Electro-Optical Effect and Crystals

BBO,   KTP,   KD*P,  LN, RTP crystals for E-O

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 (Δn) is Δn = 0.5no3γ63E if both the directions of light propagation and electric field are along the z-axis, where no is refractive index without electric field and γ63 is electro-optic coefficient of KD*P.   

If a linearly polarized light passes through an E-O crystal, the phase retardation (Γ ) will be induced by Δn: Γ = 2πΔnL/λ,  where L is the crystal length, λ the light wavelength. For KD*P, again as an example, Γ = πLno3 γ63E/λ. 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 = I0 sin2(Γ/2), where I0 is the 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 (Vπ) is defined as the voltage at which
Γ = π. For example, Vπ=λ/(2no3 γ63) for KD*P and Vπ=λd/(2no3 γ22L) for LiNbO3, where λ is light wavelength, d the distance between the electrodes and L the crystal length.    

BBO for EO

KD*P for EO

LiNbO3 for EO

KTP for EO

RTP for EO