CN108155946B - Multi-pumping phase sensitive amplifier based on high nonlinear optical fiber and generation method - Google Patents
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Abstract
The invention provides a multi-pumping phase sensitive amplifier based on a high nonlinear optical fiber and a generation method thereof, which are used for solving the problems that the existing PSA is not easy to generate four-step phase response and can not realize the phase regeneration of QPSK signals; the method comprises the following steps: n light waves interact in the four-wave mixing process to obtain the following N coupling differential equations; determining how many wavelengths participate in the four-wave mixing process; all wavelengths participating in the four-wave mixing process are listed in N coupling differential equations in the first step to calculate the complex amplitude and the phase of the output wave, and a phase sensitive amplifier is obtained; and optimizing configuration parameters of the phase sensitive amplifier by using a multi-wave model to obtain three HNLF-based multi-pump PSA (pressure swing adsorption) for QPSK (quadrature phase shift keying) signal regeneration. The invention designs the PSA with high energy efficiency by optimizing the initial power of the pump light and the signal light, and obtains the four-step phase response with lower nonlinear phase shift to carry out phase regeneration on the QPSK signal.
Description
Technical Field
The invention relates to the technical field of optical communication, in particular to a multi-pumping phase-sensitive amplifier based on a high nonlinear optical fiber and a generation method.
Background
In optical communication, a Phase Sensitive Amplifier (PSA) is widely used in the fields of low noise amplification and Phase noise cancellation. In high-speed optical communication systems, in order to accommodate the rapidly increasing network traffic, advanced modulation formats with high spectral efficiency have become a research hotspot. Currently, 100Gb/s transmission systems using QPSK modulation format have been put into commercial communication networks. In order to expand the scale of the high-speed QPSK optical network, it is important to research a regenerator for eliminating the accumulated noise in the network node transmission.
A Phase Sensitive Amplifier (PSA) can amplify an in-phase component and simultaneously attenuate a quadrature component in a Differential Phase Shift Keying (DPSK) signal, and thus can effectively suppress phase noise in the DPSK signal. Conventional PSA projects the complex amplitude of the signal onto the gain axis, and thus, for QPSK signal, it is converted into Binary Phase Shift Keying (BPSK) signal, which cannot be directly reproduced. The multi-pump PSA can realize the four-step phase response by changing the configuration parameters, and therefore, the multi-pump PSA can be suitable for the regeneration of QPSK signals.
PSA based on different nonlinear optical media, in which the ultra-fast response speed (10) of PSA based on high nonlinear fiber (HNLF) due to the kerr effect, has been widely studied at present-14s) has the characteristics of ultra-high-speed signal processing, low loss characteristic, dispersion controllability and the like, so that the PSA is unique in a plurality of PSAs. The phase sensitive amplifier based on HNLF has the characteristics of ultra-fast response speed, low loss, controllable dispersion and the like, so that the structure of PSA can be flexible and changeable. The ideal gain and corresponding curve can be obtained by reasonably adjusting the configuration parameters of the HNLF-based multi-pump phase sensitive amplifier. Two-pump degenerate PSAs due to their in-phaseThe property of amplification, anti-phase attenuation (binary step phase response) is often used to regenerate BPSK signals. For the reproduction of QPSK signals, however, a PSA with a four step phase transfer function is required. The fundamental PSA principle based on HNLF can be understood as the transfer of energy between the signal light, the pump light and the sidebands produced by four-wave mixing. HNLF-based PSAs with low dispersion slopes necessarily produce many higher order sidebands due to FWM, and therefore 7-wave models (e.g., two-pump degenerate PSAs) are often used to calculate the high-gain extinction ratio of PSAs. In this model, the higher order sidebands can contribute to phase sensitive attenuation by dissipating pump power, resulting in higher gain extinction ratios. When more wavelengths participate in the four-wave mixing (FWM) process in the PSA, the original 7-wave model needs to be extended accordingly. For multi-pump PSAs with various frequency allocations and input wave power allocations, a multi-wave numerical model is built accordingly.
Disclosure of Invention
Aiming at the technical problems that four-step phase response is not easy to generate in the conventional PSA and the phase regeneration of a QPSK signal cannot be realized, the invention provides a multi-pump phase sensitive amplifier based on a high nonlinear optical fiber and a generation method thereof, provides three phase sensitive amplifiers based on the high nonlinear optical fiber, and has four-step phase response under the condition of smaller Nonlinear Phase Shift (NPS) as far as possible by optimizing configuration parameters of the three phase sensitive amplifiers, thereby realizing the function of regenerating the QPSK signal.
