计算脉冲在非线性耦合器中演化的Matlab 程序 &I!2gf `+zr PpX % This Matlab script file solves the coupled nonlinear Schrodinger equations of
})!n1k t % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
N(1jm F % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
}JlQQ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
>Q+EqT u5R^++ %fid=fopen('e21.dat','w');
{v`wQM[ N = 128; % Number of Fourier modes (Time domain sampling points)
X^xu$d6 M1 =3000; % Total number of space steps
rSEJ2%iF* J =100; % Steps between output of space
b JBx~ T =10; % length of time windows:T*T0
**s:H'M w_ T0=0.1; % input pulse width
sgB3i`_M MN1=0; % initial value for the space output location
=e ._b 7P dt = T/N; % time step
#d| .Bx H n = [-N/2:1:N/2-1]'; % Index
~^5uOeTZ~ t = n.*dt;
s#qq%
@ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
K}Z'!+ <U u20=u10.*0.0; % input to waveguide 2
`L;I/Hp u1=u10; u2=u20;
4]dPhsey U1 = u1;
5/*ZqrJw{" U2 = u2; % Compute initial condition; save it in U
f%@Y
XGf ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
hF2
G{{8A w=2*pi*n./T;
6Jj)[ R\5= g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
np>*O }r* L=4; % length of evoluation to compare with S. Trillo's paper
ZcdS?Z2k dz=L/M1; % space step, make sure nonlinear<0.05
~RMOEH.o for m1 = 1:1:M1 % Start space evolution
MPGQ4v i& u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
BO[A1'> u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
Y0eu ^p) ca1 = fftshift(fft(u1)); % Take Fourier transform
KY"~Ta` ca2 = fftshift(fft(u2));
=_,OucKkYG c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
K1+,y1c c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
~; `i&s u2 = ifft(fftshift(c2)); % Return to physical space
J J3 vC u1 = ifft(fftshift(c1));
NKI&n]EO if rem(m1,J) == 0 % Save output every J steps.
94lmsE U1 = [U1 u1]; % put solutions in U array
W&p-Z"=) U2=[U2 u2];
{ aB_t%`w MN1=[MN1 m1];
]
2b@mX z1=dz*MN1'; % output location
0 /H1INve end
/aPq9B@ end
hi
]+D= S hg=abs(U1').*abs(U1'); % for data write to excel
h|-r t15 ha=[z1 hg]; % for data write to excel
hB^"GYZ t1=[0 t'];
9B%"7MVn hh=[t1' ha']; % for data write to excel file
jgO{DNe(= %dlmwrite('aa',hh,'\t'); % save data in the excel format
ER|5_ figure(1)
Q;^([39DI waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
t)v#y!Ci" figure(2)
$qE JO=v waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
^#Z(&/5f0 Cn{UzSKfs 非线性超快脉冲耦合的数值方法的Matlab程序 o1g[(zky 97&6i TYA 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。
[ z&y]~ 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
N4}h_mh^' >l7
o/*4 WW_X:N~~e\ N C sUC % This Matlab script file solves the nonlinear Schrodinger equations
lA ,%'+- % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
]O \6.>H % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
+0 a',`yc % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
xFvSQ`sp =kCpCpET C=1;
mee-Qq:} M1=120, % integer for amplitude
n/ 8fv~zU M3=5000; % integer for length of coupler
o^NQ]BdH8
N = 512; % Number of Fourier modes (Time domain sampling points)
9wwvh'T&NK dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
Y{S/A * X T =40; % length of time:T*T0.
ofi']J{R dt = T/N; % time step
=o-q u^T^u n = [-N/2:1:N/2-1]'; % Index
.9E`x>C t = n.*dt;
Q{a!D0;4v ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
2 n7[Op w=2*pi*n./T;
:kUH>O g1=-i*ww./2;
K A< g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
Ay_<?F+& g3=-i*ww./2;
un/R7 " P1=0;
[v& _MQ P2=0;
pp-Ur?PM P3=1;
du qu}*Jw P=0;
!XicX9n for m1=1:M1
N" 8o0> p=0.032*m1; %input amplitude
l&yR-FJ7KY s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
{P3,jY^ s1=s10;
f9 rToH s20=0.*s10; %input in waveguide 2
ML]?`qv ' s30=0.*s10; %input in waveguide 3
0O:TKgb&C. s2=s20;
b9v Kux s3=s30;
xv ja p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
X >**M %energy in waveguide 1
z/ i3 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
2<O
hO
^ %energy in waveguide 2
j C@^/rMh p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
y^XwJX-f %energy in waveguide 3
N7;2BUIXJ for m3 = 1:1:M3 % Start space evolution
ew Lr+8 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
N;w1f"V} s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
qzLRA.#f^ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
F0yh7MItV sca1 = fftshift(fft(s1)); % Take Fourier transform
AD5t uY sca2 = fftshift(fft(s2));
#eaey+~ sca3 = fftshift(fft(s3));
J>'o,"D sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
`?$R_u Fh: sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
" c]Mz&z sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
&@Q3CC DS s3 = ifft(fftshift(sc3));
r`krv-,O$ s2 = ifft(fftshift(sc2)); % Return to physical space
I;`V*/s 8" s1 = ifft(fftshift(sc1));
JrQN-e! end
IFE C_F> p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
g &za/F p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
Oo0$n]*;W p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
IKU - P1=[P1 p1/p10];
?e@Ff"Y@e P2=[P2 p2/p10];
RsY<j& f P3=[P3 p3/p10];
J3zb_!PPE P=[P p*p];
qV}zV\Nz end
0I cyi#N figure(1)
+ ]__zm/^ plot(P,P1, P,P2, P,P3);
N7E[wOP }C'z$i( y 转自：
http://blog.163.com/opto_wang/
