计算脉冲在非线性耦合器中演化的Matlab 程序 u*S-Pji,x n1 Wo<$# % This Matlab script file solves the coupled nonlinear Schrodinger equations of
#iiXJnG % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
`x:O&2 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
&} rmDx % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
1a ]P+-@u[ &v/>P1Z
G %fid=fopen('e21.dat','w');
e~ZxDAd N = 128; % Number of Fourier modes (Time domain sampling points)
)z_5I (?& M1 =3000; % Total number of space steps
3
,f3^A J =100; % Steps between output of space
9*2Q'z}_ T =10; % length of time windows:T*T0
.WVIdVO7 T0=0.1; % input pulse width
/8? u2
q MN1=0; % initial value for the space output location
UrmnHc>}c dt = T/N; % time step
edL sn>\*# n = [-N/2:1:N/2-1]'; % Index
7PW7&]-WQ t = n.*dt;
_u9bZ' u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
KIGMWS^^ u20=u10.*0.0; % input to waveguide 2
@s|G18@ u1=u10; u2=u20;
U1)!X@F{ U1 = u1;
D=jtXQF U2 = u2; % Compute initial condition; save it in U
vNQ|tmn ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
RgD %pNhI w=2*pi*n./T;
)B9 /P >c g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
; w<r/dK L=4; % length of evoluation to compare with S. Trillo's paper
FmhT^ dz=L/M1; % space step, make sure nonlinear<0.05
v[\Z^pccgj for m1 = 1:1:M1 % Start space evolution
n65fT+; u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
:I^4ILQCD u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
9Dyw4'W.N ca1 = fftshift(fft(u1)); % Take Fourier transform
R %JEx3)0m ca2 = fftshift(fft(u2));
mG%cE(j*D c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
nTsPX Tat c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
nZ`=Up p ) u2 = ifft(fftshift(c2)); % Return to physical space
.yb8<q s u1 = ifft(fftshift(c1));
-./ Y if rem(m1,J) == 0 % Save output every J steps.
R!WeSgKCs U1 = [U1 u1]; % put solutions in U array
7 A U2=[U2 u2];
VKi3z%kwK MN1=[MN1 m1];
kEg~yN z1=dz*MN1'; % output location
Ds\f?\Em end
/sl# M end
^fM=|.? hg=abs(U1').*abs(U1'); % for data write to excel
)' 2vUt`_7 ha=[z1 hg]; % for data write to excel
wDs#1`uTq t1=[0 t'];
}J= z O8OL hh=[t1' ha']; % for data write to excel file
x_EU.924uY %dlmwrite('aa',hh,'\t'); % save data in the excel format
5a* Awv} figure(1)
/ `w'X/'VJ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
ND5E`Va5R figure(2)
,aa
%{ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
7p18;Z+6>X ^N ~Jm&I 非线性超快脉冲耦合的数值方法的Matlab程序 1xwq:vFC. +Jc-9Ko\c; 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。
16I(S 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
qj?I*peK) U3 w*z6OG ,qlFk| A| 1 z[blNs& % This Matlab script file solves the nonlinear Schrodinger equations
>2)!w % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
I3?:KVa % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
~0 n9In% % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
{XYf"ONi Vs[!WJ
7 C=1;
!Jo.Un7 M1=120, % integer for amplitude
QLTE`t5w3' M3=5000; % integer for length of coupler
W&^2Fb N = 512; % Number of Fourier modes (Time domain sampling points)
yDw^xGws dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
.{ ]=v T =40; % length of time:T*T0.
t,; b*ZR dt = T/N; % time step
H
%PIE1_ n = [-N/2:1:N/2-1]'; % Index
NPR{g!tK% t = n.*dt;
* -9b!>5eD ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
:Ee5:S w=2*pi*n./T;
#D! 3a%u0 g1=-i*ww./2;
j Ns eD g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
VAR/" g3=-i*ww./2;
h O:X\:G P1=0;
Xq%!(YD| P2=0;
"i*Gi
\U P3=1;
8|,-P=%t P=0;
v 6?<)M% for m1=1:M1
:Zd# }P p=0.032*m1; %input amplitude
>Y/1%Hp9 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
]H<C Rw s1=s10;
R:JS)>B s20=0.*s10; %input in waveguide 2
H\!u5o&}` s30=0.*s10; %input in waveguide 3
-.WVuc` s2=s20;
-/&6}lD s3=s30;
j|WaW nl= p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Bj7\ {x,? %energy in waveguide 1
egi?Qg p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
2=N YBOE %energy in waveguide 2
I@q>ES! 1H p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
Qi7^z; %energy in waveguide 3
jW",'1h<n for m3 = 1:1:M3 % Start space evolution
9Au+mIN s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
7 3(T+6` s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
?-'Q-\j s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
|q Nrj~n@ sca1 = fftshift(fft(s1)); % Take Fourier transform
U^0vLyqW^5 sca2 = fftshift(fft(s2));
A1f]HT sca3 = fftshift(fft(s3));
0+:.9*g=k sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
{UZli[W1 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
c\4n 7m,y sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
C 12 7he s3 = ifft(fftshift(sc3));
k*c:%vC! s2 = ifft(fftshift(sc2)); % Return to physical space
J0p,P.G s1 = ifft(fftshift(sc1));
qc'tK6=jp end
+msHQk5#$m p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
|2 wff? p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
Da-(D<[0 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
5\Y/s o= P1=[P1 p1/p10];
P e wPl0 P2=[P2 p2/p10];
]:E]5&VwV} P3=[P3 p3/p10];
16G v?
I
h P=[P p*p];
3Ob"r` end
j*:pW;)^ figure(1)
kdYl>M plot(P,P1, P,P2, P,P3);
*E)Y?9u" ^]R0d3?>\ 转自：
http://blog.163.com/opto_wang/
