[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 ePr&!Tz#  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of d/ARm-D  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of ]b\yg2  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear q
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%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 JTr vnA  
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%fid=fopen('e21.dat','w'); V#XppYU  
N = 128;                       % Number of Fourier modes (Time domain sampling points) K%a%a6k`  
M1 =3000;              % Total number of space steps F$ #U5}Q  
J =100;                % Steps between output of space ~rDZ?~%  
T =10;                  % length of time windows:T*T0 @ o3T  
T0=0.1;                 % input pulse width rf>0H^r  
MN1=0;                 % initial value for the space output location 3on7~*  
dt = T/N;                      % time step iH/6M  
n = [-N/2:1:N/2-1]';           % Index JBXrFC;  
t = n.*dt;   E7.2T^o;M  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 P!H_1RwXKC  
u20=u10.*0.0;                  % input to waveguide 2 x[$z({Yf  
u1=u10; u2=u20;                 bmfI~8  
U1 = u1;   [P&7i57  
U2 = u2;                       % Compute initial condition; save it in U 1DE1.1  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. ]L9s%]o  
w=2*pi*n./T; MCS8y+QK  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 4kBaB  
L=4;                           % length of evoluation to compare with S. Trillo's paper ^G4Py<s  
dz=L/M1;                       % space step, make sure nonlinear<0.05 4)@mSSfn.  
for m1 = 1:1:M1                                    % Start space evolution Q4+gAS9  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS iPd[l{85Z  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 7JEbH?lEN  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform -=~| ."O  
   ca2 = fftshift(fft(u2)); n/SwP  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation _a6[{_Pc  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   H@q?v+2  
   u2 = ifft(fftshift(c2));                        % Return to physical space Hea;?4Vg  
   u1 = ifft(fftshift(c1)); ^>jwh  
if rem(m1,J) == 0                                 % Save output every J steps. \/: {)T~  
    U1 = [U1 u1];                                  % put solutions in U array bYEy<7)x  
    U2=[U2 u2]; jz qyk^X  
    MN1=[MN1 m1]; -I&m:A$4*  
    z1=dz*MN1';                                    % output location %Z):>
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  end L3@82yPo!  
end FFu9&8Y  
hg=abs(U1').*abs(U1');                             % for data write to excel j@SQ~AS  
ha=[z1 hg];                                        % for data write to excel +y&Tf#.V/A  
t1=[0 t']; >8k_n  
hh=[t1' ha'];                                      % for data write to excel file /atW8 `&  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format VU&7P/\f%  
figure(1) @\f^0^G  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn n ~shK<!C  
figure(2) yXHUJgjl/  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn @cFJeOC|  
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非线性超快脉冲耦合的数值方法的Matlab程序 n)^i/ nXb'  
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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。   I'uSp-Sfy  
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 orWbU UC  
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%  This Matlab script file solves the nonlinear Schrodinger equations j)<IRD^  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of ;<j0f~G`  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear `HZ;NRr  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 uBNn6j  
8B\2Zfe  
C=1;                           dep=&  
M1=120,                       % integer for amplitude #~C]ZrK  
M3=5000;                      % integer for length of coupler Qo;
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N = 512;                      % Number of Fourier modes (Time domain sampling points) Exc9` 7%.  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. v(ZYS']d2  
T =40;                        % length of time:T*T0. 56zL"TF`  
dt = T/N;                     % time step B9NWW6S  
n = [-N/2:1:N/2-1]';          % Index ihIVUu-M  
t = n.*dt;   {L/tst#C  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. |mGFts}0o'  
w=2*pi*n./T; qI#;j%V  
g1=-i*ww./2; 0n;< ge&~R  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; ]6TATPIr  
g3=-i*ww./2; i{`FmrPO~  
P1=0; &#!4XOyB  
P2=0; amOnqH-(  
P3=1; 18+)`M-5o  
P=0; a@@)6FM  
for m1=1:M1                 Yu)NO\3&  
p=0.032*m1;                %input amplitude GP?M!C,/}k  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 wr$M$i:  
s1=s10; bN]+_ mF  
s20=0.*s10;                %input in waveguide 2 C8Qa$._  
s30=0.*s10;                %input in waveguide 3 $$Oey)*  
s2=s20; bpH^:fyLU`  
s3=s30; +nXK-g;)'  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   xv(9IEjt0  
%energy in waveguide 1 "Zl5<  
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   JBE!j-F  
%energy in waveguide 2 x:),P-~w  
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   }<@b=_>S  
%energy in waveguide 3 S- pV_Ff  
for m3 = 1:1:M3                                    % Start space evolution ~<_2WQ/$  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS ADDSCY=,  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; r'^Hg/Jzt  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; }1Gv)l7  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform Z>)Bp/-  
   sca2 = fftshift(fft(s2)); jQ2Ot<  
   sca3 = fftshift(fft(s3)); PsnWWj?c  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   ^p[rc@+  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); >O*IQ[r-  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); :=u?Fqqws  
   s3 = ifft(fftshift(sc3)); /?@3.3sl_  
   s2 = ifft(fftshift(sc2));                       % Return to physical space ^l9N48]|?  
   s1 = ifft(fftshift(sc1)); _ba>19csq%  
end 2NC.Z;  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); M?Dfu .t  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); X-6de>=  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); #gRM i)(F  
   P1=[P1 p1/p10]; [DJ|`^eKD  
   P2=[P2 p2/p10]; xF;kTBRi  
   P3=[P3 p3/p10]; 2%LLSa  
   P=[P p*p]; g)#W>.Asd  
end /|tJ6T1LrB  
figure(1) 1_9<3,7  
plot(P,P1, P,P2, P,P3); }&cu/o4  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~