Sparse etching optimization method of non-uniform FBG (Fiber Bragg Grating)

Abstract

The invention discloses a sparse etching optimization method for a non-uniform FBG (Fiber Bragg Grating), which comprises the following steps of: in the etching design process of the non-uniform FBG, concluding a non-uniform etching problem as an etching position optimization selection problem, and enabling the etching process of the non-uniform FBG to be equivalent to an extraction process of the uniform FBG, and the sparse etching of the non-uniform FBG grating is realized by solving the optimal etching position extraction vector. According to the method, sparse etching of the FBG can be completed, the approximate effective refractive index, namely approximate grating performance, is obtained with the etching amount far smaller than the number of uniform FBGs, the grating performance can be guaranteed, meanwhile, the grating etching number can be remarkably reduced, on one hand, the process complexity can be reduced, and the loss of optical signals can be reduced; on the other hand, the structural strength of the grating can be improved, the problem that the strength stability of the optical fiber is reduced due to local excessive etching of the optical fiber is avoided, and the method has important significance in engineering application.

Description

Technical Field

[0001] The invention belongs to the technical field of optical fiber gratings, and in particular relates to a sparse etching optimization method for a non-uniform FBG grating. Background Art

[0002] Non-uniformly etched fiber Bragg gratings (FBGs) have significant advantages and necessity in modern fiber-optic communications and sensing technologies. Compared with uniform FBGs, non-uniform FBGs can achieve more complex and versatile spectral characteristics by finely controlling the grating period and refractive index modulation. For example, non-uniform FBGs can broaden the reflection spectrum by modulating the grating period or refractive index, thereby covering a wider wavelength range, which is particularly important in broadband fiber-optic communications and broadband spectrometers. Non-uniform FBGs can be designed with a reflection spectrum with multiple reflection peaks, enabling them to filter or reflect multiple wavelengths simultaneously, which has important applications in wavelength division multiplexing (WDM) systems. By finely designing the refractive index modulation and periodic variation of the grating, non-uniform FBGs can achieve specific spectral responses, such as asymmetric reflection spectra or transmission spectra with special shapes, to meet the needs of specific applications. In some applications, by designing non-uniform FBGs, the dispersion effect in optical fiber transmission can be compensated and the signal transmission quality and distance can be improved. In addition, non-uniform FBGs exhibit higher sensitivity and accuracy in sensing stress, temperature, and refractive index changes, optimizing the sensor response to specific parameters.

[0003] As optical fiber communication systems become more complex and diversified, non-uniform FBGs can provide more flexible and efficient optical signal processing methods, such as multi-wavelength filtering and dynamic wavelength selection, to meet the high bandwidth and performance requirements of modern communication systems. In the fields of structural health monitoring, temperature monitoring, and biosensing, non-uniform FBGs can provide higher measurement accuracy and sensitivity to meet the growing demand for sensor performance in these fields. Non-uniform FBGs are increasingly used in integrated photonics, and they can be integrated into more complex photonic circuits to achieve miniaturized, high-performance optical signal processing and sensing functions.

[0004] However, how to reduce the amount of grating etching while ensuring the performance of the FBG grating and avoid local excessive etching of the optical fiber causing a decrease in the strength stability of the optical fiber has always been one of the difficult problems plaguing the industry. Summary of the invention

[0005] In order to solve the technical problems existing in the prior art, the object of the present invention is to provide a sparse etching optimization method for a non-uniform FBG grating.

[0006] In order to achieve the above purpose and the above technical effect, the technical solution adopted by the present invention is:

[0007] A sparse etching optimization method for a non-uniform FBG grating comprises the following steps:

[0008] In the process of non-uniform FBG grating etching design, the non-uniform etching problem is summarized as the problem of optimizing the selection of etching positions. The etching process of the non-uniform FBG grating is equivalent to the extraction process of the uniform FBG grating. By solving the optimal etching position extraction vector, the sparse etching of the non-uniform FBG grating is achieved.

