计算脉冲在非线性耦合器中演化的Matlab 程序 [t*-s1cq I]Z"?T % This Matlab script file solves the coupled nonlinear Schrodinger equations of
}{[p<pU$C % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
_+Uf5,.5yU % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
7p{2&YhB % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
,0?3k b86c[2 %fid=fopen('e21.dat','w');
20M]gw] N = 128; % Number of Fourier modes (Time domain sampling points)
m$g{& M1 =3000; % Total number of space steps
Hx9lQ8 J =100; % Steps between output of space
$SzuUI T =10; % length of time windows:T*T0
"msPH<D T0=0.1; % input pulse width
V9;IH<s: MN1=0; % initial value for the space output location
7!e kINQ dt = T/N; % time step
oP:OurX8V n = [-N/2:1:N/2-1]'; % Index
C2L=i3R t = n.*dt;
2W/*1K} u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
?zYR;r2'b) u20=u10.*0.0; % input to waveguide 2
&hWYw+yH\ u1=u10; u2=u20;
wFJ*2W: U1 = u1;
WaiM\h?=# U2 = u2; % Compute initial condition; save it in U
(cp$poo ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
OjK+`D_C w=2*pi*n./T;
xfqU
atC g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
)<T2J0* L=4; % length of evoluation to compare with S. Trillo's paper
Qqp= dz=L/M1; % space step, make sure nonlinear<0.05
!!])~+4pP for m1 = 1:1:M1 % Start space evolution
LEAU3doK; u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
G%%5lw!y' u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
'~x jaa;. ca1 = fftshift(fft(u1)); % Take Fourier transform
O5JG!bGE_F ca2 = fftshift(fft(u2));
HZ89x|Hk_ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
&qm:36Y7Xg c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
- ysd`& u2 = ifft(fftshift(c2)); % Return to physical space
mvyOwM u1 = ifft(fftshift(c1));
{dvsZJj if rem(m1,J) == 0 % Save output every J steps.
?cD_\~ U1 = [U1 u1]; % put solutions in U array
g7K<"Z {M U2=[U2 u2];
J^mm"2 MN1=[MN1 m1];
l YjPrA]TC z1=dz*MN1'; % output location
>UV=k :Q end
t k+t3+ end
(2/i1)Cq hg=abs(U1').*abs(U1'); % for data write to excel
:]`JcJ ha=[z1 hg]; % for data write to excel
{<2q t1=[0 t'];
.j`8E^7< hh=[t1' ha']; % for data write to excel file
(=tu~ ^ %dlmwrite('aa',hh,'\t'); % save data in the excel format
wOR#sp& figure(1)
W\z<p P waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
T{Yk/Z/}? figure(2)
J 77*Ue^ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
!6*4^$i#o DE$T1pFV 非线性超快脉冲耦合的数值方法的Matlab程序 U,,rB( A~'p~@L 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。
0Pg@%>yb~ 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
zi,":KDz# d)v!U+-|' Jv D`RUh \6,Z<.I % This Matlab script file solves the nonlinear Schrodinger equations
62>/0_m5 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
/gE9 W % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
''CowI % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
cqb]LC Q8bn|#` C=1;
2spK#0n.HV M1=120, % integer for amplitude
uF]+i^+ M3=5000; % integer for length of coupler
oX[I4i%G N = 512; % Number of Fourier modes (Time domain sampling points)
#M8>)o c dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
13I~
T =40; % length of time:T*T0.
O9)k)A]`O dt = T/N; % time step
Y\{lQMCy n = [-N/2:1:N/2-1]'; % Index
~;nW+S$o
t = n.*dt;
GoG_4:^#h ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
v0|"[qGb w=2*pi*n./T;
]w9syz8X g1=-i*ww./2;
Td![Id g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
zuBfkW95+ g3=-i*ww./2;
BsN~Z!kd P1=0;
}/Y)^ P2=0;
R]_fe4Y0 P3=1;
{>.qo<k P=0;
p9iCrqi for m1=1:M1
H3qL&xL p=0.032*m1; %input amplitude
iTeFy-Ct s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
JT 5+d , s1=s10;
8R.`* s20=0.*s10; %input in waveguide 2
0 mR s30=0.*s10; %input in waveguide 3
vX}mwK8
s2=s20;
lV2MRxI s3=s30;
|c!lZo/ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
&bS!>_9 %energy in waveguide 1
eR5+1b p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
&E8fd/s=k %energy in waveguide 2
+PkN~m` p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
=_H)5I_\ %energy in waveguide 3
.@]M'S^1 for m3 = 1:1:M3 % Start space evolution
c)=UX_S! s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
9i#K{CkC| s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
]lzOz<0q s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
@GE:<'_:{ sca1 = fftshift(fft(s1)); % Take Fourier transform
E{6X-C[)v sca2 = fftshift(fft(s2));
*g/@-6 sca3 = fftshift(fft(s3));
V3}$vKQ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
MFLw^10(T sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
78<QNlKn sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
7q: s3 = ifft(fftshift(sc3));
.[#bOp* s2 = ifft(fftshift(sc2)); % Return to physical space
;= {Z Bx s1 = ifft(fftshift(sc1));
Q Ph6
p3bg end
F`YxH*tO7 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
Fgg4QF p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
JSm3ZP|GqJ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
H0i\#)Xs P1=[P1 p1/p10];
tc<t%]c P2=[P2 p2/p10];
uu582%tiG P3=[P3 p3/p10];
prg8Iq'w P=[P p*p];
\:wLUGFl5 end
{01wW1 figure(1)
K1>(Fs$ plot(P,P1, P,P2, P,P3);
yw)Ztg) A?829< 转自:
http://blog.163.com/opto_wang/