Is there refraction upon frustrated total internal reflection

[Christofer Br]

In frustrated total internal reflection, is there refraction corresponding to the refractive index difference between the first and third medium or does the light continue in straight line as it is usually depicted in graphic representations of the frustrated total internal reflection?

 

[jambaugh]

I believe the answer to your question is no. Refraction occurs because of the change in phase-time-distance relations when the wave passes across the interface between mediums. In total internal reflection the relationship between phase, time and distance remains the same and thus the reflected wave must be a symmetric reflection of the incident wave.

 

[Christofer Br]

I believe the answer to your question is no. Refraction occurs because of the change in phase-time-distance relations when the wave passes across the interface between mediums. In total internal reflection the relationship between phase, time and distance remains the same and thus the reflected wave must be a symmetric reflection of the incident wave.

You meant the transmitted wave at the end, right? For clarity, I was asking if the ray transmitted through the gap is "bent" (refracted) in relation to the ray in the first medium if there's a difference in refractive index between the two higher index media

 

[jambaugh]

I see. I missed the "frustrated" component. Between the mediums of the same index of refraction there will be no net angular refraction. Again this is necessary due to continuity of the phase-time-position relationships of the waves. You may have a lateral offset of the waves (offset parallel to wave front) due to the shift in phase as the light traverses the intermediate gap but the direction can't change.

Short of actually bending space-time, i.e. considering gravitational effects, the only way the beam could change direction between regions of equivalent index of refraction with whatever intermediate medium you might imagine provided it's uniformly coplanar (no prisms) would be for there to be a frequency shift.

 

[Tom.G]

If extending the FTIR situation to prisms is valid, this might be informative.
(about 40% down the page from: http://blog.teachersource.com/2011/11/26/two-prisms-four-demos/)

RECOMBINING SPECTRUM COLORS
Isaac Newton also wondered if the colors of the spectrum could be recombined to again make white light. To do this he used a second prism arranged as shown. He proved that this was possible. What’s interesting is that the light beams exiting the second prism are not on the same line, but they are PARALLEL. And, because the slit is not infinitely narrow, these beams are not infinitely narrow and therefore can mix to create white light.

Cheers,
Tom

 

[tech99]

... You may have a lateral offset of the waves (offset parallel to wave front) due to the shift in phase as the light traverses the intermediate gap but the direction can't change.

So far as I understand it, evanescent waves do not convey information and so do not have a defined speed of propagation. Therefore, I expect zero time delay across the gap between the two prisms. The following paper talks about this:-
https://www.osapublishing.org/josa/abstract.cfm?uri=josa-61-8-1035

 

[jambaugh]

Oh! I see. This is very interesting. Near field coupling across the gap sets up a parallel wave at the surface across the gap. The gap is basically a wave-guide. The information is being conveyed nearly parallel to the interface so there should be edge effects where the coupling builds up but within the beam area there's a fixed phase shift (possibly zero) independent of gap width because that phase shift will, I expect, be proportional to the incident angle. Does this sound correct?

It would also imply that for a pulse the transmitted light will spread out significantly over time. Is that observed?

I apologize for my over simplifications. There's much more going on then I understood there to be.

 

[tech99]

Oh! I see. This is very interesting. Near field coupling across the gap sets up a parallel wave at the surface across the gap. The gap is basically a wave-guide. The information is being conveyed nearly parallel to the interface so there should be edge effects where the coupling builds up but within the beam area there's a fixed phase shift (possibly zero) independent of gap width because that phase shift will, I expect, be proportional to the incident angle. Does this sound correct?

It would also imply that for a pulse the transmitted light will spread out significantly over time. Is that observed?

I apologize for my over simplifications. There's much more going on then I understood there to be.

I am very interested in the topic of evanescent waves and induction field coupling.
I agree with what you are saying except I am not sure why you suggest pulse spreading?

 

[jambaugh]

I am very interested in the topic of evanescent waves and induction field coupling.
I agree with what you are saying except I am not sure why you suggest pulse spreading?

Imagine you are riding one point of the wave front as the beam approaches the interface. You reach the interface and then are refracted parallel to it. You start moving within the interface parallel to its boundaries. As you do, your wave's energy is dissipated by the emission on the far side of the interface but at the same time it is replenished by more waves incoming on the near side so long as you're within the span where the beam is hitting the interface. So "when you cross" is spread out over a an interval of time much longer than the gap width divided by c.

I'm thinking that for a square wave amplitude pulse the spreading should exponentially decay toward the following steady state. The exponential constant would be proportional to the coupling, a function of the thickness of the gap interface.

I think that it would act (over time) like resonant coupling between the two interfaces except that the instead of a stationary resonating interface one has the traveling evanescent wave.