CN112733073A - Multi-core optical fiber crosstalk detection method based on coupling power theory - Google Patents
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Abstract
The invention discloses a multi-core optical fiber crosstalk detection method based on a coupling power theory, which redefines a coupling mode equation of the coupling mode theory, assumes that the rest random part of a phase function is stable and the statistical average is zero, calculates the average power, converts a variable of the average power and rewrites the variable to obtain a power coupling coefficient which changes longitudinally, obtains the average power coupling coefficient, obtains crosstalk according to the return stroke of the coupling mode, detects the known quantity of a crosstalk formula model in real time during detection and obtains the crosstalk of an optical fiber through the crosstalk formula calculation. According to the method, a coupling mode equation after the bending and torsion information is added is re-determined from a coupling mode theory, the actual disturbance situation is better met, and the power coupling coefficient is re-deduced on the basis of the actual disturbance situation and a crosstalk deduction formula in the prior art, so that a more accurate crosstalk detection model is obtained, and the detection of the optical fiber crosstalk through the model is more accurate.
Description
Technical Field
The invention relates to a crosstalk detection method, in particular to a multi-core optical fiber crosstalk detection method based on a coupling power theory, and belongs to the field of optical fiber manufacturing.
Background
With the rapid development of network and broadband services, the internet traffic has increased at a rate of about 100 times every 10 years since 2000, and the transmission capacity of a conventional Single-Mode Single-Core Fiber (SM-SCF) has also increased exponentially under the development of advanced technology, and has reached the shannon transmission limit of 100 Tb/s. Therefore, when the transmission capacity of the single-core optical fiber reaches a bottleneck, the multi-core optical fiber technology is produced.
The multicore fiber has been highlighted by foreign related organizations since its development, and the united states OFS and japan NICT and Sumitomo companies are mainly used among them. In the multi-core fiber research, a multi-core fiber model is usually established by a research worker, taking a dual-core fiber as an example, assuming that optical power is input from one of fiber cores, solving according to a coupling mode equation derived by the predecessor to obtain a normalized mode amplitude analytical solution of the dual-core fiber, and then obtaining corresponding normalized transmission power so as to obtain an inter-core crosstalk formula. This is the calculation of the multicore fiber crosstalk formula from the angle of the coupled mode theory. However, in practical situations, due to uncertain factors such as bending and torsion existing in the laying and using processes, optical fiber transmission does not present a fluctuation form of the coupling mode theory any more, and in such a situation, the coupling power theory is more effective and accurate.
The equation obtained by the existing power coupling theory is that both the bending radius and the torsion rate are taken as random terms and are treated as a stable random process, but no relation between the bending and the torsion rate exists in the phase of the propagation constant, so that the equation does not accord with the actual situation in the experiment, and the finally obtained crosstalk result and the actual crosstalk error are large.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a multi-core optical fiber crosstalk detection method based on a coupling power theory, which is more in line with the actual disturbance situation and improves the accuracy of crosstalk detection.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
a multi-core optical fiber crosstalk detection method based on a coupling power theory is characterized by comprising the following steps:
the method comprises the following steps: redefining a coupling mode equation of a coupling mode theory;
step two: assuming that the rest random part of the phase function is stable and the statistical average is zero, calculating the average power;
step three: rewriting the average power conversion variable;
step four: obtaining a power coupling coefficient which changes longitudinally;
step five: obtaining an average power coupling coefficient;
step six: and crosstalk is obtained according to the coupling mode return path, the known quantity of the crosstalk formula model is detected in real time during detection, and the crosstalk of the optical fiber is obtained through calculation of a crosstalk formula.
2. The multi-core optical fiber crosstalk detection method based on the coupled power theory as claimed in claim 1, wherein: the step one is specifically
Known from the known coupled power equation
Where P is the average power of the core m and hmnIs the power coupling coefficient; to represent longitudinal variation, a local propagation constant difference Δ β 'is defined'mn，
△βmn＝βm-βn (28- 3)
The coupled mode equation of redefining the coupled mode theory is
3. The multi-core optical fiber crosstalk detection method based on the coupled power theory as claimed in claim 1, wherein: the second step is specifically that
Assuming that the remaining random portion of the phase function is stationary and statistically averaged to zero, < δ f (z) 0>, the average power at z 0 can be obtained using equation (29)
Is simplified into
4. The multi-core optical fiber crosstalk detection method based on the coupled power theory as claimed in claim 1, wherein: the third step is specifically that
The conversion variable ζ is ξ - η, which can be obtained
The random part of the phase function, δ f, is a stationary random process with an autocorrelation function, R (ζ), of<δf(η+ζ)δf*(η)>The variance is 1, the first integral of equation (32) yields the fiber length z, and the autocorrelation function contributes only to the order of the correlation length, so equation (32) is rewritten to
5. The multi-core optical fiber crosstalk detection method based on the coupled power theory as claimed in claim 1, wherein: the fourth step is specifically that
Longitudinally varying power coupling coefficient, where power spectral density S (Δ β'mn) Is a fourier transform of the autocorrelation function;
the autocorrelation function is an exponential autocorrelation function with a power coupling coefficient of
This is a fourier transform of a lorentz function.
