array data values ​​are between 0 and 1, and use 30% of the spectrum response data and phase response data as test set data, and the remaining 70% as training set data; S3.

2. Construct a variational autoencoder model, and use the variational autoencoder model trained with the spectrum response data to infer and reconstruct the new spectrum data using the trained variational autoencoder model to generate the spectrum response model VAE(λ) of the chip at different wavelengths. S3.3, construct a recurrent neural network model, and use the phase response data to train the recurrent neural network model, use the trained recurrent neural network model to predict and analyze the phase response under new wavelength conditions, and generate a phase response model RNN(λ); S3.

4. Based on the spectrum response model and the phase response model predicted by the recurrent neural network model, a comprehensive transmission model of the chip at different wavelengths is generated, and the full width at half maximum of the spectrum bandwidth is calculated; S3.

5. Use the comprehensive transmission model to calculate the average transmission efficiency of the chip within the target wavelength range to evaluate the performance of the photonic interconnect core; In S3.2, a variational autoencoder model is constructed, and the variational autoencoder model trained with the spectrum response data x is used to infer and reconstruct the new spectrum data using the variational autoencoder model after training to generate the spectrum response model VAE(λ) of the chip at different wavelengths. The specific method is as follows: S3.2.

1. Construct the encoder network and decoder network in the variational autoencoder model; Encoder Network: Decoder network: Where x is the spectrum response data; z is the latent variable output from the encoder; μ φ (x) and is the parameterized neural network output; S3.2.

2. Use the variational lower bound as the optimization objective to train the variational autoencoder model: Among them, D KL is the KL divergence; φ is the encoder network parameter; q φ (z|x) is the approximate posterior distribution learned by the encoder network of the variational autoencoder model; θ is the decoder network parameter; q φ (z|x) is the conditional distribution of the input data generated by the decoder network of the variational autoencoder model; p(z) is the prior distribution of the latent variable z; The reconstruction error term represents the expected value of the logarithmic probability of generating the input data x under the condition of a given latent variable z; D KL (q φ (z|x)||p(z)) is the KL divergence term, which is used to measure the approximate posterior distribution q of the encoder output φ The difference between (z|x) and the prior distribution p(z); S3.2.

3. Use the trained variational autoencoder model to perform latent variable inference on the new spectrum data to generate reconstructed data of the spectrum response. And generate the spectrum response model VAF(λ); z~q φ (z|x); in, is the data reconstructed from the latent variable z by the decoder of the variational autoencoder model; μ θ is the mean of the reconstructed data output by the decoder; In S3.3, a recurrent neural network model is constructed, and the phase response data is used to train the recurrent neural network model. The trained recurrent neural network model is used to predict and analyze the phase response under the new wavelength condition, and a phase response model RNN(λ) is generated. The specific method is as follows: S3.3.

1. Build a recurrent neural network model, train the recurrent neural network model using phase response data, and optimize the loss function h t =f(W hh h t-1 +W xh x t +b h ); y t =W hy h t +b y ; Among them, h t is the hidden state at time step t; x t is the phase response data; y t is the output prediction; W hh is the weight matrix from hidden state to hidden state; W xh is the weight matrix from phase response data to hidden state; W hy is the weight matrix from hidden state to output; b h is the bias vector of the hidden state; b y is the bias vector of the output layer; Where T is the number of time steps; y t is the predicted value at time step t; is the actual value at time step t; S3.3.

