| tianmen |
2011-06-12 18:33 |
求解光孤子或超短脉冲耦合方程的Matlab程序
计算脉冲在非线性耦合器中演化的Matlab 程序 i9;27tT~< nEd
M_JPv % This Matlab script file solves the coupled nonlinear Schrodinger equations of [T 4 pgt'H % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 'Gl;Ir^ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear =s0g2Zv"\ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 cK|rrwa0 7}d$*C %fid=fopen('e21.dat','w'); P(pd0,%i;a N = 128; % Number of Fourier modes (Time domain sampling points) Eg`R|CF M1 =3000; % Total number of space steps 8lOZIbwS J =100; % Steps between output of space $v:gBlj%" T =10; % length of time windows:T*T0 Mr=}B6` T0=0.1; % input pulse width rkfQr9Vc MN1=0; % initial value for the space output location emv ;m/&8 dt = T/N; % time step m|[\F#+C n = [-N/2:1:N/2-1]'; % Index }%!FMXe t = n.*dt; gHi~nEH u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 'f-
u20=u10.*0.0; % input to waveguide 2 8Wdkztp/S u1=u10; u2=u20; GB<R7J U1 = u1; _\,rX\ U2 = u2; % Compute initial condition; save it in U (B>)2: T1 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. \;-=ODC w=2*pi*n./T; iN<(O7B; g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 7.Ml9{M/i L=4; % length of evoluation to compare with S. Trillo's paper S)"##-~`T dz=L/M1; % space step, make sure nonlinear<0.05 9 m\)\/V for m1 = 1:1:M1 % Start space evolution |.b%rVu u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS >oft :7p u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; [as-3&5S ca1 = fftshift(fft(u1)); % Take Fourier transform d[Rb:Yw ca2 = fftshift(fft(u2)); c8#T:HM|` c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation Zk]k1]u*5 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift *>e~_{F u2 = ifft(fftshift(c2)); % Return to physical space 6Cl+KcJH u1 = ifft(fftshift(c1)); ljup#:n if rem(m1,J) == 0 % Save output every J steps. Lzh9DYU6 U1 = [U1 u1]; % put solutions in U array @+?+6sS U2=[U2 u2]; qs!>tw MN1=[MN1 m1]; $Hp.{jw z1=dz*MN1'; % output location <TI3@9\qXE end cy1\u2x_` end L"[IOV9S hg=abs(U1').*abs(U1'); % for data write to excel IIq"e~"Vs ha=[z1 hg]; % for data write to excel RRx`}E9, t1=[0 t']; `]K,'i{R hh=[t1' ha']; % for data write to excel file RI(=HzB %dlmwrite('aa',hh,'\t'); % save data in the excel format |yLk5e~@- figure(1) gWFL waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn \HCOR, `T figure(2) `6rrXU6| waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn uyL72($ so} l# 非线性超快脉冲耦合的数值方法的Matlab程序 7 ,$ axvLw d4ic9u*D 在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。 1 h<fJzh Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 azvDvEWCQZ yrO?Np S&n[4* clHM8$ % This Matlab script file solves the nonlinear Schrodinger equations (tJ91SBl % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of Nt HbwU, % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear xC)7eQn/R % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 (F_w>w.h 6yN"
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Q7 C=1; -<O JqB M1=120, % integer for amplitude >/b^fAG M3=5000; % integer for length of coupler
LlU'_}> N = 512; % Number of Fourier modes (Time domain sampling points) w]n4KR4 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. M6\7FP6G T =40; % length of time:T*T0. h>dxBN dt = T/N; % time step gC0;2 n = [-N/2:1:N/2-1]'; % Index pw!@Q?R t = n.*dt; l x7Kw% ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. 3KtAK9PT w=2*pi*n./T; _=uviMuE g1=-i*ww./2; Y]~IY?I g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 9 >%+bA( g3=-i*ww./2; 6mwvI4) P1=0; 8AryIgy>@ P2=0; j?( c}!} P3=1; Bgf=\7;5 P=0; VW {,:Ya for m1=1:M1 {-Yee[d<? p=0.032*m1; %input amplitude Cgo9rC~] s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 S:#e8H_7m] s1=s10; N9pwWg&<+ s20=0.*s10; %input in waveguide 2 fO#?k<p s30=0.*s10; %input in waveguide 3 $iwIF7,\P s2=s20; +B# qu/By s3=s30; RXM}hqeG p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); iNXFk4 %energy in waveguide 1 )]wuF` p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); pOKeEW<q %energy in waveguide 2 .`Sw,XL5 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); {f-XyF1` %energy in waveguide 3 wajZqC2yg for m3 = 1:1:M3 % Start space evolution ~*,Wj?~+7 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS ^eobp.U s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; b]w[*<f? s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; # J]~ sca1 = fftshift(fft(s1)); % Take Fourier transform $}db /hY* sca2 = fftshift(fft(s2)); V(r`.75 sca3 = fftshift(fft(s3)); b) Ux3PB sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift b )Tl* sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); nz[
m3] sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); Y!M~#oqio s3 = ifft(fftshift(sc3)); a/b92*&k s2 = ifft(fftshift(sc2)); % Return to physical space ]9s\_A9 s1 = ifft(fftshift(sc1)); J)#S-ZB+'k end nW11wtiO. p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); ^Wm*-4 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); 1#]B^D p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); w]F!2b! P1=[P1 p1/p10]; >4~#%& P2=[P2 p2/p10]; 3+%nn+m P3=[P3 p3/p10]; t?HF-zQ P=[P p*p]; s@PLS5d" end =D5wqCT(Q figure(1) lM$t!2pRB plot(P,P1, P,P2, P,P3); Wa<-AZnh p.5e:
i^LJ 转自:http://blog.163.com/opto_wang/
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