A parameter matching and optimization method based on saturable absorber self-induced grating

Abstract

The present application relates to a kind of parameter matching and optimization method based on saturable absorber self-induced grating, comprising: step 1: numerical simulation;Small signal absorption coefficient and grating length are scanned, corresponding self-induced grating reflection spectrum is calculated, and the key performance indicators of self-induced grating reflection spectrum are extracted, to build the influence relationship diagram between grating performance;Through the influence relationship diagram, the parameter extreme value band that meets the target performance requirement is directly determined;Step 2: I scanning;The transmittance under small signal condition is calculated, and the equivalent small signal absorption coefficient of nonlinear absorber is determined;Step 3: determine parameter search range;According to engineering constraint, the feasible small signal absorption coefficient and grating length interval are determined;Step 4: joint screening grating length;According to the constraint of each performance index, the feasible interval of grating length is obtained by taking intersection;Step 5: parameter matching is completed.The present application improves design efficiency and reduces experimental debugging cost.

Description

Technical Field

[0001] This invention belongs to the field of fiber laser design and nonlinear optical parameter optimization technology, specifically relating to a parameter matching and optimization method based on a saturable absorber self-induced grating. Background Technology

[0002] With the development of fiber laser technology, single-frequency fiber lasers, due to their narrow linewidth, high coherence, and good stability, have significant application value in precision measurement, coherent communication, and fiber optic sensing. To obtain stable single-frequency output, it is usually necessary to introduce an effective longitudinal mode selection and feedback mechanism within the laser cavity.

[0003] On the other hand, nonlinear optical effects are widespread in fiber lasers, especially the nonlinear absorption effect based on saturable absorbers, which can form self-induced periodic optical modulation structures, i.e., self-induced gratings, under certain conditions. These gratings do not require external writing and have advantages such as simple structure and strong tunability, showing potential application prospects in fiber laser mode selection and feedback control.

[0004] However, existing research largely focuses on the physical mechanisms of self-induced gratings or experimental and numerical analyses under single-parameter conditions. There is a lack of systematic design methods for the synergistic matching relationship between grating structural parameters (such as grating length) and saturable absorber material parameters (such as saturation power and small-signal absorption coefficient). In practical design processes, relevant parameters often rely on experience or repeated experiments for adjustment, resulting in a degree of uncertainty and making it difficult to quickly obtain parameter combinations that meet target performance under multi-parameter coupling conditions.

[0005] Therefore, there is an urgent need for a method that can comprehensively consider the matching relationship between grating parameters and nonlinear material parameters and be used to guide the design of self-induced grating performance, so as to improve the design efficiency and repeatability of single-frequency fiber lasers. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a parameter matching and optimization method based on a saturable absorber self-induced grating; This invention establishes an equivalent model that includes grating structure parameters and nonlinear absorption characteristics based on the working mechanism of a single-frequency fiber laser.

[0007] When a strong pump light propagates in an optical fiber, it interacts with the medium through nonlinear effects (such as the Kerr effect and photoinduced absorption changes), forming a periodic refractive index modulation within the fiber, thus constituting a self-induced grating. When a weak probe light propagates within the self-induced grating, its reflectivity varies with frequency, forming a reflection spectrum. The bandwidth, peak value, and modulation depth of the reflection spectrum are related to the grating length. saturation power of nonlinear absorbers and small signal absorption coefficient These parameters are closely related; in this invention, software based on the above equivalent model can calculate and analyze the key performance indicators of the self-induced grating to evaluate the matching relationship between grating performance and parameters. These performance indicators may include, but are not limited to: 3 dB bandwidth, maximum reflectivity, etc. and reflection modulation depth .

[0008] In a laser cavity, the saturable absorption effect of a nonlinear absorber only occurs when the input power is high. Reaching or exceeding the saturation power of the material The effects are only clearly visible under certain conditions. When the input power is high enough to saturate the material, the location of the system's response extrema is primarily determined by the grating length. With small signal absorption coefficient The impact, and on The specific numerical sensitivity is relatively small. Therefore, in parameter matching analysis, it can be... The conditions are considered met, thus the focus of the analysis is placed on... and The combined effect on the performance of self-induced gratings is used to determine the combination of key parameters and optimize the reflection spectrum characteristics of the grating.

[0009] Terminology Explanation: 1. Small signal absorption coefficient This refers to the linear absorption capacity of an absorber for a light signal when the incident light intensity is much lower than the material's saturation intensity; the unit is m. -1 Its physical meaning is the exponential decay rate of light intensity per unit propagation length. For a length of... The absorber has a low power transmittance. Satisfying the relation This parameter characterizes the intrinsic absorption capacity of a material when no saturation effect occurs.

