[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 @ZtvpL}e  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of cK'}+  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 'N/u<`)  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear y~wN:  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 N'?#g`*KW  
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%fid=fopen('e21.dat','w'); kuv+TN  
N = 128;                       % Number of Fourier modes (Time domain sampling points) cZAf?,>u  
M1 =3000;              % Total number of space steps 
BuS[(  
J =100;                % Steps between output of space +aOX{1w  
T =10;                  % length of time windows:T*T0 .<6'*XR  
T0=0.1;                 % input pulse width /=KE
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MN1=0;                 % initial value for the space output location 4"Mq]_D  
dt = T/N;                      % time step 3GXmyo:o$  
n = [-N/2:1:N/2-1]';           % Index KnUVR!H|  
t = n.*dt;   e)|5P  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 H~W
=#Cx  
u20=u10.*0.0;                  % input to waveguide 2 vP,$S^7$  
u1=u10; u2=u20;                 EHrr}&  
U1 = u1;   H)5"<=]  
U2 = u2;                       % Compute initial condition; save it in U Q 2B  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. l^rQo_alk  
w=2*pi*n./T; 66scBi_d  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T =an0PN  
L=4;                           % length of evoluation to compare with S. Trillo's paper ]m#*4  
dz=L/M1;                       % space step, make sure nonlinear<0.05 i_p-|I:hQ  
for m1 = 1:1:M1                                    % Start space evolution 6e"Lod_ L  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS (ZQ?1Qxo  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; m5cRHo<9Y  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform (.kzJ\x  
   ca2 = fftshift(fft(u2)); eU\_m5xl"  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation LmPpt3[  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   mH )i  
   u2 = ifft(fftshift(c2));                        % Return to physical space Z5[g[Q  
   u1 = ifft(fftshift(c1)); {
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if rem(m1,J) == 0                                 % Save output every J steps. @R;&PR#5  
    U1 = [U1 u1];                                  % put solutions in U array
U=[isi+7  
    U2=[U2 u2]; BxB B](  
    MN1=[MN1 m1]; JG{`tTu  
    z1=dz*MN1';                                    % output location !'>,37()  
  end >txeo17Ba\  
end c;88Wb<|W  
hg=abs(U1').*abs(U1');                             % for data write to excel wM!dz&  
ha=[z1 hg];                                        % for data write to excel V2$M`|E  
t1=[0 t']; (SByN7[gb  
hh=[t1' ha'];                                      % for data write to excel file iK8jX?  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format rW`l1yi*$  
figure(1) cuL/y$+EY  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn 1eI_F8I U  
figure(2) k{cPiY^  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn Fp>nu_-"  
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非线性超快脉冲耦合的数值方法的Matlab程序 &5hs W1`  
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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。   C4gzg  
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 ]^<\a=U  
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%  This Matlab script file solves the nonlinear Schrodinger equations &5QvUn
  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of KIY9?B=+  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear qpq(<  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 /`j2%
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C=1;                           'a"Uw"/p[  
M1=120,                       % integer for amplitude :)%cL8Nz]$  
M3=5000;                      % integer for length of coupler W?n/>DML  
N = 512;                      % Number of Fourier modes (Time domain sampling points) Q<(aU{  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. $dug"[  
T =40;                        % length of time:T*T0. j3j^cO[8v  
dt = T/N;                     % time step =
]1g*~%  
n = [-N/2:1:N/2-1]';          % Index JY3!jt
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t = n.*dt;   7t+H94KG7  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. R#s_pW{op  
w=2*pi*n./T; 18]Q4s8E  
g1=-i*ww./2; X,D ]S@  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 2m9qg-W  
g3=-i*ww./2; +P.JiH`\=  
P1=0; VREDVLQT  
P2=0; t<%+))b  
P3=1; B)
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P=0; e1hf{:&/G@  
for m1=1:M1                 {~#d_!(  
p=0.032*m1;                %input amplitude D!i|KI/  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 juxAyds  
s1=s10; "tu*(>'~5  
s20=0.*s10;                %input in waveguide 2 5[~C!t;  
s30=0.*s10;                %input in waveguide 3 !$<Kp6  
s2=s20; ::@JL  
s3=s30; #z}0]GJKj  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   !e('T@^u6u  
%energy in waveguide 1 !04^E  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   S(lqj6aa}  
%energy in waveguide 2 -?Cu-'  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   &iT^IkA{  
%energy in waveguide 3 KVoM\ttP  
for m3 = 1:1:M3                                    % Start space evolution U\>k>|Jr{  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS 1;vwreJ  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; S5~(3I )v  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 7<k@{xI/  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform "WH &BhQYD  
   sca2 = fftshift(fft(s2)); CS0q#?  
   sca3 = fftshift(fft(s3)); V=c?V
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   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   l!ZzJ&  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); m`jGBSlw_  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); )4H0Bz2G  
   s3 = ifft(fftshift(sc3)); In*0.   
   s2 = ifft(fftshift(sc2));                       % Return to physical space 2 S2;LB  
   s1 = ifft(fftshift(sc1)); biVsbxYurq  
end Me^L%%:@  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); ;}k_  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); @== "$uRw  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); rK4 pYo  
   P1=[P1 p1/p10]; i(xL-&{  
   P2=[P2 p2/p10]; fqn;,!D?9  
   P3=[P3 p3/p10]; 'Y/8gD~.  
   P=[P p*p]; k0xm-  
end B&}lYo  
figure(1) Zm#,Ike?#  
plot(P,P1, P,P2, P,P3); |^#Z!Hp_Y  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~