In order to achieve the purpose, the technical scheme of the invention is realized as follows: a multi-pumping phase sensitive amplifier generating method based on high nonlinear optical fiber comprises the following steps:
the method comprises the following steps: n optical waves interact in the four-wave mixing process, including pump light, signal light and generated four-wave mixing sidebands, and the following N coupling differential equations are obtained by omitting some special-structure phase sensitive amplifiers:
wherein A isiComplex amplitudes of N light waves, i ═ 1,2 …, N; a. thei(z)、z、α、
Ap、Am、Aq、Δβi,q,q,oRespectively representing i wave amplitude, distance of light wave in optical fiber, optical fiber loss, n amplitude conjugate of light wave generated by four-wave mixing, pump wave amplitude, m amplitude of light wave generated by four-wave mixing, o amplitude conjugate of light wave generated by four-wave mixing, q amplitude of light wave generated by four-wave mixing, and phase mismatch, delta βi,p,m,n＝βp+βm-βi-βnβ denotes the optical wave transmission constant β ═ 1/2 ═ β2Wherein β2Second order dispersion coefficient of optical fiber, βp、βm、βi、βnRespectively the transmission constants of different light waves p, m, i and n; gamma 2 pi n2/λAeffIs the nonlinear coefficient of the optical fiber, n2Is the nonlinear refractive index of the optical fiber, AeffIs the effective mode field area;
step two: determining how many wavelengths participate in the four-wave mixing process;
step three: all wavelengths participating in the four-wave mixing process are listed in N coupling differential equations in the first step to calculate the complex amplitude and the phase of the output wave, and a phase sensitive amplifier is obtained;
step four: and optimizing configuration parameters of the phase sensitive amplifier by using a multi-wave model to obtain the expected gain and phase characteristics of the phase sensitive amplifier, thereby obtaining the multi-pump phase sensitive amplifier for regenerating the QPSK signal.
The method for determining the specific number of wavelengths participating in the four-wave mixing process comprises the following steps: finding all wavelength combinations capable of meeting the energy conversion relation in the N wavelengths; classifying the found wavelength combinations into a non-degenerate four-wave mixing process and a degenerate four-wave mixing process; sorting the found repeated combinations in a non-degenerate four-wave mixing process and a degenerate four-wave mixing process respectively, and recording a process representing the same four-wave mixing as an FWM process; all sorted FWM processes are used to calculate the complex amplitude of the output wave by means of N coupled differential equations.
The method of calculating the complex amplitude of the output wave is to calculate the modal propagation constants β for all the light waves, based on the previously determined wavelength combinations of the FWM process and the frequencies ω of the individual wavelengthsiThe phase mismatch Δ β of all FWM processes is calculatedi,p,m,n＝βp+βm-βi-βp(ii) a Respectively writing N coupling differential equations according to the sorted FWM process, initializing input light waves, and determining power and phase parameters of a pump, a signal and a four-wave mixing sideband at the initial time; and performing integral calculation on the listed N coupling difference equations to solve the output complex amplitude and phase of each light wave.
The output signal of a two-pump non-degenerate phase sensitive amplifier capable of achieving a four-step phase transfer function with the aid of third-order sidebands is expressed as:
wherein A is the output signal including the phase phisIs the phase of the input signal, m1Is its weight coefficient.
The output signal of a two-pump non-degenerate phase sensitive amplifier capable of achieving a four-step phase transfer function with a fifth-order sideband is represented as:
wherein A is the output signal including the phase phisIs the phase of the input signal, m2Is its weight coefficient.
The signal conversion is achieved using a third type of multi-harmonic phase sensitive amplifier, and the resulting output signal of the amplitude-preserving multi-harmonic phase sensitive amplifier is expressed as:
wherein A is inputThe output signal contains a phase phisIs the phase of the input signal, m3And m4Is its weight coefficient.