2. Use the trained recurrent neural network model to predict the phase response under new wavelength conditions and generate a phase response model RNN(λ): in, is the predicted output at time step t+1, which is the phase response under the new wavelength condition; x t+1 is the input phase data under the new wavelength condition at time step t+1; In S3.4, based on the spectrum response model VAE(λ) and the phase response model RNN(λ) predicted by the recurrent neural network model, a comprehensive transmission model M(λ) of the chip at different wavelengths is generated, and the full width at half maximum FWHM of the spectrum bandwidth is calculated. The specific method is as follows: M(λ)={VAE(λ),RNN(λ)}; FWHM = λ2-λ1; Wherein, M(λ) is the comprehensive transmission model of the photonic interconnect chip at wavelength λ; VAE(λ) is the spectrum response model generated by the variational autoencoder at wavelength λ; RNN(λ) is the phase response model predicted by the recurrent neural network at wavelength λ; λ1 and λ2 represent the two wavelength boundaries of the spectrum response curve at half maximum intensity, respectively; FWHM is the full width at half maximum of the spectrum response, which represents the width between two wavelengths where the spectrum intensity is half of the peak value; In S3.5, the average transmission efficiency η of the chip within the target wavelength range is calculated using the comprehensive transmission model M(λ). avg , evaluate the performance of the photonic interconnect core, the specific method is as follows: Among them, η avg is the average transmission efficiency of the photonic interconnect chip within the target wavelength range; N is the number of wavelength points; λ i is the i-th wavelength point within the target wavelength range; P input (λ i ) is the wavelength λ i The optical signal power input to the photonic interconnect chip; P output (λ i ) is the wavelength λ i The optical signal power output from the photonic interconnect chip is shown below.

2. The performance testing and calibration method of a photonic interconnect chip based on a deep machine learning algorithm according to claim 1 is characterized in that: In S1, the wavelength and power of the light source are set, the output of the light source is calibrated using an optical power meter, the output power and wavelength of the light source are recorded, and the root mean square error of the light source power over time is calculated. The specific steps are as follows: S1.

1. Select the test light source and use the light source control device to set the wavelength and output power of the light source; S1.

2. Connect the light source to the optical power meter and adjust the control parameters of the light source device to match the light source output power with the light source output power setting value; S1.

3. Record the output power and wavelength of the light source, and record the wavelength, output power, test date and environmental conditions of the light source; S1.

4. Continuously collect optical power meter data and calculate the root mean square error (RMSE) of the light source output power, as follows: Among them, P i is the output power of the light source measured for the i-th time; P mean is the average output power of all measured values; n is the number of measurements.

3. The performance testing and calibration method of a photonic interconnect chip based on a deep machine learning algorithm according to claim 2 is characterized in that: In S2, the light source optical signal is input into the photonic interconnect chip, the chip output optical power and reflected optical power are measured, the connection loss and alignment loss between the optical fiber and the chip are considered, the insertion loss and return loss are calculated, and the efficiency and reflection characteristics of the chip in the process of transmitting the optical signal are analyzed. The specific steps are as follows: S2.

1. Use a high-precision fiber coupler to align the light source signal with the input end of the photonic interconnect chip, and record the input power P of the light source signal. input ; S2.

2. Connect an optical power meter to the output end of the chip to measure the output power P of the optical signal passing through the chip. output , use an optical reflectometer at the input end of the photonic interconnect chip to measure the reflected optical signal power P reflected ; S2.

3. Calculate the insertion loss compensation value ΔP caused by angle deviation angular,IL and the insertion loss compensation value ΔP caused by lateral offset lateral,IL , and finally calculate the insertion loss IL; S2.

4. Calculate the return loss compensation value ΔP caused by end face reflection reflection,RL , and finally calculate the return loss RL; S2.

5. Insertion loss IL is the power ratio of the light source optical signal lost when passing through the photonic interconnect chip. The lower the insertion loss, the higher the transmission efficiency of the chip. Return loss RL represents the reflection characteristics inside the chip. The higher the return loss, the less reflection.

4. The performance testing and calibration method of a photonic interconnect chip based on a deep machine learning algorithm according to claim 3 is characterized in that: In S2.3, the insertion loss compensation value ΔP caused by the angle deviation is calculated. angular,IL and the insertion loss compensation value ΔP caused by lateral offset lateral,IL , and finally calculate the insertion loss IL. The specific method is as follows: Total insertion loss compensation value: ΔP alignment,IL =ΔP angular,IL +ΔP lateral,IL ; Insertion loss: Where n1 is the refractive index of the optical fiber; n2 is the refractive index of the photonic interconnect chip material; θ is the angular deviation between the optical fiber axis and the normal line of the input end face of the photonic interconnect chip; d is the lateral offset between the core of the optical fiber and the center of the input optical path of the chip; w0 is the radius of the optical fiber emission beam, that is, the spot size of the beam at the input end of the chip; In S2.4, the return loss compensation value ΔP caused by the end face reflection is calculated. reflection,RL , and finally calculate the return loss RL. The specific method is as follows: Total insertion loss compensation value: ΔP alignment,RL =ΔP reflection,RL ; Return loss: Among them, n1 is the refractive index of the optical fiber; n2 is the refractive index of the photonic interconnect chip material.

