Using fractional Fourier transform nonlinear effects in optical fiber link monitoring methods

Abstract

The present invention proposes a method for monitoring the nonlinear effect of an optical fiber link by fractional Fourier transformation, FRFT, by calculating an optimal fractional order of the FRFT of the frequency-domain signal propagating through an optical fiber link, calculating the chromatic dispersion of an optical fiber link based on the optimal fractional order, compensating for chromatic dispersion to the signal, calculating an optimal fractional order of the FRFT for the time-domain signal following the compensation for chromatic dispersion, calculating the time-domain chirp caused by the nonlinear effect of an optical fiber link based on the optimal fractional order, and monitoring the nonlinear effect of an optical fiber link based on the absolute value of the calculated time-domain chirp. The method can be used for quantitatively monitoring the nonlinear effect of an optical fiber link in an optical fiber communication system consisting of different types of optical fibers.

Claims

1. A method for monitoring the nonlinear effect of an optical fiber link by fractional Fourier transformation, FRFT, comprising: step one, performing coherent demodulation for an optical signal propagating through an optical fiber link to obtain a real part E .sub.I and an imaginary part E.sub.Q of an electric field of the optical signal, and next, calculating the complex electric field of the optical signal by E=E.sub.I+jE.sub.Q, where j is an imaginary unit; step two, performing Fourier transformation for the complex field of the optical signal obtained in the step one to obtain the complex field in frequency domain; step three, performing FRFT for the complex field in frequency domain obtained in the step two, calculating an optimal fractional order of the FRFT; step four, calculating the chromatic dispersion of an optical fiber link based on the optimal fractional order obtained in the step three; step five, compensating for the chromatic dispersion based on the chromatic dispersion of the optical fiber link obtained in the step four to obtain a signal following the dispersion compensation; step six, performing an inverse Fourier transformation for the signal following the dispersion compensation obtained in the step five to obtain a complex field in time domain; step seven, performing FRFT for the complex field in time domain obtained in the step six, calculating the optimal fractional order of the FRFT; step eight, calculating the chirp coefficient of the complex field in time domain based on the optimal fractional order obtained in the step seven; and step nine, obtaining an absolute value of the chirp coefficient obtained in the step eight.

2. The method for monitoring the nonlinear effect of an optical fiber link by FRFT according to claim 1, wherein, a method for searching for the optimal fractional order of the FRFT in the step three and step seven includes maximizing a variance of a fractional amplitude spectrum, comprising: calculating the variance of fractional amplitude spectrum obtained by FRFT with different fractional order, the fractional order corresponding to the maximum value of the variance of a fractional amplitude spectrum is an optimal fractional order; to be special, a fractional order .sub.i changes to .sub.i=.sub.i-1+ in a range of [0, 2] based on a fixed step length , performing FRFT for each fractional order, respectively, calculating a variance .sub.i of the fractional amplitude spectrum of each FRFT, further calculating the maximum value of all of the variances of the fractional amplitude spectrum, and the resulting fractional order corresponding to the maximum value of the variance of the fractional amplitude spectrum is an optimum fractional order.

3. The method for monitoring the nonlinear effect of an optical fiber link by FRFT according to claim 1, wherein, in the step five, the complex field in frequency domain obtained in the step two is multiplied by a dispersion function, {tilde over (E)}.sub.Comp()={tilde over (E)}()e.sup.jCD.sup.2, where represents a .sup.ECom (.sup.W) frequency.

4. The method for monitoring the nonlinear effect of an optical fiber link by FRFT according to claim 1, wherein, in the step 4, the concrete method of calculating the chromatic dispersion of an optical fiber link based on the optimal fractional order obtained in the step three is: based on the optimal fractional order .sub.optimum obtained in the step three, calculating the chromatic dispersion of an optical fiber link, that is $\mathrm{CD}=-\frac{\cot \left(\frac{}{2}.Math.{}_{\mathrm{optimum}}\right)}{2.Math..Math..Math.S^2},$ where S is a scale factor in the FRFT, the value thereof is S={square root over (N)}, and N is the number of samples of a signal.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0029] FIG. 1 is a flowchart of a method for monitoring the nonlinear effect of an optical fiber link by FRFT in the present invention and embodiments;

