计算脉冲在非线性耦合器中演化的Matlab 程序 f0BdXsV# g mI>,.&eo % This Matlab script file solves the coupled nonlinear Schrodinger equations of
6l4mS~/ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
b&5lY p"d % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
hjQ~uqbg % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
;j)FnY=: - ._+J_ts %fid=fopen('e21.dat','w');
PxfY&;4n! N = 128; % Number of Fourier modes (Time domain sampling points)
w#g#8o >' M1 =3000; % Total number of space steps
X 51Yfr J =100; % Steps between output of space
T0]*{k(FR T =10; % length of time windows:T*T0
s$ a09x T0=0.1; % input pulse width
!eUDi( MN1=0; % initial value for the space output location
Nq@+'<@p$ dt = T/N; % time step
ubmrlH\d n = [-N/2:1:N/2-1]'; % Index
L^{|uP15N t = n.*dt;
'_$uW&{NI u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
@ S 7sr- u20=u10.*0.0; % input to waveguide 2
$&2UTczp u1=u10; u2=u20;
Vo"RO$%ow* U1 = u1;
qVs\Y3 u( U2 = u2; % Compute initial condition; save it in U
:,DM*zBV p ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
hsw9(D>jp w=2*pi*n./T;
Bk+{RN(w g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
"1-}A(X L=4; % length of evoluation to compare with S. Trillo's paper
"hdvHUz dz=L/M1; % space step, make sure nonlinear<0.05
p}<w#p
| for m1 = 1:1:M1 % Start space evolution
L*x[?x;)@ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
MX ;J5(Ae u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
i}~SDY ca1 = fftshift(fft(u1)); % Take Fourier transform
0p@k({ ] < ca2 = fftshift(fft(u2));
DzheoA-+L' c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
UDL
RCS8i c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
A.5i"Ci[ie u2 = ifft(fftshift(c2)); % Return to physical space
3ux0 Jr2yT u1 = ifft(fftshift(c1));
\{EpduwZ if rem(m1,J) == 0 % Save output every J steps.
Dxk+P!!K U1 = [U1 u1]; % put solutions in U array
ykFJ%sw3X U2=[U2 u2];
Z*FrB58 MN1=[MN1 m1];
%b^ OeWip z1=dz*MN1'; % output location
1NcCy! + end
U. @*`Fg end
IO/4.m-aN# hg=abs(U1').*abs(U1'); % for data write to excel
XduV+$ 03 ha=[z1 hg]; % for data write to excel
[S@}T
zE t1=[0 t'];
}E7:ihy hh=[t1' ha']; % for data write to excel file
a:_I %dlmwrite('aa',hh,'\t'); % save data in the excel format
ts8+V<g figure(1)
TET` b7G waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
"C*B,D*}: figure(2)
{$1J=JbE waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
_kY#D; `:r ,<Q~b%(3 非线性超快脉冲耦合的数值方法的Matlab程序 g38&P3/ 84{Q\c 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
ZlojbL@|4 Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
"rAY.E] %xQ.7~ _A~4NW{U7 5~yNqC % This Matlab script file solves the nonlinear Schrodinger equations
8j4z{+'TQ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
@+WQ ^ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
L.=w?%:H= % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
)$Z=t-q @EoZI~
C=1;
E~kG2x{a M1=120, % integer for amplitude
^xZ
e2@ M3=5000; % integer for length of coupler
3.)b4T N = 512; % Number of Fourier modes (Time domain sampling points)
nJbbzQ,e dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
Ea( ,aVlj T =40; % length of time:T*T0.
5p
+ZD7jK dt = T/N; % time step
A4QcQ" n = [-N/2:1:N/2-1]'; % Index
P%MfCpyj t = n.*dt;
{W\T"7H ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
:h1pBEiH w=2*pi*n./T;
?J,AB #+ g1=-i*ww./2;
y4Er @8I` g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
( 7DXRcr< g3=-i*ww./2;
n$:IVX"2b P1=0;
Urgtg37 P2=0;
nP UqMn' P3=1;
^W7X(LQ*+ P=0;
Ux2U*a ; for m1=1:M1
1J? dK|% b p=0.032*m1; %input amplitude
L Z~"VV^ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
&J !aw s1=s10;
| / }\6L] s20=0.*s10; %input in waveguide 2
c={Ft* N s30=0.*s10; %input in waveguide 3
!JBae2Z s2=s20;
5TUNX^AW s3=s30;
*x>3xQq& p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Y $ -3v. %energy in waveguide 1
%5\3Aw p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
Yif *"oO %energy in waveguide 2
\VSATL:] p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
~l~Tk6E M %energy in waveguide 3
[\ Qr. 2 for m3 = 1:1:M3 % Start space evolution
HvxJj+X9 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
g-vg6@6 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
C}5M;|%3) s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
~ np,_yI sca1 = fftshift(fft(s1)); % Take Fourier transform
rNl.7O9b sca2 = fftshift(fft(s2));
26n^Dy>} sca3 = fftshift(fft(s3));
/VHi > sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
n,O5".aa< sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
3^= +gsc sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
OU7 %V)X5 s3 = ifft(fftshift(sc3));
8p1ziz`4>$ s2 = ifft(fftshift(sc2)); % Return to physical space
ZlKw_Sq: s1 = ifft(fftshift(sc1));
FP"$tt ( end
;PyZ?Z; p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
m?[5J)eR p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
{I{:GcS p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
V84*0&q OW P1=[P1 p1/p10];
#hw/^AaD- P2=[P2 p2/p10];
i.1U|Pi P3=[P3 p3/p10];
pe&UQ C^ P=[P p*p];
!8tS|C#2 end
/Y^8SO4 figure(1)
c3
&m9zC plot(P,P1, P,P2, P,P3);
q 1 k { D';eTy Y 转自：
http://blog.163.com/opto_wang/