[0010] 2. A nonlinear absorber is an optical material whose absorption coefficient changes with the intensity of incident light. It exhibits high absorption at low incident light intensities; as the light intensity increases and approaches or exceeds the saturation intensity, the absorption coefficient decreases. Its absorption characteristics can be expressed as follows: ,in The saturation strength is defined as [value]. The nonlinear absorber described in this invention primarily refers to materials with a saturable absorption effect.

[0011] The technical solution of this invention is as follows: A parameter matching and optimization method based on a saturable absorber self-induced grating, applied to a single-frequency fiber laser, includes: Step 1: Numerical simulation; Small signal absorption coefficient within a predetermined parameter range With grating length A scan is performed, the corresponding self-induced grating reflection spectrum is calculated, and key performance indicators such as 3 dB bandwidth, maximum reflectivity, and reflection modulation depth of the self-induced grating reflection spectrum are extracted to construct... A graph showing the relationship between the parameters and grating performance; this graph visually identifies the extreme value bands of parameters that meet the target performance requirements. The predetermined parameter refers to the small signal transmittance. , The value range is 0.1–0.9.

[0012] The grating length L refers to the equivalent length of the saturable absorber that forms a self-induced grating effect within the laser cavity; Step 2: I scan; Under the condition that the nonlinear absorber enters the saturation operating range, the transmittance of the nonlinear absorber as a function of incident light intensity is obtained, and the transmittance under small signal conditions is obtained by fitting the response curve. Determine the equivalent small-signal absorption coefficient of the nonlinear absorber. ; Step 3: Determine the parameter search range; Determine feasible small-signal absorption coefficients based on engineering constraints. and grating length range; Step 4: Jointly screen grating lengths; Based on the constraints of each performance index on L, the intersection is taken to obtain the feasible range of grating length; each performance index includes 3dB bandwidth, maximum reflectivity and reflection modulation depth; Step 5: Parameter matching complete; The parameters of the self-induced grating are matched to achieve the coordinated optimization of the nonlinear absorber and the grating length.

[0013] According to a preferred embodiment of the present invention, step 1, calculating the corresponding self-induced grating reflection spectrum, includes: Inside the saturable absorber, the master mode probe field The probe field propagates along the fiber segment, and its evolution is described by coupled differential equations in the forward and reverse propagation directions; the complex amplitudes of the probe field in the forward and reverse propagation directions are respectively... and The propagation equation is: ; ; ; ; Wherein, coupling coefficient This indicates the self-absorption modulation effect of the master mode on the probe field. This indicates the coupling strength between forward and reverse fields; The effective modulus radius of the material, The saturation power of the nonlinear material is given by ; z represents the spatial coordinates along the length of the grating, with a value range of . And define the direction of light propagation along the positive z direction as the +z direction; Indicates the amplitude of the pump light field; and These represent the signal photoelectric field envelopes propagating along the +z and -z directions, respectively. The instantaneous absorption coefficient follows the standard saturable absorption model, as shown below: ; in, The small-signal absorption coefficient is given in the standard saturable absorption model. The saturation behavior is determined by the coupling strength parameter. Equivalent representation; The incident light intensity; Saturated light intensity; In order to increase light intensity Instantaneous absorption coefficient under action; The forward and reverse fields of the probe light were obtained through numerical iteration. and The spatial distribution of the grating is defined based on the relationship between the input optical power and the output reflected optical power, and the expression is: ; in, This represents the frequency offset between the probe field frequency and the dominant mode light frequency. By scanning different frequency offsets, the reflection spectrum of the grating structure can be obtained. Indicates frequency offset The self-induced grating reflectivity is as follows; This represents the electric field reflected by the probe field propagating in the reverse direction at z = 0; This represents the electric field of the positive probe incident into the grating; Based on the established coupled-wave theoretical model, relevant parameter ranges are defined, including the small-signal transmittance. The theoretical predetermined range is set at 0.1–0.9; Subsequently, the grating length was... With small signal absorption coefficient Perform a parametric scan; among which, Take a depth of 0.5–2.5 m. Take 0–10 m -1 ; Parametric scanning refers to the scanning of the grating length. With small signal absorption coefficient Discrete transformations are performed, and the coupled wave equation, i.e. the propagation equation, is solved for each set of parameter combinations to obtain the corresponding self-induced grating reflection spectrum.

[0014] According to a preferred embodiment of the present invention, in step 1, The relationship between the influence on grating performance and other parameters was obtained by solving the coupled-wave equations and performing a parametric scan; the specific process is as follows: After obtaining the reflection spectrum of the self-induced grating, key performance indicators are extracted from it, including: maximum reflectivity. Reflection modulation depth 3 dB bandwidth; Subsequently, and Using the key performance indicators as function values ​​and the x and y axes respectively, we obtain the following results. The relationship between the influence of the grating spectral properties and the spectral characteristics is shown in the figure.