[0009] Further, it is characterized by comprising the following steps:

[0010] S1. Clarify the equivalent transmission characteristics of the FBG grating to be designed and obtain the equivalent transmission matrix T;

[0011] S2. Obtain the target transmission matrix of the FBG grating to be designed

[0012] S3, define the etching position extraction vector Θ;

[0013] S4. Set constraints and solve the optimal etching position extraction vector to achieve sparse etching of non-uniform FBG grating.

[0014] Furthermore, in step S1, the equivalent transmission matrix T is expressed as:

[0015]

[0016] Where, κ is the coupling coefficient, which indicates the intensity of refractive index modulation; L is the grating length; is the ratio of the refractive index modulation amplitude to the average refractive index; n0 is the average refractive index of the grating; Δn is the refractive index modulation amplitude; is an imaginary number; Δβ is the mismatch, which is defined as: n eff is the effective refractive index of the optical fiber, λ is the wavelength of the incident light, B is the Bragg wavelength of FBG;

[0017] When the wavelength of the incident light is at the Bragg wavelength, that is, λ = λ B When , the adaptation amount is zero, and the equivalent transmission matrix T of formula (1) is simplified to:

[0018]

[0019] At this time, the FBG grating to be designed for the Bragg wavelength λ B The reflection coefficient is the largest, and the corresponding reflection spectrum R(λ B ) and the transmission spectrum H(λ B ) are:

[0020]

[0021]

[0022] Further, in step S3, the elements in the etching position extraction vector Θ are defined as:

[0023]

[0024] When position n is an etching area, the element value corresponding to the etching position extraction vector is 1, otherwise it is 0;

[0025] Assuming that the number of equivalent uniform FBG grating etching layers is N, the length of Θ is N.

[0026] Further, in step S4, the actual transmission matrix of the non-uniform FBG grating is With the target transfer matrix The error of and the number of etching positions are taken as constraints at the same time. By solving formula (6), the number of etchings can be reduced while ensuring the performance of the FBG grating:

[0027]

[0028] Among them, ||·|| F represents the Frobenius norm, ||·||0 is the 0 norm, and α and β are weight coefficients respectively.

[0029] Furthermore, the genetic iteration method is used to solve formula (6), which includes the following steps:

[0030] Step 1: Input the grating average refractive index n0, refractive index modulation amplitude Δn, grating period Λ, grating length L and grating etching layer number N;

[0031] Step 2: Generate a population of random binary vectors The size is P × N, where P is the population size;

[0032] Step 3: Population The nth row of is defined as individual n, and the fitness G(n) corresponding to the individual n of the population is calculated;

[0033] Step 4: define the iterative search count q=1 and the iterative termination threshold K;

[0034] Step 5: Calculate the fitness of all individuals in the qth population based on step 3, and select the individual with the smallest fitness

[0035] Step 6: Define the individual reproduction coefficient m=1;

[0036] Step 7: Define two random numbers From the qth population Select two individuals

[0037] Step 8: Define an intersection point And cross the two individuals obtained in step 6 to get a new individual:

[0038]

[0039] and will As a new species The mth row of , and let m = m + 1;

[0040] Step 9: Generate a random number At the same time, define the mutation threshold ε, and judge that if ν<ε, generate a random number 1≤z≤N and Take the inverse and get If ν ≥ ε, then the step 10 is directly executed without performing the negation operation;

[0041] Step 10: If m < P, jump to step 6, otherwise output the new population and proceed to the next step;

[0042] Step 11: Set q = q + 1 and judge, if q < K, jump to step 5, otherwise output the optimal individual

[0043] At this point, the optimal etching position extraction vector is obtained The position corresponding to the non-zero elements in Θ is the etching area.

[0044] Furthermore, in step 3, the population The nth row of is defined as individual n, and the steps of calculating the fitness G(n) corresponding to the individual n of the population include:

[0045] Step 3.1: Calculate the equivalent refractive index vector

[0046] Step 3.2: Initialize the transmission matrix

[0047] Step 3.3: Calculate the propagation constant of the i-th grating layer i=1,…,N;

[0048] Step 3.4: Calculate the propagation sub-matrix of the i-th grating layer;

[0049] Step 3.5: Update i=i+1;

[0050] Step 3.6: If i < N, jump to step 3.3, otherwise continue to step 3.7;

[0051] Step 3.7: Output the fitness of individual η in the population.

