计算脉冲在非线性耦合器中演化的Matlab 程序 Wvqhl
'J d\Zng!Z ' % This Matlab script file solves the coupled nonlinear Schrodinger equations of
Ve=b16H % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
ZN6Z~SL_i~ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
r GkyGz8> % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
kN>!2UfNS <t,x RB k %fid=fopen('e21.dat','w');
XUw/2"D'? N = 128; % Number of Fourier modes (Time domain sampling points)
T )})
pt!V M1 =3000; % Total number of space steps
y==CT Y@ J =100; % Steps between output of space
fzA9'i` T =10; % length of time windows:T*T0
m4g$N) T0=0.1; % input pulse width
" v GW2~*) MN1=0; % initial value for the space output location
X7 w Ky(g dt = T/N; % time step
E"@wek.- n = [-N/2:1:N/2-1]'; % Index
-^57oU t = n.*dt;
?rIx/>C9 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
BB'OCN u20=u10.*0.0; % input to waveguide 2
M[u A@ u1=u10; u2=u20;
HmwT ~ U1 = u1;
* 4Izy14e U2 = u2; % Compute initial condition; save it in U
p$>l7?h ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
#,.Hr#3nI w=2*pi*n./T;
_[y/Y \{I g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
p^_y U_ L=4; % length of evoluation to compare with S. Trillo's paper
AK #1]i~ dz=L/M1; % space step, make sure nonlinear<0.05
wT\49DT"7 for m1 = 1:1:M1 % Start space evolution
9mFE?J u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
PuO&wI]: u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
<|\Lm20 G] ca1 = fftshift(fft(u1)); % Take Fourier transform
[mHdG2X ca2 = fftshift(fft(u2));
n}V_,:Z c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
'ah[(F<*@e c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
P2*<GjV`S/ u2 = ifft(fftshift(c2)); % Return to physical space
L^F y#p u1 = ifft(fftshift(c1));
J'2X&2 if rem(m1,J) == 0 % Save output every J steps.
w- {c.x U1 = [U1 u1]; % put solutions in U array
yOg+iFTr U2=[U2 u2];
^ BL" wk MN1=[MN1 m1];
~!3r&( z1=dz*MN1'; % output location
i@ BtM9: end
TuY CR>P[ end
e*n@j hg=abs(U1').*abs(U1'); % for data write to excel
Q dp )cT ha=[z1 hg]; % for data write to excel
*|E[L^ t1=[0 t'];
t. '!`5G hh=[t1' ha']; % for data write to excel file
2T TdH) %dlmwrite('aa',hh,'\t'); % save data in the excel format
rc>6.sM
% figure(1)
J Sg$wi8 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
*cnNu T figure(2)
0P(!j_2m waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
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[!{ +&"zU GTIc 非线性超快脉冲耦合的数值方法的Matlab程序 L u0x
(/ eNu7~3k } 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
|B2+{@R Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
&l[$*<P5V ?KI, cl %9RF /[>sf[X\I9 % This Matlab script file solves the nonlinear Schrodinger equations
UOmY-\ &c % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
zZC9\V}R % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
ivz5H (b % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
m<g~H4 o\)F}j&b#= C=1;
O5t[ M1=120, % integer for amplitude
t@Nyr& |D M3=5000; % integer for length of coupler
2Q"K8=s N = 512; % Number of Fourier modes (Time domain sampling points)
l ?^4!&Nm dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
]P2"[y T =40; % length of time:T*T0.
I y3GE[ dt = T/N; % time step
m7>JJX3=< n = [-N/2:1:N/2-1]'; % Index
y Ej^=pw t = n.*dt;
AjgF6[ B ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
x~j`@k,; w=2*pi*n./T;
/_#q@r4ZQ g1=-i*ww./2;
Nl(3Xqov g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
!1Cy$}w g3=-i*ww./2;
<nK? L cP P1=0;
W1FI mlXS P2=0;
@[i4 ^ P3=1;
az|N-?u P=0;
nmi|\mof for m1=1:M1
.Twk {p p=0.032*m1; %input amplitude
y% b F & s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
?_"ik[w} s1=s10;
f!
.<$ih s20=0.*s10; %input in waveguide 2
^4Ah_ U s30=0.*s10; %input in waveguide 3
yD6[\'% s2=s20;
r s?R: + s3=s30;
y[_Q- p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
'1)$' %energy in waveguide 1
\qK &q p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
yw3$2EW %energy in waveguide 2
-n<pPau2 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
g]yBA7/S" %energy in waveguide 3
A;|D:;x3G for m3 = 1:1:M3 % Start space evolution
qXtC^n@x s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
p >t#@Eu| s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
Y6L ~K? s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
kO*$"w#X[p sca1 = fftshift(fft(s1)); % Take Fourier transform
KC#q@InK sca2 = fftshift(fft(s2));
4G>H sca3 = fftshift(fft(s3));
?r 2 ` Q sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
fG(SNNl+D sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
)Z ? Ym.0/ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
9dUravC7 s3 = ifft(fftshift(sc3));
|(LZ9I s2 = ifft(fftshift(sc2)); % Return to physical space
oVe| M ss6 s1 = ifft(fftshift(sc1));
zY!j:FT1HY end
Gc; {\VU p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
s '\U ap p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
~-J]W-n p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
[ )dXI IM P1=[P1 p1/p10];
C" T;Qp~B P2=[P2 p2/p10];
vv+z'(l P3=[P3 p3/p10];
&_|#. P=[P p*p];
-Z
U gx$ end
hUMf"=q+ figure(1)
]cMqahaY plot(P,P1, P,P2, P,P3);
2!J&+r hPePB= 转自：
http://blog.163.com/opto_wang/
