Page 364 - Electrical Properties of Materials

346 Optoelectronics

Photorefractive materials represent a rather special class of crystals which
are both electro-optic and photoconductive. Some representatives of these ma-
terials are LiNbO 3 ,Bi 12 SiO 20 and BaTiO 3 . I shall return to them in the next
section.
Nonlinear materials are usually characterized by relating the dielectric po-
larization, P, to the electric field. The linear relationship given by eqn (10.5)
χ (1) is the linear susceptibility may be generalized and written in the form,
(what we called before simply $ %
2
susceptibility and denoted by P = 0 χ (1) E + χ (2) E + χ (3) E 3 . (13.3)
χ), and χ (2) and χ (3) are known
as the quadratic and cubic In some materials the nonlinearity may be more conveniently expressed
susceptibilities. with the aid of the index of refraction as

I is the intensity, n 0 is the index n = n 0 + n 2 I. (13.4)
of refraction under linear condi-
Intensity dependent absorption is also possible. In fact one of the very
tions, and n 2 is the measure of
interesting devices to be presented in Section 13.11 operates on that basis.
nonlinearity.
13.5 Volume holography and phase conjugation
I have already mentioned (Section 12.13) some of the interesting optical phe-
nomena holography can produce. I shall now briefly talk about one particular
Photosensitive medium branch of holography, known as volume holography, and discuss what hap-
pens in the simplest possible case, when both the reference beam and the
object wave
object beam are plane waves (Fig. 13.6). The distinguishing feature of volume
θ holography is that the recording process takes place in the volume of the
photosensitive material.
Let us now do a little mathematics. The amplitudes of the two waves may
be written in the form,
θ
A ref = A 10 exp[ik(x cos θ + y sin θ)] (13.5)
reference wave A obj = A 20 exp[ik(x cos θ – y sin θ)], (13.6)
Interference pattern
leading to the interference pattern (note that the intensity, I, is proportional to
y
the square of the amplitude),
2
I =|A ref + A obj | = A 2 + A 2 +2A 10 A 20 cos(2ky sin θ). (13.7)
x 10 20
Fig. 13.6 It may now be seen from the above equation that the intensity varies periodic-
Two plane waves incident upon a ally in the y-direction with a period,
photosensitive medium.
2π λ
= = , (13.8)
2k sin θ 2n sin θ
which is nothing else but the Bragg relation once more. The symbol, ,is
usually referred to as the grating spacing.
r1 is the amplitude of the modu-
After recording comes the processing (a black art for all known photo-
lation ( r1 r0 ). We may call
sensitive materials) with a result that the interference pattern is turned into
r a dielectric grating or, consid-
a modulation of the dielectric constant, that is, the end product is a dielectric
ering that the dielectric constant
constant varying as
affects the phase, a volume phase
hologram. r = r0 + r1 cos(2ky sin θ). (13.9)