CN110543746B - Method for optimally designing ring core optical fiber - Google Patents
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Abstract
The invention relates to a method for optimally designing a ring core optical fiber, which establishes a nonlinear relation between an optical fiber design parameter and an inter-mode coupling integral coefficient through a BP neural network, and simultaneously quickly finds an optimal structure with the minimum inter-mode coupling coefficient by using a genetic algorithm under the condition of meeting the structural limitation condition of a drawing process, thereby realizing the quick design of the ring core optical fiber with low loss and low mode group coupling. The method innovatively utilizes the coupling integral coefficient of the ring-core optical fiber as an optimization target to train the neural network, and breaks the conventional principle that the conventional multimode optical fiber mainly depends on increasing the difference of the effective refractive index between modes in the theory of realizing low coupling between the modes. Meanwhile, the output value of the neural network is used as a fitness function value of the genetic algorithm, and compared with the traditional electromagnetic field simulation calculation, the fitness function value is obtained, and the loop-core optical fiber design optimization process is quicker.
Description
Technical Field
The invention relates to the technical field of optical communication, in particular to a method for optimally designing a ring core optical fiber.
Background
As the capacity of the existing single-mode optical fiber communication system gradually approaches its theoretical limit, the spatial multiplexing optical fiber communication system that can further increase the transmission capacity of a single optical fiber has attracted much attention in recent years, and is considered as one of the main choices of the next-generation optical fiber communication technology. At present, optical fibers supporting a space division multiplexing optical fiber communication system are mainly of two types, namely few-mode optical fibers and multi-core optical fibers. Compared with the latter, the few-mode fiber has higher capacity density and more compact line devices (such as optical amplifiers and the like). However, the major problem faced by the few-mode fiber-based mode division multiplexing communication system is that, as the number of multiplexing modes increases, the complexity of a multiple-input multiple-output (MIMO) equalization module coupled between compensation modes is also increased, which is not favorable for further expansion of the mode division multiplexing communication system. To solve the above problem, the mainstream way to reduce the coupling efficiency between the modes (or groups) is to increase the effective refractive index difference between the adjacent conduction modes (or groups) of the optical fiber, so as to ensure low crosstalk between the adjacent modes (or groups) over a certain transmission distance. This means that MIMO is not needed or only partial MIMO is used to compensate for the strong coupling between degenerate modes within a group, thereby reducing MIMO complexity and increasing the mode scalability of the system. However, considering the weak guiding condition of the optical fiber and the material loss during the optical fiber preparation process, the maximum refractive index difference between the core and the cladding of the few-mode optical fiber cannot be usually too large, which means that the effective refractive index difference between the adjacent modes (groups) cannot be increased at once.
In addition, most of the existing optical fiber designs are based on repeated electromagnetic calculation or test methods, and the search for the optical fiber design with the optimal performance under special conditions is time-consuming and high in complexity.
Disclosure of Invention
The invention provides a method for optimally designing a ring core optical fiber, aiming at overcoming the defects of long time consumption and high complexity of finding the optimal performance optical fiber design under special conditions in the optical fiber design in the prior art.
The method establishes the nonlinear relation between the optical fiber design parameters and the mode group intercoupling integral coefficients through the BP neural network, and simultaneously quickly finds the optimal structure with the minimum intermode coupling coefficient by using a genetic algorithm under the condition of meeting the structural limitation condition of a drawing process, thereby realizing the quick design of the low-loss and low-mode group intercoupling annular core optical fiber.
Based on the coupling mode theory, the invention utilizes the special radial gradient change of the refractive index of the ring-core optical fiber and innovatively utilizes the coupling integral coefficient of the ring-core optical fiber as the measure of the crosstalk degree between adjacent conduction modes (groups), thereby breaking the conventional that the prior multimode optical fiber mainly depends on increasing the effective refractive index difference between the modes in the low coupling theory. Meanwhile, the coefficient is used as an optimization target to train the neural network, the output value of the neural network is used as a fitness function value of a genetic algorithm to search for the optimal optical fiber design under special conditions, and compared with the traditional electromagnetic field simulation calculation, the fitness function value is obtained, and the loop-core optical fiber design optimization process is quicker.
