A high-speed semiconductor laser frequency-time mapping modeling method

Abstract

The application discloses a high-speed semiconductor laser frequency-time mapping modeling method, belongs to the field of optoelectronic technology, and aims to provide a high-efficiency modeling method capable of quickly predicting time-domain output response of a high-speed semiconductor laser under arbitrary waveform modulation based on measured frequency-domain scattering parameters. In the application, firstly, a static P-I curve of the high-speed semiconductor laser is measured by using an optical power detection module; then, scattering parameters of the high-speed semiconductor laser under different biases and different modulation frequencies are collected by using a scattering parameter measurement module, and a dynamic P-I curve is constructed; an arbitrary modulation waveform is firstly decomposed into multiple frequency components through Fourier transform or Fourier series; each frequency component is subjected to polynomial fitting through the dynamic P-I curve of the corresponding frequency to obtain an output waveform of each component; and then, the output waveforms of all the frequency components are superposed to reconstruct a complete time-domain response, so that the high-speed semiconductor laser high-speed modulation dynamic characteristics under different biases can be accurately characterized without solving complex carrier rate equation groups.

Description

Technical Field

[0001] This invention belongs to the field of high-speed semiconductor laser modeling technology in optoelectronics, specifically relating to a frequency-time mapping modeling method for high-speed semiconductor lasers. Background Technology

[0002] High-speed semiconductor lasers, as mainstream electro-optical conversion devices, are widely used in scenarios such as short-distance optical interconnects in data centers, 5G / 6G mobile fronthaul networks, and microwave photonic signal processing. Accurate modeling of the time-frequency domain response of high-speed semiconductor lasers is a crucial foundation for performance evaluation and transmission link optimization of high-speed optical communication systems. An efficient and unified time-frequency joint modeling method can provide key technical support for the rapid and accurate prediction of the dynamic characteristics of high-speed semiconductor lasers.

[0003] Currently, there are two main types of modeling and characterization methods for high-speed semiconductor lasers: single-time-domain modeling and time-frequency domain joint modeling. Single-time-domain modeling mainly includes rate equation physical modeling and deep learning data-driven modeling. Rate equation physical modeling relies on the physical mechanism of carrier-photon coupling within the laser to establish a set of differential equations, which can accurately characterize the dynamic characteristics of high-speed semiconductor lasers, such as relaxation oscillations. However, this modeling method is prone to numerical non-convergence, and the computational cost of multi-parameter iterative solutions is high. Deep learning data-driven modeling achieves modeling by training the input-output waveform mapping relationship through neural networks, but it is highly dependent on the oscilloscope's sampling resolution and measurement sensitivity, resulting in poor model generalization ability. Time-frequency domain joint modeling utilizes high-precision frequency-domain transformation to achieve joint modeling, mainly including the inverse Fourier transform method and the equivalent circuit modeling method. The inverse Fourier transform method directly solves the impulse response from the scattering parameters, which is simple in process. However, frequency domain truncation easily introduces truncation errors and time-domain non-causality, and it cannot describe the bias-related dynamic characteristics of high-speed semiconductor lasers. The equivalent circuit modeling method establishes an equivalent circuit model by fitting frequency domain parameters, which simplifies the originally complex solution process. However, the circuit parameters of the model change with DC bias, making it difficult to extract high-precision parameters. Summary of the Invention

[0004] This invention addresses the shortcomings of existing high-speed semiconductor laser modeling methods by providing a frequency-time mapping modeling method for high-speed semiconductor lasers, which features a simple process, high-precision dynamic characterization, and compatibility with various high-speed digital or analog modulation formats.

[0005] A method for frequency-time mapping modeling of high-speed semiconductor lasers, characterized by the following steps and principles:

[0006] Step 1: Construct a high-speed semiconductor laser measurement device, including a high-speed semiconductor laser, a bias module, a scattering parameter measurement module, an optical power detection module, and a control and signal processing module. The DC terminal of the high-speed semiconductor laser is electrically connected to the bias module, the RF terminal of the high-speed semiconductor laser is electrically connected to the scattering parameter measurement module, and the output terminal of the high-speed semiconductor laser is optically connected to either the optical power detection module or the scattering parameter measurement module. The control and signal processing module is sequentially connected to the bias module, the scattering parameter measurement module, and the optical power detection module for data transmission.

