| 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 {kG;."S+K @ay|]w % This Matlab script file solves the coupled nonlinear Schrodinger equations of W^|J/Y48 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of K051usm % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear UFk!dK+ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 D?J#u;h~f !3?~#e{_ %fid=fopen('e21.dat','w'); p.aE N = 128; % Number of Fourier modes (Time domain sampling points) M%;"c?g M1 =3000; % Total number of space steps >gGil|I J =100; % Steps between output of space |P~q/Wff T =10; % length of time windows:T*T0 Av[Ud
*~ T0=0.1; % input pulse width +yIL[D MN1=0; % initial value for the space output location L,%Z9 dt = T/N; % time step 'W+i[Ep5Q n = [-N/2:1:N/2-1]'; % Index lG
<yJ~{ t = n.*dt; }_vM&.GFlL u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 6.UKB<sV u20=u10.*0.0; % input to waveguide 2 8iOO1I?+ u1=u10; u2=u20; (6o:4|xl0 U1 = u1; /6smVz@O U2 = u2; % Compute initial condition; save it in U t@r#b67WJe ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. )ZeLaa P w=2*pi*n./T; ac3_L$X[ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T @7]\y7D L=4; % length of evoluation to compare with S. Trillo's paper <YSg~T dz=L/M1; % space step, make sure nonlinear<0.05 fxOE]d8v for m1 = 1:1:M1 % Start space evolution e
%& u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS }eI`Qg u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; CJ:uYXJJ:z ca1 = fftshift(fft(u1)); % Take Fourier transform KDX$.$# ca2 = fftshift(fft(u2)); IF^[^^v+H c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation ` )]lUvR c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift ^YqbjL u2 = ifft(fftshift(c2)); % Return to physical space +{'lZa u1 = ifft(fftshift(c1)); :K:f^o]s if rem(m1,J) == 0 % Save output every J steps. ;i/"$K U1 = [U1 u1]; % put solutions in U array 3m3
EXz U2=[U2 u2]; >b3@>W MN1=[MN1 m1]; >
Z]P]e z1=dz*MN1'; % output location ` v>/
end .$UTH@;7 end l,^xX=, hg=abs(U1').*abs(U1'); % for data write to excel 1x8(I&i ha=[z1 hg]; % for data write to excel \?r$&K]4 t1=[0 t']; 4Sqvhz hh=[t1' ha']; % for data write to excel file f8R+7Ykx %dlmwrite('aa',hh,'\t'); % save data in the excel format eS*
*L3 figure(1) ktU9LW~ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn Ls lM$
figure(2) .fbYB,0w waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn QZ#3Bn%B5 w<btv]X1 非线性超快脉冲耦合的数值方法的Matlab程序 LPb]mC6# ,!jR:nApE 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。 ;B*L1'FF%t 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 \f6lT3"VN sw[<VsxjR 3e#x)H/dr 1V#0\1sj % This Matlab script file solves the nonlinear Schrodinger equations Pkj T&e) % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of s z;=mMr/Z % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear }{P&idkv % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 D`1I;Tb# GOUY_&}tL C=1; ZCj>MA M1=120, % integer for amplitude ^ b=5 6~[ M3=5000; % integer for length of coupler [^h/(a` N = 512; % Number of Fourier modes (Time domain sampling points) -Mr{+pf dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. f S(^["*G T =40; % length of time:T*T0. yjeqv-7 dt = T/N; % time step B9%yd*SJ n = [-N/2:1:N/2-1]'; % Index ]kyle3#-~ t = n.*dt; kt;}]O2%R ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. ~3LhcU- w=2*pi*n./T; >ly&+3S g1=-i*ww./2; ]!n*V/g g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; P9 W<gIO g3=-i*ww./2; ;JMOsn}8 P1=0; .;]YJy P2=0; pyu46iE) P3=1; ---Ks0\V P=0; nC-c8y for m1=1:M1 .%-6&%1 p=0.032*m1; %input amplitude ,{#RrF e s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 d,Im&j_Z s1=s10; 8#[%?}tK s20=0.*s10; %input in waveguide 2 f(EYx)gZ s30=0.*s10; %input in waveguide 3 m0dFA<5- s2=s20; {s9y@c*15. s3=s30; -MVNXAKnZ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); \c5#\1< %energy in waveguide 1 Fm-q=3 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); mtiO7w"M\7 %energy in waveguide 2 ?yK%]1O p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); _47j9m]f %energy in waveguide 3 ]%vGC^ for m3 = 1:1:M3 % Start space evolution #dxJ# s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS F$"MFdc[ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; 6!gtve_
s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; r7]?g~zb sca1 = fftshift(fft(s1)); % Take Fourier transform Q"l"p:n%n sca2 = fftshift(fft(s2)); >*<6 zQf sca3 = fftshift(fft(s3)); < e7<t9 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift \N-|
iq sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); e0G}$
as sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); ebl)6C s3 = ifft(fftshift(sc3)); U{U:8== s2 = ifft(fftshift(sc2)); % Return to physical space khKv5K#) s1 = ifft(fftshift(sc1)); [qjAq@@N#q end K%aPl~e p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 5<:VJC< p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); JsWq._O{/ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); Nv*E .|G P1=[P1 p1/p10]; 76u/WC>B P2=[P2 p2/p10]; X*c_^g{ P3=[P3 p3/p10]; 6x (L&>F P=[P p*p]; Cnc\sMDJ\B end /I`bh figure(1) _taHf %\4 plot(P,P1, P,P2, P,P3); \r1kbf7? F'Y2f6B 转自:http://blog.163.com/opto_wang/
|
|