A method and system for measuring threshold enhancement factor size using spectral effective width

Abstract

The application discloses a method for measuring threshold enhancement factor size by using spectral effective width, and belongs to the technical field of laser design; the method comprises the following steps: encoding a PRBS signal; based on the phase of the PRBS signal, modulating a fiber laser at a preset modulation depth to obtain a power spectral density function after phase modulation; performing denoising processing on the power spectral density function after phase modulation to obtain a spectral effective width; and measuring the threshold enhancement factor size according to the spectral effective width. The application also provides a system for measuring threshold enhancement factor size by using spectral effective width. The application provides a spectral effective width calculation method, and aims to solve the problems of large calculation error and incomplete application of the spectral effective width in the existing simulation.

Description

Technical Field

[0001] This invention relates to the field of laser design technology, and more specifically to a method and system for measuring the threshold enhancement factor using the effective spectral width. Background Technology

[0002] In high-power, narrow-linewidth fiber lasers, broadening the seed source laser spectrum through pseudo-random binary sequence (PRBS) phase modulation combined with a master oscillator power amplifier (MOPA) structure has proven to be an effective means of suppressing nonlinear effects such as stimulated Brillouin scattering (SBS). The SBS threshold enhancement factor is an important indicator for suppressing the SBS effect. In 1968, Denariez et al. investigated the SBS gain information in different liquids (Denariez, Marguerite, Bret, Georges, “Investigation of Rayleigh Wings and Brillouin-Stimulated Scattering in Liquids,” in Physical Review, vol. 171, no. 1, pp. 160–171, February 1968), and presented the relationship between SBS gain and linewidth. Currently, the effective spectral width (Δνm) and Brillouin linewidth (ΔνB) are widely accepted for simply calculating the SBS threshold enhancement factor. Among them Pth and These are the threshold powers with and without phase modulation, respectively. This refers to the threshold enhancement factor. In 2021, the International Organization for Standardization (ISO) specified the use of D4σ (second moment) to measure the beam width (diameter) of a laser beam. Therefore, in simulations, this method is commonly used to calculate the effective width of the synthesized spectrum. Specifically, it involves using the intensity information of the spectral lines to calculate the second moment of the intensity distribution function, thus obtaining the effective spectral width. This allows for the rapid calculation of the SBS threshold enhancement factor of the system, providing a criterion for evaluating the effectiveness of the system design in simulations.

[0003] For phase-modulated optical signals, the second-moment method has drawbacks: calculating the effective spectral width is complex (usually requiring numerical codes), and the results are easily affected by vertical shifts in the measured intensity distribution, making it highly sensitive to noise in the signal and resulting in calculations that deviate significantly from reality. Therefore, the second-moment method is not suitable for calculating the effective spectral width of PRBS-modulated optical signals, and consequently, the SBS threshold enhancement factor of the amplified system cannot be quickly measured. Thus, we need to redefine the method for calculating the effective spectral width to improve the accuracy of calculating the SBS threshold enhancement factor. Summary of the Invention

[0004] The purpose of this invention is to provide an efficient method and system for measuring the size of the threshold enhancement factor using the effective spectral width.

[0005] To address the aforementioned technical problems, this invention provides a method for measuring the threshold enhancement factor using the effective spectral width, comprising the following steps:

[0006] Encode PRBS signals;

[0007] Based on the phase of the PRBS signal, the fiber laser is modulated at a preset modulation depth to obtain the phase-modulated power spectral density function.

[0008] The phase-modulated power spectral density function is denoised to obtain the effective spectral width.

[0009] The threshold enhancement factor is measured based on the effective spectral width.

[0010] Preferably, encoding the PRBS signal specifically includes the following steps:

[0011] The characteristics of the PRBS waveform are controlled by a sequence:

[0012] {a j}={a0,a1········a N-1} (2)

[0014] Where: {a j} is a variable with a period of N, whose discrete values ​​are -1 and +1; when the code pattern generator has a code pattern of n, the period N = 2. n -1; If an element is randomly selected from the sequence, the probability of a different value becomes P. r+1 = (1 + 1 / N) / 2 and P r-1 = (1 - 1 / N) / 2, where P r-1 +P r+1 =1; In order to form a continuous waveform in the sequence, a continuously repeating sequence x(t) and a single period x N (t) can be written as:

[0015]

[0016] Where: T is the modulation time of a single bit, and * denotes convolution; assuming the basic shape p(t) of a single symbol is the same for both types of symbols, it is written as:

[0017]

[0018] Then the intermediate non-periodic signal x N (t) is achieved by using a time interval of T N =NT uses a comb function to expand in time, represented as a convolution, thus producing a periodic sequence:

[0019]

[0020] Where: j, k∈Z are used to specify discrete instants in time.