[0007] Step 2: Connect the output terminal of the high-speed semiconductor laser to the optical power detection module. The control and signal processing module controls the bias module to output a DC current from 0 to 1. Bmax A high-speed semiconductor laser is driven, and the output optical power of the high-speed semiconductor laser measured by the optical power detection module under each bias current is recorded to obtain a static PI curve. The I0 of each bias current is then calculated. B The static slope efficiency is denoted as s. L (I B ; 0);

[0008] Step 3: Connect the output of the high-speed semiconductor laser to the scattering parameter measurement module. The control and signal processing module controls the scattering parameter measurement module to perform a frequency sweep test and records each bias current I from Step 2. B The transmission parameters S below 21 (I B jf m ) and reflection parameter S 11 (I B jf m ), where f m This is the sweep frequency;

[0009] Step 4: Calculate each frequency f according to the following formula. m The dynamic PI curve is calculated using the following formula:

[0010] ,

[0011] In the formula, p L (I; jf m () represents the frequency f m The corresponding output optical power complex vector contains both amplitude and phase information, s L (I B jf m ) represents frequency f m The bias current is I B Dynamic slope efficiency under these conditions;

[0012] Step 5: Construct arbitrary modulation waveform iin (t) Perform Fourier series decomposition, and calculate the DC component and the k-th frequency component of the decomposed waveform according to the following formula:

[0013] ,

[0014] ,

[0015] Where f0=1 / T0 represents the fundamental frequency of the decomposed waveform, T0 is the period of the decomposed waveform, and arg[·] represents the complex angle of the complex number;

[0016] Step 6: Combining the reflection parameters measured in Step 3, the frequency components of the actual injected high-speed semiconductor laser are expressed as follows:

[0017] ,

[0018] In the formula, Re{·} represents taking the real part of the complex number, I k and Φ k These represent the current amplitude and phase of the k-th frequency component, respectively.

[0019] Step 7: The frequency components obtained in Step 6 are processed through the dynamic PI curve of the corresponding frequency components of the high-speed semiconductor laser established in Step 4, and then at the DC bias point I... DC Polynomial fitting is performed at the specified point, and the output waveform corresponding to each frequency component is calculated as follows:

[0020] ,

[0021] Among them, c k,n N represents the coefficient term in the polynomial fitting derivation of the k-th frequency component. k This is the fitting order for the frequency component;

[0022] Step 8: Superimpose the output waveforms of all frequency components obtained in Step 7, and combine them with DC bias I. DC Based on the corresponding output optical power, the high-speed semiconductor laser under arbitrary modulation waveform i is calculated. in The time-domain output response under (t) modulation is expressed as:

[0023] .

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

[0025] (1) The present invention constructs a dynamic PI curve based on scattering parameters to realize the direct mapping from frequency domain measurement to time domain response of high-speed semiconductor laser, without the need to solve complex coupling rate equations;

[0026] (2) The present invention can accurately characterize the dynamic characteristics of high-speed semiconductor lasers under different bias currents and is suitable for modulation scenarios with a large dynamic range.

[0027] (3) The model established by this invention does not limit the type of modulation signal and is compatible with various digital modulation formats such as NRZ and PAM4. It also supports analog modulation signals such as multi-tone sine modulation and envelope modulation, and can quickly predict the time domain response of high-speed semiconductor lasers under different modulation waveforms, with a wide range of applications. Attached Figure Description

[0028] Figure 1 This is a schematic diagram of the apparatus for the high-speed semiconductor laser frequency-time mapping modeling method described in this invention.

[0029] Figure 2 The image shows the effect of dynamic PI curve modeling for the frequency-time mapping of the high-speed semiconductor laser described in this invention.