[0015] According to a preferred embodiment of the present invention, in step 1, by A graph showing the relationship between the parameters and grating performance visually identifies the extreme value bands of parameters that meet the target performance requirements; including: The extreme value band of a parameter refers to the value of the small-signal absorption coefficient. With grating length In the constructed two-dimensional parameter space, what maximizes the reflectivity? Reflection modulation depth And the parameter combination region where the 3 dB bandwidth spectral performance index is at a relatively good level.

[0016] Further preferred, or superior level, refers to: maximum reflectivity Reflection modulation depth and 3 dB bandwidth .

[0017] According to a preferred embodiment of the present invention, in step 2, the response curve is fitted to obtain the transmittance under small signal conditions. ;include: When fitting the response curve, the nonlinear transmission characteristics of the saturable absorber are described by the following formula: ; in, This represents the saturation absorption amplitude. For saturation intensity, This refers to unsaturated transmittance. This indicates that the saturable absorber is in operation when the incident light intensity is... Instantaneous transmittance at time; Small signal transmittance Transmittance is defined as the transmittance when the incident light intensity approaches zero. .

[0018] According to a preferred embodiment of the present invention, in step 3, the grating length The value range is set to 0.5–2.5 m.

[0019] According to a preferred embodiment of the present invention, graphene, carbon nanotubes, or transition metal chalcogenides are selected as nonlinear absorbers.

[0020] The beneficial effects of this invention are as follows: 1. This invention proposes a method based on small signal absorption coefficient. A self-induced grating design method that matches the grating length L parameter. This is achieved through analysis... and The influence of grating spectral performance on the parameter matching relationship was investigated to achieve the maximum reflectivity. Reflection modulation depth The quantitative analysis of key performance parameters such as 3 dB bandwidth provides a clear theoretical basis for grating structure design.

[0021] 2. Obtained through parametric scanning The distribution pattern of grating performance in the parameter space is studied, and the parameter matching range that meets the target spectral performance requirements is determined accordingly. This enables synergistic optimization between nonlinear absorber parameters and grating length, avoiding performance trade-offs caused by adjusting a single parameter.

[0022] 3. The method proposed in this invention can directly determine a reasonable parameter range during the system design stage, providing an intuitive and quantifiable design basis for the design of self-induced grating structures in single-frequency fiber lasers or other optical systems, thereby improving system design efficiency and reducing experimental debugging costs.

[0023] 4. The method of the present invention has good versatility and can be applied to various types of nonlinear absorbing materials and different optical fiber structure systems. It does not depend on specific materials or device structures and has strong engineering applicability. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of the equivalent model of the grating; Figure 2 To build The relationship between the effect and grating performance is shown in the diagram: Figure 3 Schematic diagrams of different structural forms of self-inducing gratings and their simulation equivalent models; Figure 4 This is a typical reflectance spectrum of a self-induced grating. Detailed Implementation

[0025] The present invention will be further defined below with reference to the accompanying drawings and embodiments, but is not limited thereto.

[0026] Example 1 This invention, based on the working mechanism of a single-frequency fiber laser, establishes an equivalent grating model that includes grating structure parameters and nonlinear absorption characteristics, such as... Figure 1 As shown.

[0027] A parameter matching and optimization method based on a self-induced grating of a saturable absorber (nonlinear absorber), applied to a single-frequency fiber laser, includes: Step 1: Numerical simulation; Small signal absorption coefficient within a predetermined parameter range With grating length A scan is performed, the corresponding self-induced grating reflection spectrum is calculated, and key performance indicators such as 3 dB bandwidth, maximum reflectivity, and reflection modulation depth of the self-induced grating reflection spectrum are extracted to construct... A graph showing the relationship between the grating and its performance is generated. This graph allows for a visual identification of the extreme value bands of parameters that meet the target performance requirements, thus providing a quantitative basis for selecting the grating length.

[0028] To cover almost all practically available two-dimensional materials or saturable absorbers, low signal transmittance is required. The theoretical range can be set to 0.1–0.9, and the transmittance of materials in actual engineering generally falls within this range. The lower limit of the equivalent grating length is determined by the space required for component connection, and is usually not less than 0.25 m; regarding the upper limit, on the one hand, simulation results show that when the grating length reaches 2.5 m, the system response has reached an extreme value, and further increasing the length is not very meaningful for calculation; on the other hand, an excessively long grating is not conducive to maintaining the advantages of the equivalent grating. Therefore, combining the above upper and lower limits, the small signal absorption coefficient is calculated by formula. It can be guaranteed Parameter matching analysis with grating length L has universal applicability. The predetermined parameter refers to small signal transmittance. , The value range is 0.1–0.9.

