A method for solving the threshold gain of semiconductor laser

Abstract

The technical field of semiconductor laser threshold gain solution of the present invention discloses a method for solving the threshold gain of a semiconductor laser, including the following steps: according to the parameters related to the physical structure of the laser, the transmission coefficient is calculated through the transmission matrix; the longitudinal mode mode interval based on the FP cavity laser is calculated to determine multiple longitudinal mode modes; a loop body is constructed, and the scanning process of the loop body is performed in a longitudinal mode mode of the FP cavity laser using the dichotomy method, and the inner loop ends, and the threshold gain and lasing wavelength are extracted; an outer loop is executed, and the inner loop is executed in a new mode; the outer loop is repeatedly executed, and when the wavelength value is greater than the wavelength range set by the outer loop, the outer loop is terminated, and the threshold gain and lasing wavelength in each mode are output. The method disclosed by the present invention not only improves the speed and accuracy of the threshold gain measurement, but also can respond to the changes in the characteristics of the laser in real time, providing a more efficient and reliable tool for the design and optimization of semiconductor lasers.

Description

Technical Field

[0001] The invention relates to the technical field of semiconductor laser threshold gain solution, and in particular to a method for solving the semiconductor laser threshold gain. Background Art

[0002] Semiconductor lasers are widely used in communications, medical treatment, measurement and other fields. One of the key indicators of their performance is threshold gain. Threshold gain is the minimum gain level required for the laser to reach the excited state, which directly affects the power output, efficiency and stability of the laser. Accurately measuring and controlling the threshold gain of semiconductor lasers is crucial to improving laser performance and optimizing design.

[0003] Traditionally, the measurement methods of semiconductor laser threshold gain mainly include spectral measurement method, current-light output characteristic curve method and pulse excitation method. Although these methods can provide information about the laser threshold gain, they usually have problems such as long measurement time, insufficient accuracy or slow response to changes in laser characteristics. For example, the spectral measurement method often requires complex spectral instruments and long measurement time, while the current-light output characteristic curve method may not be able to quickly and accurately reflect changes in threshold gain due to the limitation of system response time.

[0004] In recent years, transfer matrix theory has been applied to the design and optimization of optical devices as an effective optical analysis tool. By describing the propagation behavior of light in multilayer media, this theory can analyze and predict the performance of optical devices in detail. However, the application of transfer matrix theory to the rapid scanning of the threshold gain of semiconductor lasers still faces technical challenges. Current application research focuses on the analysis of static states, and lacks effective methods for the dynamic characteristics and real-time scanning of lasers. Summary of the invention

[0005] In order to solve the above technical problems, the present invention provides a method for solving the threshold gain of a semiconductor laser, which not only improves the speed and accuracy of threshold gain measurement, but also can respond to changes in laser characteristics in real time, providing a more efficient and reliable tool for the design and optimization of semiconductor lasers.

[0006] To achieve the above object, the technical solution of the present invention is as follows:

[0007] A method for solving the threshold gain of a semiconductor laser comprises the following steps:

[0008] Step 1, obtaining the structural related parameters of the known semiconductor laser from its physical structure, and constructing the transmission matrix of the laser light field according to the related structural parameters; calculating the transmission coefficient through the transmission matrix, and obtaining the functional relationship between the transmission coefficient and the net field gain and the wavelength;

[0009] Step 2, calculating the longitudinal mode interval based on the FP cavity laser, and determining multiple longitudinal mode modes of the FP cavity laser according to the longitudinal mode interval;

[0010] Step 3, constructing a loop body including the functional relationship, wherein the loop body includes an outer loop and an inner loop, wherein the outer loop is used for mode switching, and the inner loop updates the wavelength and the net field gain, executes the transmission matrix model to obtain the transmission coefficient; and presets the inner loop end judgment value and the outer loop wavelength range;