[0021] Preferably, based on the phase of the PRBS signal, the fiber laser is modulated at a preset modulation depth to obtain the phase-modulated power spectral density function, specifically including the following steps:

[0022] Analysis of power spectral density and modulation frequency f based on PRBS signal phase modulation onto a modulated fiber laser. cr Code type n and modulation amplitude k p Relationship:

[0023] The electric field of a linearly polarized single-frequency laser can be expressed as:

[0024]

[0025] in: The amplitude is constant in the laser field. For simplicity, this amplitude is ignored when calculating the power spectral density. We also center the spectral shift carrier frequency ωc around ω = 0. According to the expression given in equation (5), the MLS coding phase φ(t) is expressed as:

[0026]

[0027] Where: k p It is the inter-peak phase modulation amplitude, defined as the inter-peak modulation voltage and the half-wave voltage V of the phase modulator. π π times; here, the laser electric field E(t) is an infinitely repeating periodic sequence with a period of N, taking two different values ​​exp(ikp / 2) and exp(-ikp / 2);

[0028] The power spectral density (PSD) of the laser field is given by the Wiener-Chinchin theorem via the Fourier transform of the PACF:

[0029]

[0030] It is the power spectral density and modulation frequency f cr Code type n and modulation amplitude k p Relational expressions;

[0031] The phase-modulated power spectral density function is given by equation (9):

[0032]

[0033] The calculated power spectral density function after phase modulation, under different code patterns, shows that the shape of the power spectral density after PRBS phase modulation is determined by sinc. 2 Envelope expanded.

[0034] Preferably, the fiber laser is a high-power narrow-linewidth fiber laser.

[0035] Preferably, the phase-modulated power spectral density function is denoised to obtain the effective spectral width, specifically including the following steps:

[0036] In the normalized phase-modulated power spectral density function, the equivalent spectral width is calculated using the traditional second-order moment method to obtain the matrix;

[0037] The effective spectral width is obtained based on the matrix and the spectral density threshold.

[0038] Preferably,

[0039] The spectral density threshold is 4% of the spectral peak value.

[0040] Preferably, the effective spectral width is obtained based on the matrix and the spectral density threshold, specifically including the following steps:

[0041] Set all points in the matrix below 4% of the spectral peak value to 0 to obtain the effective spectral width.

[0042] The present invention also provides a system for measuring the magnitude of the threshold enhancement factor using the effective spectral width, comprising:

[0043] The encoding module is used to encode PRBS signals;

[0044] The phase modulation module is used to modulate the fiber laser based on the phase of the PRBS signal at a preset modulation depth to obtain the phase-modulated power spectral density function.

[0045] The denoising module is used to denoise the phase-modulated power spectral density function to obtain the effective spectral width.

[0046] The threshold enhancement factor size measurement module is used to measure the size of the threshold enhancement factor based on the effective spectral width.

[0047] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0048] This invention provides a method for calculating the effective spectral width, aiming to solve the problems of large errors and incomplete application in the calculation of the effective spectral width in existing simulations. Attached Figure Description

[0049] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0050] Figure 1 This is a flowchart illustrating a method for measuring the size of a threshold enhancement factor using the effective spectral width according to the present invention.

[0051] Figure 2 This is a schematic diagram of the power spectral density of a PRBS signal with a modulation frequency of 10 GHz and code patterns of 5, 7, 9, and 11. Detailed Implementation

[0052] Numerous specific details are set forth in the following description to provide a full understanding of the invention. However, the invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0053] The terminology used in one or more embodiments of this specification is for the purpose of describing particular embodiments only and is not intended to be limiting of the one or more embodiments of this specification. The singular forms “a,” “described,” and “the” as used in one or more embodiments of this specification and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used in one or more embodiments of this specification refers to and includes any or all possible combinations of one or more associated listed items.

