|Aug14-07, 11:29 AM||#1|
I have some questions about birefringence. I have searched in vain on
the Internet and in a few books (it's tough to find books on
Usually determining how rays propagate after birefringence is simple
because the light is incident normally and the ne of the e-ray is
But in my situation, I need to analyze light that is incident at an
angle. Moreover, the ne is also not known. As in only the maximum ne
is known but ne as you know varies with the angle between the o-ray
and the optic axis (if I am not wrong). So, ne should also change with
the incident angle. Does anyone have an equation that takes in the
incident angle, the max ne and the no and finds the walkoff angle +
One more question: is birefringence expressed purely by differences in
ne and no? So, suppose I know the ne for a given situation, I should
be able to find the difference in angle between the o-ray and e-ray
using only Snell's law? Or is there a separate equation for Poynting
I am rather confused about these topics. Basically, I understand
birefringence conceptually but I have been unable to find appropriate
equations to apply for specific optical systems involving
birefringence. Hope some of you can help me with this. Even if you
don't know the answers to the questions, it would be helpful if you
can point me to some good sources either online or on paper.
|Aug14-07, 10:53 PM||#2|
|Aug18-07, 09:28 AM||#3|
Thanks for your help and the links. I think I have figured this out. Tell me if I am doing it right.
I believe this is the equation that expresses the ne (not the max ne) in this case with respect to the theta. First, I am not sure what the theta is. Is it the angle of refraction of the e-ray with respect to the surface normal? Or is it the angle between the optic axis and the e-ray? I think it is the latter because the ne must depend on the angle between the polarisation state and the optic axis (that is what birefringence is all about). But I am not sure... so can someone tell which is right?
So, once I know what this angle is. I can solve the system of equations below to find the ne and the angle of refraction of the e-ray.
After this, I can calculate the walkoff angle with the equation below. Here also, I am not sure which ne this is (I know the differential must be the first equation above but how about the other ne)? Is the max ne or is it the ne calculated earlier?
Once the walkoff angle is calculated, I can sum up the two angles (angle of refraction and walkoff angle) to find the actual angle of the e-ray with respect to the normal, can't I?
Summary of steps:
1. Find refraction angle of e-ray using snell's law and ne equation
2. Find walkoff angle using ne equation, refracted angle and ne found earlier
3. Sum up two angles to obtain the actual angle of the e-ray with respect to the normal in any biref crystal
So, I should be able to find the angle of e-ray inside a birefringent prism depending on the angle it is incident at.
Is there anything wrong with any step in my approach?
Thanks for the help.
|Aug20-07, 08:20 PM||#4|