[0052] Furthermore, in step 3.4, the propagation sub-matrix of the i-th grating layer is expressed as:

[0053]

[0054] Furthermore, in step 3.7, the fitness of the individual η in the population is expressed as:

[0055]

[0056] Compared with the prior art, the present invention has the following beneficial effects:

[0057] The present invention discloses a sparse etching optimization method for a non-uniform FBG grating, comprising the following steps: in the process of etching design of the non-uniform FBG grating, the non-uniform etching problem is summarized as an optimization selection problem of etching positions, the etching process of the non-uniform FBG grating is equivalent to the extraction process of the uniform FBG grating, and the sparse etching of the non-uniform FBG grating is realized by solving the optimal etching position extraction vector. The sparse etching optimization method for the non-uniform FBG grating provided by the present invention can complete the sparse etching of the fiber Bragg grating, and obtain a close equivalent refractive index, that is, a close grating performance, with an etching amount far less than the number of uniform FBG gratings. While ensuring the grating performance, the number of grating etchings can be significantly reduced. On the one hand, the process complexity can be reduced and the loss of optical signals can be reduced. On the other hand, the structural strength of the grating can be improved, and the problem of decreased fiber strength stability caused by local excessive etching of the optical fiber can be avoided. It is of great significance in engineering applications. DETAILED DESCRIPTION

[0058] The present invention is described in detail below so that the advantages and features of the present invention can be more easily understood by those skilled in the art, thereby making a clearer and more definite definition of the protection scope of the present invention.

[0059] A brief summary of one or more aspects is given below to provide a basic understanding of these aspects. This summary is not an exhaustive overview of all conceived aspects, and is neither intended to identify the key or critical elements of all aspects nor to define the scope of any or all aspects. Its only purpose is to give some concepts of one or more aspects in a simplified form as a prelude to a more detailed description that will be given later.

[0060] The present invention discloses a sparse etching optimization method for a non-uniform FBG grating, comprising the following steps:

[0061] In the process of non-uniform FBG grating etching design, the non-uniform etching problem is summarized as the problem of optimizing the etching position, and the non-uniform FBG is equivalent to an extraction form of the uniform FBG. Before selecting the etching position, the present invention first needs to clarify the equivalent transmission characteristics of the FBG to be designed, that is, the form of the equivalent transmission matrix. Assume that the Bragg wavelength of the FBG to be designed is λ B , then its equivalent transmission matrix can be expressed as:

[0062]

[0063] Where, κ is the coupling coefficient, which indicates the intensity of refractive index modulation; L is the grating length; is the ratio of the refractive index modulation amplitude to the average refractive index; n0 is the average refractive index of the grating; Δn is the refractive index modulation amplitude; is an imaginary number; Δβ is the mismatch, which is defined as: n eff is the effective refractive index of the optical fiber, λ is the wavelength of the incident light, B is the Bragg wavelength of FBG.

[0064] When the wavelength of the incident light is at the Bragg wavelength, that is, λ = λ B When , the adaptation amount is zero, and the transmission matrix of formula (1) can be simplified as:

[0065]

[0066] At this time, FBG has a Bragg wavelength λ B The reflection coefficient is the largest, and the corresponding reflection spectrum R(λ B ) and the transmission spectrum H(λ B ) are:

[0067]

[0068]

[0069] Therefore, for a specific filtering characteristic, the target transmission matrix of FBG can be determined according to the above process, and the target transmission matrix is The present invention equates the etching process of the non-uniform FBG to the extraction process of the uniform FBG. The present invention first defines the etching position extraction vector θ, and the elements in the extraction vector are defined as:

[0070]

[0071] When position n is an etched area, the element value corresponding to the etched position extraction vector is 1, otherwise it is 0. Assuming that the number of grating etching layers of the equivalent uniform FBG is N, the length of Θ is N.

