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;