[0029] The grating length L is the length of the grating, not the length of the laser cavity. Specifically, the grating length L is not the physical length of a single device; rather, it refers to the equivalent operational length of the saturable absorber within the laser cavity, forming a self-induced grating effect. This length is determined by the optical propagation path formed by the connection of related devices within the cavity, i.e., the overall optical path length from the entry of light into the nonlinear absorption region to the completion of one effective interference modulation. For example, in a typical fiber optic structure, the effective grating length can be constituted by the fiber path formed by the connection of devices such as circulators, couplers, fiber segments, and the saturable absorber; therefore, this length is usually the sum of the lengths of several fiber segments. Figure 3 Two common structural diagrams of self-induced gratings and their corresponding equivalent model diagrams are given, with the definition of the equivalent grating length L marked in both cases to illustrate how the effective grating length is determined in different structures. Although the specific structural forms may differ, the definition of the equivalent grating length L remains consistent. Figure 3 (a) is a schematic diagram of a self-induced grating structure based on a fiber optic ring mirror structure; Figure 3 (b) is a schematic diagram of a self-induced grating structure based on a circulator-fiber Bragg grating structure; Figure 3 (c) in the figure represents the equivalent simulation model of the fiber optic ring mirror structure; Figure 3 (d) in the figure represents the simulation equivalent model of the circulator-fiber Bragg grating structure;

[0030] The two cavity types mentioned above differ in their input methods and feedback paths, but their physical essence lies in forming a stable standing wave field in an unpumped nonlinear medium through actual or equivalent reflection mechanisms, thereby inducing an equivalent grating with frequency-selective characteristics. Therefore, from a theoretical modeling perspective, these two types of cavity types can be described within a unified coupled-wave theory framework.

[0031] Step 2: I scan; To achieve parameter matching between the laser cavity and the nonlinear absorber, the transmittance of the nonlinear absorber as a function of incident light intensity was obtained under the condition that the nonlinear absorber is in its saturation operating range. This response curve was then fitted to obtain the transmittance under small-signal conditions. Determine the equivalent small-signal absorption coefficient of the nonlinear absorber. ; It comprehensively reflects the material properties of the nonlinear absorber and the structure of the optical fiber it carries, including but not limited to the structural properties of tapered optical fibers, D-type optical fibers, etc. Step 3: Determine the parameter search range; Determine feasible small-signal absorption coefficients based on engineering constraints (such as fiber length, cavity space limitations, etc.). and grating length range; for example, the minimum length limit of an optical fiber embedded cavity structure will correspond to The upper limit.

[0032] Step 4: Jointly screen grating lengths; Based on the constraints of various performance indicators on L, the intersection is taken to obtain the feasible range of grating length; if necessary, further fine-tuning can be performed within the feasible range using quantitative data from the figure to meet the target performance requirements. The performance indicators include 3 dB bandwidth, maximum reflectivity, and reflection modulation depth.

[0033] Based on various performance indicators, the grating length The constraints can be used to further determine the feasible range of grating length. The performance indicators mainly include maximum reflectivity. Reflection modulation depth And a 3 dB bandwidth. By analyzing the parameter scanning results, the grating length range corresponding to each performance index meeting the target requirements can be obtained. For example, while ensuring... Not lower than the set threshold While maintaining sufficient modulation depth and ensuring the 3 dB bandwidth meets frequency selectivity requirements, the corresponding grating length ranges can be determined. Then, by taking the intersection of these ranges, a feasible grating length range that simultaneously satisfies multiple performance requirements can be obtained. If necessary, the parameters can be further fine-tuned within this feasible range using quantitative distribution data from the influence relationship diagram to meet the performance requirements of specific application scenarios.

[0034] Step 5: Parameter matching complete; The above steps complete the parameter matching of the self-induced grating, achieving synergistic optimization of the nonlinear absorber and grating length. This provides a quantitative design basis for single-frequency fiber lasers or other optical systems.

[0035] The purpose of this method is to determine the nonlinear absorption coefficient. The appropriate matching relationship between the grating length L and the maximum reflectivity was analyzed. Reflection modulation depth By studying the relationship between spectral performance indicators such as 3 dB bandwidth and parameter variations, a feasible range of grating lengths that simultaneously meet the above performance requirements can be determined.

[0036] In parameter design, determining this feasible range indicates that a reasonable matching relationship has been established between the nonlinear absorber parameters and the grating length. Since practical optical system designs typically do not require unique parameter values, but rather can achieve the target performance within a certain range, obtaining this feasible range completes the parameter matching. In specific applications, specific parameters can be selected within this range according to actual needs.

