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2.3 Chromatic Aberration
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Despite the advantages of diffractive lenses discussed in the previous
chapter, they are dispersive and suffer from large chromatic aberration. The
effect of this chromatic aberration on fiber coupling must be examined if
diffractive lenses are to be used in fiber applications.
The focal length of a diffractive lens is a function of wavelength and
varies according to, 29 (W-fr)/. 2
where
and fo are the design wavelength and focal length of the lens,
respectively, and f(X.) is the focal length at a wavelength X. The transmittance
function of this diffractive lens is given by, 29
-j—— r 2
t(r) = e ^6, 2.16
When illuminated by a monochromatic plane wave of wavelength X the
amplitude transmitted by the lens is approximately,
Uo(r) = e"V x/ . 2.17
This may be rewritten using Equation 2.15 as
Uo(r) =e'"kf e' x 2.18
The phase change in waves due to chromatic aberration is thus, 30