[0030] Figure 3 The diagram shows the effect of constructing a 30 GBaud NRZ modulated signal and an analog amplitude envelope modulated signal to output the time-domain waveform via a dynamic PI curve, as per the present invention. Detailed Implementation

[0031] The present invention will be further described below with reference to the accompanying drawings and embodiments. The described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0032] like Figure 1 As shown, the output terminal of the high-speed semiconductor laser is first connected to the optical power detection module to measure different bias currents I. B Static slope efficiency s L (I B ; 0), then connect the output of the high-speed semiconductor laser to the scattering parameter measurement module to measure different bias currents I B Different frequencies f m Scattering parameter S 21 (I B jf m ) and S 11 (I B jf m Based on the above measurement data, a dynamic PI curve of a high-speed semiconductor laser is constructed. Then, the arbitrary modulation waveform is decomposed into multiple frequency components by Fourier decomposition or series decomposition. Each frequency component is then fitted with the dynamic PI curve at the corresponding frequency to obtain the output waveform of each frequency component by polynomial fitting. Finally, the output waveforms of all frequency components are superimposed to reconstruct the complete time-domain response.

[0033] To better explain the technical invention, the principles and methods of the invention are briefly described below:

[0034] Dynamic slope efficiency s of high-speed semiconductor lasers L (I B jf m ) is defined as the corresponding bias current I B Modulation frequency f m The change in output optical power caused by a change in the unit modulation current is expressed as:

[0035] (1)

[0036] In the formula, δ represents the small change of the small signal, i L (jf m f is the modulation frequency. m The modulation current phasor, p L (I B ;jf m ) is the bias current I B The output optical power phasor.

[0037] Meanwhile, high-speed semiconductor lasers can be equivalently represented as electro-optic two-port networks, and their frequency domain characteristics can be fully characterized by scattering parameters. Furthermore, their normalized dynamic slope efficiency can be derived from the scattering parameters.

[0038] (2)

[0039] Substituting equation (2) into equation (1) and integrating both sides of the equation with respect to the injected current, we can obtain the high-speed semiconductor laser at the modulation frequency f. m The output optical power is expressed as follows:

[0040] (3)

[0041] As can be seen, formula (3) contains both the amplitude and phase information of the output optical power. By going through different modulation frequencies, the dynamic PI curve of the high-speed semiconductor laser can be obtained.

[0042] Furthermore, in order to achieve quantitative prediction of the output time-domain waveform by the model, for any constructed modulation current waveform i in (t) can be expanded into a Fourier series, expressed as:

[0043] (4)

[0044] In the formula, f0 = 1 / T0 represents the fundamental frequency of the decomposed waveform, T0 represents the period of the decomposed waveform, and i k φk Let A and B represent the current amplitude and phase of the k-th frequency component, respectively, and they can be expressed as:

[0045] (5)

[0046] (6)

[0047] When the order k=0, it can be used to characterize the input bias current I of a high-speed semiconductor laser. DC Its expression is:

[0048] (7)

[0049] Simultaneously considering the impedance mismatch at the RF input port of the high-speed semiconductor laser, the AC component of the actual injected laser needs to be corrected by the reflection coefficient, and its kth frequency component is expressed as:

[0050] (8)

[0051] In the formula, Re{·} represents taking the real part of the complex number, I k and Φ k These represent the current amplitude and phase of the k-th frequency component after considering impedance mismatch, respectively.

[0052] To better represent the mathematical model of the dynamic PI curve of a high-speed semiconductor laser, we here use its DC bias point I... DC The polynomial fitting method is used at this point, which is expressed as follows:

[0053] (9)

[0054] Where a n The coefficients represent the polynomial fitting coefficients, where N is the maximum order of the fit, and ΔI = II. DC This represents the AC modulation current of the corresponding high-speed semiconductor laser.