[0037] Example 2 The parameter matching and optimization method based on a self-induced grating of a saturable absorber (nonlinear absorber) as described in Example 1 differs in that: Step 1 involves calculating the corresponding self-induced grating reflection spectrum, including: Inside the saturable absorber, the master mode probe field The probe field propagates along the fiber segment, and its evolution is described by coupled differential equations in the forward and reverse propagation directions; the complex amplitudes of the probe field in the forward and reverse propagation directions are respectively... and The propagation equation is: ; ; ; ; Wherein, coupling coefficient This indicates the self-absorption modulation effect of the master mode on the probe field. This indicates the coupling strength between forward and reverse fields; The effective modulus radius of the material, The saturation power of the nonlinear material is given by ; z represents the spatial coordinates along the length of the grating, with a value range of . And define the direction of light propagation along the positive z direction as the +z direction; Indicates the amplitude of the pump light field; and These represent the signal photoelectric field envelopes propagating along the +z and -z directions, respectively. The instantaneous absorption coefficient follows the standard saturable absorption model, as shown below: ; in, The small-signal absorption coefficient is given in the standard saturable absorption model. The saturation behavior is determined by the coupling strength parameter. Equivalent representation; The incident light intensity; The saturation light intensity; In order to increase light intensity Instantaneous absorption coefficient under action; In practical applications, the relevant parameters in the above model (such as the effective modulus radius) saturation power and small signal absorption coefficient The parameters (e.g., nonlinear material properties, fiber structure parameters, and specific laser cavity implementation) can be set or measured based on the nonlinear material properties used, and then substituted into the model for numerical calculation. In the specific numerical calculation process, to facilitate analysis and reduce the influence of irrelevant parameters on the results, some parameters unrelated to material properties are fixed. For example, the central reflectivity of currently commercial fiber Bragg gratings (FBGs) is typically about 0.5 (±3%), so a typical value of 0.5 is used in the model calculation. Simultaneously, for single-mode fiber structures, the effective mode radius... Primarily determined by the fiber structure, it remains essentially constant under a given fiber type, therefore a fixed value is used in the calculation.

[0038] By solving the equations, the principal mode field is obtained. After determining the steady-state spatial distribution, the coupling coefficient varying along the fiber axis can be further calculated. and The propagation process of the probe light in a saturable absorbing medium is numerically solved by substituting it into the coupled propagation equation of the probe field.

[0039] During the calculation, assume the probe light originates from one end of the grating. The initial conditions for the forward propagation field at the incident point are: When the probe light propagates to the other end of the grating At that time, the reflectivity at the end face Under the influence of , a back-propagating light field is generated, and its boundary conditions are as follows: Because the probe light is only injected in a single pass and... A single reflection occurs at the point where the wave originates, but no stable standing wave forms inside the structure. Therefore, its propagation is determined solely by the reflectivity at the right end. It is determined by the structure of the left end, and is unrelated to the structural form of the left end.

[0040] Under the above boundary conditions, the forward and reverse fields of the probe light are obtained through numerical iteration. and The spatial distribution of the grating is defined based on the relationship between the input optical power and the output reflected optical power, and the expression is: ; in, This represents the frequency offset between the probe field frequency and the dominant mode light frequency. By scanning different frequency offsets, the reflection spectrum of the grating structure can be obtained. Indicates frequency offset The self-induced grating reflectivity; This represents the electric field reflected by the probe field propagating in the reverse direction at z = 0; This represents the electric field of the positive probe incident into the grating; Figure 4A typical reflection spectrum of a self-induced grating is given. Figure 4 In the diagram, the horizontal axis represents FrequencyOffset (MHz), which is the frequency offset. The vertical axis represents Reflectance (au), which is the reflectance of the self-induced grating. Wherein, a 3 dB bandwidth represents a decrease in reflectivity to half of its maximum reflectivity (i.e., The corresponding frequency range; maximum reflectivity. Reflectance at the peak of the reflection spectrum; reflection modulation depth This represents the difference between the maximum reflectance and the background reflectance in the reflection spectrum, used to characterize the reflection modulation capability of the grating. These three parameters allow for a quantitative evaluation of the grating's spectral characteristics. No further measurement of other parameters is necessary.

[0041] Based on the established coupled-wave theoretical model, relevant parameter ranges are defined, including the small-signal transmittance. The theoretical predetermined range is set at 0.1–0.9; Coupled-wave theory is a theoretical method used to describe the interaction and energy exchange between light waves propagating in different directions in spatially modulated or nonlinear media. In this work, the optical field can be represented as the superposition of forward and backward waves propagating along the grating axis, and the interaction between them is characterized by coupled differential equations. Based on this, by introducing an intensity-dependent absorption effect caused by saturable absorption, the coupling coefficient is made nonlinear, thereby establishing a coupled-wave theoretical model and equations suitable for the system of this invention.

[0042] This range covers the transmission characteristics of most practically usable two-dimensional materials or saturable absorbers. In actual engineering, the transmittance of materials usually falls within this range.

[0043] For structural parameters that are independent of materials, typical values ​​are used in the calculations. For example, the central reflectivity of currently commercial fiber Bragg gratings (FBGs) is typically around 0.5 (±3%), so a typical value of 0.5 is used in the model calculations. Meanwhile, for single-mode fiber structures, the effective mode radius is... Primarily determined by the fiber structure, it remains essentially constant under a given fiber type, therefore a fixed value is used in the calculation.

