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
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