[0054] It should be understood that although the terms first, second, etc., may be used to describe various information in one or more embodiments of this specification, such information should not be limited to these terms. These terms are only used to distinguish information of the same type from one another. For example, first may also be referred to as second without departing from the scope of one or more embodiments of this specification, and similarly, second may also be referred to as first. Depending on the context, the word "if" as used herein may be interpreted as "when," "when," or "in response to a determination."

[0055] The present invention will now be described in further detail with reference to the accompanying drawings:

[0056] This invention provides a method for measuring the magnitude of the threshold enhancement factor using the effective spectral width, comprising the following steps:

[0057] Encode PRBS signals;

[0058] Based on the phase of the PRBS signal, the fiber laser is modulated at a preset modulation depth to obtain the phase-modulated power spectral density function.

[0059] The phase-modulated power spectral density function is denoised to obtain the effective spectral width.

[0060] The threshold enhancement factor is measured based on the effective spectral width.

[0061] Preferably, encoding the PRBS signal specifically includes the following steps:

[0062] The characteristics of the PRBS waveform are controlled by a sequence:

[0063]

[0064] Where: {a j} is a variable with a period of N, whose discrete values ​​are -1 and +1; when the code pattern generator has a code pattern of n, the period N = 2. n -1; If an element is randomly selected from the sequence, the probability of a different value becomes P. r+1 = (1 + 1 / N) / 2 and P r-1 = (1 - 1 / N) / 2, where P r-1 +P r+1 =1; In order to form a continuous waveform in the sequence, a continuously repeating sequence x(t) and a single period x N (t) can be written as:

[0065]

[0066] Where: T is the modulation time of a single bit, and * denotes convolution; assuming the basic shape p(t) of a single symbol is the same for both types of symbols, it is written as:

[0067]

[0068] Then the intermediate non-periodic signal x N (t) is achieved by using a time interval of T N =NT uses a comb function to expand in time, represented as a convolution, thus producing a periodic sequence:

[0069]

[0070] Where: j, k∈Z are used to specify discrete instants in time.

[0071] Preferably, based on the phase of the PRBS signal, the fiber laser is modulated at a preset modulation depth to obtain the phase-modulated power spectral density function, specifically including the following steps:

[0072] Analysis of power spectral density and modulation frequency f based on PRBS signal phase modulation onto a modulated fiber laser. cr Code type n and modulation amplitude k p Relationship:

[0073] The electric field of a linearly polarized single-frequency laser can be expressed as:

[0074]

[0075] in: The amplitude is constant in the laser field. For simplicity, this amplitude is ignored when calculating the power spectral density. We also center the spectral shift carrier frequency ωc around ω = 0. According to the expression given in equation (5), the MLS coding phase φ(t) is expressed as:

[0076]

[0077] Where: k p It is the inter-peak phase modulation amplitude, defined as the inter-peak modulation voltage and the half-wave voltage V of the phase modulator. π π times; here, the laser electric field E(t) is an infinitely repeating periodic sequence with a period of N, taking two different values ​​exp(ikp / 2) and exp(-ikp / 2);

[0078] The power spectral density (PSD) of the laser field is given by the Wiener-Chinchin theorem via the Fourier transform of the PACF:

[0079]

[0080] It is the power spectral density and modulation frequency f cr Code type n and modulation amplitude k p Relational expressions;

[0081] The phase-modulated power spectral density function is given by equation (9):

[0082]

[0083] The calculated power spectral density function after phase modulation, under different code patterns, shows that the shape of the power spectral density after PRBS phase modulation is determined by sinc. 2 Envelope expanded.

[0084] Preferably, the fiber laser is a high-power narrow-linewidth fiber laser.

[0085] Preferably, the phase-modulated power spectral density function is denoised to obtain the effective spectral width, specifically including the following steps:

[0086] In the normalized phase-modulated power spectral density function, the equivalent spectral width is calculated using the traditional second-order moment method to obtain the matrix;

[0087] The effective spectral width is obtained based on the matrix and the spectral density threshold.

[0088] Preferably,

[0089] The spectral density threshold is 4% of the spectral peak value.

[0090] Preferably, the effective spectral width is obtained based on the matrix and the spectral density threshold, specifically including the following steps:

[0091] Set all points in the matrix below 4% of the spectral peak value to 0 to obtain the effective spectral width.

