Page 241 - Introduction to Information Optics

226 4. Switching with Optics

The change in refractive index induced by the EO effect will produce a phase
change to the optical beam passing through the crystal. The total phase change
over an interaction length L (equal to the electrode length) is a function of the
refractive index change An. It is expressed by

(4.35)
/ 0
where /L 0 is the free-space wavelength.
Electrically induced index change can be directly used for phase modulation.
Amplitude modulation can be achieved via phase modulation, either by using
interferometric techniques (Mach-Zehnder modulator, balanced bridge
switch) or by phase-matched control in directional couplers.

4,3.2.1,1. Waveguide Phase Modulator
A typical waveguide phase modulator with two electrode configurations is
shown in Fig. 4.20. If the electrodes are placed on either side of the waveguide
(Fig. 4.20a), the horizontal component of the electric field is used. If one
electrode is placed directly over the waveguide (Fig. 4.20b), the vertical
component of the field is used. The crystal orientation must be chosen to use
the largest electro-optic coefficient. For a LiNbO 3 modulator, the largest
electro-optic coefficient, T 33, should be used, and the orientation of the crystal
is shown in Fig. 4.20a for the TE wave polarized in the plane of the substrate.
LiNbO 3 waveguides are commonly fabricated using the Ti in-diffusion
process. In the process, Ti stripes with a thickness of 50-60 nm and a width of
5 /mi are evaporated onto a LiNbO 3 crystal and in-diffused at a proper
temperature for a few hours. This creates waveguides with Gaussian index
distribution in depth. The maximum index increase at the surface of the
LiNbO 3 waveguide is typically a few hundredths.
Using the scheme shown in Fig. 4.20a, the relationship between the effective
electro-optically induced index change and the applied voltage can be ex-
pressed as

(436)

where d is the interelectrode gap and F is the overlap integral between the
applied electric field and the optical mode. The phase change over an
interaction length L is thus expressed as

nnf, VL
A^-^T,, —F. (4.37)
A n " d