[0055] Next, I of each frequency component k cos(2πkf0t+Φ k Substituting these values ​​into the polynomial fitting expansion of the dynamic PI curve for the corresponding frequency, and simultaneously considering the phase change of the dynamic PI curve, the output waveform of each frequency component is expressed as follows:

[0056] (10)

[0057] In the formula c k,n N represents the coefficient term in the polynomial fitting expansion derivation of the k-th frequency component. kTo determine the maximum fitting order for this frequency component, and in order to balance fitting accuracy with avoiding overfitting, this invention uses the relative increment of the coefficient of determination as the order selection criterion, defining the relative increment ΔR of the coefficient of determination between adjacent fitting orders. 2 (m):

[0058] (11)

[0059] In the formula, R 2 (m), R 2 (m-1) represent the determination coefficients for the m-th and m-1-th order polynomial fittings, respectively. A decision tolerance ε is set, and the fitting order is increased sequentially from order 1. If the relative increment corresponding to the order increase satisfies ΔR... 2 If (m) < ε, then it is determined that further increasing the order will not significantly improve the fitting accuracy, so the order is stopped and the m-1 order is selected as the optimal fitting order for this frequency component.

[0060] Finally, the output waveforms of all frequency components are superimposed, combined with the DC bias I. DC The corresponding output optical power yields the complete time-domain response of the high-speed semiconductor laser as follows:

[0061] (12)

[0062] In the formula, K represents the total number of frequency components considered, which is obtained by dividing the highest operating frequency of the dynamic PI curve of the high-speed semiconductor laser by the fundamental frequency of the signal and rounding down.

[0063] Example 1

[0064] In this embodiment, a high-speed semiconductor laser with a center wavelength of 1546.5 nm is used as the modeling device. First, a static PI curve test is performed. The output terminal of the high-speed semiconductor laser is connected to the optical power detection module. The bias module outputs a DC current to drive the high-speed semiconductor laser under test. The bias current I... B The optical power detection module scans from 0 mA to 80 mA in 1 mA steps, synchronously acquiring the output optical power to obtain a static PI curve, and then calculating the corresponding bias current I. B Static slope efficiency s L (I B From ; 0), it can be determined that the threshold current of this high-speed semiconductor laser is 6.50 mA, and in I B Its static slope efficiency is s at a bias current of 40 mA. L (I B ; 0)=0.12 W / A.

[0065] Subsequently, scattering parameter testing of the high-speed semiconductor laser was performed. The output terminal of the high-speed semiconductor laser was connected to the scattering parameter measurement module. The control and signal processing module controlled the scattering parameter measurement module to perform a frequency sweep test, with the sweep frequency f. m Range from 10 MHz to 40 GHz in 10 MHz steps, bias current I B Similarly, the test was conducted in 1 mA increments from 0 mA to 80 mA, with the control and signal processing module recording scattering parameters and the measurement module obtaining different frequencies f. m With different bias currents I B Frequency domain transmission parameters S 21 (I B jf m ) and reflection parameter S 11 (I B jf m According to formula (3), the dynamic PI curve p of the high-speed semiconductor laser within the measurement range can be established. L (I B jf m ),like Figure 2 As shown.

[0066] In this embodiment, the baud rate is 30 GBaud, the modulation format is non-return-to-zero (NRZ), and the pseudo-random coding pattern length is 2. 10 The input is a bit-based digital modulation format with a peak-to-peak input current of 40 mA. Fourier series decomposition of the NRZ waveform yields a fundamental frequency f0 = 29.30 MHz (calculated by dividing the signal baud rate of 30 GBaud by the code length 2). 10 (derived from bit); based on the above Figure 2 The maximum frequency of the established dynamic PI curve is 40 GHz. The total number of effective frequency components K is calculated to be 1365 (obtained by dividing 40 GHz by the signal fundamental frequency of 29.30 MHz and rounding down). The current amplitude and initial phase corresponding to each frequency component are obtained synchronously, and the DC bias I of its input waveform is obtained according to formula (7). DC It is 40 mA.