Drawing the spectrum distribution diagrams of pump light, signal light and sidebands of three phase sensitive amplifiers, namely the third-order double-pump non-degenerate phase sensitive amplifier, the fifth-order double-pump non-degenerate phase sensitive amplifier and the amplitude-preserving multi-harmonic phase sensitive amplifier, wherein 4 input lights are arranged in the third-order double-pump non-degenerate phase sensitive amplifier and the fifth-order double-pump non-degenerate phase sensitive amplifier, 6 input lights are arranged in the amplitude-preserving multi-harmonic phase sensitive amplifier, and the total 11 light waves including the input pump light, the input signal light, the input sidebands and sidebands generated by the FWM participate in the amplitude-preserving multi-harmonic phase sensitive amplifier; a set of 11 coupled differential equations is used to represent the amplitudes Ai, i of all the light waves participating in the FWM process in the three phase sensitive amplifiers as 1,2 …, 11; the 11 lightwaves can constitute a total of 610 combinations satisfying the FWM process, including 560 non-degenerate four-wave mixing processes and 50 degenerate four-wave mixing processes; sorting the FWM process combinations to obtain 70 different non-degenerate four-wave mixing processes and 25 different degenerate four-wave mixing processes; calculates different frequencies omega in each FWM processiA mode propagation constant of; the input wave is initialized, power and phase parameters of the input wave are determined, and the 11 coupling differential equations are solved and integrated, so that the amplitude and the phase of all waves can be obtained.
Adopts a section of material with the length of 600m, the zero dispersion wavelength of 1542nm and the nonlinear coefficient of 10W-1km-1Attenuation of 0.65dB/km and dispersion slope of 0.026ps nm-2km-1Given a second pump wavelength lambdap2At 1544nm, the signal light is at a wavelength interval δ λ of about 0.3nm from the signal light, and other wavelengths can be selected from the second pump wavelength λ p2And the wavelength interval δ λ;
in a three-order two-pump nondegenerate phase sensitive amplifier, the initialization power is optimized respectively as follows: two pump light powers Pp2Are 14.1dBm and Pp314.1dBm, and signal light power Ps 2dBm, threeSide band of order P3s is 2dBm, the power of other wavelengths is set to be lower than-50 dBm, and when an ideal four-step phase response function capable of realizing QPSK signal regeneration is presented, the gain extinction ratio can reach 5.7 dB;
in a five-order two-pump nondegenerate phase-sensitive amplifier, two pump powers are optimized to Pp1＝Pp212.3dBm, signal optical power Ps2dBm and fifth order sideband power P 5s2 dBm; when a four-step phase response function is obtained, the gain extinction ratio can reach 3.6 dB;
in an amplitude-preserving multi-harmonic phase sensitive amplifier, the power of three pump lights is optimized to be Pp1＝Pp2＝Pp310dBm, signal light Ps2dBm, third harmonic power P3s2dBm and fifth harmonic power P5sThe other optical power is set to be lower than-50 dBm, which is 2dBm, and the gain variation is only 0.5dBm when the phase transfer function of the fourth step is obtained.
The invention has the beneficial effects that: a multi-wave numerical model of HNLF-based multi-pump PSA that can be adapted for use with light waves having a plurality of different frequencies, powers, and phase assignments; the 11-wave model can be suitable for most of PSA design based on HNLF, and the complicated design process of PSA can be greatly simplified by initializing input light waves and solving 11 coupled differential equations through numerical integration; three schemes for reducing nonlinear phase shift of HNLF-based multi-pump PSA are provided by using an 11-wave model, and four-step phase response can be obtained; when the nonlinear phase shifts are 0.31, 0.20 and 0.18, respectively, a PSA with high energy efficiency is designed by optimizing the initial power of the pump light and the signal light, and the lower nonlinear phase shift results in a four-step phase response that can be used for phase regeneration of a QPSK signal.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a graph of frequency distribution for a multi-pump PSA.
Fig. 2 is a graph of the amplitude of three PSA output signals according to the present invention in the complex plane, a third order two-pump degenerate PSA: point-line; five-stage two-pump degenerate PSA: a dashed line; amplitude-preserving multi-harmonic PSA: solid line.
Fig. 3 shows the spectral distribution of three PSAs of the present invention, with the dashed lines representing the input optical waves, wherein (a) is a third-order two-pump nondegenerate phase-sensitive amplifier, (b) is a fifth-order two-pump nondegenerate phase-sensitive amplifier, and (c) is an amplitude-preserving multi-harmonic phase-sensitive amplifier.
FIG. 4 is a graph of phase sensitive gain versus input signal phase for verification according to the present invention, dotted line: three-order double-pump degenerate PSA; dotted line: five-stage double-pump degenerate PSA; solid line: amplitude preserving multi-harmonic PSA.
FIG. 5 is a diagram of the relationship between the phase of the output signal and the phase of the input signal during the verification of the present invention, the dotted line: three-order double-pump degenerate PSA; dotted line: five-stage double-pump degenerate PSA; solid line: amplitude preserving multi-harmonic PSA.
