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Lecture3-228a

Lecture3-228a - Lecture 3 Wave Propagation in Dielectrics...

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ECE 228A Fall 2011 Daniel J. Blumenthal 3.1 Lecture 3 - Wave Propagation in Dielectrics and Basic Dielectric Properties

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ECE 228A Fall 2011 Daniel J. Blumenthal 3.2 Maxwell s Equations ∇× h = i + d t e = b t d = 0 b = 0 where e and h are the electric and magnetic feld vectors d and b are the electric and magnetic displacement vectors No ±ree charge.
ECE 228A Fall 2011 Daniel J. Blumenthal 3.3 Constitutive Relations d = ε 0 e + p b = μ 0 ( h + m ) p and m are the electric and magnetic polarizations of the medium ε 0 and μ 0 are the electric and magnetic permeabilities of vacuum e and h are the electric and magnetic ±eld vectors d and b are the electric and magnetic displacement vectors

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ECE 228A Fall 2011 Daniel J. Blumenthal 3.4 Electric Susceptibility χ (Isotropic) P = ε 0 χ ij E Isotropic Media: χ is a complex number The real part determines the index (velocity) and the imaginary part determines the gain or absorption. Isotropic media: Vacuum, gasses, glasses (optical fbers) Anisotropic media: Semiconductors, crystalline materials.
ECE 228A Fall 2011 Daniel J. Blumenthal 3.5 Electric Susceptibility χ (Anisotropic media) P = ε 0 χ ij E P i = 0 ij E j P x = 0 ( xx E x + xy E y + xz E z ) Anisotropic Media: χ is a complex second rank tensor One can always choose a coordinate system such that off axis elements are zero. These are the principal dielectric axes of the crystal. We will only use the principal coordinate system. z z y y x x E P E P E P 33 0 22 0 11 0 = = =

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ECE 228A Fall 2011 Daniel J. Blumenthal 3.6 Principal Axes D = ε 0 E + P D = E ) 1 ( ) 1 ( ) 1 ( 33 0 33 22 0 22 11 0 11 χ + = + = + = D, E and P are not parallel in general. D and E are related by the electric permeability tensor ε Principal axes can always be chosen such that D and E are parallel and the off diagonal elements of ε are zero.
ECE 228A Fall 2011 Daniel J. Blumenthal 3.7 Wave Propagation in Lossless, Isotropic Media Lossless: σ =0, χ is real, ε is real. Isotropic: χ , ε are scalors (not tensors). ∇× e = i + b t = 0 + μ h t h = i + d t ( e ) = μ ( h ) t = μ 2 d 2 t = μ ε 2 e 2 t ( e ) = 2 e − ∇ ( e ) 2 e = μ 2 e 2 t Wave Equation

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ECE 228A Fall 2011 Daniel J. Blumenthal 3.8 Wave Equation e ( x , y , z , t ) = Re[ E ( x , y , z ) e i ω t ] 2 E + 2 μ ε E = 0 2 E + k 2 E = 0 where k = = n / c c = 1 / 0 0 n = 0 0
ECE 228A Fall 2011 Daniel J. Blumenthal 3.9 Radiation and Atomic Systems Chapter 5, Yariv

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Lecture3-228a - Lecture 3 Wave Propagation in Dielectrics...

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