Contents
function [ras,rap,tas,tap]=fresnel(thetad,n)
FRESNEL computes Fresnel Reflection and Transmission
SYNTAX: [ras,rap,tas,tap]=fresnel(theta,n);
where ras,rap,tas,tap are Reflection and Transmission coeffcients for Amplitude for S and P polarization. identified as rho and tau in text Chapter 6. Input theta is in degrees, n is index of refracton, which may be complex.
EXAMPLE:
(1) S polarized reflection of typical glass for varying angle
>> thetad=[0:10:90]; >> [ras,rap,tas,tap]=fresnel(thetad,1.5); >> RS=abs(ras).^2 RS = 0.0400 0.0417 0.0471 0.0578 0.0772 0.1120 ... 0.1766 0.2996 0.5386 1.0000 >> by Chuck DiMarzio Northeastern University September, 2001 Based on FORTRAN code by C. D. and Mike Healy, 1991
(2) S polarized reflection at normal incidence for different materials
>> n=[1.3,1.5,2.4,4]; >> [ras,rap,tas,tap]=fresnel(0,n); >> RS=abs(ras).^2 RS = 0.0170 0.0400 0.1696 0.3600 >>
!! This file may be copied, used, or modified for educational and !! research purposes provided that this header information is not !! removed or altered, and provided that the book is cited in !! publications, as DiMarzio, Charles A., Optics for Engineers, !! CRC Press, Boca Raton, FL, 2011. !! http://www.crcpress.com !! Other distribution is prohibited without permission.
Convert to radians and compute amplitude coefficients
theta=thetad*pi/180; % amplitude reflection coefficient s polarized ras=(cos(theta)-sqrt(n.^2-(sin(theta)).^2))./... (cos(theta)+sqrt(n.^2-(sin(theta)).^2)); % amplitude reflection coefficient p polarized rap=-( sqrt(n.^2-(sin(theta)).^2) -n.^2.*cos(theta) )./... ( sqrt(n.^2-(sin(theta)).^2) +n.^2.*cos(theta) ); % amplitude transmission coefficient s polarized tas=1.+ras; % amplitude transmission coefficient p polarized tap=(1.+rap)./n;