FIG. 6 is a graph of phase sensitive gain versus input signal phase for parameter optimization according to the present invention, dotted line: three-order double-pump degenerate PSA; dotted line: five-stage double-pump degenerate PSA; solid line: amplitude preserving multi-harmonic PSA.
FIG. 7 is a diagram of the relationship between the phase of the output signal and the phase of the input signal during the parameter optimization of the present invention, dotted line: three-order double-pump degenerate PSA; dotted line: five-stage double-pump degenerate PSA; solid line: amplitude preserving multi-harmonic PSA.
FIG. 8 is a graph of phase sensitive gain versus input signal phase for an amplitude preserving multi-harmonic PSA of the present invention at different relative phases Φ, dotted line: phi is 0; dotted line: phi is 0.5 pi; solid line: phi is 1 pi; dot-dash line: Φ is 1.5 pi.
FIG. 9 is a graph of the phase of the output signal versus the phase of the input signal for an amplitude preserving multi-harmonic PSA of the present invention at different relative phases Φ, dotted line: phi is 0; dotted line: phi is 0.5 pi; solid line: phi is 1 pi; dot-dash line: Φ is 1.5 pi.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without inventive effort based on the embodiments of the present invention, are within the scope of the present invention.
A method for generating a multi-pump phase sensitive amplifier based on high non-linear optical fiber, as shown in FIG. 1, has N optical waves interacting in FWM process, including pump light, signal light and generated FWM sidebands. After ignoring some special structures of the PSA, the following N coupled differential equations can be obtained, where Ai(i ═ 1,2 …, N) is the complex amplitude of the N optical waves:
wherein A isi(z)、z、α、Ap、
Aq、Δβi,q,q,oRespectively showing i wave amplitude, distance of light wave in optical fiber, optical fiber loss, n amplitude conjugate of light wave generated by four-wave mixing, pump wave amplitude, o amplitude conjugate of light wave generated by four-wave mixing, q amplitude and phase mismatch of light wave generated by four-wave mixing, delta βi,p,m,n＝βp+βm-βi-βnΔ β is the phase mismatch, βp、βm、βi、βnRespectively the transmission constants of different light waves p, m, i and n; gamma 2 pi n2/λAeffFor fiber nonlinear coefficients, n in the equation2And AeffRespectively being non-linear of the optical fibreThe coupling equation is composed of five components, the fiber loss, the self-phase modulation (SPM) effect, the cross-phase modulation (XPM) effect, the non-degenerate four-wave mixing (ND-FWM) effect and the degenerate four-wave mixing (D-FWM) effect, the FWM efficiency depends on the phase mismatch Δ βi,p,m,n＝βp+βm-βi-βpThe "β" in the equation for the different subscripts indicates the mode propagation constants of the different light waves.
In the N-wave model for multi-pump PSA, the ND-FWM and D-FWM processes occur simultaneously between wavelengths due to the complexity of FWM occurring in multi-pump PSA. All wavelengths participating in the FWM process need to be listed in the above-mentioned N coupling differential equations, and the expected gain and phase characteristics of the PSA can be obtained by optimizing the configuration parameters of the PSA. And determining how many wavelengths participate in the FWM process becomes a key to this process.
The determination of the specific number of wavelengths involved in the FWM process will be briefly described below. First, all wavelength combinations that can satisfy the energy conversion relationship need to be found among N wavelengths, for example: omegai+ωn＝ωp+ωmAnd ωi+ωo＝2ωq，ωi，ωn，ωp，ωm，ωo，ωqRepresenting the angular frequencies of the different light waves i, n, p, m, o and q, respectively. The second step is to sort the combinations found into a non-degenerate four-wave mixing (ND-FWM) process and a degenerate four-wave mixing (D-FWM) process. The combinations of repetitions found are subsequently sorted in the two FWM processes, for example ω1+ω4＝ω2+ω3，ω4+ω1＝ω2+ω3，ω1+ω4＝ω3+ω2，ω4+ω1＝ω3+ω2These four combinations represent the same FWM process and can only be denoted as one FWM process. And finally, calculating the complex amplitude of the output wave by using the formula (1) in all the prepared FWM processes.
