计算脉冲在非线性耦合器中演化的Matlab 程序 w%F~4|F N\{Xhr7d % This Matlab script file solves the coupled nonlinear Schrodinger equations of
=REMSej % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
))m\d * % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
y(/"DUx % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
v&Xsyb0CaM y,'M3GGl %fid=fopen('e21.dat','w');
+*&bgGhT N = 128; % Number of Fourier modes (Time domain sampling points)
Z$
q{!aY M1 =3000; % Total number of space steps
?e( y/ J =100; % Steps between output of space
[w*YH5kX T =10; % length of time windows:T*T0
mU@pRjq= T0=0.1; % input pulse width
_wMx KM MN1=0; % initial value for the space output location
A)6xEeyR dt = T/N; % time step
+l'l*< n = [-N/2:1:N/2-1]'; % Index
Kv(2x3(" t = n.*dt;
[Z~h!} u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
!YX$4_I u20=u10.*0.0; % input to waveguide 2
mY6d+ u1=u10; u2=u20;
WOBLgM,| U1 = u1;
fNR2(8;} U2 = u2; % Compute initial condition; save it in U
Wk<he F ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
C:z+8w t w=2*pi*n./T;
wJc~AP)I%z g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
Y$JGpeq8w L=4; % length of evoluation to compare with S. Trillo's paper
A#NJ8_ dz=L/M1; % space step, make sure nonlinear<0.05
N8*6sK. for m1 = 1:1:M1 % Start space evolution
9~3;upWu! u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
s4V-brCM$| u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
6!F@?3qCyg ca1 = fftshift(fft(u1)); % Take Fourier transform
T($d3Nn1 ca2 = fftshift(fft(u2));
0QJ
: c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
h&5bMW c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
K|^PHe u2 = ifft(fftshift(c2)); % Return to physical space
fv@mA -- u1 = ifft(fftshift(c1));
FTu6%~M/ if rem(m1,J) == 0 % Save output every J steps.
1,Ams U1 = [U1 u1]; % put solutions in U array
a
]~Rp U2=[U2 u2];
>-S? rXO MN1=[MN1 m1];
jGm`Qg{< z1=dz*MN1'; % output location
SXqWq end
P}"=67$ end
zEM c) hg=abs(U1').*abs(U1'); % for data write to excel
d `MTc ha=[z1 hg]; % for data write to excel
rF@njw@ t1=[0 t'];
D;?cf+6$ hh=[t1' ha']; % for data write to excel file
'%Fg+cZN\ %dlmwrite('aa',hh,'\t'); % save data in the excel format
K Eda6zZH figure(1)
.4CCR[Het waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
y~ 2C2'7 figure(2)
F#b^l} waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
c/Dk*.xy< T'^ Do/ 非线性超快脉冲耦合的数值方法的Matlab程序 x."R_> 8NF93tqD6 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。
ztS:1\ 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
|.#G G7F^S 4 H<. EKgY jmORKX+) % This Matlab script file solves the nonlinear Schrodinger equations
mV>l`&K= % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
W(4Mvd % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
cMU"SO % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
s78MXS?py [,bra8f[C C=1;
@5RbMf{ M1=120, % integer for amplitude
uqotVil, M3=5000; % integer for length of coupler
hr@kU x N = 512; % Number of Fourier modes (Time domain sampling points)
#Vy8<Vy&w dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
AONEUSxJ T =40; % length of time:T*T0.
.#q]{j@Ot dt = T/N; % time step
`{KdmWhW n = [-N/2:1:N/2-1]'; % Index
8NZQTRdH t = n.*dt;
olv0w;s ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Cg8s9qE? w=2*pi*n./T;
:kMF.9U: g1=-i*ww./2;
AAXlBY6Y- g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
\V(w= g3=-i*ww./2;
F G:t2ea P1=0;
IRknD3LX P2=0;
oNEjlV* P3=1;
+dG3/vV P=0;
+^<s' for m1=1:M1
{1eW*9 p=0.032*m1; %input amplitude
<rihi:4K s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
\Ota~A s1=s10;
Z g.La<# s20=0.*s10; %input in waveguide 2
h`n)
b s30=0.*s10; %input in waveguide 3
y9Q#%a8V s2=s20;
9,?7mgZp s3=s30;
rD;R9b"J p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
]*Cq'<h$ %energy in waveguide 1
^qY?x7mx1 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
S[;d\Z]~ %energy in waveguide 2
XiL[1JM
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
G"F)t(iX %energy in waveguide 3
6}cN7wnm
j for m3 = 1:1:M3 % Start space evolution
uXo uN$& s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
|}o6N5) s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
im3BQIPR s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
^)E#
c sca1 = fftshift(fft(s1)); % Take Fourier transform
60R]Q sca2 = fftshift(fft(s2));
+;ylld sca3 = fftshift(fft(s3));
M<nH sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
w{WEYS sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
gX|We}H sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
Y 8n*o3jM s3 = ifft(fftshift(sc3));
$(]E$ek s2 = ifft(fftshift(sc2)); % Return to physical space
:+_ s1 = ifft(fftshift(sc1));
~f:"Q(f+ end
y 2C Jk~ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
h e[2, p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
iv
~<me0F p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
"-Yj~ P1=[P1 p1/p10];
1)#dgsa P2=[P2 p2/p10];
}60/5HNr P3=[P3 p3/p10];
| Rj"}SC P=[P p*p];
C jGQ end
/PKu",Azj figure(1)
F!<!)_8Q plot(P,P1, P,P2, P,P3);
/5Sd?pW; !'#GdRstv 转自:
http://blog.163.com/opto_wang/