[0044] Subsequently, the grating length was... With small signal absorption coefficient Perform a parametric scan; among which, Take a depth of 0.5–2.5 m. Take 0–10 m -1 ; Parametric scanning refers to adjusting the grating length within the aforementioned parameter range. With small signal absorption coefficient Discrete transformations are performed, and the coupled-wave equation (propagation equation) is solved for each set of parameters to obtain the corresponding self-induced grating reflection spectrum. In the specific calculation process, values ​​are taken at equal intervals within each parameter range. and Each set of 50 discrete points is selected, thus forming 50 × 50 sets of parameter combinations.

[0045] In step 1, The relationship between the influence on grating performance and other parameters was obtained by solving the coupled-wave equations and performing a parametric scan; the specific process is as follows: After obtaining the reflection spectrum of the self-induced grating, key performance indicators are extracted from it, including: maximum reflectivity. Reflection modulation depth 3 dB bandwidth; Subsequently, and Using the key performance indicators as function values ​​and the x and y axes respectively, we obtain the following results. A graph showing the relationship between the parameters and the grating's spectral properties. This graph characterizes the combined effect of the two parameters on the grating's performance.

[0046] Figure 2 for Relationship between grating performance indicators: Figure 2 In the middle, (a) is A schematic diagram illustrating the impact of the equivalent grating's 3 dB bandwidth; (b) is... For equivalent grating Schematic diagram of the impact; (c) is For the equivalent grating reflection modulation depth Impact For the maximum reflectivity of the equivalent grating A diagram illustrating the impact.

[0047] In step 1, through A graph showing the relationship between the parameters and grating performance visually identifies the extreme value bands of parameters that meet the target performance requirements; including: By analyzing the influence relationship diagram, the parameter value range that meets the target spectral performance requirements can be determined. The parameter extremum band refers to the range of small-signal absorption coefficients. With grating length In the constructed two-dimensional parameter space, to maximize reflectivity Reflection modulation depth And the parameter combination region where the 3 dB bandwidth spectral performance index is at a relatively good level.

[0048] Small signal absorption coefficient In the two-dimensional parameter space formed by the grating length L, the region of parameter combinations that simultaneously satisfy the above conditions is defined as the parameter extremum zone.

[0049] Since different application scenarios have different focuses on various performance indicators, the combination of parameters that meets the performance requirements is usually not a single value point, but rather forms a certain range within the parameter space. Within this range, the various spectral performance indicators of the equivalent grating can maintain a relatively balanced performance, thereby avoiding a situation where an improvement in one performance leads to a significant degradation in other performances.

[0050] exist In the graph showing the relationship between performance parameters and grating performance, color mapping represents the numerical values ​​of each performance parameter. Red and blue correspond to higher and lower values ​​of the performance parameters, respectively, while the white area represents the intermediate transition region, corresponding to the boundary areas where performance parameters change significantly. Generally, a smaller 3 dB bandwidth is more beneficial to the frequency selectivity of the grating; therefore, the blue area corresponds to the region with better performance. and A larger value is more beneficial to the grating's reflection modulation capability; the red area corresponds to the region with superior performance. By observing the spatial overlap of the superior performance regions in the parameter distribution diagrams, the small-signal absorption coefficient can be determined. With equivalent grating length The optimal range for each performance indicator does not completely overlap in the parameter space. Therefore, during matching, the spatial overlap area of ​​each parameter should be comprehensively considered, and a compromise should be made to ensure the overall balance of grating performance. In practice, this matching range can be determined by directly referring to the drawn graph, thereby achieving fast, intuitive, and repeatable parameter selection.

[0051] Determining the target grating length Then, according to the above The relationship diagram should be selected based on the corresponding small-signal absorption coefficient. This leads to the design or selection of nonlinear absorber structures. Specifically, the small-signal transmittance of the absorbing material can be altered by adjusting its thickness, concentration, or effective action length. In order to achieve the goal Value. For example, in the realization of two-dimensional material saturable absorbers, the small signal transmittance can be adjusted by changing the number of material layers or the deposition coverage area, thereby obtaining the desired small signal absorption coefficient.

[0052] By selecting those that meet this condition and By combining parameters, a reasonable match can be achieved between the nonlinear absorber parameters and the grating length, thereby realizing the synergistic optimization of the cavity structure and the absorber structure.

[0053] Based on the relationship diagram obtained from the parameter scanning results, the optimal level refers to: maximum reflectivity. Reflection modulation depth and 3 dB bandwidth .

[0054] In step 2, the response curve is fitted to obtain the transmittance under small signal conditions. ;include: When fitting the response curve, the nonlinear transmission characteristics of the saturable absorber are described by the following formula: ; in, This represents the saturation absorption amplitude. For saturation intensity, This refers to unsaturated transmittance. This indicates that the saturable absorber is in operation when the incident light intensity is... Instantaneous transmittance at a given time; that is, the normalized transmittance of a material to incident light, reflecting its nonlinear transmission characteristics as light intensity changes.