In addition, theIn calculating the complex amplitude of the output wave, it is first necessary to calculate the mode propagation constants β of all the optical waves according to the wavelength combinations of the FWM process and the frequencies ω of the respective wavelengths determined previouslyiI 1,2 …, N, the phase mismatch Δ β for all FWM processes needs to be calculatedi,p,m,n＝βp+βm-βi-βn. And then writing N coupling difference equations according to the sorted FWM, and initializing the input optical wave, namely determining power and phase parameters of the pump, the signal and the sideband at the beginning. And finally, performing integral calculation on the listed N coupling difference equations to solve the output complex amplitude and phase of each light wave.
Three multi-pump PSAs for QPSK signal regeneration will be described next. The first two-pump non-degenerate PSA, capable of implementing a four-step phase transfer function with third-order sidebands, has an output signal that can be expressed as,
the second is a two-pump non-degenerate PSA, with its fifth order sidebands also enabling a fourth order step phase transfer function, whose output signal can be expressed as,
however, both PSAs additionally introduce amplitude noise because the signal output amplitude is subject to PSA phase sensitive gain.
To suppress this apparent phase-amplitude noise, a third type of multi-harmonic PSA can be used to achieve the conversion of the following signals into an amplitude-preserving multi-harmonic PSA:
wherein A is the output signal including the phase phisAnd phi is the phase of the input signal, miI is 1-4 as weightAnd (4) the coefficient.
The amplitude preserving multi-harmonic PSA achieves compression of phase while preserving signal amplitude through the action of multiple optical waves. The output signal traces in the complex plane for the three-order sideband assisted two-pump non-degenerate PSA (dotted line), the five-order sideband assisted two-pump non-degenerate PSA (dashed line) and the amplitude-preserving multi-harmonic PSA (solid line) are plotted in fig. 2, respectively, with the single circle as the input signal, according to equations (2) - (4). In contrast to a two-pump non-degenerate PSA, an amplitude-preserving multi-harmonic PSA is capable of preserving the amplitude of a signal in addition to being able to compress phase.
A multi-wave model is respectively utilized to simulate three PSA schemes of a third-order double-pump non-degenerate phase sensitive amplifier, a fifth-order double-pump non-degenerate phase sensitive amplifier and an amplitude-preserving multi-harmonic phase sensitive amplifier. Through simulation, a four-step phase response is achieved with the PSA optimized for configuration parameters.
Fig. 3 shows the spectral distribution of pump light, signal light, and sidebands, respectively, in three PSAs. As shown by the dashed lines in fig. 3, the first two PSAs, a third two-stage two-pump non-degenerate phase sensitive amplifier and a fifth two-stage two-pump non-degenerate phase sensitive amplifier, have 4 inputs, while the third PSA, an amplitude-preserving multi-harmonic phase sensitive amplifier, has 6 inputs. In PSA for QPSK signal phase regeneration, not too many high order sidebands are generated since too high a non-linear phase shift is not required. Thus, in the last PSA, a total of 11 optical waves including the input pump light, the input signal light, the input sidebands and the FWM generated sidebands participate in the entire process. Compared to this, the first two PSAs are less involved in light waves in the FWM process.
The amplitudes Ai, i of all the light waves participating in the FWM process in these three PSAs are then represented by a set of 11 coupled differential equations, 1,2 …, 11. According to the previous procedure for determining the number of FWM's, the 11 light waves can constitute 610 combinations satisfying the FWM energy conversion, including 560 ND-FWM and 50D-FWM procedures. These FWM combinations were then trimmed to yield 70 different ND-FWM and 25 different D-FWM processes. After determining the specific number of FWM processes, the respective FWM processes are calculatedMedium different frequency omegaiIs constant. Finally, the input wave is initialized, for example, the power and phase parameters of the input wave are determined, and the 11 coupling differential equations are solved and integrated, so that the amplitude and the phase of all the waves can be obtained.
The 11 wave number value model has three different input cases for these three different multi-pump PSA schemes. Scheme 1: in a two-pump nondegenerate PSA based on third-order sideband assistance, there are four input waves, each ωp2、ωs、ω3sAnd ωp3. As shown by the dashed line in fig. 3(a), which depends primarily on ωs+ω3s＝ωp2+ωp3The ND-FWM procedure of (a) to achieve regeneration of the QPSK signal. Scheme 2: in a two-pump non-degenerate PSA based on fifth-order sideband assistance, there are four input waves, ω, respectively, that differ from case 1p1、ωs、ω5sAnd ωp2. As shown by the dashed lines in fig. 3(b), they depend primarily on ωs+ω5s＝ωp1+ωp2The ND-FWM process to obtain a four step phase response. Scheme 3: in amplitude-preserving multi-harmonic PSA, there are three input pump lights, one input signal light, and two input sidebands, which are ω, respectivelyp1、ωp2、ωp3、ωs、ω3sAnd ω5sThis PSA can obtain a four-step phase response with little fluctuation in amplitude, as shown in fig. 3 (c).