[0092] The present invention also provides a system for measuring the magnitude of the threshold enhancement factor using the effective spectral width, comprising:

[0093] The encoding module is used to encode PRBS signals;

[0094] The phase modulation module is used to modulate the fiber laser based on the phase of the PRBS signal at a preset modulation depth to obtain the phase-modulated power spectral density function.

[0095] The denoising module is used to denoise the phase-modulated power spectral density function to obtain the effective spectral width.

[0096] The threshold enhancement factor size measurement module is used to measure the size of the threshold enhancement factor based on the effective spectral width.

[0097] To better illustrate the technical effects of the present invention, the present invention provides the following specific embodiments to illustrate the above technical process:

[0098] Example 1: A method for measuring the magnitude of the threshold enhancement factor using the effective spectral width:

[0099] This invention provides a method for calculating the effective spectral width, aiming to solve the problems of large errors and limited application in existing simulation methods for calculating the effective spectral width. The method for calculating the spectral width after PRBS phase modulation is as follows: Figure 1 As shown, it includes the following steps:

[0100] 1) Calculate the SBS threshold enhancement factor for high-power narrow-linewidth fiber amplifiers.

[0101] Since the Brillouin gain spectrum is Lorentz-shaped, the interaction between the incident pump light and the backscattered light is considered under steady-state conditions (continuous pump light). Given the relatively small Brillouin frequency shift, the pump wave and the Stokes wave can be approximated as having the same fiber loss. Furthermore, the incident pump light and the back-propagating Stokes light are linearly polarized along the same direction and their polarization states remain unchanged during propagation. Therefore, a general calculation model for estimating the classical values ​​of Smith and K.ng for stimulated Brillouin scattering can be obtained:

[0102]

[0103] Among them: A eff The effective core area of ​​the optical fiber is taken as 2.6 × 10⁻⁶. -10 m 2 g0 is the peak Brillouin gain, which is approximately 2 × 10⁻⁶. -11 m / W, The effective fiber length is given by α, where α is the fiber loss coefficient derived from (10 / L)log(P0 / P). L It is derived that L is the fiber length, and P0 and P L These represent the optical input power and output power, respectively, and G is the threshold gain coefficient.

[0104] The specific expression for the threshold gain coefficient G is:

[0105]

[0106] In the formula: v B =2nv A ω / c is the Brillouin frequency shift, approximately 16 GHz, where n is the refractive index in the fiber, taking a value of 1.45, and v... A The velocity of sound is taken as 5.9 × 10⁻⁶. 3 m / s, ω is the laser angular frequency, taken as 1.7534 × 10⁻⁶ m / s. 15 rad / s, where c is the speed of light in vacuum 3 × 10⁻⁶ rad / s. 8 m / s. k is the Boltzmann constant, taken as 1.38 × 10⁻⁶. -23 m 2 Kgs -2 K -1 T is the absolute temperature, taken as 293 K, and the phonon decay rate Γ = 2π / 17.5 ns. -1 = 2π × 57.1 × 10 6 s -1 v0 is the pump wave frequency, approximately 3.07 × 10⁻⁶. 14 Hz.

[0107] P th and The threshold powers in the system with and without phase modulation are obtained using equation (1), and the SBS threshold enhancement factor can be used. To obtain.

[0108] 2) Encoding PRBS signals:

[0109] The characteristics of the PRBS waveform are controlled by a sequence:

[0110] {a j}={a0,a1········a N-1} (2)

[0111] Where: {a j} is a variable with a period of N, whose discrete values ​​are -1 (if the bit is symbol 0) and +1 (if the bit is symbol 1). When the code generator has a code pattern of n, the period N = 2. n -1. If an element is randomly selected from the sequence, the probability of a different value becomes P. r+1 = (1 + 1 / N) / 2 and P r-1 = (1 - 1 / N) / 2, where P r-1 +P r+1 =1. To form a continuous waveform in the sequence, a continuously repeating sequence x(t) and a single period x N (t) can be written as:

[0112]

[0113] Where: T is the modulation time of a single bit (equal to the modulation frequency f) cr The reciprocal of (), and * denotes convolution. Assume the basic shape p(t) of a single symbol is the same for both types of symbols. They are typically a rectangular function, constant for the entire duration T, otherwise 0, and can therefore be written as:

[0114]

[0115] Then the intermediate non-periodic signal x N (t) can be obtained by using a time interval of T. N =NT comb functions are used to expand in time. This operation can be represented as convolution, thus producing periodic sequences.