[0011] Step 4, using the dichotomy method to perform a cyclic scanning process in a longitudinal mode of the FP cavity laser, during which the square of the absolute value of the current maximum transmission coefficient is preset ; By comparing the square of the absolute value of the maximum transmission coefficient obtained by the current wavelength and the net field gain and The size of determines the updated wavelength scanning step and value; when When the value is greater than the preset inner loop end judgment value, the inner loop ends, and the net field gain value and its corresponding wavelength at this time are extracted as the threshold gain and lasing wavelength;

[0012] Step 5, execute the outer loop to perform mode jump, execute the inner loop in the new mode, repeat step 4, and extract the threshold gain and lasing wavelength in the new mode;

[0013] Step 6, repeat step 5, when the wavelength value is greater than the wavelength range set by the outer loop, end the outer loop and output the threshold gain and lasing wavelength in each mode.

[0014] In the above scheme, in step 1, the structure-related parameters include central wavelength, wavelength range, net field gain range, coupling coefficient, effective refractive index value, laser cavity length, left end face reflectivity, right end face reflectivity, left end face phase, right end face phase and group refractive index.

[0015] In the above scheme, in step 1, the transmission coefficient It is expressed as:

[0016] ;

[0017] In the formula, is the transmission matrix The fourth item.

[0018] In the above scheme, in step 2, based on the longitudinal mode spacing of the FP cavity laser The calculation formula is as follows:

[0019] ;

[0020] In the formula, is the wavelength size, is the group refractive index in the laser cavity, is the laser cavity length.

[0021] In the above scheme, in step 3, the preset inner loop end judgment value is , denoted as , the preset outer loop wavelength range is , is the central wavelength, is the longitudinal mode spacing of the FP cavity laser.

[0022] In the above scheme, in step 4, in the inner loop, the wavelength update setting is:

[0023] ;

[0024] The initial scan step length is = , is the longitudinal mode spacing of the FP cavity laser;

[0025] The net field gain range is:

[0026] .

[0027] In the above scheme, in step 4, before the inner loop starts, the square of the absolute value of the current maximum transmission coefficient is preset is an initial value; the square of the absolute value of the maximum transmission coefficient in the net field gain interval is selected as the comparison value, recorded as , and Compare, record the corresponding wavelength and net field gain value, and decide to update the scanning step length and Values, where the binary search is used Value to update: If ,but , not updated ;if ,but , ;when When , the inner loop ends and the corresponding wavelength and net field gain value are output.

[0028] In the above scheme, in step 5, when the inner loop is executed and the outer loop is executed, the updated wavelength starting point is set to the calculated corresponding wavelength plus the longitudinal mode interval of the FP cavity laser, that is:

[0029] ;

[0030] In the formula, is the longitudinal mode spacing of the FP cavity laser.

[0031] In the above scheme, in step 4, the inner loop in each outer loop is set to be repeated a maximum of 100 times, and the number of inner loops is recorded as cc. If the threshold gain and lasing wavelength are not found between 100 times, the wavelength jumps to search in the next mode.

[0032] Through the above technical solution, the method for solving the threshold gain of a semiconductor laser provided by the present invention has the following beneficial effects:

[0033] By using the binary method to update the wavelength update step, the wavelength can quickly converge to the lasing wavelength within a longitudinal mode; the mode theory is used to search for mode jumps, and by presetting the distance between two lasing wavelengths as the size of a longitudinal mode, the lasing wavelength in the next mode after finding a lasing wavelength is quickly located, which greatly improves the numerical solution rate. This method not only improves the speed and accuracy of threshold gain measurement, but also can respond to changes in laser characteristics in real time, providing a more efficient and reliable tool for the design and optimization of semiconductor lasers. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art are briefly introduced below.