5. The performance testing and calibration method of a photonic interconnect chip based on a deep machine learning algorithm according to claim 4 is characterized in that: In S4, different input signal conditions are set, the output signal of the photonic interconnect chip is measured to generate an eye diagram, and a frequency scan is performed to obtain the frequency response characteristics of the chip, and the signal-to-noise ratio and bit error rate are calculated to evaluate the signal and data transmission quality of the photonic interconnect chip. The specific steps are as follows: S4.

1. Set the output power and wavelength of the optical signal source, use a bit error rate tester to collect the output signal of the photonic interconnect chip at the receiving end, generate an eye diagram, and use the eye diagram data to calculate the signal-to-noise ratio and bit error rate; S4.

2. Set the scanning range and step size, use the spectrum analyzer to perform frequency scanning on the output of the photonic interconnect chip, and measure the output power and phase response of the chip; In S4.1, the signal-to-noise ratio SNR and the bit error rate BER are calculated using the eye diagram data. The specific method is as follows: Among them, P signal is the signal power, which is the average power of the ideal digital signal part represented in the eye diagram; P noise is the noise power, which is the average power of the jitter and fuzzy area; Number of Error Bits is the number of error bits; Total Number of Transmitted Bits is the total number of transmitted bits.

6. The performance testing and calibration method of a photonic interconnect chip based on a deep machine learning algorithm according to claim 5 is characterized in that: In S5, the photonic interconnect chip is placed in an environment with adjustable temperature, temperature data is collected in real time, the influence factor of material thermal expansion is introduced and the temperature coefficient is calculated, and the output power change of the photonic interconnect chip under different temperature conditions is analyzed. The specific steps are as follows: S5.

1. Calculate the wavelength change Δλ of the optical signal caused by thermal expansion of the photonic interconnect chip material: The thermal expansion coefficient of the photonic interconnect chip material is α, the initial length is L0, the initial wavelength is λ0, and the temperature change is ΔT, then the length change ΔL is: ΔL=L0αΔT; Wavelength change Δλ: ΔT = T - T0; Among them, L0 is the initial length, the initial physical length of the photonic interconnect chip before the temperature changes; ΔT is the temperature change; T is the current temperature; T0 is the reference temperature; S5.

2. Calculate the temperature coefficient TCR considering the effect of wavelength change caused by thermal expansion on output power: in: ΔP output =P output (T)-P output (T); Then the corrected temperature coefficient TCR is: Among them, ΔP output is the change of the output optical power of the photonic interconnect chip under the temperature change ΔT; P output,0 is the output optical power at reference temperature T0; P output (λ0) is the optical power output by the photonic interconnect chip at the initial wavelength λ0; P output (λ0+Δλ) is the output optical power after wavelength change; S5.

3. Establish the optical output power model of output power, temperature change ΔT and wavelength change Δλ: P output (T)=P output,0 (1+TCR·ΔT); It can also be expressed as: P output (T)=P output,0 +k·(T-T0)+m·(λ0α(T-T0)); Where k = ΔP output / ΔT, represents the direct temperature variation coefficient of light output power; It indicates the temperature effect caused by the change of optical output power with wavelength; S5.4, according to the optical output power model P output (T) Analyze the performance of photonic interconnect chips under different temperature conditions, as follows: S5.4.

1. If k is positive, it means that the output power increases with the increase of temperature; if k is negative, it means that the output power decreases with the increase of temperature. By comparing P output (T), chips with large output power variations are sensitive to temperature changes; S5.4.

2. If m·(λ0α)>0, wavelength change will enhance the effect of temperature on output power; if m·(λ0α)≤0, wavelength change will weaken the effect of temperature on output power.

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