When an electric field (E) is applied to an electro-optic (E-O) crystal, the refractive index of E-O crystal will change linearly to electric field. The phenomenon is called linear electro-optic effect.
If a linearly polarized light passes th rough an E-O crystal, the phase retardation (G) will be induced by ?n to G = 2p ?n L, where L is crystal length, for KD*P as an example, G = pLn3o r63 E/?. It is clear that the phase of light will change together with electric field (E). This is called electro-optic Phase modulation. If two crossed polarizers are placed at input and output ends of E-O crystal separately as shown in Fig.32, the output intensity of light will be l =Io sin2 (G/2), where Io is input intensity. That means the intensity or amplitude of light can also be modulated by electric field. This is called amplitude modulation
There are two kinds of E-O modulations. One is longitudinal E-O modulation if the directions of electric field and light propagation are the same (as shown in Fig.1). The KDP isomorphic crystals are normally used in this scheme. If the directions of electric field and light propagation are perpendicular, it is called transverse E-O modulation (as shown in Fig2.). The LiNbO3, MgO:LiNbO3, ZnO:LiNbO3, BBO and KTP crystals are usually employed in this scheme.
The half-wave voltage (vp) is defined as the voltage which makes G = p. for example, Vp =?/(2nr63) for KD*P and Vp =?d/(2n r22 L) for LiNbO3, where ? is light wavelength and d is the distance between the electrodes.