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%--------------------------- Huygens.m -----------------------
%
% Propagation and Interference of Waves - Part 2
%
%
%					Lecture 5
%					Chemistry 455
% 					Summer Quarter 1995
%					James B. Callis, Instructor
%
%
% Press any key to continue
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% A Point Radiator a la Huygens.
%
% Let us start by considering a point source of radiation 
% as it sends out waves in two spatial dimensions. For this
% system, the amplitude at a fixed instant of time, t = 0, 
% varies in two spatial dimensions as follows:
%
% 	A(x, y ) = A1*sin(2pi*sqrt((x-xo)^2 + (y-yo)^2)/lam)
%
% Where xo and yo are the position coordinates of the radiator. 
% Let us plot such a point source radiator for a wavelength of 
% 500 nm over the spatial region from 0 to 2500 nm in steps of
% 50 nm. Let us place the radiator at 0 in the x direction and 
% 1250 nm in the y direction. 
%
% Press any key to continue
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% Here are the constants:
xo = 0; % x coordinate of Huygen's source
yo = 1250e-9; % y coordinate of Huygen's source
lam = 500e-9;% Wavelength of light, m
Dx = 100e-9; % Spatial Increment, m
Lx = 2500e-9; % max spatial dimension in x dimension, m
Ly = 2500e-9;  % max spatial dimension in y dimension, m
%
% Now make up the space vectors along x and y:
x = 0:Dx:Lx; % look over 2500 nm in x
y = 0:Dx:Ly; % look over 2500 nm in y
% Press any key to continue
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% Now calculate the mesh grid
[X,Y] = meshgrid(x,y);
% Now calculate all of the x,y points
amp = sin(2*pi*sqrt((X-xo).^2 + (Y-yo).^2)/lam); % Note dot
% Calculation is finished, press any key to see plot
pause
contour(x,y,amp)
axis('square')
title('Huygens Point Radiator')
xlabel('Distance Along X Dimension, m')
ylabel('Distance Along Y Dimension, m')
pause
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% Diffraction as the Superposition of Amplitudes.
%
% Let us now consider two point sources of radiation placed at
% two different positions along the y axis. For this system, 
% the Amplitude at a fixed instant of time, t = 0, varies in 
% two spatial dimensions as follows:
%
%	A(x, y ) = sin(2*pi*sqrt(x^2 + (y-y1)^2)/lam)
%			   +sin(2pi*sqrt(x^2 + (y-y2)^2)/lam)
%
% Where y1 = 750 nm and y2 = 1750 nm are the y position 
% coordinates of the radiators. Let us plot these point source 
% radiators for a wavelength of 500 nm over the spatial region 
% from 0 to 3000  nm in steps of 100 nm.
% Press any key to continue
pause
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clear
% Here are the constants:
y1 = 750e-9; % x coordinate of Huygen's source
y2 = 1750e-9; % y coordinate of Huygen's source
lam = 500e-9;% Wavelength of light, m
Dx = 100e-9; % Spatial Increment, m
Lx = 3000e-9; % max spatial dimension in x dimension, m
Ly = 3000e-9;  % max spatial dimension in y dimension, m
%
% Now make up the space vectors along x and y:
x = 0:Dx:Lx; % look over 2500 nm in x
y = 0:Dx:Ly; % look over 2500 nm in y
% Press any key to continue
pause
clc
% Now calculate the mesh grid
[X,Y] = meshgrid(x,y);
% Now calculate all of the x,y points
amp = sin(2*pi*sqrt(X.^2 + (Y-y1).^2)/lam) + ... % continued
sin(2*pi*sqrt(X.^2 + (Y-y2).^2)/lam);
% Calculation is finished, press any key to see plot
pause
contour(x,y,amp)
axis('square')
title('Two Huygens Point Radiators')
xlabel('Distance Along X Dimension, m')
ylabel('Distance Along Y Dimension, m')
pause