[0035] Figure 1 A schematic flow chart of a method for solving a threshold gain of a semiconductor laser disclosed in an embodiment of the present invention;

[0036] Figure 2 It is a flow chart of the loop process of the loop body;

[0037] Figure 3 Flowchart for solving the transmission matrix for a single wavelength at different net field gains and finding the transmission coefficient;

[0038] Figure 4 is a schematic diagram of a FP cavity laser;

[0039] Figure 5 This is a schematic diagram of the solution results of the FP cavity;

[0040] Figure 6 Schematic diagram of the standard DFB laser structure with AR / HR coating;

[0041] Figure 7 This is a schematic diagram of the solution results for a standard DFB laser with AR / HR coating;

[0042] Figure 8 For AR / AR coating Schematic diagram of the phase-shifted DFB laser structure;

[0043] Fig. 9 For AR / AR coating Schematic diagram of the solution results of the phase-shifted DFB laser;

[0044] Fig.10 The solution method of the present invention is applied to AR / AR coating Schematic diagram of the spectrum of the phase-shifted DFB laser in the main mode lasing gain;

[0045] Fig.11 The solution method of the present invention is applied to AR / AR coating Schematic diagram of the spectrum of the phase-shifted DFB laser when it is in the first-order side film lasing gain on the right;

[0046] Fig.12 The solution method of the present invention is applied to AR / AR coating Schematic diagram of the spectrum of the phase-shifted DFB laser at the first-order side film lasing gain on the left;

[0047] Fig.13 The solution method of the present invention is applied to AR / AR coating Schematic diagram of the transformation curve of the transmission coefficient of the phase-shifted DFB laser with the net field gain at the main mode lasing wavelength.

[0048] In the figure, 1, waveguide layer; 2, active area; 3, left end surface; 4, right end surface. DETAILED DESCRIPTION

[0049] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the accompanying drawings in the embodiments of the present invention.

[0050] The present invention provides a method for solving the threshold gain of a semiconductor laser, such as Figure 1 As shown, the following steps are included:

[0051] Step 1, obtain the structural related parameters of the known semiconductor laser from its physical structure, construct the transmission matrix of the laser light field according to the related structural parameters, calculate the transmission coefficient through the transmission matrix, and obtain the functional relationship between the transmission coefficient and the net field gain and the wavelength.

[0052] Structure-related parameters include central wavelength ,wavelength Interval, net field gain Interval, coupling coefficient , effective refractive index value , laser cavity length , left end face reflectivity , right end face reflectivity And the corresponding left and right end face reflection phase , group refractive index .

[0053] The transmission matrix includes FP cavity laser transmission matrix, standard DFB laser transmission matrix and multi-segment DFB laser transmission matrix.

[0054] (1) The transmission matrix of the FP cavity laser can be expressed as:

[0055] ;

[0056] In the formula, is the complex propagation constant; The range of the transfer matrix description starts from End point , are two arbitrary values ​​in the cavity length direction and satisfy ; is the refractive index in the FP cavity, It is the net field gain and does not vary with the position in the cavity or the wavelength.

[0057] The total transmission matrix of the FP cavity laser can be written as:

[0058] ;

[0059] in, are the reflectivity of the left and right end faces of the laser, ; , , , is the transmission matrix Elements in

[0060] Transmission coefficient of FP cavity laser It can be expressed as:

[0061] ;

[0062] in, for The fourth item in .

[0063] (2) The transmission matrix of a standard (single-section) DFB laser can be expressed as:

[0064] ;

[0065] ;

[0066] ;

[0067] ;

[0068] ;

[0069] in, , , Used to simplify the transfer matrix formula, are two arbitrary values ​​in the cavity length direction and satisfy , is the average wave number, is the effective refractive index in the cavity, c is the speed of light, is the Bragg wave number, is the grating coupling coefficient, is the initial phase of the grating, is the detuning constant, is the Bragg angular frequency, is the angular frequency, is the group velocity, is the DFB net field gain, which is a constant value in the cavity.

