Ronald Driggers, Editor-in-Chief
The author is with Shimadzu Corporation, 1, Nishinokyo kuwabara-cho, Nakagyo-ku, Kyoto, 604-8511 Japan.
A new and useful method for obtaining diffraction efficiencies from
holograms manufactured practically is presented. Applying the
rigorous coupled-wave analysis, we express each difference between the
practical and the ideal as a mathematical component that can be easily
integrated. In Part 1 the effects due to thickness change in the
hologram layer (observed frequently after the development process)
are treated. Although uniform swelling or shrinking causes a simple
reconstruction wavelength or incidence-angle shift, nonuniform
thickness extends the capacity of the Bragg condition matching,
creating a diffraction efficiency curve in the asymmetric
profile. Other characteristics of diffraction are also
maintained. A refractive-index change has an effect that is similar
to the thickness change. Higher-order terms in permittivity
modulation create negligible effects in general holograms when used at
or near the simple first-order Bragg condition.
© 1998 Optical Society of America
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Definition of the holographic grating used in this
paper: (a) before and (b) after thickness change and shear
effect during processing, (c) relationship between the grating
parameters before and after processing.
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Vector diagram of incident light and diffracted light.
Exposure model geometry used in the calculations.
Diffraction efficiencies of each reflection order from an
unaffected standard hologram: (a) with cover plate, (b)
without cover plate.
Diffraction efficiencies of each transmission order from
an unaffected standard hologram: (a) with cover plate, (b)
without cover plate.
Relations between the first reflection diffraction and
swelling rate m: (a), (b) Bragg condition
matching parameter B
3,1,1 and diffraction
efficiency with constant m; (c), (d) m
and diffraction efficiency while m is expressed as a linear
function; (e)–(h) m and diffraction efficiency
while m is expressed as a parabolic function with (e),
3 = 3 and (g), (h)
3 = 10.
Relationships between the first reflection diffraction
and mean index n̅
3: (a) Bragg
condition matching parameter B
3,1,1 and (b)
diffraction efficiency with constant n̅
Influence of higher-order permittivity modulation on
reflection diffractions: (a) normal grating period with
c,3,1 = 0.05 (standard); (b)
normal grating period with Δε
c,3,1 = 0.05
c,3,2 = 0.025; (c) half-grating
period with Δε
c,3,1 = 0.05; (d)
half-grating period with Δε
c,3,1 = 0.05 and
c,3,2 = 0.025.
Absolute error from unity in the case of a swollen
hologram, shown as a dotted curve in Fig. 6(d).
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