| 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 n`2LGc[rP ^)0b= (. % This Matlab script file solves the coupled nonlinear Schrodinger equations of K1[(%<Gp % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of kCZxv"Ts % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 71!'k>]h % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 d2[R{eNX= ,1|0]: %fid=fopen('e21.dat','w'); u<K{=94!e N = 128; % Number of Fourier modes (Time domain sampling points) h^=9R6im M1 =3000; % Total number of space steps ~k780 J =100; % Steps between output of space MgUjB~)Y T =10; % length of time windows:T*T0 muKCCWy# T0=0.1; % input pulse width M"|({+9eG MN1=0; % initial value for the space output location @86?!0bt dt = T/N; % time step _"c:Z !L n = [-N/2:1:N/2-1]'; % Index ;}E$>]*Yn t = n.*dt; YB3?Ftgw u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 El4SL'E@ u20=u10.*0.0; % input to waveguide 2 _&|<(m&." u1=u10; u2=u20; ;iTZzmB U1 = u1; {;E]#=| U2 = u2; % Compute initial condition; save it in U LQ3J$N ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. ;P!x/Ct w=2*pi*n./T; <n{-&;> g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T Rg6/6/ IN L=4; % length of evoluation to compare with S. Trillo's paper ~e#QAaXD#5 dz=L/M1; % space step, make sure nonlinear<0.05 "6zf-++% for m1 = 1:1:M1 % Start space evolution SQJ
}$#= u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS *zTEK:+_ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; V4qv7 ca1 = fftshift(fft(u1)); % Take Fourier transform 6P U]I+ ca2 = fftshift(fft(u2)); FCA]zR1 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation @]xHt&j c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift q_[V9 u2 = ifft(fftshift(c2)); % Return to physical space l~c# X3E u1 = ifft(fftshift(c1)); [ %:%C]4 if rem(m1,J) == 0 % Save output every J steps. o0\d`0-el U1 = [U1 u1]; % put solutions in U array d<+@cf_9 U2=[U2 u2]; HlC[Nu^6U MN1=[MN1 m1]; (4oO8aBB z1=dz*MN1'; % output location VSW"/{Lp end L+J) end K6M_b?XekA hg=abs(U1').*abs(U1'); % for data write to excel ZtH{2j0 ha=[z1 hg]; % for data write to excel Gn}^BJN t1=[0 t']; 6qH^&O][ hh=[t1' ha']; % for data write to excel file odNHyJS0 %dlmwrite('aa',hh,'\t'); % save data in the excel format a0=>@? figure(1) YqNI:znm- waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn v!77dj 6I figure(2) hR(p{$-T waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn sTChbks :1,xs e 非线性超快脉冲耦合的数值方法的Matlab程序 Xl\yOMfp 7zEpuw 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。 BFH=cs 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 nMU[S+ h(MS>= {H[3[ sm96Ye{O{ % This Matlab script file solves the nonlinear Schrodinger equations T,SCK^ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of 3JcI}w % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear UgAG2 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 m.DC L$4nbOu\~ C=1; ;/|3U7{c M1=120, % integer for amplitude IM9P5?kJ
? M3=5000; % integer for length of coupler [>wvVv N = 512; % Number of Fourier modes (Time domain sampling points) F|{F'UXj| dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. kV:C=MLI T =40; % length of time:T*T0. tDwj~{a~ dt = T/N; % time step 9_I#{? n = [-N/2:1:N/2-1]'; % Index W9%B9~\G;+ t = n.*dt; 9d1 Gu" ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. r,-9]?i w=2*pi*n./T; vB;$AFh{ g1=-i*ww./2; rN5;W g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; @!:_r5R~N g3=-i*ww./2; nps"nggk P1=0; tF=Y3W+L P2=0; %eDJ]\*^X P3=1; CKgbb4;<m[ P=0; 1?N$I}? for m1=1:M1 k=8L hO p=0.032*m1; %input amplitude bhg
OLh# s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 l<YCX[%E s1=s10; Z5%T pAu[ s20=0.*s10; %input in waveguide 2 J0a#QvX! s30=0.*s10; %input in waveguide 3 xzjG|"a[GB s2=s20; hDc)\vzr s3=s30; jFThW N p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); <=7N2t)s4 %energy in waveguide 1 k>;a5'S p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); RFzMah?Q=j %energy in waveguide 2 KXTx{R p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); z~+gche> %energy in waveguide 3 I'%(f@u~ for m3 = 1:1:M3 % Start space evolution 8`S6BkfC| s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS 8
y+N l&"V s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; wM#BQe3t# s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 1[Ffl^\ARp sca1 = fftshift(fft(s1)); % Take Fourier transform *2tG07kI sca2 = fftshift(fft(s2)); TSCc=c sca3 = fftshift(fft(s3)); p-1
\4 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift oHI/tS4
_ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); sB>ZN3ptH^ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); J4;Fk s3 = ifft(fftshift(sc3)); b$Ch2Qz0q s2 = ifft(fftshift(sc2)); % Return to physical space ^&-H"jF s1 = ifft(fftshift(sc1)); ^S'tMT_ end _$Hx:^p: p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); A}cGag+sp p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); WJN}d-S=^ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); uRu)iBd D P1=[P1 p1/p10]; <dA1n:3o P2=[P2 p2/p10]; l-mf~{ P3=[P3 p3/p10]; !j|93* P=[P p*p]; 6bW:&IPQ; end \d)~. 2$G* figure(1) V*U*_Y plot(P,P1, P,P2, P,P3); :n?K[f?LfY /P-Eg86V' 转自:http://blog.163.com/opto_wang/
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