[0067] Combining the reflection parameters at the corresponding frequency components, the amplitude and phase of the frequency component current after considering impedance mismatch are calculated according to formula (8) to obtain the frequency current components of the actual injected laser. Each frequency component is then passed through the dynamic PI curve of the corresponding frequency at the DC bias point I. DCPolynomial fitting is performed at 40 mA; the decision tolerance for the relative increment of the coefficient of determination is set to ε = 0.005%. This decision tolerance is used to select the optimal fitting order for the dynamic PI curve at each frequency component, with the maximum fitting order determined to be 5. Taking the 900th frequency component as an example, the coefficient of determination R for polynomial fitting of orders 1 to 4 is... 2 (m) are 0.999309, 0.999695, 0.999989, and 0.999994, respectively, corresponding to the relative increments ΔR of adjacent orders. 2 The values ​​of (m) are 0.0386%, 0.0294%, and 0.0005%, respectively. Therefore, considering the decision tolerance ε, the third order is selected as the optimal fitting order for the dynamic PI curve of the 900th frequency component.

[0068] The output waveforms of all 1365 frequency components are calculated based on the fitting coefficients of each frequency component. The output waveforms of all frequency components are superimposed using formula (12) and combined with DC bias I. DC The corresponding output optical power p L (I DC ; 0)=4.0087mW, finally reconstructing the complete time-domain output response of the high-speed semiconductor laser, such as Figure 3 As shown in (a).

[0069] Example 2

[0070] In this embodiment, the dynamic PI curve p of the high-speed semiconductor laser is established. L (I B jf m The process is the same as in Example 1, except that in Example 1, an NRZ digital modulation format waveform is constructed, while in this example, an analog modulation waveform is constructed to reconstruct its time domain response.

[0071] This embodiment constructs an amplitude envelope modulation analog waveform as input, using a high-frequency carrier superimposed with two baseband sinusoidal signals to form a multi-tone envelope modulation waveform. The carrier frequency is 20 GHz, while the frequencies of the two baseband sinusoidal signals are 2 GHz and 5 GHz, respectively. The peak-to-peak value of the input current is 52.4811 mA. Fourier series decomposition is performed on this analog waveform, and the fundamental frequency f0 = 1 GHz is calculated (derived from the greatest common divisor of the baseband modulation signal frequencies). Figure 2 The maximum frequency of the established dynamic PI curve is 40 GHz. The total number of effective frequency components K is calculated to be 40 (obtained by dividing 40 GHz by the signal fundamental frequency of 1 GHz). At the same time, the current amplitude and initial phase corresponding to each frequency component are solved, and the DC bias I of its input signal is obtained according to formula (7). DC It is 50 mA.

[0072] Combining the reflection parameters of each frequency component, the amplitude and phase of the current of each frequency component after considering impedance mismatch are calculated according to formula (8) to obtain the current of each frequency component injected into the laser. Each frequency component is then passed through the dynamic PI curve at the corresponding frequency, at the DC bias point I. DC Polynomial fitting is performed at 50 mA; the decision tolerance for the relative increment of the coefficient of determination is set to ε = 0.005%. This decision tolerance is used to select the optimal fitting order for the dynamic PI curve at each frequency component, with the maximum fitting order determined to be 5. Taking the 18th frequency component as an example, the coefficient of determination R for polynomial fitting of orders m from 1 to 5 is... 2 (m) are 0.996902, 0.998888, 0.999940, 0.999992, and 0.999993, respectively, corresponding to the relative increments ΔR of adjacent orders. 2 The values ​​of (m) are 0.1992%, 0.1053%, 0.0052%, and 0.0001%, respectively. Therefore, considering the decision tolerance ε, the fourth order is selected as the optimal fitting order for the dynamic PI curves of the 18 frequency components.

[0073] The output waveforms of all 40 frequency components are calculated based on the fitting coefficients of each frequency component. The output waveforms of all frequency components are superimposed using formula (12) and combined with DC bias I. DC The corresponding output optical power p L (I DC ; 0)=5.2119 mW, and finally the time-domain output response of the high-speed semiconductor laser under the analog modulation waveform is reconstructed, such as Figure 3 As shown in (b).