6. The multi-core optical fiber crosstalk detection method based on the coupled power theory as claimed in claim 5, wherein: the fifth step is specifically that
To avoid numerical solutions of the coupled power equation, the average value of the power coupling coefficient over the torque is
The average power coupling coefficient obtained by bringing formula (34) into formula (35) is
Wherein
7. The multi-core optical fiber crosstalk detection method based on the coupled power theory as claimed in claim 2, wherein: the sixth step is specifically that
From the coupled power equation of equation (27), the crosstalk can be found as
In the case of very little crosstalk, it is denoted as
Compared with the prior art, the invention has the following advantages and effects: the multi-core optical fiber crosstalk detection method based on the coupling power theory starts from the coupling mode theory, re-determines the coupling mode equation after the bending and torsion information is added, and is more consistent with the actual disturbance situation, and re-deduces the power coupling coefficient on the basis of the actual disturbance situation and the crosstalk deduction formula in the prior art, so that a more accurate crosstalk detection model is obtained, and the optical fiber crosstalk is detected more accurately through the model. The method provided by the invention considers the actual situation, leaves the phase relation of bending and disturbance in the actual situation, and better fits the bending and twisting situations in the actual optical fiber wiring, and the detection result of the method provided by the invention is more fit with the actual test result.
Drawings
Fig. 1 is a flowchart of a multi-core optical fiber crosstalk detection method based on a coupling power theory according to the present invention.
Fig. 2 is a diagram comparing crosstalk results simulation of an embodiment of the present invention with the prior art.
FIG. 3 is a diagram illustrating a comparison between crosstalk values at different bending radii for an embodiment of the present invention and the prior art.
Detailed Description
To elaborate on technical solutions adopted by the present invention to achieve predetermined technical objects, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, it is obvious that the described embodiments are only partial embodiments of the present invention, not all embodiments, and technical means or technical features in the embodiments of the present invention may be replaced without creative efforts, and the present invention will be described in detail below with reference to the drawings and in conjunction with the embodiments.
The present invention is developed based on the coupled power theory of the prior art, and therefore, in order to more fully illustrate the technical solution of the present invention, the coupled power theory of the prior art is illustrated in detail as follows:
the theory of coupled power first appeared in d.marcues in the us in 1971, which will be described here in a summary using zhengsi.
Considering the irregularities caused by bending and stress fluctuation during actual use, the known coupled mode equation
After adding the perturbation, the following form can be written:
wherein f (z) describes the actual bend (bend radius R)b) And the phase function of the twisting effect (twist rate γ). Suppose that
κmn＝-jCmnexp[j(βm-βn)z]f(z) (3)
Equation (2) can be written as:
considering lossless, power flow density conservation:
the following expression can be obtained by reusing equation (4):
wherein represents a complex conjugate. Interchanging the second terms m, n in the formula to obtain:
due to the amplitude term in equation (7)
It cannot be constant zero, so the following relationship of coupling coefficients can be obtained:
further, it can be obtained from the formula (3):
assuming that f (z) is a stationary random variable, its autocorrelation function is assumed to be gaussian first, and the derivation process is similar for the remaining two cases:
where is the variance, σ2Is the correlation length of (f), (z). The average power per mode is:
Pm＝<|Am|2> (11)
the symbol < represents the overall average. From formulas (2) and (11):
where Δ βmn＝βm-βn. And satisfies Δ βmμ+△βμn＝△βmn. Assuming that the initial point of the optical waveguide is located at z ═ 0, an approximate solution of equation (2) can be obtained at a z point sufficiently close to z ═ 0:
the solution of equation (13) is based on first order perturbation theory, which is applicable to cases where the coupling is very weak or where z is so small that A isμ(z) and Aμ(0) In the case of very small differences. A. theμ(0) Independent of statistical fluctuations, the values are therefore identical to the mean values. Ignore CmnA higher-order term of the middle-second order or higher, obtained by substituting formula (13) into formula (12):
in the above formula because
<f(z)>＝0
(15)
Thus, CmnThe first power term of (a) is zero. c. represents a complex conjugate term in formula (14). Using equation (10) and the following relationship:
△βnμ＝-△βμn (16)
the following can be obtained:
it is assumed here that z>>D and σ2Small enough to ensure the accuracy of the approximate solution of equation (2-69). The integral term in equation (2-73) can be written as:
