[分享]求解光孤子或超短脉冲耦合方程的Matlab程序 [复制链接]

计算脉冲在非线性耦合器中演化的Matlab 程序
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of I5%#A/|z  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of j0wpaIp  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
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%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 D\H;_k8  
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%fid=fopen('e21.dat','w'); m8ApiGG  
N = 128;                       % Number of Fourier modes (Time domain sampling points) gJFx#s0?6.  
M1 =3000;              % Total number of space steps P Y&(ObC  
J =100;                % Steps between output of space 3xX^pjk  
T =10;                  % length of time windows:T*T0 p[^a4E_v  
T0=0.1;                 % input pulse width 1OI/,y8}  
MN1=0;                 % initial value for the space output location UURYK~$K:  
dt = T/N;                      % time step
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n = [-N/2:1:N/2-1]';           % Index BN>t"9XpW  
t = n.*dt;   G2y
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u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 $p;<1+!  
u20=u10.*0.0;                  % input to waveguide 2 =bHS@h8N<  
u1=u10; u2=u20;                 Rt+ak}  
U1 = u1;   YZdV0-S  
U2 = u2;                       % Compute initial condition; save it in U x>!bvZ2  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. uB1>.Pvxb  
w=2*pi*n./T; CK=
TD`$w  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T ;R[w}#Sm  
L=4;                           % length of evoluation to compare with S. Trillo's paper tv 7"4$T  
dz=L/M1;                       % space step, make sure nonlinear<0.05 EA``G8Vn>  
for m1 = 1:1:M1                                    % Start space evolution xg;I::hE7X  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS ZJf:a}=h  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; ^B?brH}  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform % B^BN|r  
   ca2 = fftshift(fft(u2)); E' _6v  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation UbDpSfub  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   Ys@OgdS@:  
   u2 = ifft(fftshift(c2));                        % Return to physical space `k.0d`3(  
   u1 = ifft(fftshift(c1)); G%F}H/|R  
if rem(m1,J) == 0                                 % Save output every J steps. %M5{-pJ|C  
    U1 = [U1 u1];                                  % put solutions in U array k-!Jww  
    U2=[U2 u2]; uA[c$tBe  
    MN1=[MN1 m1]; +4g H=6  
    z1=dz*MN1';                                    % output location f`K[oCfu  
  end {oftZXwf  
end s1>d)2lX  
hg=abs(U1').*abs(U1');                             % for data write to excel /~1Ew  
ha=[z1 hg];                                        % for data write to excel @L,4JPk  
t1=[0 t']; Q+7+||RW  
hh=[t1' ha'];                                      % for data write to excel file N?s`a;Q[=  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format [/Sk+ID  
figure(1) Ib(G!oO:E-  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn /T<))@$  
figure(2) =/e
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waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn `lcQ Yd<,4  
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非线性超快脉冲耦合的数值方法的Matlab程序 Qf($F,)K  
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在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   ]o?r(1  
Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 =Cc]ugl7-  
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%  This Matlab script file solves the nonlinear Schrodinger equations hS'!JAM>Q  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of 25Uw\rKeO  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear j8)rz  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 G{74o8  
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C=1;                           y>>)Yo&|  
M1=120,                       % integer for amplitude 3gv@JGt7`  
M3=5000;                      % integer for length of coupler B9dc*  
N = 512;                      % Number of Fourier modes (Time domain sampling points) 37b6w6{D  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. : G'a
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T =40;                        % length of time:T*T0. VHm.uL_UW  
dt = T/N;                     % time step 8?hZ5QvA(j  
n = [-N/2:1:N/2-1]';          % Index 0at['zw  
t = n.*dt;   \Mzr[dI  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. ~e_  
w=2*pi*n./T; \0n<6^y  
g1=-i*ww./2; oU|_(p"e|  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 0TaN#  
g3=-i*ww./2; 3b?8<*  
P1=0; ?vP6~$*B  
P2=0; JAX`iQd  
P3=1; (#BOcx5J]  
P=0; w<u@L  
for m1=1:M1                 Van=dzG  
p=0.032*m1;                %input amplitude []G@l. ]W  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 K;ocs?rk/  
s1=s10; uD\rmO{  
s20=0.*s10;                %input in waveguide 2 =I0J1Ob  
s30=0.*s10;                %input in waveguide 3 K'f^=bcI  
s2=s20; w7c0jIf{  
s3=s30; n_(f"Uv  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   lnGg1/
  
%energy in waveguide 1 g:s|D hE[  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   4Uhh]/  
%energy in waveguide 2 5<M$ XT  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   8 ,W*)Q  
%energy in waveguide 3 TBZhL  
for m3 = 1:1:M3                                    % Start space evolution R*?!xDJ  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS @RZbo@{~  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; i|rCGa0}  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; V4&a+MJ@  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform ibn\&}1  
   sca2 = fftshift(fft(s2)); nErr&{C  
   sca3 = fftshift(fft(s3)); EE*|#  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   Qxfds`4V9i  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 1vYa&!  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); ,$Cr9R&/  
   s3 = ifft(fftshift(sc3)); H<tU[U=G  
   s2 = ifft(fftshift(sc2));                       % Return to physical space b7y#uL1AE  
   s1 = ifft(fftshift(sc1)); -p"}K~lt:  
end yg6o#;  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); xiV!\Z}  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); x)pR^t7u8  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); p +nh]  
   P1=[P1 p1/p10]; +6x}yc:yd  
   P2=[P2 p2/p10]; ktkS$  
   P3=[P3 p3/p10]; k;K-6<^h  
   P=[P p*p]; Z_a@,k:+[  
end k7& cc|y  
figure(1) =b8u8*ua  
plot(P,P1, P,P2, P,P3); bYmk5fpRG  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~