Volume hologram

Volume holograms are holograms where the thickness of the recording material is much larger than the light wavelength used for recording. In this case diffraction of light from the hologram is possible only as Bragg diffraction, i.e., the light has to have the right wavelength (color) and the wave must have the right shape (beam direction, wavefront profile). Volume holograms are also called "thick holograms" or "Bragg holograms".

Theory

Volume holograms were first treated by H. Kogelnik in 1969 cite journal
title = Coupled-wave theory for thick hologram gratings
author = H. Kogelnik
coauthors=
journal = Bell System Technical Journal
volume = 48
number =
pages = 2909
year = 1969
month =
url =
doi =
publisher = ] by the so-called "coupled-wave theory". For volume "phase" holograms it is possible to diffract 100% of the incoming reference light into the signal wave, i.e., full diffraction of light can be achieved. Volume "absorption" holograms show much lower efficiencies. H. Kogelnik provides analytical solutions for transmission as well as for reflection conditions. A good text-book description of the theory of volume holograms can be found in a book from J. Goodmancite book
title = Introduction to Fourier optics
author = J. Goodman
year = 2005
publisher = Roberts & Co Publishers] .

Bragg selectivity

In the case of a simple Bragg reflector the wavelength selectivity $Deltalambda$ can be roughly estimated by $Deltalambda/lambda\; approx\; Lambda/L$, where $lambda$ is the vacuum wavelength of the reading light, $Lambda$ is the period length of the grating and $L$ is the thickness of the grating. The assumption is just that the grating is not too strong, i.e., that the full length of the grating is used for light diffraction. Considering that because of the Bragg condition the simple relation $Lambda=lambda/(2n)$ holds, where $n$ is the refractive index of the material at this wavelength, one sees that for typical values ($lambda\; =\; 500mbox\{\; nm\},,\; L\; =\; 1mbox\{\; cm\},,\; n\; =\; 1.5$) one gets
$Deltalambda/lambda\; approx\; 10^\{-5\}$ showing the extraordinary wavelength selectivity of such volume holograms.

In the case of a simple grating in the transmission geometry the angular selectivity $DeltaTheta$ can be estimated as well: $DeltaTheta\; approx\; Lambda/d$, where $d$ is the thickness of the holographic grating. Here $Lambda$ is given by $Lambda\; =\; (lambda/$2$sinTheta$). Using again typical numbers ($lambda\; =\; 500mbox\{\; nm\},,\; d\; =\; 1mbox\{\; cm\},,\; Theta\; =\; 45\; ^circ$) one ends up with
$DeltaTheta\; approx\; 4\; imes\; 10^\{-5\}mbox\{\; rad\}\; =\; 0.002^circ$ showing the impressive angular selectivity of volume holograms.

Applications of volume holograms

The Bragg selectivity makes volume holograms very important. Prominent examples are:

*Distributed feedback lasers (DFB lasers) as well as distributed Bragg reflector lasers (DBR lasers) where the wavelength selectivity of volume holograms is used to narrow the spectral emission of semiconductor lasers.
*Holographic memory devices for holographic data storage where the Bragg selectivity is used to multiplex several holograms in one piece of holographic recording material using effectively the third dimension of the storage material.
*Fiber Bragg gratings that employ volume holographic gratings encrypted into an optical fiber.
Wavelength filters that are used as an external feedback in particular for semiconductor lasers [http://www.ondaxinc.com/ - Ondax, Inc.] [http://www.pdld.com/index.htm - PD LD, Inc.] [http://www.optigrate.com/ - Optigrate ] . Although the idea is similar to that of DBR lasers, these filters are not integrated onto the chip. With the help of such filters also high-power laser diodes become narrow-band and less temperature sensitive.

Footnotes