[0072] make represents the actual transmission matrix of the non-uniform FBG, then the present invention summarizes the etching position selection of the non-uniform FBG into the following optimization problem:

[0073]

[0074] Among them, ||·|| F represents the Frobenius norm, ||·||0 is the 0 norm, and α and β are weight coefficients respectively. The above optimization process takes the error between the actual transmission matrix and the target transmission matrix and the number of etching positions as constraints at the same time. By solving the above optimization problem, the number of etchings can be reduced while ensuring the performance of the FBG grating.

[0075] In view of the above optimization problem, the present invention adopts the idea of ​​genetic iteration to solve it, and the specific steps are as follows:

[0076] Step 1: Input the grating average refractive index n0, refractive index modulation amplitude Δn, grating period Λ, grating length L and number of grating etched layers N.

[0077] Step 2: Generate a population of random binary vectors The size is P×N, where P is the population size.

[0078] Step 3: Population The nth row of is defined as individual n, and the fitness G(n) corresponding to the population individual n is calculated. The specific steps are:

[0079] Step 3.1: Calculate the equivalent refractive index vector

[0080] Step 3.2: Initialize the transmission matrix

[0081] Step 3.3: Calculate the propagation constant of the i-th grating layer i=,…,N;

[0082] Step 3.4: Calculate the propagation matrix of the i-th grating layer:

[0083]

[0084] Step 3.5: Update i=i+1;

[0085] Step 3.6: If i < N, jump to step 3.3, otherwise continue to step 3.7;

[0086] Step 3.7: Output the fitness of the individual η in the population:

[0087]

[0088] Step 4: Define the iterative search count q=1 and the iterative termination threshold K.

[0089] Step 5: Calculate the fitness of all individuals in the qth population based on step 3, and select the individual with the smallest fitness

[0090] Step 6: Define the individual reproduction coefficient m=1.

[0091] Step 7: Define two random numbers From the qth population Select two individuals

[0092] Step 8: Define an intersection point And cross the two individuals obtained in step 6 to get a new individual:

[0093]

[0094] and will As a new species The mth row of , and let m=m+1.

[0095] Step 9: Generate a random number At the same time, define the mutation threshold ε, and judge that if ν<ε, generate a random number 1≤z≤N and Take the inverse and get If ν ≥ ε, then the step 10 is directly executed without performing the negation operation.

[0096] Step 10: If m < P, jump to step 6, otherwise output the new population and proceed to the next step;

[0097] Step 11: Set q = q + 1 and judge, if q < K, jump to step 5, otherwise output the optimal individual

[0098] At this point, the optimal etching position extraction vector can be obtained Based on the definition of formula (5), the position corresponding to the non-zero element in Θ is the etching area. The present invention can complete the sparse etching of the fiber Bragg grating, and obtain a close equivalent refractive index, that is, a close grating performance, with an etching amount far less than the uniform FBG grating amount. The above method can significantly reduce the number of grating etchings while ensuring the grating performance, reduce the process complexity and improve the structural strength of the grating, which is of great significance in engineering applications.

[0099] Parts or structures not specifically described in the present invention may adopt existing technologies or existing products and will not be described in detail here.

[0100] The above descriptions are merely embodiments of the present invention and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention specification, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A sparse etching optimization method for non-uniform FBG grating, characterized in that: The following steps are involved: In the process of non-uniform FBG grating etching design, the non-uniform etching problem is summarized as the problem of optimizing the selection of etching positions. The etching process of the non-uniform FBG grating is equivalent to the extraction process of the uniform FBG grating. By solving the optimal etching position extraction vector, the sparse etching of the non-uniform FBG grating is achieved.

2. The sparse etching optimization method for non-uniform FBG grating according to claim 1, characterized in that: The following steps are involved: S1. Clarify the equivalent transmission characteristics of the FBG grating to be designed and obtain the equivalent transmission matrix T; S2. Obtain the target transmission matrix of the FBG grating to be designed S3, define the etching position extraction vector Θ; S4. Set constraints and solve the optimal etching position extraction vector to achieve sparse etching of non-uniform FBG grating.