The method comprises the following steps:
s1: constructing a training sample of a neural network according to the universal model for optical fiber design, and preprocessing the training sample;
s2: constructing and training a BP neural network model according to the training sample preprocessed in the S1;
s3: the genetic algorithm is used to find the optimal value under the defined conditions: generating a population by taking each input design parameter as an individual, constructing a population fitness function based on a trained BP neural network, and searching the individual with the highest fitness value under a limited condition to find the optimal value of each design parameter;
s4, secondary verification result: one or more groups of parameter combinations with optimal effects can be obtained according to the optimization results of the genetic algorithm, secondary verification is carried out on the parameters through a conventional electromagnetic field calculation method, whether the optimization results are correct or not is judged, if the optimization results are correct, the results are returned to a designer, and if the optimization results are incorrect, the results are returned to S2.
Preferably, S1 comprises the steps of:
s101, determining a universal model of optical fiber design: the outer diameter of the optical fiber cladding is 125 mu m, the maximum relative refractive index difference between the core layer and the cladding is 0.008, and the core layer is designed with a four-layer structure; the core inner and outer diameters are determined to ensure a fixed number of mode groups and a radial first order conduction mode; the refractive indexes of the inner cladding layer and the outer cladding layer of the annular fiber core are consistent, and the refractive indexes of the other core layers are distributed in a step-type manner;
s102, determining input and output variables: selecting the difference between the radius of each core layer and the relative refractive index of the core layer and the cladding layer as input variables, and selecting the mode group coupling integral coefficient C between adjacent high orders of the target lm As an output variable;
s103, preparing a training sample: determine eachAfter the range and the value interval of the input variable, the coupling integral coefficient C of each input variable is obtained by an electromagnetic field calculation method lm Constructing and storing a training sample of the neural network;
s104, sample pretreatment: the sample input and output variables are preprocessed to be between 0, 1.
Preferably, the specific calculation formula of the mode group coupling integral coefficient in S102 is as follows:
e 0 denotes the vacuum permeability, j denotes
b is the maximum radius value of the mode field inside the integral; ω represents frequency;
Γ lm represents the coupling efficiency between mode l and mode m caused by random microbending perturbation, and the spatial power spectrum
And the coupling integral coefficient C lm The two items are related; delta beta lm Represents the propagation constant difference between mode i and mode m:
Δn eff for effective refractive index difference, A l And A m Normalized amplitudes representing mode i and mode m, respectively; integral of the ith mode
Can be normalized to->
ε 0 And mu 0 Respectively, the dielectric constant and the permeability in vacuum, k 0 Denotes the wave vector in vacuum, beta i Denotes the propagation constant, A i A normalized amplitude value representing mode i; r represents the radius of the optical fiber, n 0 An undistorted Refractive Index Profile (RIP) representing an ideal optical fiber;
Preferably, the preprocessing method in S104 is to normalize the maximum and minimum values of the sample input and output variables to be between [0,1], where the normalization formula is as follows:
where z is the normalized value, x is the normalized data, x min 、x max Respectively, the minimum and maximum values in the normalized data.
Preferably, S2 comprises the steps of:
s201, initializing parameters: determining the number of hidden layers of the network, the number of neurons of the hidden layers and a transfer function of the network, wherein the number of the neurons of the input layer and the number of the neurons of the output layer are respectively determined by the number of input and output variables;
s202, obtaining the optimal initial weight and threshold of the neural network: dividing the preprocessed sample data in the step S1 into a training set and a testing set, generating a population by using a genetic algorithm and taking the initial hidden layer weight and the threshold of the network as individuals, coding the population and the individuals by adopting a real number coding mode, taking the Mean Square Error (MSE) of a predicted value and a target value of a BP neural network as a population fitness value function, and selecting the highest value from all the rest individuals as the optimal initial weight and the threshold of the network according to the fitness value after crossing, variation and selection operations until the evolution times are met;
s203, training a neural network: and (4) training the BP neural network by using the optimal network initial weight and the threshold value obtained in the step (S202) until the Mean Square Error (MSE) of the predicted value and the sample value meets the requirement.
