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Lecture 7 Electro Optic Modulator The index of refraction is not constant but depends on the electric field ( )= + + Pockels Effect Kerr Effect In uniaxial crystal le , , given by + + be the principle axes of the index ellipsoid (indicatrix) so that ellipsoid is =1 But in the ---- coordinate system , , 1 + 1 + 1 1 + the general indicatrix is 2 + 1 2 + 1 2 =1 So in general there are 6 components of the index of refraction For the linear electro optic effect (Pockels effect) : ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ∆ ∆ ∆ ∆ ∆ ∆ ⎤ ⎥ ⎥ ⎥ ⎥= ⎥ ⎥ ⎥ ⎦ ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥∗ ⎥ ⎥ ⎦ The Electro-Optic Tensor Quadratic Electro Optic Effect ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ∆ ∆ ∆ ∆ ∆ ∆ ⎤ ⎥ ⎥ ⎥ ⎥= ⎥ ⎥ ⎥ ⎥ ⎦ ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ ⎤ ⎢ ⎥ ⎢ ⎥∗⎢ ⎥ ⎢2 ⎥ ⎢ 2 ⎦ ⎣2 ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ Example: GaAs Isotropic (Cubic) Crystal 0 0 0 ⎡ ⎢ =⎢ ⎢ ⎢ ⎣ 0 0 0 0 0 0 0 0 0 0 0 ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ 0 ( / ) ( = 0.9 ( / ) ( = 1.15 = 3.6 = 1.1 ∗ 10 = 1.43 ∗ 10 ) ) Example: LiNbO3 Uniaxial Crystal 0 ⎡ 0 ⎢ = ⎢ 0 ⎢ 0 ⎢ ⎣ - ̇ - ⎤ ⎥ ⎥ 0 ⎥ 0 ⎥ 0 ⎦ 0 0 = 9.6 = 6.8 = 30.9 = 32.6 1 =∆ 1 + 1 = ∆ 1 + 1 =∆ 1 1 + 1 =∆ 1 ( / ) ⃑ // For case of GaAs, let the external field ∆ 10 2 = 0, ∆ +2 1 = ( )=0 So the spherical indicatrix is changed to ellipsoid with the O.A. in the direction of the applied electric field rotating , coordinate 45 degree we get the principle axis. = =− = = = = + ∅ + ∅ − ∅ −2 +2 − + + − + [ −2 + ]+( 1 +( 1 ) +2 [ 1 )[ − +2 + − + ] ]=1 Since 1 1 + + + −2 1 2 + 1 + −2 2 + +2 ( − 1 ) =0 We should find the angle ∅ so that the coefficient of . In the case of isotropic material (GaAs) ) = 0 and ∅ = 45 . = = . So ( − So the indicatrix becomes 1 1 = +2 1 1 + −2 +2 1 + −→ =0 = (1 + = 1+ ) = Example of Phase Modulation 1. Transverse Modulation 2 ( + ∆∅) ∅= ∆∅ = 1− V K z d 2 L K 2. Longitudinal Modulation 2 ∆∅ = z V d L Example of Polarization Modulation The polarization is orientation to make the angle is 45 with the decomposed into components. = cos( − 2 ), The phase difference between = and ∆∅ = − = − − − = − − − cos( − 2 and so the light is ) is , If ∆∅ = 0 No change of polarization ∆∅ = Linear polarization ∆∅ = /2 Circular polarization ℎ Elliptical Polarization For Longitudinal Modulation , For Transverse Modulation Optical Kerri Effect: The refractive index changes in a function of the light intensity. The part of the polarization vector that gives rise to this effect is: ( )( ( )=3∈ The total Polarization is ( )= + ( ) Where = =∈ +3 ( )| − ) ( ) + ( ) ( )+3∈ ∗( ) ( )=3∈ ( )| ( )| ( )( ( )=∈ ; , , ) | ( )| ( ) ( ) ( )| =1+ = + |< = + |< ( ) >| = 2 ( ) ( ) >|. ∗( ∈ 1 ) = 2| ( )| 2 By using equation 1 and equation 2 =1+ ( ) , = ( ) ∈