[0070] The total transmission matrix of a standard (single-section) DFB laser can be written as:

[0071] ;

[0072] in, are the reflectivity of the left and right end faces of the laser, ; , , , is the transmission matrix Elements in

[0073] Transmission coefficient of a standard (single-section) DFB laser It can be expressed as:

[0074] ;

[0075] (3) Multi-segment corrugated DFB laser, part( =1,2,3…,n) can be expressed as:

[0076] ;

[0077] ;

[0078] ;

[0079] ;

[0080] ;

[0081] in, The first Two arbitrary values ​​of the segment, and satisfy is the average wave number, is the effective refractive index in the cavity, c is the speed of light, is the Bragg wave number, is the grating coupling coefficient, For the The initial phase of the segment grating, is the detuning constant, is the Bragg angular frequency, is the angular frequency, is the group velocity, For the Segment net field gain.

[0082] The transmission matrix of an n-segment DFB laser can be written as:

[0083] ;

[0084] After adding the reflectivity of the left and right end faces of the laser, the total transmission matrix of the n-segment DFB laser can be written as:

[0085] ;

[0086] in, are the reflectivity of the left and right end faces of the laser, ; , , , is the transmission matrix The elements in .

[0087] Transmission coefficient of multi-segment corrugated DFB laser It can be expressed as:

[0088] .

[0089] Step 2: Calculate the longitudinal mode interval based on the FP cavity laser, and determine multiple longitudinal mode modes of the FP cavity laser according to the longitudinal mode interval.

[0090] The present invention is deduced from the FP cavity, and it is believed that only at most one wavelength within a FP cavity mode length can reach the DFB laser threshold gain; but as the laser cavity length increases, the mode length will decrease, which is the same as the DFB laser mode conversion trend. The designer makes this setting and it can be successfully applied in the DFB laser.

[0091] Longitudinal mode spacing based on FP cavity laser The calculation formula is as follows:

[0092] ;

[0093] In the formula, is the wavelength size, is the group refractive index in the laser cavity, is the laser cavity length.

[0094] In the embodiment of the present invention, seven longitudinal modes of the FP cavity laser are determined.

[0095] Step 3, construct a loop body containing a functional relationship, the loop body includes an outer loop and an inner loop, the outer loop is used for mode jumping, the inner loop updates the wavelength and net field gain, executes the transmission matrix model to obtain the transmission coefficient; preset the inner loop end judgment value and the outer loop wavelength range.

[0096] The threshold gain condition of the inner loop process is The denominator is 0, that is →∞, it is very difficult to solve the denominator equal to zero in real situations. In this embodiment, it is considered that the square of the absolute value of the current maximum transmission coefficient When , it is considered to have reached the threshold value (lasing value), is the preset inner loop end judgment value, denoted as , and extract the corresponding wavelength and the corresponding net field gain at this moment.

[0097] The interval of finding the threshold point, that is, the preset outer loop wavelength range is the mode length of 7 FP cavity lasers, and the specific expression formula is: , is the central wavelength, is the longitudinal mode spacing of the FP cavity laser.

[0098] Step 4, using the dichotomy method to perform a cyclic scanning process in a longitudinal mode of the FP cavity laser, during which the square of the absolute value of the current maximum transmission coefficient is preset =0; by comparing the square of the absolute value of the maximum transmission coefficient obtained by the current wavelength and the net field gain and The size of determines the updated wavelength scanning step and value; when When the value is greater than the preset inner loop end judgment value, the inner loop ends, and the net field gain value and its corresponding wavelength at this time are extracted as the threshold gain and lasing wavelength.

[0099] In the inner loop, the wavelength update is set as:

[0100] ;

[0101] The initial scan step length is = , is the longitudinal mode spacing of the FP cavity laser;

[0102] The net field gain range is:

[0103] .

[0104] Before the inner loop starts, the square of the absolute value of the current maximum transmission coefficient is preset is an initial value; the square of the absolute value of the maximum transmission coefficient in the net field gain interval is selected as the comparison value, recorded as , and Compare, record the corresponding wavelength and net field gain value, and decide to update the scanning step length and Value: If ,but , not updated ;if ,but , ;when When , the inner loop ends and the corresponding wavelength and net field gain value are output.

