Is there refraction upon frustrated total internal reflection

• Christofer Br
In summary, frustrated total internal reflection does not involve refraction as the relationship between phase, time, and distance remains the same. The transmitted wave may have a lateral offset due to the phase shift, but the direction cannot change. There may be edge effects and a fixed phase shift across the gap due to near field coupling. This can be observed in the recombination of spectrum colors using two prisms, where the light beams exiting the second prism are parallel. However, evanescent waves and induction field coupling add complexity to the situation, which may result in pulse spreading over time.
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?

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.

jambaugh said:
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

Last edited:
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.

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

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gneill
jambaugh said:
... 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

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.

jambaugh said:
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?

tech99 said:
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.

1. What is frustrated total internal reflection (FTIR)?

Frustrated total internal reflection is a phenomenon that occurs when a light ray travels from a medium with a higher refractive index to a medium with a lower refractive index, and is reflected back into the original medium instead of being transmitted into the second medium.

2. What causes refraction in frustrated total internal reflection?

Refraction in frustrated total internal reflection is caused by a change in the direction and speed of the light ray as it passes through the boundary between two different mediums with different refractive indices.

3. Is there refraction upon frustrated total internal reflection?

Yes, there is refraction upon frustrated total internal reflection. This is because the light ray changes direction and speed as it passes through the boundary between two different mediums, resulting in a change in its path.

4. What is the difference between frustrated total internal reflection and total internal reflection?

The main difference between frustrated total internal reflection and total internal reflection is that in total internal reflection, the light ray is completely reflected back into the original medium, while in frustrated total internal reflection, some of the light may be transmitted into the second medium.

5. How is frustrated total internal reflection used in scientific research?

Frustrated total internal reflection is used in various scientific research fields, such as surface plasmon resonance and evanescent wave spectroscopy. It is also used in optical devices, such as optical fibers and lenses, to control the transmission and reflection of light.

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