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 $KAOJc4< e^ ZxU/e % This Matlab script file solves the coupled nonlinear Schrodinger equations of 3mCf>qj73 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of q2U8]V U) % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear =VFPZ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ] l@Mo7|w gOSFvH8FU %fid=fopen('e21.dat','w'); dPx{9Y<FzU N = 128; % Number of Fourier modes (Time domain sampling points) +T,Yf/^Fn M1 =3000; % Total number of space steps x<lY&KQ0 J =100; % Steps between output of space EsK.g/d T =10; % length of time windows:T*T0 OdWZYWj T0=0.1; % input pulse width fk)5TPc^ MN1=0; % initial value for the space output location KN\*|) dt = T/N; % time step 9cMQ51k)E n = [-N/2:1:N/2-1]'; % Index f?[0I\V[$ t = n.*dt; 8gK
<xp u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 6_vhBYLf u20=u10.*0.0; % input to waveguide 2 ynQ+yW74Z u1=u10; u2=u20; y2=`NG= U1 = u1; a|5^4 J\% U2 = u2; % Compute initial condition; save it in U u}~j NV ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. xoQ;fVNp w=2*pi*n./T; n5e1ky*9w g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 'Io2",~
M L=4; % length of evoluation to compare with S. Trillo's paper A6faRi703 dz=L/M1; % space step, make sure nonlinear<0.05 R{3vPG for m1 = 1:1:M1 % Start space evolution vk>EFm8l u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS =o? Q0 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 5k]xi)% ca1 = fftshift(fft(u1)); % Take Fourier transform >r8$vQ Gj ca2 = fftshift(fft(u2)); S`?L\R.: c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation m_;<7W&p] c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift CG397Y^ u2 = ifft(fftshift(c2)); % Return to physical space YZllfw$9 u1 = ifft(fftshift(c1)); \fjr`t] if rem(m1,J) == 0 % Save output every J steps. 7sglqf> U1 = [U1 u1]; % put solutions in U array y'#i'0eeL U2=[U2 u2]; 3l?-H|T MN1=[MN1 m1]; +@5@`"Jry z1=dz*MN1'; % output location hF4gz*Q end |w)S
&+ end |(Q !$ hg=abs(U1').*abs(U1'); % for data write to excel \'[C_+;X ha=[z1 hg]; % for data write to excel c'Mi9,q t1=[0 t']; 'v?"TZ hh=[t1' ha']; % for data write to excel file 1nAAs;`' %dlmwrite('aa',hh,'\t'); % save data in the excel format \7elqX`.yY figure(1) 9&VfbrBM waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn ^PrG5|,s figure(2) YVT\@+C' waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn 1.6Y=Mh=i[ 9@{=2 k 非线性超快脉冲耦合的数值方法的Matlab程序 HgfeSH UL<*z!y 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。 9u%S<F" 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 Vh o3I[C KsR^:_e SGK=WLGM8 2Ysl|xRo % This Matlab script file solves the nonlinear Schrodinger equations iF!r}fUU6 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of \Ng|bWR>LQ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear `j1(GQt % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ?VaAVxd29 F?EAIL C=1; n)6mfoe M1=120, % integer for amplitude trAIh}Dj M3=5000; % integer for length of coupler 1,pg7L8H N = 512; % Number of Fourier modes (Time domain sampling points) 4qe!+!#$ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. Zwm2T3@e T =40; % length of time:T*T0. BH+@!H3hf dt = T/N; % time step |',$5!:0O n = [-N/2:1:N/2-1]'; % Index 8<X,6 t = n.*dt; QT[yw6Z ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. ?Gr2@,jlD w=2*pi*n./T; PY{])z3N g1=-i*ww./2; T#:n7$M|?A g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; x+B7r&#: g3=-i*ww./2; jcVK4jW P1=0; G;k#06 P2=0; 8 "5^mj P3=1; `zmjiC P=0; `:y { for m1=1:M1 ER4j=O# p=0.032*m1; %input amplitude b0n " J` s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 mO|YX/> s1=s10; fRT4,; s20=0.*s10; %input in waveguide 2 KMo]J1o s30=0.*s10; %input in waveguide 3 g[ dI% s2=s20; B!X;T9^d s3=s30; }}4u>1,~ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); o1B8_$aYgc %energy in waveguide 1 =MCQNyf+ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); uhJnDo %energy in waveguide 2 YKtF)N;m] p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); K[/sVaPZ %energy in waveguide 3 0S}ogU[k for m3 = 1:1:M3 % Start space evolution @}[yC[' s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS `of`u B s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; G:k]tZ*` s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; (s?Rbd sca1 = fftshift(fft(s1)); % Take Fourier transform c"H59 jE sca2 = fftshift(fft(s2));
7%g8&d sca3 = fftshift(fft(s3)); 0%f}w0]: sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift sH_5.+,` sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); $wq[W,'#L sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); %D9,Femt s3 = ifft(fftshift(sc3)); Sh(W s2b7 s2 = ifft(fftshift(sc2)); % Return to physical space LLlt9(^d s1 = ifft(fftshift(sc1)); _RI!Z end A\IQM^i p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); riuG,$EX p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); Rx\.x? & p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); l%^VBv>
2 P1=[P1 p1/p10]; ~,jBm^4 P2=[P2 p2/p10]; (^)" qsB P3=[P3 p3/p10]; +?I1Og P=[P p*p]; oI2YJ2?Je8 end VP\'p1a figure(1) S>y(3E]I plot(P,P1, P,P2, P,P3); AXmW7/Sj" 9f/RD?(1O 转自:http://blog.163.com/opto_wang/
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