CN113703158B - Rapid design method of few-mode optical fiber gain profile for intermode gain equalization - Google Patents
Rapid design method of few-mode optical fiber gain profile for intermode gain equalization Download PDFInfo
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Abstract
The invention discloses a method for quickly designing a few-mode optical fiber gain section for gain equalization among modes, which quickly and efficiently realizes the design of the few-mode optical fiber gain section by simplifying a gain section design model and solving the idea. According to the method for rapidly designing the few-mode optical fiber gain profile for the intermode gain equalization, which is provided by the invention, a mathematical model is simple and easy to operate, the typical completion time under the computer-aided calculation condition is within 1 minute, the design time is obviously reduced, the solution can be realized through manual calculation under the extreme condition, and the dependence degree of the design on the computer-aided calculation is reduced.
Description
Technical Field
The invention belongs to the technical field of optical fibers, and particularly relates to a method for quickly designing a few-mode optical fiber gain profile for intermode gain equalization.
Background
Under the huge pressure of the current communication demand, space division multiplexing is a novel multiplexing scheme for improving the current communication capacity in multiples. The scheme has gained wide attention at home and abroad, and is generally considered as a key technology for solving the communication requirement at the next stage. For relay amplification of an undisrupted signal in long-distance transmission of optical communication, a basic problem of rare earth doped optical fiber suitable for requirements of a space division multiplexing optical fiber amplifier must be solved for constructing an optical amplifier of a space division multiplexing communication system.
Amplification is achieved in conventional single mode fiber communication systems primarily by rare earth doped active fiber amplifiers, of which erbium doped fiber based amplifiers have gained widespread use. The high gain characteristic of the rare earth doped fiber can be transferred to the space division multiplexing active fiber through a common preparation process, so that the problem to be solved most urgently by the space division multiplexing amplifier is that the gain difference of each mode is large, so that obvious signal power difference appears after amplification, and the system interruption probability is easily increased due to multiple accumulation in transmission, so that the bit error rate of a receiving end is increased.
The source of solving the mode gain difference problem lies in the gain profile design of the few-mode active optical fiber. The structural design of the optical fiber comprises a refractive index profile design and a gain profile design, wherein the refractive index profile design determines the characteristics of the optical fiber such as cut-off wavelength, mode number, mode field distribution, dispersion and the like, and the gain profile design determines the mode gain and the mode-to-mode gain difference of the optical fiber. The fiber refractive index profile is the most interesting issue for passive fibers for transmission, and the amplifier section focuses more on the design of the gain profile of active fibers.
The profile in the field of optical fibers refers specifically to the distribution of the profile over the cross-section of the optical fiber, for example, the refractive index profile or the gain profile of most of the few-mode optical fibers can be represented by the concentric circle structure shown in fig. 1 and 2. The optical fiber main body structure is composed of two parts: a core 1 with a high refractive index, and a cladding 2 with a low refractive index concentric with and surrounding the core. According to the difference of refractive index or doping concentration of gain particles, the fiber core 1 can be divided into a plurality of concentric circle regions, 11, 12, 13 and 14 from inside to outside in the figure, corresponding to the refractive index n1、n2、n3、n4And doping concentration ratio a1、a2、a3、a4As noted in the figures.
In the existing reports, software is written to carry out numerical operation to obtain more reasonable gain profile parameters mainly through a reverse design idea and by adopting methods such as a neural network and a genetic algorithm. At present, no commercial software exists in the design method, the model is complex, and the compiling difficulty is high, so that only few units can realize the gain section design through reverse design. The reverse design process involves a large amount of parameter adjustment and amplification characteristic calculation, and the design is time-consuming. Given a refractive index profile, the time required to perform a gain profile design once is typically over twenty hours.
Disclosure of Invention
The invention provides a method for quickly designing a few-mode optical fiber gain section for intermode gain equalization, which aims to quickly and efficiently realize the design of the few-mode optical fiber gain section by simplifying a gain section design model and a solution thought.