First, the references [ K.R.H.Botterll, G.D.Hesketh, F.Parmigiani, P.Horak, D.J.Richardson, and P.Petropoulos, "compression of gain variation in a PSA-based phase regenerator using an additional harmonic," IEEEPhoton.Technol.Lett.,26,20,2074 + 2077(2014)]The parameters in (1) are simulated. Wherein the length of the optical fiber is 300m, and the nonlinear coefficient is 11.6W-1km-1Attenuation of 0.88dB/km and dispersion slope of 0.018ps nm-2km-1. In the above-described third-order two-pump non-degenerate phase-sensitive amplifier according to scheme 1 and the fifth-order two-pump non-degenerate phase-sensitive amplifier according to scheme 2, the pump power is 17.4dBm, the signal light power is 6.4dBm, and the third-order/fifth-order sideband powers are4.4 dBm. In the amplitude-preserving multi-harmonic phase sensitive amplifier of the scheme 3, the pump power is 15.3dBm, the signal power is 7.3dBm, and the third-order/fifth-order sideband power is 2.3dBm respectively. Fig. 4 and 5 are a calculated phase sensitive gain curve and a calculated phase response curve, respectively. The results of the multi-wave model calculations are consistent with the results obtained by solving Schrodinger nonlinear equation (NLSE) by using a distributed Fourier transform (SSF) method, which are measured in the above reference documents, thereby proving the effectiveness of the multi-wave model of the invention.
Then, the configuration parameters of the above three PSAs are optimally designed by using a multi-wave model, so that the energy-efficient PSA for the phase regeneration of the QPSK signal is obtained. Adopts a section of material with the length of 600m, the zero dispersion wavelength of 1542nm and the nonlinear coefficient of 10W-1km-1Attenuation of 0.65dB/km and dispersion slope of 0.026ps nm-2km-1And given a second pump wavelength λ p2At 1544nm, the signal light is at a wavelength interval δ λ of about 0.3nm from the signal light, and other wavelengths can be represented by λ p2And the wavelength interval δ λ.
In a three-order two-pump nondegenerate phase-sensitive amplifier in scheme 1, the initialization power is optimized as follows, namely two pump light powers (Pp)2，Pp3) 14.1dBm and 14.1dBm, signal optical power (Ps) of 2dBm, third order sidebands (P)3s) was 2 dBm. But otherwise the power at other wavelengths in figure 3 is set below-50 dBm. The dotted lines in fig. 6 and 7 are the calculated phase sensitive gain curve and phase transfer function, respectively, for the PSA. When an ideal four-step phase response function capable of realizing reproduction of a QPSK signal is presented, the gain extinction ratio can reach 5.7 dB.
In the five-stage two-pump nondegenerate phase-sensitive amplifier of scheme 2, two pump powers are optimized to 12.3dBm respectively, namely Pp1＝Pp212.3dBm, the signal optical power and the fifth-order sideband power are both set to 2dBm, i.e., Ps＝2dBm，P 5s2 dBm. The PSA phase-sensitive gain and phase transfer function obtained at this time can be seen in dashed lines in fig. 6 and 7. When a four-step phase response function is obtained, the gain extinction ratio can be obtainedReaching 3.6 dB.
In a scheme 3 amplitude-preserving multi-harmonic phase sensitive amplifier, the three pump light powers are optimized to 10dBm, i.e., Pp1＝Pp2＝Pp3The signal light, 3 rd order harmonic and 5 th order harmonic powers were each set to 2dBm, P, 10dBms＝P3s＝P5sThe power of other light waves is set to be lower than-50 dBm except for 2 dBm. The solid curves in fig. 6 and fig. 7 are the phase sensitive gain curve and the phase transfer function, respectively. The gain variation is only 0.5dBm when it obtains a phase transfer function of four steps.
In the above simulation, a four-step phase response was obtained by optimizing the input power of the PSA using an 11-wave model. In these schemes, however, the desired nonlinear phase shifts (Φ) of each otherNL＝γPpL) are different, and the nonlinear phase shift can in turn determine the magnitude of the PSA gain, with the minimum nonlinear phase shift required for amplitude-preserving multi-harmonic PSA. In addition, the required nonlinear phase shift can be reduced by making the input signal optical power the same as the input sideband power.
