Page 369 - Electrical Properties of Materials

Acousto-optic interaction 351

Conventional
mirror

Phase
conjugate
mirror
Fig. 13.11
A divergent beam reflected by
(a) a conventional mirror, (b) a phase
(a) (b) conjugate mirror.

13.6 Acousto-optic interaction

We have seen that periodic variation of the dielectric constant within a volume
of material may help to produce a diffracted beam by the mechanism of Bragg
interaction. The periodic variation may be achieved by using photosensitive
and photorefractive materials, but there is one more obvious possibility which
we shall now discuss. An acoustic wave propagating in a material will cause a
strain, and the strain may cause a change in the dielectric constant (refractive
index). The relationship between the change in the dielectric constant and the
strain is given by the so-called strain–optic tensor. In the simplest case, when
only one coefficient needs to be considered, this may be written in the form,

1
= pS, (13.10)
r
where p is the photoelastic coefficient, and S is the strain. Thus, we can produce
a volume hologram simply by launching an acoustic wave. But is a volume
hologram much good if it moves? Well, it is all relative. For us anything mov-
ing with the speed of sound appears to be fast, but for an electromagnetic
wave which propagates by nearly five orders of magnitude faster than a sound
wave, the hologram appears to be practically stationary. There is, however, an
effect characteristic to moving gratings that I must mention, and that is the
Doppler shift. The frequency of the electromagnetic wave is shifted by the
frequency of the acoustic wave; an effect that becomes occasionally useful in
signal processing.
Let us now work out the frequency of an acoustic wave needed to deflect an
optical wave of 633 nm wavelength (the most popular line of a He–Ne laser)
by, say, 2 . The Bragg angle is then 1 . Taking further LiNbO 3 as the material
◦
◦
in which the waves interact, we find for the grating spacing,
is the required wavelength of the
λ 633 × 10 –9 acoustic wave.
= = =7.92 μm, (13.11a)
2n sin θ 2 × 2.29 × sin 1 ◦
This is regarded as quite high
3
Noting that the velocity of a longitudinal wave in LiNbO 3 is 6.57 × 10 ms –1 frequency, which cannot be ex-
[see Table 13.3], we find for the frequency of the acoustic wave cited without exercising due care,
8
f =8.30 × 10 Hz. but nevertheless such an acous-
A device which can deflect an optical beam can, of course, be used for tic wave can be produced in bulk
modulation as well. When the acoustic wave is on, the power in the trans- LiNbO 3 and can be duly used for
mitted beam decreases, and a diffracted beam appears. Thus, by varying the deflecting an optical beam. The
amplitude of the acoustic wave, both output beams are modulated. It may be device is known as a Bragg cell.