Fundamentals of Photonics Volume 1

Starting point for beginners questions.
lobaz
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Re: Fundamentals of Photonics Volume 1

Post by lobaz »

Din wrote: Thu Jul 19, 2018 9:58 am This is not true anymore. It was true about 40 odd years ago, when all transmission holograms were considered "thin". This particular formulation leads to Raman Nath diffraction, which is not selective - all light diffracts. Today, with modern emulsions, if you record with a ref angle > ~7deg, you'll record a "thick" hologram. A "thick" hologram diffracts in the Bragg regime, and the theory behind a "thick" hologram is Kogelnik, which strongly shows selectivity for both wavelength and angle of reconstruction. But, to within some reasonable approximation, you can model a transmission hologram using this, so long as you're aware that it is an approximation.
Dinesh, do you have any hands on experience how the scalar theory holds with surface relief holograms, such as in photoresists?
Brian
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Re: Fundamentals of Photonics Volume 1

Post by Brian »

Din wrote: Thu Jul 19, 2018 9:59 am By the way, Brian, is this one of your "One question every week"? :)
Very true that I haven't been on the forum in quite some time. So catching up, the energy conservation teaser caught my eye, as I have posited it to my students.

But all the while I have been making small reflection holograms. Squeezing in attempts between the other things that consume my days. And in doing so, I still have questions. I guess I should make it "one question every month", and I'll have one ready for August. :D
Din wrote: The power in an EM wave is given by the magnitude of the Poynting vector...
The power in an EM wave spread over an area is given by the magnitude of the Poynting vector. But I know theorists don't bother with units. ;)
Din wrote: thus overall intensity pattern is sinusoidal, with a noise term I₁ + I2 (which I call the 'dc term'), which encapsulates both beams.
Exactly how I describe it, a sinusoidal function with a dc offset.
Din wrote: There are... those... with no clue on how to derive the Euler formulation of complex numbers
I don't know any undergraduate math course that teaches this, which means I have to teach it.
Din wrote: A "thick" hologram diffracts in the Bragg regime, and the theory behind a "thick" hologram is Kogelnik
"Coupled Wave Theory for Thick Hologram Gratings" downloaded and on my reading list.
lobaz
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Re: Fundamentals of Photonics Volume 1

Post by lobaz »

Brian wrote: Thu Jul 19, 2018 4:14 pm The power in an EM wave spread over an area is given by the magnitude of the Poynting vector. But I know theorists don't bother with units. ;)
Units help :)
So, for a prospective reader of this thread: the intensity I given by

I = (1/2)cεE₀²

is measured in W/m^2, i.e. it is usually the value we are interested in when we decide the exposure time.

By the way, Brian, if you are interested in the coupled wave theory, you can get some basics even from Goodman's Introduction to Fourier Optics, chapter on Holography. Optical Holography by Collier et al. is OK as well. Practical Volume Holography by Syms is also worth checking.
Brian
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Re: Fundamentals of Photonics Volume 1

Post by Brian »

lobaz wrote: Thu Jul 19, 2018 4:54 pm Units help :)
Agreed.
lobaz wrote: ... you can get some basics even from Goodman's Introduction to Fourier Optics, chapter on Holography. Optical Holography by Collier et al. is OK as well. Practical Volume Holography by Syms is also worth checking.
Thank you for the recommendations. I will look into them.
Din
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Re: Fundamentals of Photonics Volume 1

Post by Din »

lobaz wrote: Thu Jul 19, 2018 1:27 pm Dinesh, do you have any hands on experience how the scalar theory holds with surface relief holograms, such as in photoresists?
It holds quite well if the amplitude is low. As I mentioned elsewhere, if the resist is etched so that the sin wave is clipped, , which usually happens, you get additional Fourier components, but, these also follow the scalar theory. Commercial resists, such as from Towne, have emulsion depths of 1 micron, and they're usually not etched all the way to the glass, so the amplitude is low. So display holography with commercial plates follow the scalar law, and, in fact, you use the grating formula λ = dsin(θ) when we do "pseudo-colour" transmission holography. That is, you have several H1's, each for a different colour image, and copied at a different angle so that, in the final resist H2, you see several colours at the same time.

If the amplitude is high compared to the (inverse) spatial frequency, then you start to go to the vector regime. Now, you begin to get Bragg selectivity, but the reconstruction begins to become dependent on the polarisation of the recon beam. "High" means that h/d~>3, where h is the amplitude and d is the (inverse) spatial frequency.So, if the spatial frequency is 1000 l/mm, the spacing is 1 micron, and if the amplitude is much greater than 3 microns, you begin to see vector effects.

