ECE615_Lecture_18

ECE615_Lecture_18 - Lecture 18 Second Harmonic...

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Lecture 18 * 3 ( | | ) ( ) ( ) 0 ij i i V i er E i eE r r r d r ψ ψ = - = - = arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp ɶ ɶ Second Harmonic Susceptibility: Resonant Case ϖ ϖ 2 ϖ (0) 11 1 ρ = ˆ ˆ , nm nm nm nm nm nm i i V ρ ϖ ρ ρ γ ρ = - - - ɺ (1) (0) i i ϖ γ ρ ρ ρ + = - - i ρ i ρ ( 29 nm nm nm nv vm nv vm nm nm v i i V V ρ ϖ ρ ρ ρ γ ρ = - - - - ɺ is the only element in the 1 st order. 1 21 21 21 21 11 23 31 i V V t 22 21 V 23 31 V ( 21 21, exp . . V E i t c c γ γ μ ϖ = - - + [ ] (1) 21 21 exp i t ρ δ ϖ = - ( 29 (1) 21 21 21 21, i i E t γ γ ϖ ϖ γ δ μ + - + = ( 29 [ ] 21, (1) 21 21 21 1 exp E i t i γ γ μ ρ ϖ γ ϖ ϖ = - - + + 21 ρ
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( 29 31 31 31 3 1 3 1 31 31 v v v v v i i V V ρ ϖ ρ ρ ρ γ ρ = - - - - ɺ 11 33 22 0 V V V = = = 33 31 V ρ 32 21 31 11 V V ρ ρ + + 33 31 V ρ - 32 21 V ρ - 31 11 V ρ - symmetry off-resonant higher-order symmetry (2) (1) 31 31 31 32 21 i i V t ϖ γ ρ ρ + + = - [ ] (2) (2) 31 31 exp 2 i t ρ δ ϖ = - ( 32 32, exp . . V E i t c c α α μ ϖ = - - + ( 29 ( 29 32, 21, (2) 31 31 31 2 21 21 2 E E i i i β β γ γ μ μ γ ϖ ϖ δ ϖ ϖ γ + - = - - ( 29 ( 29 ( 29 32, 21, (2) 31 2 21 21 31 31 exp 2 2 E E i i t i i β γ β γ μ μ ρ ϖ ϖ ϖ γ ϖ ϖ γ = - - - - -     ( ( 31 13, ˆ ˆ ( ) tr . . ( )exp 2 . . t c c d i t c c α α α μ ρμ ρ μ ϖ
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