Page 243 - Introduction to Information Optics

228 4. Switching with Optics

Typically, the required drive voltage is traded off by the modulation band-
width. Therefore, the ratio of drive power to modulation bandwidth is usually
adopted as a figure of merit of the device. The drive voltage depends upon the
type of modulator, the electrode geometry, the optical wavelength, and the
overlap geometry. In the case of lumped electrode modulators, where the
electrode length is much smaller than the modulating radio frequency
wavelength, modulation speed is constrained by the larger of the electrical or
optical transit time and the RC charging time, where C is the electrode
capacitance, including parasitics, and R is the resistance value providing
matching to driver impedance. For the electrode configuration shown in Fig.
4.20a, the capacitance, which is proportional to the electrode length L, is
usually the main limiting factor. It is given by [14, 15]

4 39
ln
C = — (1 + £/£o) —r 1 • < - )
JT \ a
In this case, the bandwidth of the modulator is
A/ = l/(2nRC). (4.40)
Obviously, one way to increase A/ is to use a small L. However, L cannot be
arbitrarily reduced because the required drive voltage scales inversely with L,
given by

L = -^£—. (4.41)

The goal in modulator design is a high bandwidth and a low driving voltage
at the same time. Modulator performance can be characterized appropriately
by introducing the voltage-bandwidth figure of merit: F = V n/B. This par-
ameter is proportional to the voltage-length product V KL and inversely
proportional to the bandwidth-length product (EL). Here BL depends on the
modulator geometrical structure. For LiNbO 3 modulators with lumped elec-
trodes, a realistic value of the bandwidth-length product is 2.2 GHz-cm, for a
load of 50 O.
The bandwidth limitations in lumped electrode modulators can be over-
come by using modulator structures based on traveling wave (TW) electrodes,
the basic scheme of which is shown in Fig. 4.21. The electrode is designed as a
matched transmission line, and the radio-frequency drive is fed collinearly with
the propagating optical signal. In this case the bandwidth is limited by the
transit, time difference between the radio-frequency drive and the optical signal
[8,14], resulting in

I Ac
g _ _____ (4 42)
nLn RF(l - n/n RF)'