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ECE615_Lecture03

# ECE615_Lecture03 - Lecture 3 Definition of Nonlinear...

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Unformatted text preview: Lecture 3 Definition of Nonlinear Susceptibility 1 Given: Material with dipsersion and/or loss (1) Note: * is complex and frequency dependent. * Prime (‘) in (1) denotes sum over only positive frequencies Now: (2) Where Note are real And Then (3) where t t t ' ( , ) ( , ) . . ( , ) n n n n E r t E r t c c E r t = + = ∑ ∑ ch ch ch h h h χ t t t ( ) ( ) n n n E E E +- = + ch ch ch (+),(-) denote positive and negative frequencies t t ( 29 ( ) exp n n n E E i t ϖ + = ⋅- ch ch t t t ( 29 ( ) ( )* exp n n n n E E E i t ϖ- + = = ⋅ ch ch ch t ( , ) E r t ch h ( 29 ( ) exp n n n n E r E A ik r = = ⋅ ch h ch ch h h t t ( 29 ' ' ( , ) ( , ) . . exp n n n n n n E r t E r t c c A i k r t ϖ = + = ⋅- ∑ ∑ ch ch h h ch h h ( ) ( ) n n n n E E A A ϖ ϖ = = ch ch ch ch 2 Reality condition then becomes: or (4) therefore (5) Now, the field is represented by or (6) * * ( ) ( ) ( ) ( ) n n n n n n E E A A ϖ ϖ ϖ ϖ- =- = ch ch ch ch t ( 29 ( 29 ( , ) ( ) exp ( ) exp n...
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