Preferably, S3 is in particular:
firstly, determining individual and fitness value, setting initial parameters (including population scale, evolution times, cross probability and variation probability), generating population by taking input design variables as individuals, coding the population and the individuals in a real number coding mode, generating initial population, and calculating coupling integral coefficient value C by using BP neural network trained by S2 lm And further calculating a population fitness value, wherein a fitness value function is designed as:
wherein the limiting conditional function Q (X) is designed as:
when the structure limiting condition meeting the drawing process is met, the Q (X) value is 1, otherwise, the Q (X) value is 0;
on the premise of meeting the limiting condition, searching the optimal value by calculating and searching the maximum fitness value, otherwise, the fitness is always 0, which means that the optimal value under the constraint condition is not met;
and for the optimal value which does not meet the constraint condition, performing crossover, variation and selection operations until the maximum evolution times is met, and selecting the highest value from all the remaining individuals as the optimal optical fiber design parameter according to the fitness value.
Preferably, the limiting conditions in S3 are to ensure that each layer is at least greater than 0.5 μm thick, and the relative refractive index difference between adjacent layers is at least greater than 0.0005, so as to reduce the difficulty of the drawing process.
Compared with the prior art, the technical scheme of the invention has the beneficial effects that: based on the coupling mode theory, the invention utilizes the special radial gradient change of the refractive index of the ring-core optical fiber and innovatively utilizes the coupling integral coefficient of the ring-core optical fiber as the measure of the crosstalk degree between adjacent conduction modes (groups), thereby breaking the conventional that the prior multimode optical fiber mainly depends on increasing the effective refractive index difference between the modes in the low coupling theory. Meanwhile, the coefficient is used as an optimization target to train the neural network, the output value of the neural network is used as a fitness function value of a genetic algorithm to search for the optimal optical fiber design under special conditions, and compared with the traditional electromagnetic field simulation calculation, the fitness function value is obtained, and the loop-core optical fiber design optimization process is quicker.
Drawings
FIG. 1 is a schematic representation of the refractive index profile of an optical fiber according to an embodiment of the present invention at the cross-section and at the diameter line of the cross-section.
FIG. 2 is a flowchart of a method for optimally designing a ring-core optical fiber according to an embodiment of the present invention;
fig. 3 is a schematic structural diagram of a BP neural network in the embodiment of the present invention.
In the figure, 1, 2, 3, 4, 5, and 6 represent auxiliary lines.
Detailed Description
The drawings are for illustrative purposes only and are not to be construed as limiting the patent;
for the purpose of better illustrating the present embodiments, certain elements of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product;
it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.
Example 1:
in FIG. 1, (a) is a cross-sectional view of the fiber, and (b) is a refractive index profile along the diameter line of the cross-section, the ring-core fiber based on this embodiment has 4 core layers, including but not limited to the structure shown in FIG. 1, wherein the refractive index profile can be stepwise. In fig. 1, the auxiliary line 6 identifies the outer boundary of the outer cladding layer of the optical fiber, the auxiliary line 5 identifies the outer boundary of the core layer of the fiber core, i.e., the outer boundary of the fourth core layer, the auxiliary line 4 identifies the outer boundary of the third core layer, the auxiliary line 3 identifies the outer boundary of the second core layer, the auxiliary line 2 identifies the outer boundary of the first ring, and the auxiliary line 1 identifies the inner cladding boundary of the ring-shaped fiber core. The fiber cladding outer diameter is standard 125 μm and the core inner and outer diameters are determined to ensure a fixed number of mode groups and radial first order conduction modes. Radius r of core layer 1 、r 2 、r 3 Are all design input variables; (b) The core refractive index profile shown in (1) is not limited to such a profile, and the maximum core-cladding relative refractive index difference is 0.008, where the relative refractive index difference n is 1 、n 2 、n 3 、n 4 Are all design variables.
