| 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 pI<f) r 7 Fsay+a % This Matlab script file solves the coupled nonlinear Schrodinger equations of dUdT7ixo % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of |! "eWTJ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 11;zNjD| % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 UkGCyGyZ[ Y\'}a+:@Ph %fid=fopen('e21.dat','w'); Y`wSv NU N = 128; % Number of Fourier modes (Time domain sampling points) bi;1s'Y<D M1 =3000; % Total number of space steps "tpSg J =100; % Steps between output of space eb$#A _m T =10; % length of time windows:T*T0 ]')RMg zM* T0=0.1; % input pulse width 18:%~>.! MN1=0; % initial value for the space output location #C@FYOf* dt = T/N; % time step cj5+NM" n = [-N/2:1:N/2-1]'; % Index 8DaL,bi*. t = n.*dt; R@rBEW& u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 ^_mj u20=u10.*0.0; % input to waveguide 2 }*"p?L^p{ u1=u10; u2=u20; 0_t!T'jr7 U1 = u1; uY'HT|@:{ U2 = u2; % Compute initial condition; save it in U "C`Ub ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. H}
g{Cr"Ex w=2*pi*n./T; R*r#E{!V; g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T FaJ &GOM, L=4; % length of evoluation to compare with S. Trillo's paper E-g_".agO dz=L/M1; % space step, make sure nonlinear<0.05 t\ewHZG" for m1 = 1:1:M1 % Start space evolution wLr_-vJ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS <Q?F?.^e u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; V3j= Kf ca1 = fftshift(fft(u1)); % Take Fourier transform bA->{OPkT ca2 = fftshift(fft(u2)); x-3\Ls[I c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation /&94 eC c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift 6)Lk-D u2 = ifft(fftshift(c2)); % Return to physical space #>+ HlT u1 = ifft(fftshift(c1)); 6!FQzFCZq if rem(m1,J) == 0 % Save output every J steps. ]z9=}=If U1 = [U1 u1]; % put solutions in U array czd~8WgOa U2=[U2 u2]; \)|hogI|f MN1=[MN1 m1]; M =r)I~ z1=dz*MN1'; % output location #;nYg?d= end "9e\c;a end V~5jfcd hg=abs(U1').*abs(U1'); % for data write to excel Q'0d~6n&{ ha=[z1 hg]; % for data write to excel ~$?ZK]YOrx t1=[0 t']; }pu27F)& hh=[t1' ha']; % for data write to excel file C3YT1tK %dlmwrite('aa',hh,'\t'); % save data in the excel format D d</`iUq figure(1) tZG:Pr1U@ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn @sC`!Rmy'- figure(2) HC,Se.VYS waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn :20W\P<O!A LSr]S79N1 非线性超快脉冲耦合的数值方法的Matlab程序 Jz e:[MYS BR yl4 在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。 65Yv4pNL Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 #O dJ"1A| 6V01F8&w SI-Ops~e >I&5j/&}+ % This Matlab script file solves the nonlinear Schrodinger equations AkQ~k0i}b % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of hZ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear I&W=Q[m % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 w&T9;_/ }Kbb4]t|" C=1; 03 #lX(MB M1=120, % integer for amplitude G*P#]eO M3=5000; % integer for length of coupler 81
sG N = 512; % Number of Fourier modes (Time domain sampling points) '$%l7 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. Z}Ft:7 T =40; % length of time:T*T0. @r/nF5 dt = T/N; % time step ^,T(mKS n = [-N/2:1:N/2-1]'; % Index :! !at:> t = n.*dt; 0^K"> ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. XuM'_FN`A< w=2*pi*n./T; vnZC,J ` g1=-i*ww./2; !."D]i; g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; o]I\6,T/| g3=-i*ww./2; .jWC$SVR P1=0; X?qK0fS P2=0; 68WO~* P3=1; 8NAON5.! P=0; C1 GKLl~ for m1=1:M1 ^yN&ZI3P& p=0.032*m1; %input amplitude t=W}SH s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 D7Q$R:6| s1=s10; |imM#wF s20=0.*s10; %input in waveguide 2 z/@slT s30=0.*s10; %input in waveguide 3 6fEqqUeV s2=s20; aQ\$A`? s3=s30; R)s:rJQ=p p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); K} X&AJ5A %energy in waveguide 1 SbrecZ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); h^(*Tv-! %energy in waveguide 2 nazZ*lC p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); #( 146 %energy in waveguide 3 4yA+h2 for m3 = 1:1:M3 % Start space evolution O`t&ldU s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS ]:k/Y$O2 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; ^KT Y? s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; $1L>)S sca1 = fftshift(fft(s1)); % Take Fourier transform hH8oyIC sca2 = fftshift(fft(s2)); =wV<hg)C sca3 = fftshift(fft(s3)); =|y9UlsD sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift `%"\@< sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); xHLlMn4M sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); bI9~jWgGp s3 = ifft(fftshift(sc3)); +.b,AqJ/ s2 = ifft(fftshift(sc2)); % Return to physical space 1FL~ndJs s1 = ifft(fftshift(sc1)); 2E)-M9ds end bUdLs.: p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); ]dmrkZz: p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); `MN4uC p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); V1`o%;j P1=[P1 p1/p10]; WUXx;9 > P2=[P2 p2/p10]; :g=qz~2Xk P3=[P3 p3/p10]; .|>3k'<l P=[P p*p]; cO+qs[
BQ end Nv}=L
: E figure(1) `w7v*h|P plot(P,P1, P,P2, P,P3); nuMD!qu!nZ Vl=l?A8 转自:http://blog.163.com/opto_wang/
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