[0055] Small signal transmittance Transmittance is defined as the transmittance when the incident light intensity approaches zero. .

[0056] In step 3, in actual engineering implementation, the grating length The effective length of the grating is limited by the fiber optic structure and the way the devices are connected. Since nonlinear absorbers are typically embedded in the system structure via fiber optic devices, their effective grating length is determined by the total optical path length of the fiber segment within the cavity and the connected related devices; therefore, there exists a minimum achievable length. For example, in a typical fiber optic structure, the minimum fiber length after device connection is usually not less than approximately 0.5m. Therefore, the grating length... The value range is set to 0.5–2.5 m.

[0057] The determination of the upper limit of approximately 2.5 m is mainly based on a comprehensive consideration of simulation results and engineering implementation: by scanning the parameters of different grating lengths, it can be found that when Maximum reflectivity when increased to approximately 2.5 m Reflection modulation depth Key spectral performance parameters, such as the 3 dB bandwidth, have essentially reached their extreme values ​​or tended to stabilize, and further increasing the grating length has limited effect on performance improvement. Furthermore, excessively long fiber paths increase system loss and structural complexity, which is detrimental to practical engineering implementation. Therefore, the upper limit of the grating length is set at approximately 2.5 m in the parameter analysis.

[0058] Graphene, carbon nanotubes, or transition metal chalcogenides were selected as nonlinear absorbers.

[0059] In this embodiment, graphdiyne film is selected as the nonlinear absorber only to illustrate the parameter matching method of the present invention and does not constitute a limitation on the type of material. The method of the present invention is applicable to other nonlinear materials with saturable absorption characteristics that can be integrated into optical fiber systems, such as graphene, carbon nanotubes, transition metal chalcogenides, and other two-dimensional materials, but is not limited to the above-mentioned materials.

[0060] Example 3 The parameter matching and optimization method based on a self-induced grating of a saturable absorber (nonlinear absorber) as described in Embodiment 1 or 2 differs in that: A graphdiyne film was selected as the nonlinear absorber and integrated into a tapered optical fiber. Under experimental conditions, an I-scan was performed on the incident light intensity to measure the transmittance response characteristics of the nonlinear absorber as a function of the incident light intensity, i.e., the transmittance response curve. By fitting the transmittance response curve, the transmittance under small-signal conditions was obtained. The definition of the small-signal absorption coefficient is as follows: ,in, Experiments have shown that the choice of grating length is irrelevant. However, in practical system design, engineering geometric constraints must be considered: since the tapered fiber needs to be close to and embedded within the cavity structure, its length cannot be less than 0.5 m. This leads to the deduction... The feasible upper limit, i.e. This limits the parameter search range to Within.

[0061] In Within the range, the grating length is determined by combining numerical simulation results. Comprehensive screening was conducted: First, the 3 dB bandwidth constraint on the grating length was considered. Secondly, reflection modulation depth The acceptable range corresponds to Located at approximately 0.25–1.75 m; again, the maximum reflection value... The grating length must not exceed 1.5 m. Taking the intersection of the above three constraints yields the final feasible range for the grating length. .

[0062] Therefore, the selection of the grating length is not directly determined by a single definition, but rather is determined within a fixed... Under engineering constraints, the results were obtained through joint screening of multiple performance indicators. Furthermore, adjustments can be made based on specific application requirements. Within this range, the quantitative data given in the figure can be used to further refine the analysis. Detailed adjustments are made to achieve the optimal compromise of the target performance parameters.

Claims

1. A parameter matching and optimization method based on a self-induced grating of a saturable absorber, characterized in that, Applications include single-frequency fiber lasers, including: Step 1: Numerical simulation; Small signal absorption coefficient within a predetermined parameter range With grating length A scan is performed, the corresponding self-induced grating reflection spectrum is calculated, and key performance indicators such as 3 dB bandwidth, maximum reflectivity, and reflection modulation depth of the self-induced grating reflection spectrum are extracted to construct... A graph showing the relationship between the parameters and grating performance; this graph visually identifies the extreme value bands of parameters that meet the target performance requirements. The predetermined parameter refers to the small signal transmittance. , The value range is 0.1–0.9; The grating length L refers to the equivalent length of the saturable absorber that forms a self-induced grating effect within the laser cavity; Step 2: I scan; Under the condition that the nonlinear absorber enters the saturation operating range, the transmittance of the nonlinear absorber as a function of incident light intensity is obtained, and the transmittance under small signal conditions is obtained by fitting the response curve. Determine the equivalent small-signal absorption coefficient of the nonlinear absorber. ; Step 3: Determine the parameter search range; Determine feasible small-signal absorption coefficients based on engineering constraints. and grating length range; Step 4: Jointly screen grating lengths; Based on the constraints of each performance index on L, the intersection is taken to obtain the feasible range of grating length; each performance index includes 3 dB bandwidth, maximum reflectivity and reflection modulation depth; Step 5: Parameter matching complete; The parameters of the self-induced grating are matched to achieve the coordinated optimization of the nonlinear absorber and the grating length.