[0105] In this embodiment, an inner loop is set to cycle a maximum of 100 times, and the number of inner loops is recorded as cc. If the threshold gain and lasing wavelength are not found within 100 times, the wavelength jumps to search in the next mode.

[0106] Step 5, execute the outer loop to perform mode jump, execute the inner loop in the new mode, repeat step 4, and extract the threshold gain and lasing wavelength in the new mode.

[0107] When the inner loop is executed and the outer loop is executed, the starting point of the updated wavelength is set to the calculated corresponding wavelength plus the longitudinal mode interval of the FP cavity laser, that is:

[0108] .

[0109] Step 6, repeat step 5, when the wavelength value is greater than the wavelength range set by the outer loop, end the outer loop and output the threshold gain and lasing wavelength in each mode.

[0110] The specific process is as follows Figure 2 As shown, the following steps are included:

[0111] (1) Setting the wavelength range in which the mode may exist, and making the cycle start from the minimum wavelength and end at the maximum wavelength; in this embodiment, the preset outer cycle wavelength range is ,Right now ;

[0112] (2) Initializing the number of inner loops in a single mode. In this embodiment, an inner loop can be repeated up to 100 times; (3) Updating the wavelength size, executing the transmission matrix for a single wavelength under different net field gains, and obtaining its transmission coefficient, selecting the maximum transmission coefficient to iterate the initial conditions and scanning step size;

[0113] The specific process is as follows Figure 3 As shown, the following steps are included:

[0114] a. Input parameters;

[0115] b. Set the net field gain range;

[0116] c. Initialize the net field gain ;

[0117] d. Input wavelength value;

[0118] e. Judgment Is it greater than 500? If so, end; if not, calculate the transmission matrix and obtain the transmission coefficient;

[0119] f. , return to step e;

[0120] (4) Determine whether the maximum value of the transmission coefficient meets the threshold cutoff condition, that is, whether the maximum value of the transmission coefficient is greater than the preset inner loop end judgment value. If not, cc=cc+1, and determine whether cc is greater than 100. If not, repeat step (3). If cc is greater than 100, stop the loop and jump to step (5). If the threshold cutoff condition is met, output the threshold gain and its corresponding wavelength and jump to step (5).

[0121] (5) Update the longitudinal mode interval of the FP cavity laser, update the initial value of the step size, jump the wavelength to the next mode, and repeat step (2);

[0122] (6) Determine whether the wavelength value at this time is greater than the maximum wavelength value. If it is satisfied, end the process. If not, execute steps (2) to (5) until the end condition is met.

[0123] Application Example 1

[0124] A method for solving the threshold gain of a semiconductor laser provided by the present invention is applied to the parameter setting and application of an FP cavity laser. The structure of the FP cavity laser is as follows: Figure 4 As shown, the FP cavity laser has a waveguide layer 1 and an active region 2 inside, and a left end face 3 and a right end face 4 on both sides.

[0125] Set the transmission coefficient cutoff condition to , the net field gain interval is set to , the wavelength range is set to ,in is 1.310nm, where the refractive index of the cavity medium is is 3.2, the reflectivity of the left and right end faces is set to 0.3, and the end face phase is 0; the cavity length .

[0126] implement Figure 2 The process shown in FIG. 1 is a flow chart in which the transmission matrix is ​​applied to the transmission matrix of the FP cavity laser; the result is as follows Figure 5 As shown in Table 1.

[0127] Table 1 Solution results of FP cavity laser

[0128]

[0129] from Figure 5 As can be seen from Table 1, the present invention only takes 3.11 seconds to be applied to the FP cavity laser. The FP laser has a threshold gain of 120.4 cm -1 The invention can be applied to the FP cavity laser to quickly solve the threshold gain.

[0130] Application Example 2

[0131] A method for solving the threshold gain of a semiconductor laser provided by the present invention is applied to the parameter setting and application of a standard DFB laser with AR / HR coating. The structure of the standard DFB laser is as follows: Figure 6 As shown, the standard DFB laser has a waveguide layer 1 and an active region 2 inside, and a left end face 3 and a right end face 4 on both sides.