In both of the previous two schemes, the phase difference between the pump and signal light determines the gain and phase response of the PSA, while the relative phase Φ between the pump light causes only a shift in the gain and phase curve. While the relative phase between the pump lights plays a significant role in the last scheme. The gain and phase curves for the case 3 amplitude preserving multi-harmonic phase sensitive amplifier are plotted in fig. 8 and 9, respectively, when the relative phases between the pump light are 0, 0.5 pi, pi and 1.5 pi rad, respectively. As can be seen from fig. 8 and 9, the gain curve changes with the change of the relative phase Φ, and the corresponding phase response curve also changes, so that the phase response no longer satisfies the fourth step. Thus, in amplitude-preserving multi-harmonic PSA (scheme 3), to obtain a four-step phase response, we must ensure that the relative phase Φ between the pumps is an integer multiple of 2 π.
The invention introduces a multiwave numerical model for researching HNLF-based multi-pump PSA, which can be suitable for the conditions of a plurality of lightwaves with different frequencies, powers and phase distributions, and researches three PSAs suitable for QPSK signal regeneration by utilizing the numerical model; by optimally adjusting each input power, the three PSAs can respectively obtain four-step phase response with lower nonlinear phase shifts of 0.31, 0.20 and 0.18rad, and the energy-efficient PSA is very beneficial to the regeneration of QPSK signals. The nonlinear phase shift is the product of the fiber nonlinear coefficient, the pump power and the fiber length, and the nonlinear phase shift required for generating four-step phase response is different because the required pump power is different under different configurations. In addition, the 11-wave model can be suitable for most PSA designs based on HNLF, and when the needed PSA is designed, the complicated design process of the PSA can be greatly simplified by initializing input light waves and solving 11-coupled differential equation sets through numerical integration.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (6)
1. A method for generating a multi-pumping phase sensitive amplifier based on a high nonlinear optical fiber is characterized by comprising the following steps:
the method comprises the following steps: n optical waves interact in the four-wave mixing process, including pump light, signal light and generated four-wave mixing sidebands, and the following N coupling differential equations are obtained by omitting some special-structure phase sensitive amplifiers:
wherein A isiComplex amplitudes of N light waves, i ═ 1,2 …, N; a. thei(z)、z、α、
Ap、Am、
Aq、Δβi,q,q,oRespectively representing i wave amplitude, distance of light wave in optical fiber, optical fiber loss, n amplitude conjugate of light wave generated by four-wave mixing, pump wave amplitude, m amplitude of light wave generated by four-wave mixing, o amplitude conjugate of light wave generated by four-wave mixing, q amplitude of light wave generated by four-wave mixing, and phase mismatch, delta βi,p,m,n＝βp+βm-βi-βnβ denotes the optical wave transmission constant β ═ 1/2 ═ β2Wherein β2Second order dispersion coefficient of optical fiber, βp、βm、βi、βnRespectively the transmission constants of different light waves p, m, i and n; gamma 2 pi n2/λAeffIs the nonlinear coefficient of the optical fiber, n2Is the nonlinear refractive index of the optical fiber, AeffIs the effective mode field area;
step two: determining how many wavelengths participate in the four-wave mixing process;
step three: all wavelengths participating in the four-wave mixing process are listed in N coupling differential equations in the first step to calculate the complex amplitude and the phase of the output wave, and a phase sensitive amplifier is obtained;
step four: optimizing configuration parameters of the phase sensitive amplifier by using a multi-wave model to obtain the expected gain and phase characteristics of the phase sensitive amplifier and obtain a multi-pump phase sensitive amplifier for regenerating QPSK signals;
the method for determining the specific number of wavelengths participating in the four-wave mixing process comprises the following steps: finding all wavelength combinations capable of meeting the energy conversion relation in the N wavelengths; classifying the found wavelength combinations into a non-degenerate four-wave mixing process and a degenerate four-wave mixing process; sorting the found repeated combinations in a non-degenerate four-wave mixing process and a degenerate four-wave mixing process respectively, and recording a process representing the same four-wave mixing as an FWM process; calculating the complex amplitude of the output wave in all the sorted FWM processes through N coupling differential equations;
the method of calculating the complex amplitude of the output wave is to calculate the modal propagation constants β for all the lightwaves, based on the determined wavelength combinations and frequencies of the individual wavelengths of the FWM processωiThe phase mismatch Δ β of all FWM processes is calculatedi,p,m,n＝βp+βm-βi-βp(ii) a Respectively writing N coupling differential equations according to the sorted FWM process, initializing input light waves, and determining power and phase parameters of a pump, a signal and a four-wave mixing sideband at the initial time; and performing integral calculation on the listed N coupling difference equations to solve the output complex amplitude and phase of each light wave.
