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Unformatted text preview: Lecture 2: Dispersion in Materials 5 nm Course Info Course webpage Is now up and running www.ecepurdue.edu/~shalaev Let me know what you think! Topics ? Format ? Direct questions Ask questions any time. Big comments on the nano course are most welcome! Speed of the EM wave: Compare 2 2 1 1 r r c v = = Previous Lecture: Maxwell + Wave Equation 2 2 2 r t = E E and general wave Equation: Where c 2 = 1/( ) = 1/((8.85x1012 C 2 /m 3 kg) (4 x 107 m kg/C 2 )) = ( 3.0 x 10 8 m/s) 2 ( 29 ( 29 2 2 2 2 , 1 , r t r t v = U U t Refractive index is defined by: Optical refractive index 1 r c n v = = = + Note: Including polarization results in same wave equation with a different r c becomes v 3.0 3.4 index: n Refractive Index Various Materials 2.0 1.0 0.1 1.0 10 ( m ) Refractive in ( 29 ( 29 ( 29 { } , Re , exp z t z ikz i t = + E E ( 29 ( 29 2 2 2 2 2 , , t n t c = E r E r t Derived from wave equation Dispersion Relations Dispersion relation: = (k) Substitute: Result: 2 2 2 2 n k c = Check this! 2 2 2 2 c k n = 1 r g d c c c dk k n v = = = = + k g v Phase velocity: Group velocity: ph v k A z Absorption and Dispersion of EM Waves EM wave: ( 29 ( 29 ( 29 { } , Re , exp z t z ikz i t = + E E 2 2 2 2 c k n = Dispersion relation k n c = ' '' n n in = + Absorbing materials can be described by a complex n: '' ' '' n in n i n i + = +  follows that: Transparent materials can be described by a purely real refractive index n ( 29 ' '' ' '' 2 k n in n i n i c c c = + = +  It follows that: Investigate + sign: ( 29 ( 29 , Re , exp 2 z t z i z z i t = + E E Traveling wave Decay ' ' n kn c = = Note: n acts as a regular refractive index 2 '' 2 '' n kn c =  =  is the absorption coefficient Summary and Future Directions Maxwells Equations f = D = B =  B E t = + D H J t Curl Equations lead to 2 2 2 2 2...
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 Fall '08
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