[0132] Set the transmission coefficient cutoff condition to , the net field gain interval is set to , the wavelength range is set to , where the Bragg wavelength (central wavelength) is 1.310nm, and the effective refractive index , group refractive index , anti-reflection coating is set on the left end face , the phase is , high reflective coating is set on the right end face , phase is 0, cavity length , .

[0133] implement Figure 2 The cycle flow is shown in Figure 1, where the transmission matrix model applies the transmission matrix of a standard DFB laser. The result is Figure 7 As shown in Table 2.

[0134] Table 2 Solution results of standard DFB laser with AR / HR coating

[0135]

[0136] from Figure 7 As can be seen from Table 2, the standard DFB laser applied to AR / HR coating in the present invention only takes 2.58s to solve the threshold gain and its side mode lasing gain. The main mode lasing wavelength of the standard DFB laser with AR / HR coating can be found nearby is 1308.4nm, and the threshold gain is 58.5 cm -1 , and find the lasing position and lasing gain of its side mode, which is consistent with the actual situation. The present invention can be applied to the standard DFB laser to quickly solve the threshold gain.

[0137] Application Example 3

[0138] The method for calculating the threshold gain of a semiconductor laser provided by the present invention is applied to AR / AR coating. Parameter setting and application of phase-shifted DFB laser, The phase-shifted DFB laser structure is as follows: Figure 8 As shown, The phase-shifted DFB laser has a waveguide layer 1 and an active region 2 inside, and a left end face 3 and a right end face 4 on both sides.

[0139] Set the transmission coefficient cutoff condition to , the net field gain interval is set to , the wavelength range is set to , where the Bragg wavelength 1.310nm, anti-reflection coating is set on both the left and right end faces , phase is 0, cavity length .

[0140] The phase-shifted DFB laser is a type of multi-segment DFB laser. Here, the phase shift position is set to 1 / 2 of the cavity length; the number of segments is set to 2, and an additional The phase of the two sections is designed to be the effective refractive index , group refractive index , the length is , .

[0141] implement Figure 2The cycle flow is shown in FIG. 1 , where the transmission matrix model applies the transmission matrix of a multi-segment DFB laser; the result is shown in FIG. Fig. 9 As shown in Table 3.

[0142] Table 3 Phase-shifted DFB laser solution results

[0143]

[0144] from Fig. 9 As can be seen from Table 3, the present invention is applied to AR / AR coating. The phase-shifted DFB laser takes only 6.40 seconds to solve the threshold gain and side mode lasing gain. AR / AR coating can be found nearby The main mode lasing wavelength of the phase-shifted DFB laser is 1309.9nm and the threshold gain is 113.6cm -1 , and find the lasing position and lasing gain of its side mode, which is consistent with the actual situation; here, because the lasing wavelength in the third-order side mode on the right side exceeds the preset wavelength range, the lasing wavelength and threshold gain are not found. The present invention can be applied to the rapid solution of threshold gain of multi-segment DFB lasers.

[0145] The results of Example 3 were analyzed and the results were as follows: Figures 10 to 13 As shown, Fig.10 The input master mode threshold gain , the wavelength range is Spectrum of

[0146] Fig.11 is the input first-order submode threshold gain , the wavelength range is Spectrum of

[0147] Fig.12 is the input first-order submode threshold gain , the wavelength range is Spectrum of

[0148] Fig.13 Enter the main mode lasing wavelength value When , the transmission coefficient changes with the gain. Since the accurate solution value is After that, you need to continue to refine the decimal point. At this time, enter The lasing value will not be greater than .

[0149] from Figures 10 to 13 It can be seen that the main mode lasing wavelength and threshold gain, side mode lasing wavelength and corresponding lasing gain required by the present invention are accurate, which further proves the feasibility and accuracy of the present invention.