The technical scheme adopted by the invention is as follows:
a method for quickly designing a few-mode optical fiber gain profile for intermode gain equalization is characterized by comprising the following steps:
s1, obtaining refractive index profile parameters of the optical fiber, including the radius of each concentric circle and the refractive index of each layer;
s2, judging whether the optical fiber belongs to a step multilayer structure or not according to the refractive index profile parameters obtained in the step S1; if not, determining the number n of layers of the gain profile; if yes, go to S3;
s3: if the optical fiber is of a step multilayer structure, directly using the layered structure of the refractive index profile in the design of the gain profile to obtain the corresponding doping layering number n of the gain particles;
s4: obtaining the number m of modes supported by the optical fiber and the field distribution of each mode according to the refractive index profile by the aid of a classical solution method or simulation software
S5: calculating a filling factor matrix gamma of each mode in each doping layer according to the field distribution and the layering structure of each modemnWherein matrix element γijFill factor at j layer for i mode, i.e.The power of the ith mode at the jth layer is simply calculated as the ratio of the total power carried by the mode:
s6: using a fill factor matrix ΓmnThe evaluation factors of each mode are constructed, and the doping concentration coefficients of the 1 st layer to the n-th layer are respectively a1To anEvaluation factor e of the i-th modeiCan be expressed as:
when the evaluation factors are equal, obtaining the doping concentration coefficient of each layer to be solved; i.e. to solve a system of equations comprising m equations:
e1＝e2＝...＝em-1＝em＝1 (3)
the following substitution is made for,
the system of equations can be rewritten in the form of a matrix equation
ΓA＝1 (5)
Judging the magnitude relation between m and n, if m is less than n, obtaining a group of proportional relations by the equation set, wherein the proportional relations are the doping concentration ratios of all layers of the gain section; if m > n, the constraint condition of the equation set is more than the number of unknowns, the equation set is not solved, and S7 is executed.
S7: and (4) converting into a solution of the over-determined equation problem, namely finding a least square solution of the over-determined equation gamma A-1. The solution can be done manually or computer-aided. So far, the first round of parameter calculation is completed.
S8: the number of virtual subdivision levels s per level is set. The number of calculated layers divided at this time is s · n in total, but the number of doping profile layers n is not changed, and the doping concentration still has only n different values.
S9: according to the definition and formula provided by S5, calculating filling factors of each mode in each layer containing the virtual subdivision layer, and constructing a new matrix Γ S according to the following rulemn：
Where the subscript jk denotes the kth subdivided layer of the jth layer.
S10: and solving the overdetermined equation set gamma SA 1 manually or by a computer.
S11: and (5) checking the residual error of the over-determined equation under two times of calculation. And if the residual difference is larger than the set threshold delta, increasing the S, and repeating the steps S8-S11 until the threshold requirement is met, thereby completing the design.
Preferably, the method can also determine the completion of the design by directly comparing the evaluation factor difference with the threshold. That is, after S7 or S10 is finished, the corresponding evaluation factors e of each mode are directly calculated at the current timeiAnd (5) performing difference, comparing with a set threshold delta, and finishing the design if the difference is smaller than the threshold.
The invention has the beneficial effects that:
the invention does not need complex methods such as neural network, genetic algorithm and the like, does not relate to amplification characteristic calculation, and has extremely simple program compiling; the mathematical model in the invention is simple and easy to operate, the typical completion time under the computer-aided calculation condition is within a few minutes, the design time consumption is obviously reduced, and the solution can be realized through manual calculation under the extreme condition, so that the dependence degree of the design on the computer-aided calculation is reduced.
Drawings
FIG. 1 is a schematic cross-sectional view of a concentric-circle-structured few-mode optical fiber in the prior art;
FIG. 2 is a schematic diagram of a refractive index profile and a gain profile of a concentric-circle-structured few-mode optical fiber in the prior art;
fig. 3 is a flowchart of a method for rapidly designing a few-mode fiber gain profile for gain equalization between modes according to the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Aiming at the problems of high threshold, high difficulty, long time consumption and the like of the current few-mode optical fiber gain section design, the invention provides a method for quickly designing a few-mode optical fiber gain section for gain equalization among modes, which is shown in figure 3 and comprises the following steps:
s1, obtaining refractive index profile parameters of the optical fiber, such as the radius of each concentric circle and the refractive index of each layer shown in FIG. 1;
s2, judging whether the optical fiber belongs to a step multilayer structure or not according to the refractive index profile parameters obtained in the step S1; if not, determining the number n of layers of the gain profile; if yes, go to S3;
s3: if the optical fiber is of a step multilayer structure, directly using the layered structure of the refractive index profile in the design of the gain profile to obtain the corresponding doping layering number n of the gain particles;
s4: obtaining the number m of modes supported by the optical fiber and the field distribution of each mode according to the refractive index profile by the aid of a classical solution method or simulation software
S5: calculating a filling factor matrix gamma of each mode in each doping layer according to the field distribution and the layering structure of each modemnWherein matrix element γijThe filling factor of the ith pattern at the jth layer, i.e. the ratio of the power of the ith pattern at the jth layer in the total power carried by the pattern, can be simply calculated by the following formula:
s6: using a fill factor matrix ΓmnThe evaluation factors of each mode are constructed, and the doping concentration coefficients of the 1 st layer to the n-th layer are respectively a1To anEvaluation factor e of the i-th modeiCan be expressed as:
when the evaluation factors are equal, obtaining the doping concentration coefficient of each layer to be solved; i.e. to solve a system of equations comprising m equations:
e1＝e2＝...＝em-1＝em＝1 (3)
the following substitution is made for,
the system of equations may be rewritten as a matrix equation
ΓA＝1 (5)
Judging the magnitude relation between m and n, if m is less than n, obtaining a group of proportional relations by the equation set, wherein the proportional relations are the doping concentration ratios of all layers of the gain section; if m > n, the constraint condition of the equation set is more than the number of unknowns, the equation set is not solved, and S7 is executed.