2. The parameter matching and optimization method based on a saturable absorber self-induced grating according to claim 1, characterized in that, Step 1 involves calculating the corresponding self-induced grating reflection spectrum, including: Inside the saturable absorber, the master mode probe field The probe field propagates along the fiber segment, and its evolution is described by coupled differential equations in the forward and reverse propagation directions; the complex amplitudes of the probe field in the forward and reverse propagation directions are respectively... and The propagation equation is: ； ； ； ； Wherein, coupling coefficient This indicates the self-absorption modulation effect of the master mode on the probe field. This indicates the coupling strength between forward and reverse fields; The effective modulus radius of the material, The saturation power of the nonlinear material is given by ; z represents the spatial coordinates along the length of the grating, with a value range of . And define the direction of light propagation along the positive z direction as the +z direction; Indicates the amplitude of the pump light field; and These represent the signal photoelectric field envelopes propagating along the +z and -z directions, respectively. The instantaneous absorption coefficient follows the standard saturable absorption model, as shown below: ； in, The small-signal absorption coefficient is given in the standard saturable absorption model. The saturation behavior is determined by the coupling strength parameter. Equivalent representation; The incident light intensity; Saturated light intensity; In order to increase light intensity Instantaneous absorption coefficient under action; The forward and reverse fields of the probe light were obtained through numerical iteration. and The spatial distribution of the grating is defined based on the relationship between the input optical power and the output reflected optical power, and the expression is: ； in, This represents the frequency offset between the probe field frequency and the dominant mode light frequency. By scanning different frequency offsets, the reflection spectrum of the grating structure can be obtained. Indicates frequency offset The self-induced grating reflectivity is as follows; This represents the electric field reflected by the probe field propagating in the reverse direction at z = 0; This represents the electric field of the positive probe incident into the grating; Based on the established coupled-wave theoretical model, relevant parameter ranges are defined, including the small-signal transmittance. The theoretical predetermined range is set at 0.1–0.9; Subsequently, the grating length was... With small signal absorption coefficient Perform a parametric scan; among which, Take a depth of 0.5–2.5 m. Take 0–10 m -1 ; Parametric scanning refers to the scanning of the grating length. With small signal absorption coefficient Discrete transformations are performed, and the coupled wave equation, i.e. the propagation equation, is solved for each set of parameter combinations to obtain the corresponding self-induced grating reflection spectrum.

3. The parameter matching and optimization method based on a saturable absorber self-induced grating according to claim 1, characterized in that, In step 1, The relationship between the influence on grating performance and other parameters was obtained by solving the coupled-wave equations and performing a parametric scan; the specific process is as follows: After obtaining the reflection spectrum of the self-induced grating, key performance indicators are extracted from it, including: maximum reflectivity. Reflection modulation depth 3 dB bandwidth; Subsequently, and Using the key performance indicators as function values ​​and the x and y axes respectively, we plot the results. The relationship between the influence of the grating spectral properties and the spectral characteristics is shown in the figure.

4. The parameter matching and optimization method based on a self-induced grating of a saturable absorber according to claim 1, characterized in that, In step 1, through A graph showing the relationship between the parameters and grating performance visually identifies the extreme value bands of parameters that meet the target performance requirements; including: The extreme value band of a parameter refers to the value of the small signal absorption coefficient. With grating length In the constructed two-dimensional parameter space, to maximize reflectivity Reflection modulation depth And the parameter combination region where the 3 dB bandwidth spectral performance index is at a relatively good level.

5. The parameter matching and optimization method based on a saturable absorber self-induced grating according to claim 4, characterized in that, Superior level refers to: maximum reflectivity Reflection modulation depth and 3 dB bandwidth .

6. The parameter matching and optimization method based on a saturable absorber self-induced grating according to claim 1, characterized in that, In step 2, the response curve is fitted to obtain the transmittance under small signal conditions. ;include: When fitting the response curve, the nonlinear transmission characteristics of the saturable absorber are described by the following formula: ； in, This represents the saturation absorption amplitude. For saturation intensity, This refers to unsaturated transmittance. This indicates that the saturable absorber is in operation when the incident light intensity is... Instantaneous transmittance at time; Small signal transmittance Transmittance is defined as the transmittance when the incident light intensity approaches zero. .

7. The parameter matching and optimization method based on a saturable absorber self-induced grating according to claim 1, characterized in that, In step 3, the grating length The value range is set to 0.5–2.5 m.

8. A parameter matching and optimization method based on a self-induced grating of a saturable absorber according to any one of claims 1-7, characterized in that, Graphene, carbon nanotubes, or transition metal chalcogenides were selected as nonlinear absorbers.

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