计算脉冲在非线性耦合器中演化的Matlab 程序 0nBDF79 MGK?FJn_? % This Matlab script file solves the coupled nonlinear Schrodinger equations of
a;Pn.@NVq % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
E`xpZ>$mPx % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
T12Zak4.= % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
SXe1Q8; i`<L#6RBT %fid=fopen('e21.dat','w');
L%3Bp/`S N = 128; % Number of Fourier modes (Time domain sampling points)
Y^DGnx("m M1 =3000; % Total number of space steps
hi(e%da J =100; % Steps between output of space
eB_r.R{ T =10; % length of time windows:T*T0
v>nBdpjXh T0=0.1; % input pulse width
0 ;)Q MN1=0; % initial value for the space output location
.x] pJ9 dt = T/N; % time step
:.=j)ljTx n = [-N/2:1:N/2-1]'; % Index
\ntUxPox. t = n.*dt;
Qc!3y>Y=_ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
$;$vcV9* u20=u10.*0.0; % input to waveguide 2
_iDVd2X"H u1=u10; u2=u20;
oa=TlBk< U1 = u1;
HCkfw+gaV U2 = u2; % Compute initial condition; save it in U
/ece}7M ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
3 G<4rH] w=2*pi*n./T;
4Z=`; g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
oC}
u L=4; % length of evoluation to compare with S. Trillo's paper
}CZw'fhVWO dz=L/M1; % space step, make sure nonlinear<0.05
4^YE*6z for m1 = 1:1:M1 % Start space evolution
G; W2Z, u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
TF!v ,cX u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
G9am}qr ca1 = fftshift(fft(u1)); % Take Fourier transform
O^6anUV0 ca2 = fftshift(fft(u2));
[MKG5=kaE c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
F#)bGi c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
d-m.aP)y: u2 = ifft(fftshift(c2)); % Return to physical space
$%M]2_W( u1 = ifft(fftshift(c1));
hosY`"X if rem(m1,J) == 0 % Save output every J steps.
1tI=Dwx U1 = [U1 u1]; % put solutions in U array
u)r:0;5 U2=[U2 u2];
!\BM MN1=[MN1 m1];
B/;'D7i|S z1=dz*MN1'; % output location
%K=_ end
@x743}Y\ end
dS <*DP hg=abs(U1').*abs(U1'); % for data write to excel
a]%sks ha=[z1 hg]; % for data write to excel
olL? 6)gC t1=[0 t'];
d:^B2~j hh=[t1' ha']; % for data write to excel file
Z^'\()3t %dlmwrite('aa',hh,'\t'); % save data in the excel format
ZvT>A#R;l~ figure(1)
"lt5gu! `u waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
b5
NlL`g figure(2)
xYW&Mfka waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
'DpJ#w\81 ZMiOKVl 非线性超快脉冲耦合的数值方法的Matlab程序 T*=*$% vp*+Ckd 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。
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]9@ 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
96#]P 5F
^VvzNn $)8,dS <Q- m & % This Matlab script file solves the nonlinear Schrodinger equations
1 JIU5u) % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
+w?R4Sxjn % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
tk=S4/VWv % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
:Y1;= W Kdp($L9r C=1;
ZE_ M1=120, % integer for amplitude
v3XM-+Z4 M3=5000; % integer for length of coupler
0x]?rd+q8Q N = 512; % Number of Fourier modes (Time domain sampling points)
O&|<2Qr dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
]cmX f T =40; % length of time:T*T0.
bJD$!*r\%! dt = T/N; % time step
|Nj6RB7 n = [-N/2:1:N/2-1]'; % Index
Za3}:7`Gu t = n.*dt;
k1zK3I&c_ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
a@qc? w=2*pi*n./T;
2u!&Te(!9 g1=-i*ww./2;
v0E6i!D/ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
DC-d@N+ g3=-i*ww./2;
#C?M- P1=0;
66" 6> P2=0;
$8HiX6r P3=1;
%Pt){9b P=0;
SUUN_w~ for m1=1:M1
9:VUtx#}2 p=0.032*m1; %input amplitude
650qG$ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
: N$-SV s1=s10;
>-<iY4|[d s20=0.*s10; %input in waveguide 2
1TGRIe) s30=0.*s10; %input in waveguide 3
cY_ke s2=s20;
p:Lmf8EI s3=s30;
N8#j|yf p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
aVc{ aP %energy in waveguide 1
L*A-&9.p3 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
Z
f\~Cl %energy in waveguide 2
*`Vm ncv3 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
hdrsa}{g %energy in waveguide 3
}58MDpOF1 for m3 = 1:1:M3 % Start space evolution
[x>Ju&))$ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
}AJoF41X s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
s:"Sbml s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
DHw)]WB M sca1 = fftshift(fft(s1)); % Take Fourier transform
bSX/)')jU sca2 = fftshift(fft(s2));
@&WHX# sca3 = fftshift(fft(s3));
g""GQeR sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
B#SVN Lv sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
}shxEsq sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
l&qCgw s3 = ifft(fftshift(sc3));
ZCPUNtOl s2 = ifft(fftshift(sc2)); % Return to physical space
Dpw*m.f s1 = ifft(fftshift(sc1));
Cg]),S end
}P
fAf p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
_J W|3q p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
I_u/ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
Y6sX|~Zy P1=[P1 p1/p10];
#m{*]mY@ P2=[P2 p2/p10];
HRDpFMA/~ P3=[P3 p3/p10];
y3s+.5; P=[P p*p];
o1$u;}^ | end
&gY) x{ figure(1)
<c pck plot(P,P1, P,P2, P,P3);
/]xa}{^B cpltTJFg 转自:
http://blog.163.com/opto_wang/