2. The method of claim 1, wherein the output signal of the two-pump non-degenerate phase sensitive amplifier capable of implementing a four-step phase transfer function with the aid of third-order sidebands is expressed as:
wherein A is the output signal including the phase phisIs the phase of the input signal, m1Is its weight coefficient.
3. The method of claim 1, wherein the output signal of the two-pump non-degenerate phase sensitive amplifier capable of implementing a four-step phase transfer function with a five-step sideband is expressed as:
wherein A is the output signal including the phase phisIs the phase of the input signal, m2Is its weight coefficient.
4. The method of claim 1, wherein a third multi-harmonic phase sensitive amplifier is used to perform signal transformation, and the output signal of the amplitude-preserving multi-harmonic phase sensitive amplifier is expressed as:
wherein A is the output signal including the phase phisIs the phase of the input signal, m3And m4Is its weight coefficient.
5. The method for generating a multi-pump phase-sensitive amplifier based on high nonlinearity fiber according to any one of claims 2-4, wherein the spectral distribution diagrams of pump light, signal light and sidebands of three phase-sensitive amplifiers, namely a third-order two-pump nondegenerate phase-sensitive amplifier, a fifth-order two-pump nondegenerate phase-sensitive amplifier and an amplitude-preserving multi-harmonic phase-sensitive amplifier, are drawn, wherein there are 4 input lights in the third-order two-pump nondegenerate phase-sensitive amplifier and the fifth-order two-pump nondegenerate phase-sensitive amplifier, and there are 6 input lights in the amplitude-preserving multi-harmonic phase-sensitive amplifier, and there are 11 total light waves including the input pump light, the input signal light, the input sidebands and the sidebands generated by FWM that participate in the amplitude-preserving multi-harmonic phase-sensitive; a set of 11 coupled differential equations is used to represent the amplitudes Ai, i of all the light waves participating in the FWM process in the three phase sensitive amplifiers as 1,2 …, 11; the 11 lightwaves can constitute a total of 610 combinations satisfying the FWM process, including 560 non-degenerate four-wave mixing processes and 50 degenerate four-wave mixing processes; sorting the FWM process combinations to obtain 70 different non-degenerate four-wave mixing processes and 25 different degenerate four-wave mixing processes; calculates different frequencies omega in each FWM processiA mode propagation constant of; the input wave is initialized, power and phase parameters of the input wave are determined, and the 11 coupling differential equations are solved and integrated, so that the amplitude and the phase of all waves can be obtained.
6. The method of claim 5, wherein a length of 600m, zero dispersion wavelength of 1542nm, and nonlinear coefficient of 10W are used-1km-1Attenuation of 0.65dB/km and dispersion slope of 0.026ps nm-2km-1Given a second pump wavelength lambdap2At 1544nm, the signal light is at a wavelength interval δ λ of about 0.3nm from the signal light, and other wavelengths can be selected from the second pump wavelength λ p2And the wavelength interval δ λ;
in a three-order two-pump nondegenerate phase sensitive amplifier, the initialization power is optimized respectively as follows: two pump light powers Pp2Are 14.1dBm and Pp314.1dBm, signal light power Ps 2dBm, third-order sideband P3s is 2dBm, the power of other wavelengths is set to be lower than-50 dBm, and when an ideal four-step phase response function capable of realizing QPSK signal regeneration is presented, the gain extinction ratio can reach 5.7 dB;
in a five-order two-pump nondegenerate phase-sensitive amplifier, two pump powers are optimized to Pp1＝Pp212.3dBm, signal optical power Ps2dBm and fifth order sideband power P5s2 dBm; when a four-step phase response function is obtained, the gain extinction ratio can reach 3.6 dB;
in an amplitude-preserving multi-harmonic phase sensitive amplifier, the power of three pump lights is optimized to be Pp1＝Pp2＝Pp310dBm, signal light Ps2dBm, third harmonic power P3s2dBm and fifth harmonic power P5sThe other optical power is set to be lower than-50 dBm, which is 2dBm, and the gain variation is only 0.5dBm when the phase transfer function of the fourth step is obtained.
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