计算脉冲在非线性耦合器中演化的Matlab 程序 4 2ge3> zX i 'kB % This Matlab script file solves the coupled nonlinear Schrodinger equations of
)NT*bLRPQ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
sU^1wB
Rj % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
M&M 6;Ph % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
]A_`0"m.U 9H1r O8k %fid=fopen('e21.dat','w');
goWuw}? N = 128; % Number of Fourier modes (Time domain sampling points)
-m#)B~) M1 =3000; % Total number of space steps
lPAQ3t!, J =100; % Steps between output of space
w_V P
J T =10; % length of time windows:T*T0
_7y[B&g[r T0=0.1; % input pulse width
%iqD5x$OA MN1=0; % initial value for the space output location
vW@=<aS Z dt = T/N; % time step
<9b &<K: n = [-N/2:1:N/2-1]'; % Index
;}p t = n.*dt;
sNFlKQ8)Q u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
)0k53-h& u20=u10.*0.0; % input to waveguide 2
]T) 'Hb u1=u10; u2=u20;
|u p U1 = u1;
bpa?C U2 = u2; % Compute initial condition; save it in U
.*Qx\, ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
F,CT Z~ w=2*pi*n./T;
e]$s
t? g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
>=w)x,0yX L=4; % length of evoluation to compare with S. Trillo's paper
i,VMd dz=L/M1; % space step, make sure nonlinear<0.05
{id4:^u&; for m1 = 1:1:M1 % Start space evolution
@>7%qS u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
Y}KNKO; u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
MiX 43Pk] ca1 = fftshift(fft(u1)); % Take Fourier transform
iH'p>s5L ca2 = fftshift(fft(u2));
G^@5H/) c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
9: lFo= c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
+aAc9'k u2 = ifft(fftshift(c2)); % Return to physical space
a$fnh3j[ u1 = ifft(fftshift(c1));
/BL4<T f if rem(m1,J) == 0 % Save output every J steps.
?Z} &EH U1 = [U1 u1]; % put solutions in U array
(**oRw r% U2=[U2 u2];
-$g#I MN1=[MN1 m1];
#[[ e n z1=dz*MN1'; % output location
1{.9uw"2S end
DVeE 1Q end
|5 ]X| v hg=abs(U1').*abs(U1'); % for data write to excel
,`sv1xwd ha=[z1 hg]; % for data write to excel
?\n >
AC t1=[0 t'];
3$
PV2" hh=[t1' ha']; % for data write to excel file
H K% 7g %dlmwrite('aa',hh,'\t'); % save data in the excel format
z0 Z%m @ figure(1)
MWh6]gGs waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
l}P=/#</T figure(2)
_t yc gq# waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
Rk8P
ax/JK EiaW1Cs 非线性超快脉冲耦合的数值方法的Matlab程序 6wg^FD_Q bhs
_9ivw 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。
J9 I :Q<; 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
wKY_Bo/d H%{+QwzZ[j DW3G -ze J#B)C % This Matlab script file solves the nonlinear Schrodinger equations
%]7d`/ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
BL4 -7 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
IvNT6]6 P % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
|&4/n6;P$0 .eC1qWZJpd C=1;
fd9k?,zM M1=120, % integer for amplitude
J,6yYIq M3=5000; % integer for length of coupler
\^1E4C\": N = 512; % Number of Fourier modes (Time domain sampling points)
Zgb!E]V[ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
= WJ NWt> T =40; % length of time:T*T0.
A_UjC` dt = T/N; % time step
Z #m+ObHK1 n = [-N/2:1:N/2-1]'; % Index
-%4,@
x` t = n.*dt;
]{>,rK[So ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
H%lVl8oQ w=2*pi*n./T;
=?`c=z3~i$ g1=-i*ww./2;
"^iYLQOC g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
CTA 3*Gn g3=-i*ww./2;
)=-szJjXZ P1=0;
e8 b:)"R P2=0;
,"0 :3+(8; P3=1;
Yz93'HDB P=0;
AwF:Iu^3n for m1=1:M1
]J]h#ZHx p=0.032*m1; %input amplitude
M"To&?OI s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
e@YK@?^#N s1=s10;
+qdEq _ m s20=0.*s10; %input in waveguide 2
Uo ix s30=0.*s10; %input in waveguide 3
Ef{V p;] s2=s20;
'/%H3A#L s3=s30;
Yu`~U,m p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
FXU8[j0P_G %energy in waveguide 1
pI<f) r p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
_h1mF<\ X^ %energy in waveguide 2
mRK>U$v p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
dUdT7 ixo %energy in waveguide 3
YKf0dh;O for m3 = 1:1:M3 % Start space evolution
={Qi0Pvt s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
J<lO=
+mg s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
{BU; $ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Wh{tZ~ c sca1 = fftshift(fft(s1)); % Take Fourier transform
Fv`,3aNB sca2 = fftshift(fft(s2));
`~q < N sca3 = fftshift(fft(s3));
13/]DF,S"^ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
[)X\|pO & sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
~WV"SaA)*U sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
seeB S/% s3 = ifft(fftshift(sc3));
vs{s_T7Mz] s2 = ifft(fftshift(sc2)); % Return to physical space
'@P^0+B!(. s1 = ifft(fftshift(sc1));
#C@FYO f* end
K\c#ig p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
iO;
7t@]- p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
"U"Z 3 * p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
uWE^hz" P1=[P1 p1/p10];
Dv`c<+q(# P2=[P2 p2/p10];
D^;Uq8NDKq P3=[P3 p3/p10];
A&jlizN7 P=[P p*p];
R Vi uJ; end
U :_^#\p figure(1)
0_t!T'jr7 plot(P,P1, P,P2, P,P3);
uY'HT|@:{ Q&bM\;Ml 转自：
http://blog.163.com/opto_wang/