[0030] FIG. 2 is a flowchart of a method of searching for an optimal fractional order in the present invention and embodiments;

[0031] FIG. 3 is a schematic diagram of a system structure for monitoring the nonlinear effect of an optical fiber link by FRFT in the present invention and embodiments;

[0032] FIG. 4 is a structure diagram of FRFT processing modules in the present invention and embodiments;

[0033] FIG. 5 is a fractional-order amplitude spectrum diagram of a 10Gbit/s OOK optical pulses obtained by the FRFT of different orders following a dispersion compensation to the output of the optical fibers in embodiments of the present invention, wherein x-coordinates p and u are two parameters of the FRFT, respectively, and y-coordinates are an amplitude spectrum value;

[0034] FIG. 6 is a relation curve of the chirp coefficient obtained by adopting the FRFT to its time-domain signal and the maximum nonlinear phase shift of the nominal optical fiber link following a dispersion compensation of a 10 Gbit/s OOK optical pulses output from the optical fibers of different lengths in enibodiments of the present invention;

[0035] FIG. 7 is a relation curve of the chirp coefficient obtained by adopting the FRFT to its time-domain signal and the maximum nonlinear phase shift of the nominal optical fiber link following a dispersion compensation of a 20Gbit/s QPSK, optical pulses output from a standard single mode optical fiber with different launched peak powers in embodiments of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

[0036] For a better description of objects and advantages of the present invention, a further description of summary of the invention is provided in conjunction with drawings and. embodiments below.

Embodiments

[0037] The presentinvention relates to a method for monitoring of the nonlinear effect of an optical fiber link by fractional Fourier transformation (FRFT), the procedure thereof is as shown in FIG. 1, steps while specific implementations are as follows:

[0038] step one, performing coherent demodulations for an optical pulse signal propagating through an optical fiber links to obtain a real part E.sup.I and an imaginary part E.sub.Q of an electric field of the optical pulse signal, and next, calculating a complex electric field E=E.sub.I+jE.sub.Q, where j is an imaginary unit;

[0039] step two, performing Fourier transformation for the complex field of the optical pulse signal obtained in the step one to obtain a complex field in frequency domain {tilde over (E)}() where is an angle frequency of the optical pulse signal;

[0040] step three, performing FRFT for the complex field in frequency domain obtained in the step two, based on the energy focusing effect in the fractional spectrum of the chirp signal, calculating an optimal fractional order .sub.optimum of the method of searching for the optimal fractional order comprises a fractional-order spectral entropy, an optimal filtering operator, maximizing a density of zero-center normalized instantaneous amplitude spectrum, maximizing a variance of fractional-order amplitude spectrum;

[0041] step four, calculating the chromatic dispersion of the optical fiber link based on the optimal fractional order obtained in the step three;

[0042] the concrete method is: based on the optimal fractional order .sub.optimum obtained in the step three, calculating a chromatic dispersion of an optical fiber link, i.e.,

[00003]$\mathrm{CD}=-\frac{\cot \left(\frac{}{2}.Math.{}_{\mathrm{optimum}}\right)}{2.Math..Math..Math.S^2},$

where S is a scale factor in the FRIFT, the value thereof is S={square root over (N)}, and N is the number of samples of a signal;

[0043] step five, compensating for chromatic dispersion for the complex field in frequency domain obtained in the step two based on the chromatic dispersion of the optical fiber link obtained in the step four to obtain the complex field in frequency domain {tilde over (E)}.sub.Comp() following the dispersion compensation;

[0044] the concrete method is the complex field in frequency domain obtained in the step two is multiplied by a dispersion function, i.e., {tilde over (E)}.sub.Comp()={tilde over (E)}()e.sup.jCD.sup.2;

[0045] step six, performing an inverse Fourier transformation for the complex field in frequency domain {tilde over (E)}.sub.Comp () obtained in the step five to obtain a complex field in time domain E.sub.Comp;

