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import numpy as np
import pylab
import sys
def prismDiskCoupling(prismAngleInDegrees, nDisk, nPrism, diskX, coupDesc):
# Calculates incident angle for proper coupling into the disc via prism
# prismAngleInDegrees - angle of the prism faces in degrees
# diskX - x coordinate of the disk center
# coupDesc - short annotation of the situation
prismAngle = prismAngleInDegrees * np.pi / 180 # convert to radians
# critical angle for beam from prism to disk
# recall nDisk*sin(thetaDisk)=nPrism*sin(thetaPrism) where angles are
# counted from normal to the face and we want thetaDisk to be 90 degrees
# for total internal reflection, thus sin(thetaDisk)=1
thetaPrism1 = np.arcsin(nDisk / nPrism)
thetaPrismInDegrees1 = thetaPrism1 * 180 / np.pi
# find inside angle on the incident side of prism
thetaPrism2 = prismAngle - thetaPrism1
thetaPrismInDegrees2 = thetaPrism2 * 180 / np.pi #convert to degrees
# calculate refracted angle out of the prism with respect to the normal
# positive means above the normal; negative below
tempArcsin = nPrism * np.sin(thetaPrism2)
try:
thetaAir = np.arcsin(tempArcsin)
except ValueError:
print 'Error'
sys.exit('Total internal reflection at right prism face')
thetaAir = np.arcsin(tempArcsin)
thetaAirInDegrees = thetaAir * 180 / np.pi #convert to degrees
# angle in the air relative to horizon
thetaAirHorizon = thetaAir + (np.pi/2 - prismAngle)
thetaAirHorizonInDegrees = thetaAirHorizon * 180 / np.pi #convert to degrees
# -----GRAPHICAL OUTPUT-----
# PRISM
# bottom face will go from (-1,0) to (1,0) regardless of prismAngle
xFace1 = np.linspace(-1,1)
yFace1 = 0 * xFace1
# second face to the right of origin
# at prismAngle with respect to negative x-direction
xFace2 = np.linspace(1,0)
yFace2 = (1 - xFace2) * np.tan(prismAngle)
# third face to the left of origin
# at prismAngle with respect to positive x-direction
xFace3 = np.linspace(-1,0)
yFace3 = (xFace3 + 1) * np.tan(prismAngle)
# draw prism
pylab.plot(xFace1, yFace1, 'black',\
xFace2, yFace2, 'black',\
xFace3, yFace3, 'black')
# DISK
# center will be located at (diskX, -radius)
radius = 0.25
diskCenterX = diskX
diskCenterY = -radius
xDisk = diskCenterX + (radius * np.cos(np.linspace(0, 2 * np.pi)))
yDisk = diskCenterY + (radius * np.sin(np.linspace(0, 2 * np.pi)))
pylab.plot(xDisk, yDisk, 'black')
# BEAMS
# Inside Prism
# drawing line from disk contact point to face2 at angle thetaPrism
xCross = (np.tan(prismAngle) + diskX / np.tan(thetaPrism1)) /\
(1/np.tan(thetaPrism1) + np.tan(prismAngle))
yCross = -np.tan(prismAngle) * (xCross - 1)
xBeamPrism = np.linspace(diskX, xCross)
yBeamPrism = np.linspace(0, yCross)
pylab.plot(xBeamPrism, yBeamPrism, color = 'red', linewidth = 2)
# Outside Prism
xOutStart = xCross
yOutStart = yCross
xOutStop = 1.5
yOutStop = 2.0
yBeamOut = np.linspace(yOutStart, yOutStop)
xBeamOut = xOutStart + (1/np.tan(thetaAirHorizon)) * (yBeamOut - yOutStart)
# this keeps the beam from going farther than necessary
i = 0
for value in yBeamOut:
if value > 2.0:
break
else:
i +=1
# ensure same dimension
yBeamOut = yBeamOut[:i]