S7: and (4) converting into a solution of the over-determined equation problem, namely finding a least square solution of the over-determined equation gamma A-1. The solution can be performed manually or computer-aided. So far, the first round of parameter calculation is completed.
S8: the number of virtual subdivision levels s per level is set. The number of calculated layers divided at this time is s · n in total, but the number of doping profile layers n is not changed, and the doping concentration still has only n different values.
S9: according to the definition and formula provided by S5, calculating filling factors of each mode in each layer containing the virtual subdivision layer, and constructing a new matrix Γ S according to the following rulemn：
Where the subscript jk denotes the kth subdivided layer of the jth layer.
S10: and solving the overdetermined equation set gamma SA 1 manually or by a computer.
S11: and (5) checking the residual error of the over-determined equation under two times of calculation. And if the residual difference is larger than the set threshold delta, increasing the S, and repeating the steps S8-S11 until the threshold requirement is met, thereby completing the design.
Preferably, the method can also determine the completion of the design by directly comparing the evaluation factor difference with the threshold. That is, after S7 or S10 is finished, the corresponding evaluation factors e of each mode are directly calculated at the current timeiAnd (5) performing difference, comparing with a set threshold delta, and finishing the design if the difference is smaller than the threshold.
Example one
As shown in fig. 3, the method for designing the gain profile of the few-mode optical fiber for gain equalization between modes disclosed in the present invention includes the following steps for the optical fiber with the refractive index profile parameters shown in table 1 below:
and S1, acquiring the refractive index profile parameters of the optical fiber. The parameters of the refractive index profile used in this example are shown in table 1 below;
TABLE 1 refractive index parameters for a three-core fiber used in example one
| Radius (mum) | 3 | 6.26 | 10 | 14 | 20 | 62.5 |
| Refractive index | 1.4488 | 1.4512 | 1.4500 | 1.4440 | 1.4370 | 1.4440 |
The refractive index profile of the fiber is 6 layers in total. The outermost side is a cladding; the inner three layers have refractive indexes higher than that of the cladding and are multilayer regions designed relative to a gain section; the outer 3 layers are cladding and transition layers, which only affect the mode characteristics and do not incorporate the gain profile design.
And S2, judging that the optical fiber belongs to the step multilayer structure according to the refractive index profile parameters obtained in the step S1. Execution of S3;
s3: directly using the layered structure of the refractive index profile in the design of the gain profile to obtain the corresponding doping layering number 3 of the gain particles;
s4: according to the refractive index profile, 5 modes which can be supported by the optical fiber and field distribution phi of each mode are obtained by the assistance of simulation software COMSOLMUTIPhysics1～φ5；
S5: calculating a filling factor matrix gamma of each mode in each doping layer according to the field distribution and the layering structure of each modemn
S6: using a fill factor matrix ΓmnThe evaluation factors of each mode are constructed, and the doping concentration coefficients of the 1 st layer to the 3 rd layer are respectively a1To a3，A＝[a1,a2,a3]T,
The system of equations can be rewritten in the form of a matrix equation
ΓA＝1 (9)
The matrix equation m is 5, n is 3, m > n is satisfied, the constraint condition of the equation set is more than the number of unknowns, the equation set is not solved, and S7 is executed.
S7: and (4) converting into a solution of the over-determined equation problem, namely finding a least square solution of the over-determined equation gamma A-1. The solution of the over-determined equation is obtained by Matlab software aided solution as a ═ 1.280950865,0.758076479,1.303455178]T. So far, the first round of parameter calculation is completed.
