ECE615_Lecture07

ECE615_Lecture07 - Lecture 7 Time-Domain Description of...

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Unformatted text preview: Lecture 7 Time-Domain Description of Optical Nonlinearities Frequency-Domain (FD) descriptions of nonlinearities apply to monochromatic input fields. FD relates the nonlinear polarization to the input field Time-Domain (TD) descriptions of nonlinearities apply to arbitrary input fields. FD relates the nonlinear polarization to the input field TD is useful for short pulses and transient fields. FD and TD descriptions are entirely equivalent, and are chosen for convenience. ( ) P ϖ ( ) E ϖ ( ) P t ( ) E t 1 (1) where is linear response function relating response at time to input at time for all as required by causality (1) (1) ( ) ( ) ( ) P t R E t d ε τ τ τ ∞ =- ∫ ɶ ɶ (1) ( ) R τ (1) P ɶ ( ) t E ɶ ( ) t τ- (1) ( ) R τ = τ < Time-Domain to Frequency-Domain through Fourier Transform (FT/IFT) FT: (2) IFT: (3) Inverse Fourier Transform (IFT) of (1) (4) ( 29 ( ) ( ) exp E E t i t dt ϖ ϖ ∞-∞ = ⋅ ∫ ɶ ( 29 1 ( ) ( ) exp 2 E t E i t d ϖ ϖ ϖ π ∞-∞ = ⋅- ∫ ɶ...
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ECE615_Lecture07 - Lecture 7 Time-Domain Description of...

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