In our case, we coat our own resist. Our resists usually are about 1 micron - 2 micron. However, I did have to make a resist plate that was over 3 microns deep for a specific type of blazed grating, with a period of over 1000 l/mm. This grating did have Bragg selectivity (it was supposed to!), but I didn't notice any polarisation effects. However, I wasn't looking for them, so there may have been polarisarisation effects I didn't notice. The grating was designed to work for white light sources, so, if I wanted to test polarisation, I would have to reconstruct it with a laser, at different polarisations.
Din
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Re: Fundamentals of Photonics Volume 1

Post by Din »

Brian wrote: Thu Jul 19, 2018 4:14 pm The power in an EM wave spread over an area is given by the magnitude of the Poynting vector. But I know theorists don't bother with units. ;)
Units, hell! We don't even bother with constants! c is always 1! :)
lobaz
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Re: Fundamentals of Photonics Volume 1

Post by lobaz »

Din wrote: Fri Jul 20, 2018 8:33 am It holds quite well if the amplitude is low.
...
If the amplitude is high compared to the (inverse) spatial frequency, then you start to go to the vector regime. Now, you begin to get Bragg selectivity, but the reconstruction begins to become dependent on the polarisation of the recon beam. "High" means that h/d~>3, where h is the amplitude and d is the (inverse) spatial frequency.
OK, thank you. I have read the same statement somewhere, but I did not actually measured that. Good to know that your experience agrees with the theory. By the way, I wonder you still call it Bragg selectivity. I always thought that Bragg must be volumetric.
Din
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Re: Fundamentals of Photonics Volume 1

Post by Din »

lobaz wrote: Sat Jul 21, 2018 6:05 pm By the way, I wonder you still call it Bragg selectivity. I always thought that Bragg must be volumetric.
Yes, it is a misnomer. Strictly speaking, it shouldn't be called "Bragg selectivity". The reconstruction of deep amplitude surface holograms becomes more and more selective for wavelengths and angles, the range over which diffraction occurs becomes smaller and smaller, due to the vector nature of the diffraction.. With Raman Nath diffraction, all light is diffracted, no matter what angle and wavelength. But, even Raman Nath may be a misnomer, because Raman Nath diffraction is a model of diffraction by acousto-optic crystals. Low frequency acoustic waves cause the light launched into the crystal to diffract by the Raman Nath model.

I think holography had to borrow a lot of words from previous diffraction studies because it came late into the game. By the time the theories of holography were being created in the 60's, diffraction theories were a century old. So, the new holography theories simply borrowed the words from previous theories of diffraction. Consider that Bragg diffraction is associated with narrow band reconstruction of volume holograms. it's not equivalent to Bragg diffraction, which assumes a crystalline structure of repeating molecular positions. The coupled wave theory explains narrow band reconstruction of volume holograms by means of a repeating set of planes. You can associate the repeating planes of coupled wave theory with the repeating molecules of a crystal structure, and so call the reconstruction of volume holograms as "Bragg" reconstruction. But, the original Bragg reconstruction is not reconstructing anything - the crystals were already there, no one 'recorded' the crystals.

However, strictly speaking, if you associate Bragg diffraction with the reconstruction of a volume hologram, then, a piece of quartz is a hologram, even if the display holographers will insist that a piece of quartz is "not a hologram".

My feeling is that language is a form of communication of ideas or concepts, whose meaning is extracted from a cultural milieu or bias. It should not be strictly enforced like a law governing where you can park your car. if both of us agree to call this thing "an apple", both of us know what you mean when you say, "I'm going to eat an apple". If both of us agree that this thing is 'a hologram' - whether it's a set of interference lines on a medium, or simply a 3D image, then both of us know what you mean when you say, "I'm going to see a hologram"
lobaz
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Re: Fundamentals of Photonics Volume 1

Post by lobaz »

Din wrote: Mon Jul 23, 2018 10:58 am Yes, it is a misnomer. Strictly speaking, it shouldn't be called "Bragg selectivity". The reconstruction of deep amplitude surface holograms becomes more and more selective for wavelengths and angles, the range over which diffraction occurs becomes smaller and smaller, due to the vector nature of the diffraction.. With Raman Nath diffraction, all light is diffracted, no matter what angle and wavelength. But, even Raman Nath may be a misnomer, because Raman Nath diffraction is a model of diffraction by acousto-optic crystals. Low frequency acoustic waves cause the light launched into the crystal to diffract by the Raman Nath model.
Got it, no problem. Thank you.
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