[0046] step seven, performing FRFT for the complex field in time domain E.sub.comp obtained in the step six, calculating the optimal fractional order .sub.optimum of the FRFT; the method of searching for the optimal fractional order comprises a fractional-order spectral entropy, an optimal filtering operator, maximizing a density of zero-center normalized instantaneous amplitude spectrum, maximizing a variance of fractional-order amplitude spectrum;

[0047] step eight, calculating a chirp coefficient of the complex field in time domain E.sub.Comp the optimal fractional order .sub.optimum obtained in the step seven, i.e.,

[00004]$C=-\frac{\cot \left(\frac{}{2}.Math.{}_{\mathrm{optimum}}^{}\right)}{2.Math..Math..Math.S^2},$

where S is a scale factor in the FRFT, the value thereof is S={square root over (N)}, and N is the number of samples of a signal;

[0048] step nine, an absolute value |C| of the chirp coefficient of the complex field in time domain E.sub.Comp obtained in the step eight is proportional to a nonlinear phase shift caused by the nonlinear effect of the optical fiber, and therefore the absolute value |C| of the chirp coefficient of the complex field in time domain E.sub.Comp can be used for monitoring the size of the nonlinear effect of the optical fiber;

[0049] where a method that can be adopted for searching for the optimal fractional order of the FRFT in the step three and step seven includes maximizing a variance of a fractional-order amplitude spectrum, comprising:

[0050] calculating the variance of fractional amplitude spectrum obtained by FRFT with different fractional order, the fractional order corresponding to the maximum value of the variance of an amplitude of fractional spectrum is an optimal fractional order; to be special, a fractional order .sub.i changes to .sub.i=.sub.i-1+ in a range of [0, 2] based on a fixed step length i , performing FRFT for each fractional order, respectively, calculating a variance .sub.i of an amplitude spectrum of each FRFT, further calculating the maximum value of all of the variances of the amplitude spectrum, and the resulting fractional order corresponding to the maximum value of the variance of the amplitude spectrum is an optimal fractional order.

[0051] The procedure of the method of searching for an optimal fractional order of calculating an optimal fractional order of the FRFT in the step three and step seven (corresponding to the grey bolded box indicated by the 3.sup.rd and 7.sup.th arrows, respectively) is as shown in FIG. 2.

[0052] In an embodiment, a system for monitoring of the nonlinear effect of an optical fiber link by FRFT can interference-freely monitor the nonlinear effect of optical fiber links. The effect of measurement is independent of a type of an optical fiber, a modulation format and a rate of an optical fiber link signal, solves a real-time monitoring of the nonlinear effect of high-speed optical fiber link, currently.

[0053] The system (hereinafter referred to as system) upon the method for monitoring of the nonlinear effect of an optical fiber link by FRFT in the present embodiment is unnecessary to change a transmitter, and has features of simple in structure, easy to implement. The system as shown in FIG. 3 is made up of a local oscillator laser, an optical mixer, a balanced detector, an analog-digital converter, a FRFT processing module, where the fractional Fourier transformation processing module as shown in FIG. 4 comprises a memory cell, a complex field calculating unit, a Fourier transformation signal processing unit, a fractional Fourier transformation signal processing unit 1, a dispersion calculating unit, a dispersion compensation unit, a Fourier inverse transform signal processing unit, a fractional Fourier transformation signal processing unit 2, and a chirp coefficient calculating unit.

[0054] A connection among each module in the system is: an output end of the local oscillator laser is connected to one input end of the optical mixer, a four-way output of the optical mixer connects the balanced detector, a two-way output of the balanced detector connects the analog-digital converter, and the two-way output of the analog-digital converter connects the fractional Fourier transformation processing module.

