Electro-Optic Crystals

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. For KD*P crystal, for example, the change of the refractive index (Dn) is Dn = 0.5n³_or₆₃E if both the directions of light propagation and electric field are along the z-axis, where n_ois refractive index without electric field and r₆₃ is electro-optic coefficient of KD*P.

If a linearly polarized light passes through an E-O crystal, the phase retardation (G) will be induced by Dn to G = 2pDnL, where L is crystal length, for KD*P, again as an example, G = pLn³_or₆₃E/l. 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, the output intensity of light will be I = I₀sin²(G/2), where I₀ 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. 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. The LiNbO₃, MgO:LiNbO₃, ZnO:LiNbO₃, BBO and KTP crystals are usually employed in this scheme.

The half-wave voltage (V_p) is defined as the voltage at G = p, for example, Vp=l/(2n_o³r₆₃)for KD*P and Vp=ld/(2n_o³r₂₂L) for LiNbO₃, where lis light wavelength and d is the distance between the electrodes.

Longitudinal Modulator

transverse modulator