twobeamsimulator.m

This program simulates the interference pattern of two Gaussian beams.

function varargout = twobeamsimulator(varargin)
% TWOBEAMSIMULATOR M-file for twobeamsimulator.fig
%   TWOBEAMSIMULATOR simulates interference pattern for 2 Gaussian beams
%  
%   The parameters are:
%   Screen Distance:    distance from 2nd mirror (infinitely thin) to
%                       observation screen in mm 
%   z_1,z_2:            distance from position of minimal waist radius
%                       (w0_1,w0_2) to beam combiner in mm
%   Reflectivity:       reflectivity of beam combiner (1st beam 
%                       transmitted; value between 0 and 1)
%   Refractive Index:   refractive index of medium in front of
%                       and behind the beam combiner (beam combiner itself
%                       neglected)
%                      
%   w0_1,w0_2:          minimal beam waist radius in mm
%   Wavelength:         wavelength of radiation in nm
%
%   Theta:              tilt of beam combiner (in x-direction) in angular
%                       seconds
%   Calculation-Window Width:   width of observation screen
%   Number of Pixels:           larger number means better resolution but
%                               longer waiting times 
%   Number of Rays:             number of simulated beam paths                    

% Version: 1.1
% Copyright: Birk Andreas 20060704

% Begin initialization code - DO NOT EDIT
gui_Singleton = 1;
gui_State = struct('gui_Name',       mfilename, ...
                   'gui_Singleton',  gui_Singleton, ...
                   'gui_OpeningFcn', @twobeamsimulator_OpeningFcn, ...
                   'gui_OutputFcn',  @twobeamsimulator_OutputFcn, ...
                   'gui_LayoutFcn',  [] , ...
                   'gui_Callback',   []);
if nargin && ischar(varargin{1})
    gui_State.gui_Callback = str2func(varargin{1});
end

if nargout
    [varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});
else
    gui_mainfcn(gui_State, varargin{:});
end
% End initialization code - DO NOT EDIT

function twobeamsimulator_OpeningFcn(hObject, eventdata, handles, varargin)
handles.output = hObject;
guidata(hObject, handles);
initialize_gui(hObject, handles);

function varargout = twobeamsimulator_OutputFcn(hObject, eventdata, handles)
varargout{1} = handles.output;

function abstand_CreateFcn(hObject, eventdata, handles)
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end

function abstand_Callback(hObject, eventdata, handles)
handles.abstand=str2double(get(hObject,'String'));
if handles.abstand < 0
    handles.abstand=-handles.abstand;
end
guidata(hObject, handles);

function d_Callback(hObject, eventdata, handles)
handles.d=str2double(get(hObject,'String'));
if handles.d < 0
    handles.d=-handles.d;
end
guidata(hObject, handles);

function d_CreateFcn(hObject, eventdata, handles)
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end

function z1_Callback(hObject, eventdata, handles)
handles.z1=str2double(get(hObject,'String'));
if handles.z1 < 0
    handles.z1=-handles.z1;
end
guidata(hObject, handles);

function z1_CreateFcn(hObject, eventdata, handles)
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end

function z2_Callback(hObject, eventdata, handles)
handles.z2=str2double(get(hObject,'String'));
if handles.z2 < 0
    handles.z2=-handles.z2;
end
guidata(hObject, handles);

function z2_CreateFcn(hObject, eventdata, handles)
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end

function r_Callback(hObject, eventdata, handles)
handles.r=str2double(get(hObject,'String'));
if handles.r < 0
    handles.r=-handles.r;
end
guidata(hObject, handles);

function r_CreateFcn(hObject, eventdata, handles)
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end

function theta_Callback(hObject, eventdata, handles)
handles.theta=str2double(get(hObject,'String'));
guidata(hObject, handles);

function theta_CreateFcn(hObject, eventdata, handles)
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end

function breite_Callback(hObject, eventdata, handles)
handles.breite=str2double(get(hObject,'String'));
if handles.breite < 0
    handles.breite=-handles.breite;
end
guidata(hObject, handles);

function breite_CreateFcn(hObject, eventdata, handles)
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end

function pixel_Callback(hObject, eventdata, handles)
handles.pixel=str2double(get(hObject,'String'));
if handles.pixel < 0
    handles.pixel=-handles.pixel;
end
guidata(hObject, handles);

function pixel_CreateFcn(hObject, eventdata, handles)
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end

function mult_Callback(hObject, eventdata, handles)
handles.mult=str2double(get(hObject,'String'));
if handles.mult < 0
    handles.mult=-handles.mult;
end
guidata(hObject, handles);

function mult_CreateFcn(hObject, eventdata, handles)
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end

function w01_Callback(hObject, eventdata, handles)
handles.w01=str2double(get(hObject,'String'));
if handles.w01 < 0
    handles.w01=-handles.w01;
end
guidata(hObject, handles);

function w01_CreateFcn(hObject, eventdata, handles)
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end

function w02_Callback(hObject, eventdata, handles)
handles.w02=str2double(get(hObject,'String'));
if handles.w02 < 0
    handles.w02=-handles.w02;
end
guidata(hObject, handles);