As shown in fig. 2 and fig. 3, the method for optimally designing a ring-core optical fiber according to this embodiment includes the following steps:
s1: and constructing a training sample of the neural network according to the universal model for optical fiber design, and preprocessing the training sample.
S101, determining a universal model of optical fiber design: considering the drawing process and the realization difficulty, the outer diameter of the outer cladding of the model optical fiber is standard 125 μm, the maximum relative refractive index difference between the core layer and the cladding is 0.008, and the core layer is designed with a four-layer structure. The core inner and outer diameters are determined to ensure a fixed number of mode groups and radial first order conduction modes. The refractive indexes of the inner cladding layer and the outer cladding layer of the annular fiber core are consistent, and the refractive indexes of the other core layers are distributed in a step-type manner;
s102, determining input and output variables: selecting the difference between the radius of each core layer and the relative refractive index of the core layer and the cladding layer as input variables,selecting a mode group coupling integral coefficient C between adjacent high orders of a target lm As the output variable, the embodiment selects the first order and the second order, and the mode group coupling integral coefficient C between the second order and the third order 21 ，C 23 As an output variable;
the specific calculation formula of the inter-mode coupling integral coefficient in S102 is as follows:
Γ lm represents the coupling efficiency between modes l and m caused by random microbending perturbations, with the spatial power spectrum
And coupling integral coefficient C lm The two terms are related. Wherein it is present>
Representing the propagation constant difference between modes l and m, b is the maximum radius value of the mode field inside the integral, e 0 Denotes the magnetic permeability in vacuum, A l And A m The normalized amplitudes of modes l and m are indicated, respectively. Integration of the ith mode->
Can be normalized to->
Where epsilon 0 And mu 0 Respectively, the dielectric constant and the magnetic permeability in a vacuum. A. The i A normalized amplitude value representing mode i; r represents the radius of the optical fiber, n 0 Showing the undistorted Refractive Index Profile (RIP) of an ideal fiber. Wherein it is present>
The value depends on Δ β (or effective refractive index difference Δ n) eff ) Drawing process and the external stress to which the optical fiber is subjected. Coefficient C lm Depending on the magnitude of the overlap integral between the mode field amplitude profile and the refractive index gradient. Thus, by adjusting n of the fiber, assuming that the fiber environment and the drawing process are constant 0 Reducing overlap integral of mode field and refractive index gradient
The mode coupling efficiency caused by microbend disturbance can be reduced, and the conventional principle that the conventional multimode fiber mainly depends on increasing the effective refractive index difference between modes in the theory of realizing low coupling between modes is broken. In this embodiment, the first and second order, and the overlap integral C between the second and third order are selected and calculated 21 And C 23 By minimizing C 21 And C 23 The aim of reducing the coupling coefficient between the modes is achieved.
S103, preparing a training sample: after the range and the value interval of each input variable are determined, the C of each input variable is obtained by a conventional electromagnetic field calculation method 21 、C 23 Constructing and storing a training sample of the neural network;
s104, sample pretreatment: the input and output variables are preprocessed, including but not limited to normalization, to be between [0,1], and the normalization formula is as follows:
where z is the normalized value, x is the normalized data, x min 、x max Respectively, the minimum value and the maximum value in the normalized data;
s2, constructing and training a BP neural network model, and the process is as follows:
s201, initializing parameters: determining the number of hidden layers of the network, the number of neurons of the hidden layers, the transfer function of the network and the like, wherein the number of the neurons of the input layer and the output layer is respectively determined by the number of input and output variables;
s202, obtaining the optimal initial weight and threshold of the neural network: dividing the sample data in the step S1 into a training set and a testing set, generating a population by using a genetic algorithm and taking a network initial hidden layer weight and a threshold as individuals, and optimizing by taking network MSE as population fitness through continuous iteration optimization to obtain an optimal network initial weight and a threshold;
in S202, after the initial parameters (including population scale, evolution frequency, crossover probability, and variation probability) are set, the population is generated by using the initial hidden layer weight and the threshold as the individuals, the population and the individuals are encoded by using a real number encoding method, the Mean Square Error (MSE) between the predicted value and the target value of the BP neural network is used as a population fitness value function, the population is subjected to crossover, variation, and selection operations until the evolution frequency is met, and the highest value among all the remaining individuals is selected as the optimal initial network weight and the threshold according to the fitness value.