[0055] The operating procedure of the system is as follows:

[0056] first of all, mixing the optical pulse signals output by the optical fiber link and the output of the local oscillator laser in the optical mixer, obtaining a real part E.sub.I and imaginary part E.sup.Q of an electric field of the optical pulse signal through the balanced detector;

[0057] secondly, after performing an analog-to-digital conversion, the real part E.sup.I and the imaginary part E.sub.Q of the electric field of the optical pulse signal enter the memory cell in the FRFT processing module for storage, and further calculating to obtain the chirp coefficient for quantitatively monitoring the nonlinear effect of the optical fiber. To be specific, the calculating procedure of the chirp coefficient is as follows:

[0058] 1) the complex field of optical pulse signal obtained by a complex field calculating unit in the FRFT processing module is E=E.sub.I+jE.sub.Q, where j is an imaginary unit; i

[0059] 2) the Fourier transformation signal processing unit performing Fourier transformation for the complex field signals E to obtain the complex field in frequency domain {tilde over (E)}();

[0060] 3) the fractional Fourier transformation signal processing unit 1 further performing a fractional Fourier transformation for the complex field in frequency domain {tilde over (E)}() to obtain an optimal fractional order .sub.optimum, where the concrete method of obtaining .sub.optimumis: a fractional order .sub.i changes to .sub.i=.sub.i-11+ in a range of [0, 2]based on a fixed step length , performing FRFT for the complex field of the optical pulse signal corresponding to each fractional order to obtain a variance .sub.i of an amplitude spectrum of each FRFT, and further calculating the maximum value of all of the variances of the amplitude spectrum, and the resulting fractional order corresponding to the maximum value of the variance of the amplitude spectrum is an optimal fractional order .sub.optimum;

[0061] 4) a dispersion calculating unit further calculating a chromatic dispersion of an optical fiber link, i.e.,

[00005]$\mathrm{CD}=-\frac{\cot \left(\frac{}{2}.Math.{}_{\mathrm{optimum}}\right)}{2.Math..Math..Math.S^2},$

where S is a scale factor in the FRFT, the value thereof is S={square root over (N)}, and N is the number of samples of a signal;

[0062] 5) the dispersion compensation unit performing a dispersion compensation for the complex field in frequency domain {tilde over (E)}() to obtain the following:

{tilde over (E)}.sub.Comp()={tilde over (E)}()e.sup.jCD.sup.2

[0063] 6) the Fourier inverse transform signal processing unit performing an inverse Fourier transformation for the complex field in frequency domain {tilde over (E)}.sub.Comp() to obtain a complex field in time domain E.sub.Comp;

[0064] 7) the complex field in time domain E.sub.Comp enters the fractional Fourier transformation signal processing unit 2 once again to obtain the optimal fractional order .sub.optimum of the FRFT;

[0065] where the method of searching for the optimal fractional order .sub.optimum comprises a fractional-order spectral entropy, an optimal filtering operator, maximizing a density of zero-center normalized instantaneous amplitude spectrum, and maximizing a variance of fractional-order amplitude spectrum;

[0066] 8) the chirp coefficient calculating unit calculating a chirp coefficient of the complex field in time domain E.sub.Comp, i.e.,

[00006]$C=-\frac{\cot \left(\frac{}{2}.Math.{}_{\mathrm{optimum}}^{}\right)}{2.Math..Math..Math.S^2},$

where S is a scale factor in the FRFT, the value thereof is S={square root over (N)}, and N is the number of samples of a signal;

[0067] finally, taking an absolute value |C| with respect to above-mentioned chirp coefficient C, thus this absolute value is a numerical value of a quantitatively characterized nonlinear effect of an optical fiber.

[0068] The method and system for mo toring of the nonlinear effect of an optical fiber link by FRFT in the present embodiment are respectively as shown in FIGS. 1 and 3; and as seen from FIG. 3, the present embodiment is simple to be integrated, and satisfies the requirement of on-line, interference-free, and real-time monitoring of the optical fiber communication links; wherein the optical pulse signal output by the optical fiber links is mixed in the optical mixer with the output of the local oscillator laser, the real part and the imaginary part of an electric field of the optical pulse signal are obtained through the balanced detector, followed by an analog to digital conversion, the number of samples N of the analog to digital conversion is 8197.

[0069] Entering the ERFT processing module after the analog to digital conversion, and calculating to obtain the chirp coefficient of quantitative monitoring of the nonlinear effect of the optical fiber, the calculation procedure thereof is as shown in FIG. 4:

[0070] wherein the searching procedure of the optimal fractional order in the fractional Fourier transformation signal processing unit 2 is as shown in FIG. 2, the fractional order .sub.i changes to .sub.i=.sub.i-1+ in a range of [0, 2] based on a fixed step length , performing FRET for the complex field of the optical pulse signal corresponding to each fractional order to obtain the variance .sub.i of an amplitude spectrum of each FRFT, and further calculating the maximum value of all of the variances of the amplitude spectrum, and the resulting fractional order corresponding to the maximum value of the variance of the amplitude spectrum is an optimal fractional order .sub.optimum.