function w02_CreateFcn(hObject, eventdata, handles)
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end

function lambda_Callback(hObject, eventdata, handles)
handles.lambda=str2double(get(hObject,'String'));
if handles.lambda < 0
    handles.lambda=-handles.lambda;
end
guidata(hObject, handles);

function lambda_CreateFcn(hObject, eventdata, handles)
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end

function n_Callback(hObject, eventdata, handles)
handles.n=str2double(get(hObject,'String'));
guidata(hObject, handles);

function n_CreateFcn(hObject, eventdata, handles)
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end

function calculate_Callback(hObject, eventdata, handles)
breite=1e-3*handles.breite;
pixel=round(handles.pixel);
abstand=1e-3*handles.abstand;
z1=1e-3*handles.z1;
z2=1e-3*handles.z2;
w01=1e-3*handles.w01;
w02=1e-3*handles.w02;
lambda=1e-9*handles.lambda;
n=handles.n;
r=handles.r;
theta=pi/648000*handles.theta;
mult=round(handles.mult);
k=2*pi*n/lambda;
z01=n*pi*w01^2/lambda;
z02=n*pi*w02^2/lambda;
t=1-r;
versatz=tan(theta)*abstand;
pixel2=round((breite+versatz)/breite*pixel*2);
Et1=zeros(pixel2);
Et2=zeros(pixel2);
randfield=rand(2,mult)*(breite+versatz)-(breite+versatz)/2;
for N=1:mult
    x=randfield(1,N);
    y=randfield(2,N);     
    xd1=x;
    xd2=x+tan(theta)*abstand;
    yd1=y;
    yd2=y;
    zd1=z1+abstand;
    zd2=z2+abstand/cos(theta);
    w1=sqrt(w01^2*(1+(zd1/z01)^2));
    w2=sqrt(w02^2*(1+(zd2/z02)^2));
    R1=zd1*(1+(z01/zd1)^2);
    R2=zd2*(1+(z02/zd2)^2);
    ix=ceil(randfield(1,N)/breite*pixel+pixel2/2);
    iy=ceil(randfield(2,N)/breite*pixel+pixel2/2);   
    xc=ceil(randfield(1,N)/breite*pixel+pixel2/2)-(randfield(1,N)...
        /breite*pixel+pixel2/2);
    yc=ceil(randfield(2,N)/breite*pixel+pixel2/2)-(randfield(2,N)...
        /breite*pixel+pixel2/2);
    xf=(randfield(1,N)/breite*pixel+pixel2/2)-floor(randfield(1,N)...
        /breite*pixel+pixel2/2);
    yf=(randfield(2,N)/breite*pixel+pixel2/2)-floor(randfield(2,N)...
        /breite*pixel+pixel2/2);   
    A=t*w01/w1*exp(-(xd1^2+yd1^2)/w1^2)*exp(-i*(k*zd1-atan(zd1/z01)))...
        *exp(-i*k*(xd1^2+yd1^2)/(2*R1));  
    Et1(iy-1,ix)=Et1(iy-1,ix)+xf*yc*A;
    Et1(iy,ix-1)=Et1(iy,ix-1)+xc*yf*A;
    Et1(iy-1,ix-1)=Et1(iy-1,ix-1)+xc*yc*A;
    Et1(iy,ix)=Et1(iy,ix)+xf*yf*A;  
    A=r*w02/w2*exp(-(xd2^2+yd2^2)/w2^2)...
        *exp(-i*(k*zd2-atan(zd2/z02)))*exp(-i*k*(xd2^2+yd2^2)/(2*R2));   
    Et2(iy-1,ix)=Et2(iy-1,ix)+xf*yc*A;
    Et2(iy,ix-1)=Et2(iy,ix-1)+xc*yf*A;
    Et2(iy-1,ix-1)=Et2(iy-1,ix-1)+xc*yc*A;
    Et2(iy,ix)=Et2(iy,ix)+xf*yf*A;   
end
I=(Et1+Et2).*conj(Et1+Et2);
I=I/sum(sum(I));
[zl,sp]=size(I);
I=I(floor(zl/2)-floor(pixel/2)+1:floor(zl/2)+floor(pixel/2),floor(sp/2)...
    -floor(pixel/2)+1:floor(sp/2)+floor(pixel/2));
assignin('base','I',I);
P=angle(Et1+Et2);
P=P(floor(zl/2)-floor(pixel/2)+1:floor(zl/2)+floor(pixel/2),floor(sp/2)...
    -floor(pixel/2)+1:floor(sp/2)+floor(pixel/2));
assignin('base','P',P);
figure;
surf(P);
shading interp;
view(2);
colorbar;
figure;
surf(I);
shading interp;
view(2);
colorbar;

function initialize_gui(fig_handle, handles)
handles.breite=5;
handles.pixel=100;
handles.abstand=100;
handles.z1=100;
handles.z2=100;
handles.w01=1.5;
handles.w02=1.5;
handles.lambda=532;
handles.n=1;
handles.r=0.5;
handles.theta=0;
handles.mult=3e5;
guidata(handles.figure1, handles);