ECE615_Lecture02

ECE615_Lecture02 - Lecture 2 Third-Order Polarization P(t =...

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Lecture 2 Third-Order Polarization Third-Harmonic Generation (THG) (1) (2) Energy-level description Geometry of the interaction 1 tildenosp2char tildenosp2char (3) (3) 3 0 ( ) ( ) P t E t ε χ = tildenosp2char ( ) cos( ) . . i t E t t e c c ϖ ϖ - = Ε = Ε + 3 3 1 4 4 cos ( ) cos3 cos t t t ϖ ϖ ϖ = + tildenosp2char (3) (3) 3 (3) 3 3 1 0 4 4 ( ) cos3 cos P t t t ε χ ϖ χ ϖ = Ε + Ε ϖ ϖ 3 ϖ (3) χ 3 ϖ ϖ ϖ ϖ
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2 Intensity-Dependent Refractive Index 2 nd term in (2) is nonlinear contribution to refractive index n experienced by a wave at ω. Represented as: Where: = linear refractive index = nonlinear refractive index = intensity of the incident wave 0 2 n n n I = + 0 n (3) 2 2 0 0 3 2 n n c χ ε = 2 0 0 1 2 I n c ε = Ε
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3 -Bulk material then acts as a positive lens, causing the beam toconverge. -Self-focusing can cause optical damage. nonuniform transverse intensity distribution positive lens nonlinear material Self-focusing A nonuniformintensity cross-section beam (e.g. Gaussian beam) through a nonlinear refractive index material, results in an increased refractive index for the high intensity regions of the beam.
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