[0116]

[0117] Where: j, k∈Z are used to specify discrete instants in time.

[0118] 3) Based on the phase modulation of the PRBS signal in a high-power, narrow-linewidth fiber laser, the power spectral density and modulation frequency f are analyzed.cr Code type n and modulation amplitude k p Relationship:

[0119] The linearly polarized single-frequency laser electric field in the scheme can be expressed as:

[0120]

[0121] in: The amplitude is constant in the laser field. For simplicity, this amplitude is ignored when calculating the power spectral density, and the spectral shift carrier frequency ωc is centered at ω = 0. According to the expression given in equation (5), the MLS coding phase φ(t) can be expressed as:

[0122]

[0123] Where: k p It is the inter-peak phase modulation amplitude, which we define as the sum of the inter-peak modulation voltage and the half-wave voltage V of the phase modulator. π The laser electric field E(t) is a π-fold increase. Here, the laser electric field E(t) is an infinitely repeating periodic sequence with a period of N, taking two different values: exp(ikp / 2) and exp(-ikp / 2).

[0124] The power spectral density (PSD) of the laser field can be given by the Fourier transform of the PACF according to the Wiener-Chinchin theorem, i.e.

[0125]

[0126] This refers to the power spectral density and the modulation frequency f. cr Code type n and modulation amplitude k p The relationship expression is as follows: The threshold enhancement factor is represented by the ratio of the intensity of the spectral line that first reaches the SBS threshold to the intensity of the unmodulated spectral line, and its relationship with the modulation depth is plotted as a reference standard.

[0127] 4) Plot the power spectral density function after phase modulation when the modulation depth is fixed (e.g., ...). Figure 2 As shown):

[0128] When the code pattern n = 5, 7, 9, 11 is selected, the modulation frequency is fixed at 10 GHz, and the modulation depth is π, the spectral line spacing Δf cr =1 / NT=f cr / N are 322.58MHz, 158.73MHz, 78.74MHz, and 39.21MHz, respectively. The power spectral density after phase modulation is given by equation (9), that is:

[0129]

[0130] The calculated power spectral density function is as follows: Figure 1 As shown, the power spectral density shape after PRBS phase modulation under different code patterns is determined by sinc 2 Envelope expanded.

[0131] 5) In normalized power spectral density, the traditional second-moment method for calculating the equivalent spectral width is affected by noise at the bottom of the spectral lines. To avoid this effect, this invention employs a novel method for calculating spectral width. It has been observed that bottom noise is negligible above approximately 4% of the spectral peak. Therefore, 4% of the peak value is used as the spectral density threshold, and all points below this threshold are removed—that is, points in the matrix below 4% of the peak value are set to 0. Only the signal intensity remains, and the final equivalent spectral width is the full width of the remaining signal. This approach avoids discarding low spectral densities that do not affect the SBS process while allowing direct calculation of the net width of the remaining spectral components.

[0132] 6) Calculate the system threshold enhancement factor according to the relationship between the SBS threshold enhancement factor and the effective spectral width in formula (10):

[0133]

[0134] Where: Δν m and Δν B These represent the effective spectral width and Brillouin linewidth (~35MHz), respectively. (Plotted) The relationship between modulation depth and threshold enhancement factor is compared. The correlation between the threshold enhancement factor and the modulation depth is compared. A strong correlation indicates that the effective spectral width can be used to approximate the threshold enhancement factor. Thus, we obtain a new method for measuring the threshold enhancement factor using spectral width, which allows for rapid assessment of the feasibility of amplification path design in simulations.

[0135] In the several embodiments provided by this invention, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative. For instance, the division of modules, units, or units is merely a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units, modules, or components may be combined or integrated into another device, or some features may be ignored or not executed.

