NNSE618-L14-optics

NNSE618-L14-optics - 1 Lecture contents Macroscopic...

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NNSE 618 Lecture #14 1 Lecture contents Macroscopic electrodynamics: Maxwell equations Dielectric function Reflectance Electron-radiation interaction Absorption coefficient – quantum mechanical calculation Interband absorption, direct and indirect
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NNSE 618 Lecture #14 2 Optical processes Goal: understand “microscopic” reasons for optical properties We will limit ourselves to linear isotropic optics : Polarization is linear function of electric field Interaction is scalar Interaction is local and synchronous Units: 1 eV 11600 K 8065.5 cm -1 2.141x10 14 Hz 1.2398 m m From Yu and Cordona, 2003 D P D P 4 ; ) , ( ) , ( t r t r D
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NNSE 618 Lecture #14 3 Macroscopic electrodynamics: Maxwell equations Maxwell equations describing the “coupling” of electric and magnetic fields Additional relationships in isotropic media: D H B m J t B c 1 J c t D c H 4 1  4 D 0 B
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NNSE 618 Lecture #14 4 Propagation of electromagnetic waves in a medium Taking curl of the first equation and substituting D , and B , we will have a linear equation for electric field: Looking for solution in the form of plane wave (for a Fourier component): Substituting into the wave equation, obtain the dispersion relation in the medium (wavevector is complex) or It is convenient to introduce dielectric function with real and imaginary parts: t c c t c m 4 2 t i iqr e 0 m m 2 2 2 2 4 c c i q 4 ) , ( 2 1 i i q 2 2 2 2 4 c c i q
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NNSE 618 Lecture #14 5 Dielectric function, index of refraction Wavevector can be also expressed through refraction and absorption (extinction) indexes: or for m =1 In this case solution for a plane wave is:
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NNSE618-L14-optics - 1 Lecture contents Macroscopic...

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