wherein, F (D,. DELTA.. beta.)μn) Is a real function and is independent of z. Thus, the only z-related quantity of equation (17) is exp [ j (. DELTA.. beta.)mn-△βμn)z]. It has been found for the differential equation (14) with respect to the z-integral that the effect of the ripple term on the right hand side of the equation is not significant. This is because am (z) is a slowly varying term compared to the fluctuating term, and integrating the sine-cosine function is not as significant as integrating the slowly varying function. Therefore, the fluctuation term can be ignored here, and only β in the formula (17) is consideredm＝βμThe case (2) is not limited. Similarly, the following formula can be obtained:
as can be seen from the above discussion, only the non-fluctuating term contributes to the differential equation (14), and therefore only β is consideredμ＝βnThe case (1). Thus, equation (14) is expressed as:
since it is assumed that the coupling is very weak and the variation of the wave amplitude over the transmission distance z is not large, An (0) can be replaced by An (z) here, and using equations (9) and (11), it can be obtained from equation (20):
the complex conjugate term therein is such that the imaginary part of equation (20) is zero. Usually taking the variance σ2Suppose that 1 is
Equation (21) can be written as:
the above equation is the power coupling equation. Wherein h ismnIs the power coupling coefficient between optical waveguides m and n. Further, according to the formula (9):
hmn＝hnm
(24)
the above is based on the power of mode m derived at z-0. However, we can follow the same derivation, assuming the value of the wave amplitude of each mode at a certain point z ', and then calculate the power at a certain adjacent point z' +. DELTA.z. Assuming the case of weak coupling, the power of mode m at any point z 'is derived from the power of all modes at z'.
It should be noted that, here, derivation is performed only when the autocorrelation function of f (z) is a Gaussian Autocorrelation Function (GAF), the derivation processes of the other two autocorrelation functions are not repeated, and here, only the derivation result is given, that is, when the autocorrelation function of z) is an Exponential Autocorrelation Function (EAF), the power coupling coefficient h is givenmnComprises the following steps:
power coupling coefficient h when the autocorrelation function of f (z) is a Triangular Autocorrelation Function (TAF)mnComprises the following steps:
and the form of the power coupling equation is exactly the same as the form of equation (23).
The invention re-deduces the power coupling coefficient h on the basis of the abovemnRelation of (a), hmnIncluding bending and torsional disturbances, and then determining hmnI.e. the average power coupling coefficient.
As shown in fig. 1, the method for detecting crosstalk of a multi-core optical fiber based on a coupling power theory specifically includes the following steps:
known from the known coupled power equation
Where P is the average power of the core m and hmnIs the power coupling coefficient. To represent longitudinal variation, a local propagation constant difference Δ β 'is defined'mn，
△βmn＝βm-βn (28- 3)
The coupled mode equation of redefining the coupled mode theory is
Assuming that the remaining random portion of the phase function is stationary and statistically averaged to zero, < δ f (z) 0>, the average power can be obtained using equation (29) when z is 0
Is simplified into
The conversion variable ζ is ξ - η, which can be obtained
The random part of the phase function, δ f, is a smooth random process, and therefore it has an autocorrelation function, R (ζ), which is equal to<δf(η+ζ)δf*(η)>Variance is 1, note that the first integral of equation (32) yields the fiber length z, while the autocorrelation function only contributes to the order of the correlation length, so equation (32) can be rewritten as
Finally, we have derived the following longitudinally varying power coupling coefficient, where power spectral density S (. DELTA.. beta. ')'mn) Is the fourier transform of the autocorrelation function.
The autocorrelation function can be a Gaussian autocorrelation function, a triangular autocorrelation function or an exponential autocorrelation function, and is physically more practical based on an exponential autocorrelation function with a power coupling coefficient of
This is a fourier transform of a lorentz function. To avoid numerical solutions of the coupled power equation, the power coupling coefficient has an average over the torque of
The average power coupling coefficient obtained by bringing formula (34) into formula (35) is
Wherein
From the coupled power equation of equation (27), the crosstalk can be found as
In the case of very little crosstalk, this can be expressed as
As can be seen from the coupling mode equation redefined by the equation (29), the difference from the previous one is that Δ β in exp ()mnBecome delta beta'mn
△β'mnThe optical fiber has bending and twisting disturbance conditions, which are closer in practical conditions, and the transmission condition of the optical fiber under the condition of actually laying a line is better simulated.