S203, training a neural network: training the BP neural network by using the initial weight and the threshold of the optimal network obtained in the step 202 until the Mean Square Error (MSE) of the predicted value and the sample value meets the requirement;
s3, searching an optimal value under a limited condition by using a genetic algorithm: generating a population by taking each input design parameter as an individual, constructing a population fitness function based on a trained BP neural network, and searching the individual with the highest fitness value under a limited condition to find the optimal value of each design parameter;
in step S3, after setting initial parameters (including population scale, evolution times, crossover probability, and mutation probability), generating a population by using input design variables as individuals, encoding the population and the individuals by using a real number encoding method, and calculating C by using a trained BP neural network after generating an initial population 21 And C 23 And further calculating a population fitness value, wherein the fitness value function is designed as:
wherein the qualifying conditional function Q (X) is designed as:
when the structural definition condition meeting the drawing process is satisfied, the Q (X) value is 1, otherwise, the Q (X) value is 0.
On the premise of meeting the limiting condition, the maximum fitness value is searched by calculation to search the optimized value, otherwise, the fitness is always 0, which means that the optimal value under the constraint condition is not met.
And then, performing intersection, variation and selection operations until the maximum evolution times are met, and selecting the highest value from all the remaining individuals as the optimal optical fiber design parameter according to the fitness value.
In addition, the limiting conditions are that the thicknesses of all the layers are ensured to be at least more than 0.5 μm, and the relative refractive index difference of all the adjacent layers is at least more than 0.0005, so as to reduce the difficulty of the drawing process.
S4, secondary verification result: one or more groups of parameter combinations with optimal effects can be obtained according to the optimization results of the genetic algorithm, the parameters are verified for the second time through a conventional electromagnetic field calculation method, and finally the feasibility of the optimization results is determined and fed back to a designer. If the difference is large, training the neural network and optimizing and solving the genetic algorithm again;
the conventional electromagnetic field calculation method in step S4 includes, but is not limited to, finite element analysis, and solving partial differential equations.
The terms describing positional relationships in the drawings are for illustrative purposes only and are not to be construed as limiting the patent;
it should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.
Claims (6)
1. A method for optimizing the design of a ring-core optical fiber, the method comprising the steps of:
s1: constructing a training sample of a neural network according to the universal model for optical fiber design, and preprocessing the training sample; the method comprises the following steps:
s101, determining a universal model of optical fiber design: the outer diameter of the optical fiber cladding is standard 125 mu m, the maximum relative refractive index difference between the core layer and the cladding is 0.008, and the core layer is designed with a four-layer structure; the core inner and outer diameters are determined to ensure a fixed number of mode groups and a radial first order conduction mode; the refractive indexes of the inner cladding layer and the outer cladding layer of the annular fiber core are consistent, and the refractive indexes of the other core layers are distributed in a step-like manner;
s102, determining input and output variables: selecting the radius of each core layer and the relative refractive index difference between the core layer and the cladding layer as input variables, and selecting the mode group intercoupling integral coefficient C between adjacent high orders of the target lm As an output variable;
s103, preparing a training sample: after the range and the value interval of each input variable are determined, the coupling integral coefficient C under each input variable is obtained by an electromagnetic field calculation method lm Constructing and storing a training sample of the neural network;
s104, sample pretreatment: preprocessing the input and output variables of the sample to enable the input and output variables of the sample to be between [0,1 ];
s2: constructing and training a BP neural network model according to the training sample preprocessed in the S1;
s3: and (3) searching an optimal value under a limited condition by using a genetic algorithm: generating a population by taking each input design parameter as an individual, constructing a population fitness function based on the trained BP neural network, and searching the individual with the highest fitness value to find the optimal value of each design parameter under a limited condition;
s4, secondary verification result: and acquiring a plurality of groups of parameter combinations with optimal effects according to the optimization result of the genetic algorithm, carrying out secondary verification on the parameters by a conventional electromagnetic field calculation method, judging whether the optimization result is correct or not, if so, returning the result to a designer, and if not, returning to S2.