And judging the completion of the design by adopting an evaluation factor. After S7 or S10 is finished, the corresponding evaluation factors e of each mode are directly calculated at the current timeiAnd (5) performing difference, comparing with a set threshold delta, and finishing the design if the difference is smaller than the threshold. In this embodiment, S7 is used to find the evaluation factor e of each mode corresponding to aiAnd the corresponding differences are shown in table 2 below.
Table 2 example evaluation factors and differences for each mode
| |
|
|
Mode 4 | Mode 5 | |
| Evaluation factor ei | 0.992229367 | 1.001114996 | 1.020454713 | 1.004063661 | 0.98129069 |
| Difference value | - | 0.008885629 | 0.028225345 | 0.011834294 | -0.010938678 |
For the set threshold δ of 0.05, the present embodiment determines that the design is complete when the difference between the evaluation factors corresponding to the respective modes is smaller than δ as a result obtained in step S7. The gain profile design parameters obtained in this example are shown in table 3 below.
TABLE 3 example gain Profile parameters
It will be understood by those skilled in the art that the above-described types of parameters of the core, cladding and rare earth doped region are merely exemplary, and that other types of applications of the core, cladding and rare earth doped region, which are currently or later become known and may be used in the embodiments of the present invention, are also included within the scope of the present invention and are hereby incorporated by reference.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (2)
1. A method for quickly designing a few-mode optical fiber gain profile for intermode gain equalization is characterized by comprising the following steps:
s1, obtaining refractive index profile parameters of the optical fiber;
s2, judging whether the optical fiber belongs to a step multilayer structure or not according to the refractive index profile parameters obtained in the step S1; if not, determining the number n of layers of the gain profile; if yes, go to S3;
s3: if the optical fiber is of a step multilayer structure, directly using the layered structure of the refractive index profile in the design of the gain profile to obtain the corresponding doping layering number n of the gain particles;
s4: obtaining the number m of modes supported by the optical fiber and the field distribution of each mode according to the refractive index profile by the aid of a classical solution method or simulation software
S5: according to the distribution and the layered structure of each mode field, calculating a filling factor matrix gamma of each mode in each doping layermnWherein matrix element γijThe filling factor of the ith pattern at the jth layer, i.e. the ratio of the power of the ith pattern at the jth layer in the total power carried by the pattern, can be calculated by the following formula:
s6: using fill factor matrix ΓmnThe evaluation factors of each mode are constructed, and the doping concentration coefficients of the 1 st layer to the n-th layer are respectively a1To anEvaluation factor e of the i-th modeiCan be expressed as:
when the evaluation factors are equal, obtaining the doping concentration coefficient of each layer to be solved; i.e. to solve a system of equations comprising m equations:
e1＝e2＝…＝em-1＝em＝1 (3)
the following substitution is made for,
the system of equations can be rewritten in the form of a matrix equation:
ΓA＝1 (5)
judging the magnitude relation between m and n, if m is less than n, obtaining a group of proportional relations by the equation set, wherein the proportional relations are the doping concentration ratios of all layers of the gain section; if m is greater than n, the constraint condition of the equation set is more than the number of unknown numbers, the equation set is not solved, and S7 is executed;
s7: converting into a problem of solving an overdetermined equation, namely finding a least square solution of the overdetermined equation gamma A1, and solving to complete the first round of parameter calculation;
s8: setting the number s of virtual fine layers of each layer, wherein the number of divided calculated layers is s.n layers in total, but the number n of doping section layers is not changed, and the doping concentration still has n different values;
s9: according to the definition and formula provided in step S5, calculating filling factors of each mode in each layer including the virtual subdivision layer, and constructing a new matrix Γ S according to the following rulemn：
Wherein the subscript jk denotes the kth subdivided layer of the jth layer;
s10: solving an overdetermined equation set gamma SA (1);
s11: checking the residual error of the overdetermined equation under the two-time calculation; and if the residual difference is larger than the set threshold delta, increasing the S, and repeating the steps S8-S11 until the threshold requirement is met, thereby completing the design.
2. The method for rapidly designing a gain profile of a few-mode fiber for intermodal gain equalization according to claim 1, wherein:
design completion can also be determined by directly comparing the evaluation factor difference with a threshold, i.e.After S7 or S10 is finished, the corresponding evaluation factors e of each mode are directly calculated at the current timeiAnd (5) making a difference, comparing the difference with a set threshold delta, and finishing the design if the difference is smaller than the threshold.
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