% fresneliso.m - Fresnel reflection coefficients for isotropic media with either indices _or_ lambda as vectors
%
% Usage: [rs,rp] = fresnel(na,nb,theta)
%
% na,nb = refractive indices of left and right media. May be vectors if lambda is not.
% theta = incident angle(s) in degrees.  May be a vector if na and nb are vectors.
% rs,rp = reflection coefficients for p and s polarizations
%
% Modified by Andri M. Gretarsson from fresnel.m written by Orfanidi.  August 2008.

function [rs,rp] = fresnel(na,nb,theta)

if nargin==0, help fresnel; return; end

if length(na)==1
    na=ones(size(nb))*na;  
elseif length(nb)==1
    nb=ones(size(na));
end
theta = pi*theta/180;

if length(nb) == 1
    Na = 1./sqrt(cos(theta).^2/na^2 + sin(theta).^2/na^2);       
    xe = (na*sin(theta)).^2;                                     % used for s-pol        
    xm = (Na.*sin(theta)).^2;                                    % used for p-pol                    

    rs = (na*cos(theta) - sqrt(nb^2 - xe)) ./ ...
      (na*cos(theta) + sqrt(nb^2 - xe));

    if na==nb,                                               
        rp = (na - nb) / (na + nb) * ones(1,length(theta));
    else
        rp = (na*na * sqrt(nb^2 - xm) - nb*nb * sqrt(na^2 - xm)) ./ ...
            (na*na * sqrt(nb^2 - xm) + nb*nb * sqrt(na^2 - xm));
    end
elseif length(theta) == 1
    Na = 1./sqrt(cos(theta)^2./na.^2 + sin(theta)^2./na.^2);       
    xe = (na*sin(theta)).^2;                                     % used for s-pol        
    xm = (Na*sin(theta)).^2;                                    % used for p-pol                    

    rs = (na*cos(theta) - sqrt(nb.^2 - xe)) ./ ...
      (na*cos(theta) + sqrt(nb.^2 - xe));

    if na==nb,                                               
        rp = (na - nb) ./ (na + nb);
    else
        rp = (na.*na .* sqrt(nb.^2 - xm) - nb.*nb .* sqrt(na.^2 - xm)) ./ ...
            (na.*na .* sqrt(nb.^2 - xm) + nb.*nb .* sqrt(na.^2 - xm));
    end
    
else
    error('Either na and nb must have length 1 _or_ theta must have length 1.');
end