[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 _wXT9`|3  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of r.)n
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%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 50 w
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%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear XOX$uLm  
%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 62nmm/c  
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%fid=fopen('e21.dat','w'); t{UVX%b  
N = 128;                       % Number of Fourier modes (Time domain sampling points) Q=! lbW  
M1 =3000;              % Total number of space steps sDs.da#*2  
J =100;                % Steps between output of space ,7:GLkj  
T =10;                  % length of time windows:T*T0 QeF:s|[  
T0=0.1;                 % input pulse width r1F5'?NZ(0  
MN1=0;                 % initial value for the space output location G1it 3^*$  
dt = T/N;                      % time step l`~
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n = [-N/2:1:N/2-1]';           % Index gK~Z Ch  
t = n.*dt;   . AA# G  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 P'iX?+*  
u20=u10.*0.0;                  % input to waveguide 2 mvH}G8  
u1=u10; u2=u20;                 L+ew/I>:  
U1 = u1;   j&dCP
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U2 = u2;                       % Compute initial condition; save it in U ,Gy,bcv{  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. Fep@VkN  
w=2*pi*n./T; K"[jrvZ=  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T Ng<ic  
L=4;                           % length of evoluation to compare with S. Trillo's paper <zY#qFQ2  
dz=L/M1;                       % space step, make sure nonlinear<0.05 (XR}U6^v]  
for m1 = 1:1:M1                                    % Start space evolution /V0Put  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS X*#\JF4$i  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; }+lK'6  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform /T qbl^[  
   ca2 = fftshift(fft(u2)); %{
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   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation k6DJ(.n'%a  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   O.#Rr/+)  
   u2 = ifft(fftshift(c2));                        % Return to physical space [Y@}{[q5  
   u1 = ifft(fftshift(c1)); i.^UkN{  
if rem(m1,J) == 0                                 % Save output every J steps. .+Q1h61$T  
    U1 = [U1 u1];                                  % put solutions in U array f-^*p  
    U2=[U2 u2]; >9XG+f66E  
    MN1=[MN1 m1]; m.6uLaD"!}  
    z1=dz*MN1';                                    % output location m; =S]3P*  
  end sAO/yG  
end U(+QrC:  
hg=abs(U1').*abs(U1');                             % for data write to excel M`#g>~bI#R  
ha=[z1 hg];                                        % for data write to excel & :W6O)uY  
t1=[0 t']; )
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hh=[t1' ha'];                                      % for data write to excel file lpd~U2&  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format L})fYVX  
figure(1) P{s1NorKDh  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn (j:[<U
  
figure(2) k^JgCC+  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn `6Q+N=k~Z  
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非线性超快脉冲耦合的数值方法的Matlab程序 QH
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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。   ;E{
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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 F*z>B >{)  
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%  This Matlab script file solves the nonlinear Schrodinger equations WSF$xC/~  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of /Re67cMQ*  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear _;x`6LM  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 7!o
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C=1;                           ;eFV}DWW  
M1=120,                       % integer for amplitude wko9tdC=U  
M3=5000;                      % integer for length of coupler !}`[s2ji  
N = 512;                      % Number of Fourier modes (Time domain sampling points) $rjm MSxi  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 9l[C&0w#\  
T =40;                        % length of time:T*T0. b*Hk} !qH  
dt = T/N;                     % time step j$u  
n = [-N/2:1:N/2-1]';          % Index $^e_4]k  
t = n.*dt;   BD.l5~:  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. pxbuZ9w2Q  
w=2*pi*n./T; vPZ0?r
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g1=-i*ww./2; /ml+b8@  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; rCGKE`H
 
g3=-i*ww./2; _M>S=3w  
P1=0; E^w0X,0XlE  
P2=0; gpbdK?  
P3=1; _+~jZ]o N  
P=0; J1r\Cp+h0  
for m1=1:M1                 <g&GIFE,  
p=0.032*m1;                %input amplitude g p9;I*!  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 E9.1~ )  
s1=s10; PJKxh%J  
s20=0.*s10;                %input in waveguide 2 (:+Wc^0  
s30=0.*s10;                %input in waveguide 3 t1#f*G5  
s2=s20; L]X Lv9J0  
s3=s30; s}^W2  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   bL:+(/:  
%energy in waveguide 1 A6;[r #C  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   wqE
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%energy in waveguide 2 vX
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p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   tQ
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%energy in waveguide 3 *MWI`=c  
for m3 = 1:1:M3                                    % Start space evolution #Guwbg  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS p8CaD4bE  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; >^f]Lgp  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; #b&=CsW`  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform ^sJp!hi4=)  
   sca2 = fftshift(fft(s2)); Ej@N}r>X  
   sca3 = fftshift(fft(s3)); li`  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift  
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   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); esv<b>`R  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); Pj^Ccd'>=  
   s3 = ifft(fftshift(sc3)); Kna@K$6{w=  
   s2 = ifft(fftshift(sc2));                       % Return to physical space .KYDYdoS'  
   s1 = ifft(fftshift(sc1)); T< <N U"n  
end MLmk=&d  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); H[/^&1P  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); X*r?@uK
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   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); bOlb  
   P1=[P1 p1/p10]; fb!>@@9Z  
   P2=[P2 p2/p10]; 0w$1Yx~C  
   P3=[P3 p3/p10]; *u34~v16,  
   P=[P p*p]; k~1{|HxrE  
end ,v*\2oG3^  
figure(1) #/K71Y  
plot(P,P1, P,P2, P,P3); (jh0cy}|]  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~