Accordion_lattice/Accordion_2.m

clear;

% Elementary constants
c = 299792458;                  %Speed of light [m/s]
h = 6.626070040e-34;            %Planck constant [J/Hz]
hbar = h/2/pi; 
u0 = 4*pi*1e-7;                 %Vacuum permeability [N/A^2]
e0 = 1/u0/(c^2);                %Vacuum permittivity [A^2*s^4/kg/m^3]
qe = 1.6021766208e-19;          %Elementary charge [C]
G = 6.67408e-11;                %Gravitational constant [m^3/kg/s^2]
kB = 1.38064852e-23;            %Boltzmann constant [J/K]
me = 9.10938356e-31;            %Electron rest mass [kg]
mp = 1.672621898e-27;           %Proton mass [kg]
uB = qe*hbar /2/me;             %Bohr magneton [J/T]
uN = qe*hbar /2/mp;             %Nuclear magnton [J/T]
alpha = u0*qe^2*c/(2*h);        %Fine structure constant
u = 1.660539040e-27;            %Atomic mass unit [kg]
a0 = 4*pi*e0*hbar^2/me/qe^2;    %Bohr radius [m]
Ry = 13.605693009;              %Rydberg energy [eV]

%Dysprosium properties
mDy = 164*u;                    %Dysprosium mass [kg]
abuDy164 = 0.2826;              %Dy164 abundance
Polar1064 = 193*4*pi*e0*a0^3;   %Dynamical polarizability of Dy for 1064 and 532 [A^2s^4/kg]
Polar532 = 350*4*pi*e0*a0^3;

%Laser properties
lambda = 532e-9;                %Laser wavelength [m]
k = 2*pi/lambda;                %Wave number of laser [m^-1]
P0 = 10;                         %Power [W]

%Coordinate rotation y-axis for E1
theta= 4/180*pi;                       %Half angle between the beams
x = linspace(-3000,3000,1501)*1e-6;        %Definition of coordinate System
y = 0;
z = linspace(-300,300,1501)*1e-6;

[X,Z]=meshgrid(x,z);
xt= X.*cos(theta)+Z.*sin(theta);
yt = y;
zt= -X.*sin(theta)+Z.*cos(theta);

%Gaussian beam propagating in xt direction
w0 = 90e-6;                      %Beam waist at x=xt=0 (center of the trap)
xr = pi*w0.^2/lambda;            %Rayleigh length i xt-direction
wxt = w0.*sqrt(1+(xt./xr).^2);     %Radius to 1/e
P = P0/2;

E0 = sqrt(2*P./(pi*wxt.^2*c*e0)); %Electric field at time 0 , x=-f origin
E1 = E0*w0./wxt.*exp(-(zt.^2+yt.^2)./wxt.^2).*exp(-1i*k.*xt); %Electric field 1

%Coordinate rotation y-axis for E2
theta= -theta;                       %Half angle between the beams
xt= X.*cos(theta)+Z.*sin(theta);
yt = y;
zt= -X.*sin(theta)+Z.*cos(theta);

E2 = E0*w0./wxt.*exp(-(zt.^2+yt.^2)./wxt.^2).*exp(-1i*k.*xt); %Electric field 1

%Interference of the two beams
Itot = abs(E1+E2).^2 ;             %Intensity of the interference pattern

figure
imagesc(x,z,Itot)
set(gca,'YDir','normal')