Page 240 - Introduction to Information Optics

4.3. Fast Electro-optic Switches: Modulators 225

the optical gain changes as a result of carrier density variations. The inter-
dependence between AM and FM is governed by the line width enhancement
factor. As a result, spectral broadening and chirping exist, caused by the
current modulation. This usually affects the spectral stability of the output
optical signal.

4.3.2. EXTERNAL ELECTRO-OPTIC MODULATORS

4,3.2.1. Electro-optic Devices
The principle of electro-optic modulators is based on the linear electro-optic
effect (Pockels effect), which induces a change in the refractive index propor-
tional to an externally applied electrical field E. The magnitude of the
electro-optic effect depends on the electro-optic coefficients of the medium and
the applied electrical field. Using common notations [7], the refractive index
of the crystal can be described by the index ellipsoid. The linear changes in the
coefficients of the index ellipsoid due to an applied field of components Ej
( j — 1, 2, 3 corresponding to x, y, z components, respectively) can be expressed
by [7]

= I TtjEj i = 1, 2, . . . , 6, j = 1, 2, 3, (4.33)

where T fj is the electro-optic tensor. In the case of LiNbO 3, if a field E is
applied along the z axis, the induced index change seen by an optical field
polarized along the z direction is given by

n 3
An = T 33£,, (4.34)

where n e is the corresponding extraordinary index. It should be noted that
the EO effect depends on the orientation of the crystal and the direction of
the applied field. The coefficient T 33, which corresponds to the stronger
electro-optic effect for LiNbO 3 with applied field in z direction, is about
6
30 x 1CP jum/V. In GaAs, the higher index change is seen by an optical field
polarized along the x direction and the corresponding parameter Ti 3 is about
6
1.4 x 10~ /mi/V. InP has about the same value.
The electro-optic effect is a fast process, since it is mainly related to
electronic lattice transitions. The response time of the index change approaches
14
13
electronic lattice relaxation times, which range from 10~~ to 10~ s. There-
fore, potential modulators with a few hundreds GHz bandwidth can be built.