[0136] The units may or may not be physically separate. The components shown as units can be one or more physical units, meaning they can be located in one place or distributed in multiple different locations. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0137] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0138] In particular, according to embodiments disclosed in this invention, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments of this disclosure include a computer program product comprising a computer program carried on a computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via a communication component, and / or installed from a removable medium. When the computer program is executed by a central processing unit (CPU), it performs the functions defined in the methods of this invention. It should be noted that the computer-readable medium described above in this invention can be a computer-readable signal medium or a computer-readable storage medium, or any combination of the two. The computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof.

[0139] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0140] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions within the technical scope disclosed in the present invention should be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for measuring the magnitude of a threshold enhancement factor using the effective spectral width, characterized in that, Includes the following steps: The characteristics of the PRBS waveform are controlled by a sequence: ； （2）； Where: {a j } is a variable with a period of N, whose discrete values ​​are -1 and +1; when the code pattern generator has a code pattern of n, the period N=2. n -1; If an element is randomly selected from the sequence, the probability of a different value becomes P. r+1 = (1 + 1 / N) / 2 and P r-1 = (1 - 1 / N) / 2, where P r-1 +P r+1 =1; In order to form a continuous waveform in the sequence, the continuously repeating sequence x(t) and the single period x N (t) is written as: ； （3）； Where: T is the modulation time of a single bit, and * denotes convolution; assuming the basic shape p(t) of a single symbol is the same for both types of symbols, it is written as: ；（4）； Then the intermediate non-periodic signal x N (t) by using a time interval of T N =NT uses a comb function to expand in time, represented as a convolution, thus producing a periodic sequence: ；（5）； Where: j, k∈Z are used to specify discrete instants in time; Analysis of power spectral density and modulation frequency f based on PRBS signal phase modulation onto a modulated fiber laser. cr Code type n and modulation amplitude k p Relationship: The electric field of a linearly polarized single-frequency laser can be expressed as: ； （6）； in: The amplitude is constant in the laser field and is ignored when calculating the power spectral density. The spectral shift carrier frequency ωc is centered at ω=0. According to the expression given in equation (5), the MLS coding phase ϕ(t) is expressed as: ；（7）； Where: k p It is the inter-peak phase modulation amplitude, defined as the inter-peak modulation voltage and the half-wave voltage V of the phase modulator. π π times; here, the laser electric field E(t) is an infinitely repeating periodic sequence with a period of N, taking two different values ​​exp(ikp / 2) and exp(−ikp / 2); The power spectral density (PSD) of the laser field is given by the Wiener-Chinchin theorem via the Fourier transform of the PACF: ；（8）； It is the power spectral density and modulation frequency f cr Code type n and modulation amplitude k p Relational expressions; The phase-modulated power spectral density function is given by equation (9): ；（9）； Where: ∆f cr Represents spectral line spacing; The calculated power spectral density function after phase modulation, under different code types, shows that the shape of the power spectral density after PRBS phase modulation is determined by sinc. 2 Envelope unfurling; In the normalized phase-modulated power spectral density function, the equivalent spectral width is calculated using the traditional second-order moment method to obtain the matrix; The effective spectral width is obtained based on the matrix and the spectral density threshold; The phase-modulated power spectral density function is denoised to obtain the effective spectral width. The threshold enhancement factor is measured based on the effective spectral width.

2. The method for measuring the threshold enhancement factor using the effective spectral width according to claim 1, characterized in that: The fiber laser is a high-power, narrow-linewidth fiber laser.

3. The method for measuring the threshold enhancement factor using the effective spectral width according to claim 1, characterized in that: The spectral density threshold is 4% of the spectral peak value.

4. The method for measuring the threshold enhancement factor using the effective spectral width according to claim 3, characterized in that, The effective spectral width is obtained based on the matrix and the spectral density threshold, specifically including the following steps: Set all points in the matrix below 4% of the spectral peak value to 0 to obtain the effective spectral width.

5. A system for measuring the magnitude of a threshold enhancement factor using the effective spectral width, for implementing the method for measuring the magnitude of a threshold enhancement factor using the effective spectral width as described in any one of claims 1-4, characterized in that, include: The encoding module is used to encode PRBS signals; The phase modulation module is used to modulate the fiber laser based on the phase of the PRBS signal at a preset modulation depth to obtain the phase-modulated power spectral density function. The denoising module is used to denoise the phase-modulated power spectral density function to obtain the effective spectral width. The threshold enhancement factor size measurement module is used to measure the size of the threshold enhancement factor based on the effective spectral width.

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