Monochrome and Color Denisyuk Holograms from China

[Holoamateur]

Let's daydream a little bit for fun. We could have a theoretical ideal holographic recording medium, which is panchromatic sensitive and has zero absorption in whole visible spectrum and we have a tunable wavelength (400nm-760nm) SLM laser. We make 180 layers of such emulsion, which is 10 micron thickness per layer and we make (760-400)/2=180 laser exposures (2nm step of laser wavelengths), then we stack them all together, the total thickness is 10micron * 180=1800 micron=1.8 mm. Such 1.8mm thick multi-layer-multi-wavelength hologram should give us: high brightness and high color saturation as the real objects. That's the real virtual reality.

Following Collier et all* that probably would not run. Let us take ideal material, which has exact fourier-shape layers of diffraction picture. There is finite (i.e. >0) bandwidth of the reflected spectrum. It depends upon bragg's angle, refraction index of the plate, thickness of the holographic layer and laser wavelength (also depends upon your experiment scheme, details are in chapter 17.6 of the mentioned book). For example 7 nm for 633 nm. laser and 80 degrees bragg angle. It is not extinct. So, if the tunable laser has minimal step LESS than this criteria, you may get cross modulation effect.

*R.J.Collier, C.B.Burckhardt, L.H.Lin "Optical Holography", 1971 edition, chapter 17.6

Vladimir B.

[Holoamateur]

If the Bragg planes were 'sharpened", by which I assume you mean that the sinusoidal profile has become more of a square wave profile, then additional frequencies would be introduced because the 'squaring off' of the plane structure would introduce Fourier components, each of which would also diffract. The amount of diffraction from these Fourier component planes would depend on the amplitude of the Fourier component. Since the structure is still periodic, the new Fourier components' frequency would each be doubled from the fundamental, so the diffraction, and hence the 'color' of the new planes would be shifted into the UV. For example, let's say you were recording at 633. Ideally, the fringes/planes would be sinusoidal, with a frequency f = 2/633 (nm)^(-1). Let's say for whatever reason (processing, grain growth etc), the fringes/planes became square wave. Now you introduce new frequencies with frequencies of 3/633, 5/633 etc. each with amplitude 4/(pi*n) for odd n ( Here's the series from Wolfram's mathworld: http://mathworld.wolfram.com/FourierSer ... eWave.html ). The second harmonic would diffract at lambda = 633/3 = 211 nm, ie in the UV region.

Thus grain growth, for example, does not affect bandwidth, since bandwidth is dependent on the statistical frequency distribution of the planes, but it does affect the efficiency (or brightness, which is not the same as efficiency) because it takes some energy away from the fundamental frequency, ie the recording frequency, and transfers it to second, third and even higher orders.

That is amazing, that THIN layers (both phase and amplitude modulated) give higher diffraction efficiency, if transmission is described by square wave, than sinusoidal. For example 10,1% vs. 6,25% for amplitude and 40,4% comparing 33,9% in case of phase modulated. Also interesting, that some experimental evidence confirm the shape of diffraction grating is more square wave form (look at http://www.bu.edu/photonics/files/2012/ ... tonics.pdf , page 12).

Vladimir B.