3. The sparse etching optimization method for non-uniform FBG grating according to claim 2, characterized in that: In step S1, the equivalent transmission matrix T is expressed as: Where, κ is the coupling coefficient, which indicates the intensity of refractive index modulation; L is the grating length; is the ratio of the refractive index modulation amplitude to the average refractive index; n0 is the average refractive index of the grating; Δn is the refractive index modulation amplitude; is an imaginary number; Δβ is the mismatch, which is defined as: n eff is the effective refractive index of the optical fiber, λ is the wavelength of the incident light, B is the Bragg wavelength of FBG; When the wavelength of the incident light is at the Bragg wavelength, that is, λ = λ B When , the adaptation amount is zero, and the equivalent transmission matrix T of formula (1) is simplified to: At this time, the FBG grating to be designed for the Bragg wavelength λ B The reflection coefficient is the largest, and the corresponding reflection spectrum R(λ B ) and the transmission spectrum H(λ B ) are:

4. The sparse etching optimization method for non-uniform FBG grating according to claim 2, characterized in that: In step S3, the elements in the etching position extraction vector Θ are defined as: When position n is an etching area, the element value corresponding to the etching position extraction vector is 1, otherwise it is 0; Assuming that the number of equivalent uniform FBG grating etching layers is N, the length of Θ is N.

5. The sparse etching optimization method for non-uniform FBG grating according to claim 2, characterized in that: In step S4, the actual transmission matrix of the non-uniform FBG grating is With the target transfer matrix The error of and the number of etching positions are taken as constraints at the same time. By solving formula (6), the number of etchings can be reduced while ensuring the performance of the FBG grating: Among them, ||·|| F represents the Frobenius norm, ||·||0 is the 0 norm, and α and β are weight coefficients respectively.

6. The sparse etching optimization method for non-uniform FBG grating according to claim 5, characterized in that: The genetic iteration method is used to solve formula (6), which includes the following steps: Step 1: Input the grating average refractive index n0, refractive index modulation amplitude Δn, grating period Λ, grating length L and grating etching layer number N; Step 2: Generate a population of random binary vectors The size is P × N, where P is the population size; Step 3: Population The nth row of is defined as individual n, and the fitness G(n) corresponding to the individual n of the population is calculated; Step 4: define the iterative search count q=1 and the iterative termination threshold K; Step 5: Calculate the fitness of all individuals in the qth population based on step 3, and select the individual with the smallest fitness Step 6: Define the individual reproduction coefficient m=1; Step 7: Define two random numbers From the qth population Select two individuals Step 8: Define an intersection point And cross the two individuals obtained in step 6 to get a new individual: and will As a new species The mth row of , and let m = m + 1; Step 9: Generate a random number At the same time, define the mutation threshold ε, and judge that if ν<ε, generate a random number 1≤z≤N and Take the inverse and get If ν ≥ ε, then the step 10 is directly executed without performing the negation operation; Step 10: If m < P, jump to step 6, otherwise output the new population and proceed to the next step; Step 11: Set q = q + 1 and judge, if q < K, jump to step 5, otherwise output the optimal individual At this point, the optimal etching position extraction vector is obtained The position corresponding to the non-zero elements in Θ is the etching area.

7. The sparse etching optimization method for non-uniform FBG grating according to claim 6, characterized in that: In step 3, the population The nth row of is defined as individual n, and the steps of calculating the fitness G(n) corresponding to the individual n of the population include: Step 3.1: Calculate the equivalent refractive index vector Step 3.2: Initialize the transmission matrix Step 3.3: Calculate the propagation constant of the i-th grating layer Step 3.4: Calculate the propagation sub-matrix of the i-th grating layer; Step 3.5: Update Step 3.6: If i < N, jump to step 3.3, otherwise continue to step 3.7; Step 3.7: Output the fitness of individual η in the population.

8. The method for optimizing sparse etching of a non-uniform FBG grating according to claim 7, characterized in that: In step 3.4, the propagation matrix of the i-th grating layer is expressed as:

9. The sparse etching optimization method for non-uniform FBG grating according to claim 7, characterized in that: In step 3.7, the fitness of the individual η in the population is expressed as:

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