2. The method of claim 1, wherein the specific calculation formula of the mode-group coupling integral coefficient in S102 is as follows:
e 0 denotes the vacuum permeability, j denotes
b is the maximum radius value of the mode field inside the integral; ω represents frequency;
Γ lm represents the coupling efficiency between mode l and mode m caused by random microbending perturbation, and the spatial power spectrum
And the coupling integral coefficient C lm The two items are related; delta beta lm Represents the propagation constant difference between mode i and mode m:
Δn eff for effective refractive index difference, A l And A m Respectively representing the normalized amplitude values of the mode l and the mode m; integral of the ith mode
Is normalized to->
ε 0 And mu 0 Respectively, the dielectric constant and the permeability in vacuum, k 0 Denotes the wave vector in vacuum, beta i Denotes the propagation constant, A i A normalized amplitude value representing mode i; r represents the radius of the optical fiber, n 0 Representing an undistorted refractive index profile of an ideal optical fiber; />
3. The method of claim 2, wherein the preprocessing in S104 is to normalize the maximum and minimum values of the input and output variables of the sample to make the input and output variables of the sample between [0,1], and the normalization formula is as follows:
where z is the normalized value, x is the normalized data, x m i n 、x max Respectively, the minimum and maximum values in the normalized data.
4. The method for optimizing the design of the ring-core optical fiber according to claim 3, wherein S2 comprises the following steps:
s201, initializing parameters: determining the number of hidden layers of the network, the number of neurons of the hidden layers and a transfer function of the network, wherein the number of the neurons of the input layer and the number of the neurons of the output layer are respectively determined by the number of input and output variables;
s202, obtaining the optimal initial weight and threshold of the neural network: dividing the preprocessed sample data in the step S1 into a training set and a testing set, generating a population by using a genetic algorithm and taking a network initial hidden layer weight and a threshold value as individuals, coding the population and the individuals by adopting a real number coding mode, taking a mean square error of a BP neural network predicted value and a target value as a population fitness value function, and selecting a highest value from all the rest individuals as a network optimal initial weight and a threshold value according to the fitness value after crossing, variation and selection operations until the evolution times are met;
s203, training a neural network: and (4) training the BP neural network by using the initial weight and the threshold of the optimal network obtained in the step (S202) until the mean square error of the predicted value and the sample value meets the requirement.
5. The method for optimally designing the ring-core optical fiber according to claim 4, wherein S3 is specifically as follows:
firstly, determining individuals and fitness values, setting initial parameters, generating a population by taking input design variables as the individuals, coding the population and the individuals in a real number coding mode, generating an initial population, and calculating a coupling integral coefficient C by using a BP neural network trained by S2 lm And further calculating a population fitness value, wherein the fitness value function is designed as:
the qualifying conditional function Q (X) is designed as:
when the structure limiting condition meeting the drawing process is met, the Q (X) value is 1, otherwise, the Q (X) value is 0;
on the premise of meeting the limiting condition, searching the optimal value by calculating and searching the maximum fitness value, otherwise, the fitness is always 0, which means that the optimal value under the constraint condition is not met;
and for the optimal value which does not meet the constraint condition, performing crossing, variation and selection operations until the maximum evolution times are met, and selecting the highest value from all the remaining individuals as the optimal optical fiber design parameter according to the fitness value.
6. The method for optimizing the design of the ring-core optical fiber according to claim 1 or 5, wherein the limiting conditions in S3 are to ensure that the thickness of each layer is at least greater than 0.5 μm, and the relative refractive index difference between adjacent layers is at least greater than 0.0005, so as to reduce the difficulty of the drawing process.
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