[0071] FIG. 5 shows an amplitude spectrum of the fractional Fourier transformation of complex field in time domain of optical pulse sequence signal after dispersion compensations, the fractional spectrum of energy focus has the maximum variance of its amplitude spectrum, and. the corresponding fractional order is the optimal fractional order .sub.optimum. The chirp coefficient of the complex field in time domain of the optical pulse signals after a dispersion compensation calculated based on the optimal fractional order is as follows:

[00007]$\mathrm{CD}=-\frac{\cot \left(\frac{}{2}.Math.{}_{\mathrm{optimum}}\right)}{2.Math..Math..Math.S^2};$

where S is a scale factor in the FRFT, the value thereof is S={square root over (N)}, and N is the number of samples of a signal i.e., 8192, The absolute value |C| of the chirp coefficient of the complex field in time domain of an optical pulse sequence signal following the dispersion compensation is proportional to the nonlinear phase shift of the quantitatively characterized nonlinear effect of the optical fibers, therefore the |C| can be used for quantitatively characterizing the nonlinear effect of the optical fibers.

[0072] FIG. 6 is a relation of the chirp coefficient obtained from the output optical pulse sequences via the FRFT processing module and the nominal nonlinear phase shift after the optical pulse sequence signal having a pulse width of 100 picoseconds is transmitted via the standard mono-mode optical fiber of different lengths, when the peak powers of optical pulses of the present embodiment are 8.0 dBm and 18 dBm, respectively.

[0073] FIG. 7 is a relation of the chirp coefficient obtained by the FRFT processing module and the nominal nonlinear phase shift after the optical pulse sequence signals of different pulse peak value powers of the present embodiment are transmitted via the optical fibers having lengths of 10 km and 50 km, respectively. Whereby it can be seen in FIG. 7 that the system of monitoring the nonlinear effect of the optical fiber link designed based on the present invention and embodiments can quantitatively characterize the nonlinear effect of the optical fiber through the chirp coefficient and has features of monitoring conveniently, and accurately.

[0074] As can be seen from the result of FIGS. 6 and 7, the chirp coefficient obtained by the FRFT processing module can quantitatively monitor and characterize the size of the nonlinear effect of the optical fiber. Where after the optical pulse in a modulation format of OOK with 10 Gbit/s having a peak power of 18 dBm in FIG. 6 is transmitted 80 km via the monomode optical fiber, the accumulated nonlinear phase shift is 1.2 radians; the peak power of the optical pulse in a modulation format of QPSK with 20 Gbit/s in FIG. 7 varies from OdBm to 65 dBm, and after transmitting 50 km in an optical fiber, the nonlinear phase shift is also 1.2 radians. This indicates that the system of monitoring of the nonlinear effect of an optical fiber link involved in the present invention and embodiments has features of wide monitoring range and accurate measurement, and meanwhile further indicates that the present invention and embodiments satisfy the requirement of the nonlinear effect of high-speed optical fiber conimunication links undoptical networks, can be applied to an optical communication link system consisting of different types of optical fibers, and different modulation modes, in particular applicable to a high-speed optical-fiber communication system for accurately monitoring and equalizing of the nonlinear effect.

[0075] Method and system for monitoring of the nonlinear effect of an optical fiber link by FRFT in the present invention is described in detail in the foregoing, however, embodiments of the invention are not limited thereto. The embodiments are illustrated only to assist in understanding of the method of present invention and the core concept thereof; meanwhile, for those skilled in the art, both eMbodiments and application ranges will be changed based on the idea of the invention, as apparent from the foregoing, this description should not be construed as limiting the invention.

[0076] A variety of obvious changes made hereto without departing from the spirit of the method of the present invention and the scopes of claims fall within the scope of the invention.