| 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 [SPx $H)^o! % This Matlab script file solves the coupled nonlinear Schrodinger equations of {~U3|_"[pX % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of :o'x?] % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear &xnQLz:# % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 |./mPV r 6zi>Q?] 1 %fid=fopen('e21.dat','w'); ')"+ a^c N = 128; % Number of Fourier modes (Time domain sampling points) <Y]LY_( M1 =3000; % Total number of space steps G !q[NRu J =100; % Steps between output of space ue_wuZi T =10; % length of time windows:T*T0 mJSfn"b}K T0=0.1; % input pulse width C-&ymJC| MN1=0; % initial value for the space output location R
BYhU55B dt = T/N; % time step 6cH8Jr _ n = [-N/2:1:N/2-1]'; % Index <3;p>4gN t = n.*dt; IzP,)!EE u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 &9yZfp u20=u10.*0.0; % input to waveguide 2
jxog8E u1=u10; u2=u20; uz8LF47@:- U1 = u1; 40t xZFQ0 U2 = u2; % Compute initial condition; save it in U en<~_|J ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. :"%/u9<A w=2*pi*n./T; -YA,Stc- g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T aB,-E>+ L=4; % length of evoluation to compare with S. Trillo's paper 3Ua?^2l dz=L/M1; % space step, make sure nonlinear<0.05 nKx)R^]k for m1 = 1:1:M1 % Start space evolution +,76|oMsQ% u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS A8)4nOXM u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; Gw*Tz" ca1 = fftshift(fft(u1)); % Take Fourier transform WXQ@kQD ca2 = fftshift(fft(u2)); ~YYnn7) c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation GJ ^c^` c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift /F0q8j0 u2 = ifft(fftshift(c2)); % Return to physical space >i/jqT/ u1 = ifft(fftshift(c1)); cQU/z"?+ if rem(m1,J) == 0 % Save output every J steps.
^CkMk 1 U1 = [U1 u1]; % put solutions in U array 4 PK}lc U2=[U2 u2]; QaWS%0go MN1=[MN1 m1]; +?_!8N8 z1=dz*MN1'; % output location oZ'a}kF end y*
+y& end /R#zu_i hg=abs(U1').*abs(U1'); % for data write to excel 4#$#x=: ha=[z1 hg]; % for data write to excel 5UEZpxnv t1=[0 t']; WZ CI*' hh=[t1' ha']; % for data write to excel file J@3, %dlmwrite('aa',hh,'\t'); % save data in the excel format &,nv+>D figure(1) 1!#N-^qk waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn U+S=MP
}: figure(2) S6~y!J6Ok4 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn LPvp
(1 cn'>dz3v 非线性超快脉冲耦合的数值方法的Matlab程序 }%wd1`l7 v3-/ [-XB: 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。 +}:Z9AAMy 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 +-izC%G sZ `Tv[ 8U{D)KgS )jM%bUk,! % This Matlab script file solves the nonlinear Schrodinger equations #ArrQeO 5_ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of r4yz{^G
% Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear t~Q9}+ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 =2R4Z8G ;: ;E|{e C=1; xGd60"w2 M1=120, % integer for amplitude LmrdVSs_ M3=5000; % integer for length of coupler '.A!IGsj N = 512; % Number of Fourier modes (Time domain sampling points) {U5sRM|I dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. 3?93Pj3oPt T =40; % length of time:T*T0. "hIYf7r## dt = T/N; % time step &[E\2 E n = [-N/2:1:N/2-1]'; % Index A7p4M?09 t = n.*dt; N`8K1{>BH ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. -cgO]q+Oq w=2*pi*n./T; ~1G^IZ6 g1=-i*ww./2; MB]E[&Q! g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; o_:v?Y>0 g3=-i*ww./2; c{q+h V= P1=0; B,>02EZ P2=0; kg/ B<w' P3=1; U8_{MY-9} P=0; {cK<iQJ for m1=1:M1 }M07-qIX{ p=0.032*m1; %input amplitude t@%w:*& s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 j7I=2xnTWu s1=s10; @6
he!wW s20=0.*s10; %input in waveguide 2 <A3%182 s30=0.*s10; %input in waveguide 3 4I4m4^ s2=s20; 1XGg0SC s3=s30; ~ k*]Z8Z p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); iOfm:DTPr %energy in waveguide 1 =
0 ~4k# p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); Iiy5;:CX:q %energy in waveguide 2 YvY|\2^K p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); j<AOC? %energy in waveguide 3 4n,&,R r# for m3 = 1:1:M3 % Start space evolution q"d9C)Md s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS TKZtoQP% s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; :jiEn
y s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 0=ws )@[I sca1 = fftshift(fft(s1)); % Take Fourier transform FXCBX:LnvU sca2 = fftshift(fft(s2)); u8f\)m sca3 = fftshift(fft(s3)); _){|/Zd sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift z"@^'{.l sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); h+km? j sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); [LVXXjkFI s3 = ifft(fftshift(sc3)); mWviWHK s2 = ifft(fftshift(sc2)); % Return to physical space bT:u|/I s1 = ifft(fftshift(sc1)); (UkP AE end @@Ib^sB% p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
*yZ6" p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); jWdviS9&g p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); h.<f%&)F P1=[P1 p1/p10]; Tm%5:/<8 P2=[P2 p2/p10]; prJd' P3=[P3 p3/p10]; i?T-6{3I P=[P p*p]; )%C.IZ_s2 end (-C)A-Uo& figure(1) ^t0!Dbx3SE plot(P,P1, P,P2, P,P3); ( 5LCy?-6 jz!I + 转自:http://blog.163.com/opto_wang/
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