[0150] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for solving the threshold gain of a semiconductor laser, characterized in that: The steps include: Step 1, obtaining the structural related parameters of the known semiconductor laser from its physical structure, and constructing the transmission matrix of the laser light field according to the related structural parameters; calculating the transmission coefficient through the transmission matrix, and obtaining the functional relationship between the transmission coefficient and the net field gain and the wavelength; Step 2, calculating the longitudinal mode interval based on the FP cavity laser, and determining multiple longitudinal mode modes of the FP cavity laser according to the longitudinal mode interval; Step 3, constructing a loop body including the functional relationship, wherein the loop body includes an outer loop and an inner loop, wherein the outer loop is used for mode switching, and the inner loop updates the wavelength and the net field gain, executes the transmission matrix model to obtain the transmission coefficient; and presets the inner loop end judgment value and the outer loop wavelength range; Step 4, using the dichotomy method to perform a cyclic scanning process in a longitudinal mode of the FP cavity laser, during which the square of the absolute value of the current maximum transmission coefficient is preset ; By comparing the square of the absolute value of the maximum transmission coefficient obtained from the current wavelength and the net field gain and The size of determines the update wavelength scanning step and value; when When the value is greater than the preset inner loop end judgment value, the inner loop ends, and the net field gain value and its corresponding wavelength at this time are extracted as the threshold gain and lasing wavelength; Step 5, execute the outer loop to perform mode jump, execute the inner loop in the new mode, repeat step 4, and extract the threshold gain and lasing wavelength in the new mode; Step 6, repeating step 5, when the wavelength value is greater than the wavelength range set in the outer loop, ending the outer loop, and outputting the threshold gain and lasing wavelength in each mode; In step 4, in the inner loop, the wavelength update is set to: ； Set the initial scan step size to = , is the longitudinal mode spacing of the FP cavity laser; The net field gain range is: ； In step 4, before the inner loop starts, the square of the absolute value of the current maximum transmission coefficient is preset is an initial value; The square of the absolute value of the maximum transmission coefficient in the net field gain range is selected as the comparison value, which is recorded as , and Compare, record the corresponding wavelength and net field gain value, and decide to update the scanning step length and Values, where the binary search is used Value to update: If ,but , not updated ;if ,but , ;when When , the inner loop ends and the corresponding wavelength and net field gain value are output; In step 5, when the inner loop is executed and the outer loop is executed, the starting point of the updated wavelength is set to the calculated corresponding wavelength plus the longitudinal mode interval of the FP cavity laser, that is: ； In the formula, is the longitudinal mode spacing of the FP cavity laser.

2. The method for solving the threshold gain of a semiconductor laser according to claim 1, characterized in that: In step 1, the structure-related parameters include central wavelength, wavelength range, net field gain range, coupling coefficient, effective refractive index value, laser cavity length, left end face reflectivity, right end face reflectivity, left end face phase, right end face phase and group refractive index.

3. The method for solving the threshold gain of a semiconductor laser according to claim 1, characterized in that: In step 1, the transmission coefficient It is expressed as: ； In the formula, is the transmission matrix The fourth item.

4. The method for solving the threshold gain of a semiconductor laser according to claim 1, characterized in that: In step 2, based on the longitudinal mode spacing of the FP cavity laser The calculation formula is as follows: ； In the formula, is the wavelength size, is the group refractive index in the laser cavity, is the laser cavity length.

5. The method for solving the threshold gain of a semiconductor laser according to claim 1, characterized in that: In step 3, the default inner loop end judgment value is , denoted as , the preset outer loop wavelength range is , is the central wavelength, is the longitudinal mode spacing of the FP cavity laser.

6. The method for solving the threshold gain of a semiconductor laser according to claim 1, characterized in that: In step 4, the inner loop in each outer loop is set to be repeated at most 100 times, and the number of inner loops is recorded as cc. If the threshold gain and lasing wavelength are not found between 100 times, the wavelength jumps to search in the next mode.

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