Dammit!

[Din]

Dammit! Thought of this about 10 years ago. Yes, I know the joke:
How many holographers does it take to change a light bulb? 10, one to change the bulb and 9 to say, "I thought of that 10 years ago!"

About 1987, Tomasz Jannsen (owner POC) and I were talking about using the WKB approximation to model volume holograms, since I believed Kogelnik wasn't designed for the new photopolymers coming out then. Anyway, some 25 years later, ~2012, I was working on holographic diffractive waveguides for the research division of a hi-tech company that shall remain nameless; the method by which some VR/AR/MR goggles, which seemed to be an up-and-coming technology in 2012, work by diffractive waveguides. One of the problems was not being able to quantify and characterise these waveguides in photopolymers. Recalling that long-ago discussion on WKB methods with Tomasz, I wondered if it was possible to use digital holography along with a WKB approximation. Not having the tools for digital holography, I sketched out some notes and let the whole idea go. Now, here it is in JOSA B - Optical Physics!

waveguides.jpg (825.12 KiB) Viewed 117530 times

[lobaz]

I guess most researchers are on the same boat
Anyway, after reading the article, do you think that WKB approximation is a useful tool here? Not every published method is useful in the end...

[Din]

I guess most researchers are on the same boat

They're trying to characterise the refractive index profile (RIP) of the new waveguides made from polymers, which have a kind of RIP not seen before (below).

As you can see, the RIP is rapidly changing near the origin, and then varies slowly away from the origin. Such problems are ideal for applying the WKB approximation. They're splitting the profile into sections and analysing each section using a series approximation.

profile 1.jpg (105.02 KiB) Viewed 117498 times

[Din]

The actual profile didn't show up (despite it showing up on the preview!). here it is:

profile 2.jpg (173.26 KiB) Viewed 117497 times

[Din]

Having got the profile, they then solve Maxwell inserting the appropriate RIP, and then getting the transmission modes in the waveguide. You can see the modes below. The experimental setup uses a Mach Zender with the sample waveguide placed in one arm.

The attachment profile 3.jpg is no longer available

The attachment profile 3.jpg is no longer available

[Din]

The experimental setup did not show up 9again, the preview showed it!

profile 4.jpg (507.3 KiB) Viewed 117497 times

[Din]

I guess most researchers are on the same boat

Yep!

[Manul]

This is very interesting information; I haven't encountered it before. Am I correct in assuming that Kogelnik's theory doesn't work well for photopolymers, or that there are difficulties measuring hologram parameters using coupled-wave theory? And is it worth using the theory WKB to determine the properties of holograms on photopolymers, as it's more heuristic and possibly more fundamental?

[Din]

... is it worth using the theory WKB to determine the properties of holograms on photopolymers, as it's more heuristic and possibly more fundamental?

I believe so.

While Kogelnik is an approximation and more accurate theories called Rigorous Coupled Wave Theories (RCWT) exist, these more rigorous theories still assume a sinusoidal modulation. However, it's impossible to get an exact sinusoidal modulation, because the actinic reaction centres are not continuous. However, if the material is almost continuous, it can be reasonably recorded with a sinusoidal modulation and RCWT models this quite accurately. Thus, dichromated gelatin materials (DCG) can be recorded with a sinusoidal modulation and very high efficiencies are attainable; I've recorded DCG holograms with an OD of 4 (99.9% efficient). I can put up a paper on RCWT if there's any interest. However, such theoretical studies are not very useful for display holography, as you don't need theory to record a display hologram.

However, with polymers, the mechanism of the modulation is charge transfer, which, by the nature of charge transfer, makes it very difficult - if not impossible - to get a sinusoidal modulation. I have put up a paper on the mechanism of polymer recording which assumes a sinusoidal modulation, but the paper actually shows a square wave modulation ( viewtopic.php?t=11460 ).

Therefore I think that a WKB approach is particularly useful in polymer material. I think it'll give a more nuanced view.

[Manul]

This is extremely interesting; I'd like to hear your thoughts on this, if possible. As I understand it, this is related to the structural properties of DCG and photopolymers. Are we talking about thick polymer layers over 30 µm, or does the poor performance of classical theory also apply to Bayfol?