Tracing a ray of light through a spiral phase plate

[Spinnor]

Draw a single light ray through a spiral phase plate, anywhere but the middle of the plate, with the incoming ray being parallel to the axis of the spiral phase plate. On passing through the plate the ray is no longer parallel to the axis of the phase plate? Does the change in direction account for the change in the orbital angular momentum of the light?

I'm thinking in terms of classical optics where we can draw the path of a light ray.

Thanks!

 

[Andy Resnick]

Draw a single light ray through a spiral phase plate, anywhere but the middle of the plate, with the incoming ray being parallel to the axis of the spiral phase plate. On passing through the plate the ray is no longer parallel to the axis of the phase plate? Does the change in direction account for the change in the orbital angular momentum of the light?

I'm thinking in terms of classical optics where we can draw the path of a light ray.

Thanks!

For a spiral phase plate (index 'n') of thickness t(φ) = hφ/2π, a relative phase Ψ(φ)= hφ/λ (n-n₀)is generated for a ray. If the plate thickness is chosen such that h/λ (n-n₀) is an integer (say, 'm'), the optical field after the plate acquires a phase e^imφ, which is characteristic of a Laguerre-Gauss vortex beam.

 

[Spinnor]

Thanks Andy. Can we trace light rays through the phase plate, treating it like any lens in classical physics?

Thanks!

 

[Andy Resnick]

Thanks Andy. Can we trace light rays through the phase plate, treating it like any lens in classical physics?

View attachment 198795

Thanks!

I guess so- assigning an optical power to the surface may be tricky, since it's not axisymmetric. Also, skew rays become important.

I don't know what your application is, but if you want to ray trace, why not use an axicon element instead?

 

[Spinnor]

I don't know what your application is

I was trying to understand how a spiral wave plate changed the orbital angular momentum of light in a classical way and my thought process may have been flawed. Take a light ray that is parallel to to spiral wave plate axis and follow it through the wave plate. My guess is that all parallel light rays upon exiting the wave plate have their direction changed proportional to the pitch of the wave plate? That change in direction then corresponds to a change in orbital angular momentum. I know I have completely ignored the interference from the path dependent phase change but it seems in this flawed approach we still might see how orbital angular momentum change comes about. The spiral wave plate is an interesting optical element that causes a parallel light beam to diverge and rotate?

Thanks!