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19690529 Coupled Wave Theory For Thick Hologram Gratings Herwig Kogelnik

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19690529 Coupled Wave Theory For Thick Hologram Gratings Herwig Kogelnik
THE BELL SYSTEM

TECHNICAL JOURNAL
DEVOTED TO THE SCIENTIFIC AND ENGINEERING
ASPECTS OF ELECTRICAL COMMUNICATION

November

Volume 48
Copyright

©

1969,

Number

19P9

9

American Telephone and Telegraph Company

Coupled Wave Theory for Thick

Hologram Gratings
By

HERWIG KOGELNIK

(Manuscript received

A thick May

23, 1969)

coupled wave analysis is given of the Bragg diffraction of light by hologram gratings, which is analogous to Phariseau 's treatment of

acoustic gratings

and

to the

"dynamical" theory

of

X-ray

diffraction.

The

theory remains valid for large diffraction efficiencies where the incident

wave

is strongly depleted. It is

reflection holograms. Spatial

applied

to

transmission holograms and

to

modulations of both the refractive index and

the absorption constant are allowed for.

The

effects of loss

of slanted fringes are also considered. Algebraic

in the grating and

formulas and their nu-

merical evaluations are given for the diffraction efficiencies and the angular

and wavelength
I.

sensitivities of the various

hologram types.

INTRODUCTION
Holographic recording in thick media ("volume recording")

particular interest for high-capacity information storage,
4

holography and for

efficient white-light display of

high efficiency of light conversion which electric it

holograms

is

is

or fly 's eye lenses) in

In thick holograms

a variety it is

of

for color

holograms.

5-9

The

attainable with thick di-

also important for microimaging,

practical to use holographic optical

is

1-3

components

(for

and

it

may make

example, gratings

of optical systems.

light diffraction at or near the
2909

Bragg angle

2910

THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER

1969

which leads to efficient wavefront reconstruction. This is true for both transmission and reflection holograms, and both types are considered in this paper. The (volume) record of the holographic interference pattern (fringe pattern) usually takes the



References: Opt., 2, No. 4 (April 1963), pp. 393-400. Disclosure Bull., 8, No. 11 (April 1966), p. 1581. Field of Its Scattered Radiation," Opt. Spectroscopy, 15, No. 4 (October 1963), pp (March 1966), pp. 368-370. Reconstruction," Appl. Phys. Letters, 8, No. 11 (June 1966), pp. 286-287. Shankoff, T., "Phase Holograms in Dichromated Gelatin," Appl. Opt., 7, No. 10 (October 1968), pp 14, No. 5, (March 1969), pp. 159-160. Leith, E. N., Kozma, A., Upatnieks, J., Marks, J., and Massey, N., "Holographic Data Storage in Three-Dimensional Media," Appl. Opt., 5, No. 8 (August 1966), pp Klein, W. R., "Theoretical Efficiency of Bragg Devices," Proc. IEEE, 54, No. 5 (May 1966), pp

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