xBeamOut = xBeamOut[:i]
pylab.plot(xBeamOut, yBeamOut, color = 'red', linewidth = 2)
# NORMALS
# incident face normal
thetaNorm = np.pi/2 - prismAngle
# coordinates of normal outside the prism
xNormOut1 = np.linspace(xCross, xCross + 0.25)
yNormOut1 = yCross + (xNormOut1 - xCross) * np.tan(thetaNorm)
# coordinates of normal inside the prism
xNormIn1 = np.linspace(xCross, xCross - 0.25)
yNormIn1 = yCross + (xNormIn1 - xCross) * np.tan(thetaNorm)
pylab.plot(xNormOut1, yNormOut1, 'b:', \
xNormIn1, yNormIn1, 'b:', linewidth = 1.5)
# normal at the disk contact
yNorm2 = np.linspace(-0.25, 0.25)
xNorm2 = diskX + yNorm2 * 0.0
pylab.plot(xNorm2, yNorm2, 'b:', linewidth = 1.5)
# ARCS AND LABELS
# radius for all drawn arcs
arcRadius = 0.1
# arc to show thetaAir
# phiArcAir is the angle through which we are drawing
phiArcAir = np.linspace(thetaAirHorizon, thetaNorm)
xArcAir = xCross + arcRadius * np.cos(phiArcAir)
yArcAir = yCross + arcRadius * np.sin(phiArcAir)
pylab.plot(xArcAir, yArcAir, color = 'blue', linewidth = 1.0)
# annotatation of thetaAir
pylab.annotate('%.2f' % thetaAirInDegrees + u'\N{DEGREE SIGN}',\
xy = (xArcAir[29], yArcAir[29]),\
xytext=(xCross + 0.12, yCross + 0.3),\
arrowprops = dict(facecolor = 'black', arrowstyle = '->'))
# arc to show prismAngle
#phiArcPrism
phiArcPrism = np.linspace(np.pi, np.pi - prismAngle)
xArcPrism = 1 + arcRadius * np.cos(phiArcPrism)
yArcPrism = arcRadius * np.sin(phiArcPrism)
pylab.plot(xArcPrism, yArcPrism, color = 'blue', linewidth = 1.0)
# annotate prismAngle
pylab.annotate('%.2f' % prismAngleInDegrees + u'\N{DEGREE SIGN}',\
xy = (xArcPrism[29], yArcPrism[29]),\
xytext=(0.8, -0.2),\
arrowprops = dict(facecolor = 'black', arrowstyle = '->'))
# arc to show thetaPrism1
# phiArcPrism1 is the angle through which we are drawing
phiArcPrism1 = np.linspace(np.pi/2 - thetaPrism1, np.pi/2)
xArcPrism1 = diskX + arcRadius * np.cos(phiArcPrism1)
yArcPrism1 = arcRadius * np.sin(phiArcPrism1)
pylab.plot(xArcPrism1, yArcPrism1, color = 'blue', linewidth = 1.0)
# annotatation of thetaPrism1
pylab.annotate('%.2f' % thetaPrismInDegrees1 + u'\N{DEGREE SIGN}',\
xy = (xArcPrism1[29], yArcPrism1[29]),\
xytext=(diskX - 0.2, 0.3),\
arrowprops = dict(facecolor = 'black', arrowstyle = '->'))
# arc to show thetaPrism2
# phiArcPrism2 is the angle through which we are drawing
phiArcPrism2 = np.linspace(thetaNorm + thetaPrism2 + np.pi,\
thetaNorm + np.pi)
xArcPrism2 = xCross + arcRadius * np.cos(phiArcPrism2)
yArcPrism2 = yCross + arcRadius * np.sin(phiArcPrism2)
pylab.plot(xArcPrism2, yArcPrism2, color = 'blue', linewidth = 1.0)
# annotation of thetaPrism2
pylab.annotate('%.2f' % thetaPrismInDegrees2 + u'\N{DEGREE SIGN}',\
xy = (xArcPrism2[29], yArcPrism2[29]),\
xytext=(xCross - 0.2, yCross + 0.5),\
arrowprops = dict(facecolor = 'black', arrowstyle = '->'))
# General annotation and axis set-up
pylab.text(-1.4, 1.7, coupDesc)
pylab.text(-1.4, 1.55, 'nDisk = %.3f' % nDisk)
pylab.text(-1.4, 1.4, 'nPrism = %.3f' % nPrism)
pylab.xlim(-1.5, 1.5)
pylab.ylim(-0.5, 2.0)
pylab.title(coupDesc)
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