From bc5f1eea9b5718c3e32d4cc0ea8b384983be6d93 Mon Sep 17 00:00:00 2001
From: Eugeniy Mikhailov <evgmik@gmail.com>
Date: Wed, 17 Oct 2012 22:30:58 -0400
Subject: split coupling function and its demo to separate scripts

---
 prism_disk_coupling.m | 152 ++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 152 insertions(+)
 create mode 100644 prism_disk_coupling.m

(limited to 'prism_disk_coupling.m')

diff --git a/prism_disk_coupling.m b/prism_disk_coupling.m
new file mode 100644
index 0000000..40e0980
--- /dev/null
+++ b/prism_disk_coupling.m
@@ -0,0 +1,152 @@
+function prism_disk_coupling(prism_angle_in_degrees, n_disk, n_prism, coupling_description)
+%% Calculates incident angle for proper coupling into the disc via prism
+% prism_angle_in_degrees -  angle of the prism faces in degrees
+% coupling_description   -  short annotation of the situation
+%  for example:
+%    coupling_description='Rutile prism, MgF_{2} disk, p-polarization';
+
+prism_angle = prism_angle_in_degrees*pi/180; 
+
+%% critical angle for beam from prism to disk
+% 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_prism_in_degrees=theta_prism*180/pi
+
+%% now lets see what angle it does with other face of the prism
+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_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
+theta_air_in_degrees=theta_air*180/pi
+
+%% angle in the air relative to horizon
+theta_air_rlh=(theta_air+prism_angle);
+theta_air_rlh_in_degrees=theta_air_rlh*180/pi
+
+%% Lets make a picture
+% 1st face of the prism lays at y=0 and spans from x=-1 to x=1
+x_face_1=linspace(-1,1);
+y_face_1=0*x_face_1;
+% 2nd face to the right of origin  and at angle prism_angle with respect to negative x direction
+x_face_2=linspace(1,0);
+y_face_2=(1-x_face_2)*tan(prism_angle);
+% 3rd face to the left of origin  and at angle prism_angle with respect to negative x direction
+x_face_3=linspace(-1,0);
+y_face_3=(x_face_3+1)*tan(prism_angle);
+
+%% draw prism
+figure(1); hold off;
+plot(x_face_1, y_face_1, 'k-', x_face_2, y_face_2, 'k-', x_face_3, y_face_3, 'k-');
+hold on
+
+%% disk center will be located in point (0,-R);
+R=.25;
+dc_x=0; dc_y=-R;
+x_disk=dc_x+R*cos(linspace(0,2*pi));
+y_disk=dc_y+R*sin(linspace(0,2*pi));
+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_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_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_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);
+y_out_1=y_out_strt+tan(theta_air_rlh)*(x_out_1-x_out_strt);
+plot(x_out_1, y_out_1, 'r-');
+
+%% draw normal at the point of 1st face intersection
+theta_norm_rlh=pi/2-prism_angle;
+% coordinates of normal outside the prism
+x_norm_out=linspace(x_cross_1,1);
+y_norm_out=y_cross_1+(x_norm_out-x_cross_1)*tan(theta_norm_rlh);
+
+% coordinates of normal inside the prism
+x_norm_in=linspace(x_cross_1,0);
+y_norm_in=y_cross_1+(x_norm_in-x_cross_1)*tan(theta_norm_rlh);
+plot(x_norm_out, y_norm_out, 'b-', x_norm_in, y_norm_in, 'b-');
+
+%% arc to show theta_air
+R_arc=.1; 
+phi_arc=linspace(theta_air_rlh,theta_norm_rlh);
+x_arc_air=x_cross_1+R_arc*cos(phi_arc);
+y_arc_air=y_cross_1+R_arc*sin(phi_arc);
+plot(x_arc_air, y_arc_air, 'b-');
+%% annotation theta_air_in_degrees
+str=sprintf('theta_{a}=%.1f',theta_air_in_degrees);
+str=strcat('\',str,'^{o}');
+text(x_arc_air(end)+.05,y_arc_air(end), str);
+
+%% normal at the disk contact
+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_prism
+R_arc=.1; 
+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_prism_in_degrees);
+str=strcat('\',str,'^{o}');
+text(x_arc_prism(1)+0.05, y_arc_prism(1), str);
+
+%% arc to show theta_prism_2
+R_arc=.1; 
+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_prism_in_degrees_2);
+str=strcat('\',str,'^{o}');
+text(x_arc_prism_2(1)+.05,y_arc_prism_2(1), str);
+
+%% arc to show prism angle
+R_arc=.1; 
+phi_arc=linspace(pi, pi-prism_angle);
+x_arc=1+R_arc*cos(phi_arc);
+y_arc=0+R_arc*sin(phi_arc);
+plot(x_arc, y_arc, 'b-');
+%% annotate prism angle
+str=sprintf('theta_{prism}=%.1f',prism_angle_in_degrees);
+str=strcat('\',str,'^{o}');
+text(.52, 0.06, str);
+
+
+%% General annotation
+str=sprintf('n_{disk}=%.3f',n_disk);
+text(-0.9,1.1, str);
+
+str=sprintf('n_{prism}=%.3f',n_prism);
+text(-0.9,1.2, str);
+
+text(-0.9, 1.3, coupling_description);
+
+% force same aspect ratio for axis
+axis([-1,1,-0.5,1.5],'equal');
+
+%% output of the plot to the file
+print('prism_disk_coupling.eps','-depsc2');
+print('prism_disk_coupling.png');
+
+end
-- 
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