The present application is further described below by way of specific comparison.
Two power coupling coefficients are compared:
originally:
wherein Δ βmn＝βm-βn
After modification:
wherein
Simulations were performed for crosstalk calculation for a longitudinally evolved discrete variation model (DCM), a generalized semi-analytical model (USAM), and a modified Coupled Power Theory (CPT), as shown in fig. 2. The results were very consistent.
A simulation of the crosstalk values at different bend radii is shown in fig. 3. Since the longitudinal evolution discrete variation model (DCM) is not suitable for the condition of large bending radius, the crosstalk value thereof becomes larger as the bending radius becomes larger, and the crosstalk variation trend of the modified coupling power theory and the common semi-analytical model (USAM) is approximately consistent, and the power coupling theory angle is close to the actual situation.
Although the present invention has been described with reference to a preferred embodiment, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (7)
1. A multi-core optical fiber crosstalk detection method based on a coupling power theory is characterized by comprising the following steps:
the method comprises the following steps: redefining a coupling mode equation of a coupling mode theory;
step two: assuming that the rest random part of the phase function is stable and the statistical average is zero, calculating the average power;
step three: rewriting the average power conversion variable;
step four: obtaining a power coupling coefficient which changes longitudinally;
step five: obtaining an average power coupling coefficient;
step six: and crosstalk is obtained according to the coupling mode return path, the known quantity of the crosstalk formula model is detected in real time during detection, and the crosstalk of the optical fiber is obtained through calculation of a crosstalk formula.
2. The method for detecting the crosstalk of the multi-core optical fiber based on the coupling power theory as claimed in claim 1, wherein: the step one is specifically
Known from the known coupled power equation
Where P is the average power of the core m and hmnIs the power coupling coefficient; to represent longitudinal variation, a local propagation constant difference Δ β 'is defined'mn，
△βmn＝βm-βn (28-3)
The coupled mode equation of redefining the coupled mode theory is
3. The method for detecting the crosstalk of the multi-core optical fiber based on the coupling power theory as claimed in claim 1, wherein: the second step is specifically that
Assuming that the remaining random portion of the phase function is stationary and statistically averaged to zero, < δ f (z) 0>, the average power at z 0 can be obtained using equation (29)
Is simplified into
4. The method for detecting the crosstalk of the multi-core optical fiber based on the coupling power theory as claimed in claim 1, wherein: the third step is specifically that
The conversion variable ζ is ξ - η, which can be obtained
The random part of the phase function, δ f, is a stationary random process with an autocorrelation function, R (ζ), of<δf(η+ζ)δf*(η)>The variance is 1, the first integral of equation (32) yields the fiber length z, and the autocorrelation function contributes only to the order of the correlation length, so equation (32) is rewritten to
5. The method for detecting the crosstalk of the multi-core optical fiber based on the coupling power theory as claimed in claim 1, wherein: the fourth step is specifically that
Longitudinally varying power coupling coefficient, where power spectral density S (Δ β'mn) Is the fourier transform of the autocorrelation function;
the autocorrelation function is an exponential autocorrelation function with a power coupling coefficient of
This is a fourier transform of a lorentz function.
6. The method for detecting crosstalk of the multi-core optical fiber based on the coupling power theory as claimed in claim 5, wherein: the fifth step is specifically that
To avoid numerical solutions of the coupled power equation, the power coupling coefficient has an average over the torque of
The average power coupling coefficient obtained by bringing formula (34) into formula (35) is
Wherein
7. The method for detecting crosstalk of the multi-core optical fiber based on the coupling power theory as claimed in claim 2, wherein: the sixth step is specifically that
From the coupled power equation of equation (27), the crosstalk can be found as
In the case of very little crosstalk, it is denoted as
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| CN114647924A (en) * | 2021-12-28 | 2022-06-21 | 苏州大学 | Actual multi-core fiber nonlinear crosstalk calculation model based on segmentation idea |
| CN115455355A (en) * | 2022-09-16 | 2022-12-09 | 苏州大学 | Method and device for detecting intermode crosstalk of multi-core few-mode optical fiber |
| CN116865849A (en) * | 2023-06-11 | 2023-10-10 | 苏州大学 | High-torsion-rate weak-coupling multi-core optical fiber crosstalk detection method and device |
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