Page 643 - Introduction to Information Optics

11,2. Information Display Using Acousto-Optic Spatial Light Modulators 62'
When SQ/4 — 0.45n, the normalized intensity drops to about one half. Using
the definition of Q and knowing that A = vj'f B, we write

SQ/4 = 0.45*.

where f B is the center frequency at which the Bragg condition is satisfied and
t' s is the sound velocity in the acoustic medium. We then find that the
bandwidth is

1.8r sA
= 2% (11.14)
A L

The situation is shown in Fig. 1.1.8.
It seems from the above equation that the bandwidth may be increased by
reducing the interaction length L. However, there is a limit to this procedure.
The limit is set by the angular spread of the incident light X/D, where D is the
width of the light. As L becomes smaller, the spread of the sound becomes
larger. For efficient interaction, the angular spread of the sound must be
approximately equal to that of the light; i.e., A/L ~ A/D so that every plane
wave of light can interact with the sound. Hence, Eq. (11.14) becomes

1.8u
B

1 -

fa ~&B ft fa

Fig. 11.8. Bandwith estimation.