From 6efadc24f8d3898b871114158afe1bcb3d00b378 Mon Sep 17 00:00:00 2001
From: Eugeniy Mikhailov <evgmik@gmail.com>
Date: Sat, 9 Jul 2011 16:03:44 -0400
Subject: subindexes expanded, rutile coef match experiment

---
 coupling_angles.m | 44 ++++++++++++++++++++++----------------------
 1 file changed, 22 insertions(+), 22 deletions(-)

(limited to 'coupling_angles.m')

diff --git a/coupling_angles.m b/coupling_angles.m
index ca7dcf0..9d31848 100644
--- a/coupling_angles.m
+++ b/coupling_angles.m
@@ -10,29 +10,29 @@ prism_angle = prism_angle_in_degrees*pi/180;
 n_rutile_o = 2.4885;
 n_rutile_e = 2.75324;
 
-n_p=n_rutile_o
+n_prism=n_rutile_e ; % for horizontal or p polarization
 
 %% disk material index of refraction
 % Magnesium Fluoride (MgF2)  see http://refractiveindex.info/?group=CRYSTALS&material=MgF2
 n_MgF2_o = 1.3751;
 n_MgF2_e = 1.38679;
 
-n_d=n_MgF2_o
+n_disk=n_MgF2_o
 
 %% critical angle for beam from prism to disk
-% recall n_d*sin(theta_d)=n_p*sin(theta_p) where angles are counted from normal to the face
-% and we want theta_d to be 90 degrees for the total internal reflection
-theta_p=asin(n_d/n_p);
+% recall n_d*sin(theta_disk)=n_prism*sin(theta_prism) where angles are counted from normal to the face
+% and we want theta_disk to be 90 degrees for the total internal reflection
+theta_prism=asin(n_disk/n_prism);
 % convert to degrees
-theta_p_in_degrees=theta_p*180/pi
+theta_prism_in_degrees=theta_prism*180/pi
 
 %% now lets see what angle it does with other face of the prism
-theta_p_2=(prism_angle - theta_p);
-theta_p_in_degrees_2=theta_p_2*180/pi
+theta_prism_2=(prism_angle - theta_prism);
+theta_prism_in_degrees_2=theta_prism_2*180/pi
 
 %% now we calculate refracted angle out of the prism into the air with respect to the normal
 % positive means above the normal
-asin_arg=n_p*sin(theta_p_2);
+asin_arg=n_prism*sin(theta_prism_2);
 if (abs(asin_arg)>1) error('quiting: at the right prism face  we experienced total internal reflection'); end
 theta_air=asin(asin_arg);
 % convert to degrees
@@ -68,16 +68,16 @@ plot(x_disk,y_disk,'k-')
 
 %% beam trace inside the prism
 % crossing of the beam with 1st (right) face of the prism
-% we are solving cot(theta_p)*x=tan(prism_angle)*(1-x)
-x_cross_1=tan(prism_angle)/(tan(prism_angle)+cot(theta_p));
-y_cross_1=x_cross_1*cot(theta_p);
+% we are solving cot(theta_prism)*x=tan(prism_angle)*(1-x)
+x_cross_1=tan(prism_angle)/(tan(prism_angle)+cot(theta_prism));
+y_cross_1=x_cross_1*cot(theta_prism);
 x_beam_prism_1=linspace(0,x_cross_1);
-y_beam_prism_1=x_beam_prism_1*cot(theta_p);
+y_beam_prism_1=x_beam_prism_1*cot(theta_prism);
 plot(x_beam_prism_1, y_beam_prism_1, 'r-');
 
 %% beam out of prism
 x_out_strt=x_cross_1;
-y_out_strt=x_cross_1*cot(theta_p);
+y_out_strt=x_cross_1*cot(theta_prism);
 
 if (abs(theta_air_rlh)<pi/2) x_out_stop=1; else x_out_stop=0; end
 x_out_1=linspace(x_out_strt, x_out_stop);
@@ -111,33 +111,33 @@ y_norm_in=linspace(0.,0.5);
 x_norm_in=y_norm_in*0;
 plot(x_norm_in, y_norm_in, 'b-');
 
-%% arc to show theta_p
+%% arc to show theta_prism
 R_arc=.1; 
-phi_arc=linspace(pi/2-theta_p,pi/2);
+phi_arc=linspace(pi/2-theta_prism,pi/2);
 x_arc_prism=R_arc*cos(phi_arc);
 y_arc_prism=R_arc*sin(phi_arc);
 plot(x_arc_prism, y_arc_prism, 'b-');
 %% annotation theta_air_in_degrees
-str=sprintf('theta_{p}=%.1f',theta_p_in_degrees);
+str=sprintf('theta_{p}=%.1f',theta_prism_in_degrees);
 str=strcat('\',str,'^{o}');
 text(x_arc_prism(1)+0.05, y_arc_prism(1), str);
 
-%% arc to show theta_p_2
+%% arc to show theta_prism_2
 R_arc=.1; 
-phi_arc=linspace(theta_norm_rlh+theta_p_2+pi,theta_norm_rlh+pi);
+phi_arc=linspace(theta_norm_rlh+theta_prism_2+pi,theta_norm_rlh+pi);
 x_arc_prism_2=x_cross_1+R_arc*cos(phi_arc);
 y_arc_prism_2=y_cross_1+R_arc*sin(phi_arc);
 plot(x_arc_prism_2, y_arc_prism_2, 'b-');
 %% annotation theta_air_in_degrees
-str=sprintf('theta_{p2}=%.1f',theta_p_in_degrees_2);
+str=sprintf('theta_{p2}=%.1f',theta_prism_in_degrees_2);
 str=strcat('\',str,'^{o}');
 text(x_arc_prism_2(1)+.05,y_arc_prism_2(1), str);
 
 
-str=sprintf('n_d=%.3f',n_d);
+str=sprintf('n_{disk}=%.3f',n_disk);
 text(0,1.1, str);
 
-str=sprintf('n_p=%.3f',n_p);
+str=sprintf('n_{prism}=%.3f',n_prism);
 text(0,1.2, str);
 
 % force same aspect ratio for axis
-- 
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