Claims

1. A method for frequency-time mapping modeling of high-speed semiconductor lasers, characterized in that, Includes the following steps: Step 1: Construct a high-speed semiconductor laser measurement device, including a high-speed semiconductor laser, a bias module, a scattering parameter measurement module, an optical power detection module, and a control and signal processing module. The DC terminal of the high-speed semiconductor laser is electrically connected to the bias module, the RF terminal of the high-speed semiconductor laser is electrically connected to the scattering parameter measurement module, and the output terminal of the high-speed semiconductor laser is optically connected to either the optical power detection module or the scattering parameter measurement module. The control and signal processing module is sequentially connected to the bias module, the scattering parameter measurement module, and the optical power detection module for data transmission. Step 2: Connect the output terminal of the high-speed semiconductor laser to the optical power detection module. The control and signal processing module controls the bias module to output a DC current from 0 to 1. Bmax A high-speed semiconductor laser is driven, and the output optical power of the high-speed semiconductor laser measured by the optical power detection module under each bias current is recorded to obtain a static PI curve. The I0 of each bias current is then calculated. B The static slope efficiency is denoted as s. L (I B ; 0); Step 3: Connect the output of the high-speed semiconductor laser to the scattering parameter measurement module. The control and signal processing module controls the scattering parameter measurement module to perform a frequency sweep test and records each bias current I from Step 2. B The transmission parameters S below 21 (I B jf m ) and reflection parameter S 11 (I B jf m ), where f m This is the sweep frequency; Step 4: Calculate each frequency f according to the following formula. m The dynamic PI curve is calculated using the following formula: ， In the formula, p L (I; jf m () represents the frequency f m The corresponding output optical power complex vector contains both amplitude and phase information, s L (I B ;jf m ) represents frequency f m The bias current is I B Dynamic slope efficiency under these conditions; Step 5: Construct arbitrary modulation waveform i in (t) Perform Fourier series decomposition, and calculate the DC component and the k-th frequency component of the decomposed waveform according to the following formula: ， ， Where f0=1 / T0 represents the fundamental frequency of the decomposed waveform, T0 is the period of the decomposed waveform, and arg[·] represents the complex angle of the complex number; Step 6: Combining the reflection parameters measured in Step 3, the frequency components of the actual injected high-speed semiconductor laser are expressed as follows: ， In the formula, Re{·} represents taking the real part of the complex number, I k and Φ k These represent the current amplitude and phase of the k-th frequency component, respectively. Step 7: The frequency components obtained in Step 6 are processed through the dynamic PI curve of the corresponding frequency components of the high-speed semiconductor laser established in Step 4, and then at the DC bias point I... DC Polynomial fitting is performed at the specified point, and the output waveform corresponding to each frequency component is calculated as follows: ， Among them, c k,n N represents the coefficient term in the polynomial fitting derivation of the k-th frequency component. k This is the fitting order for the frequency component; Step 8: Superimpose the output waveforms of all frequency components obtained in Step 7, and combine them with DC bias I. DC Based on the corresponding output optical power, the high-speed semiconductor laser under arbitrary modulation waveform i is calculated. in The time-domain output response under (t) modulation is expressed as: 。 2. The frequency-time mapping modeling method for high-speed semiconductor lasers according to claim 1, characterized in that, In the testing device, the scattering parameter measurement module should have both an electrical port and an optical port. The electrical port is electrically connected to the radio frequency terminal of the high-speed semiconductor laser, and the optical port is optically connected to the output terminal of the high-speed semiconductor laser, in order to complete the measurement of the scattering parameters of the high-speed semiconductor laser.

3. The frequency-time mapping modeling method for high-speed semiconductor lasers according to claim 1, characterized in that, In step 4, the dynamic slope efficiency is derived from the static slope efficiency combined with the scattering parameters. The expression for the dynamic slope efficiency is s. L (I B ;jf m )=s L (I B ; 0)· The dynamic PI curve containing amplitude and phase information is obtained by integrating the injected current. After traversing all bias current and modulation frequency points, the dynamic PI curve of the high-speed semiconductor laser is formed.

4. The frequency-time mapping modeling method for high-speed semiconductor lasers according to claim 1, characterized in that, In step 5, any modulation waveform i in (t) can include various digital modulation waveforms such as non-return-to-zero code (NRZ) and pulse amplitude modulation code (PAM), or it can be an analog signal waveform. Different types of signals can share all the modeling processes from step 1 to step 8.

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