Note Set 1 - EM Review-1

# Note Set 1 - EM Review-1 - Essentials of Electromagnetic...

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Set 1 - Essentials of Electromagnetic Field Theory 1 Essentials of Electromagnetic Field Theory Maxwell’s equations serve as a fundamental tool in photonics Updated: 8/18/2009 11:15 AM © 2009 Henry Zmuda

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Set 1 - Essentials of Electromagnetic Field Theory 2 Light is an Electromagnetic Wave Electromagnetic waves are described by Maxwell’s Equations We will make minimal use of Maxwell’s Equations, but we will use them to establish fundamental results. © 2009 Henry Zmuda
Set 1 - Essentials of Electromagnetic Field Theory 3 Maxwell’s Equations (as used for optics) 00 CS C SS enclosed SV S B E E d B da tt D H H d D da J da D D da dv Q B B da ρρ ∂∂ ∇× = − = = ∇= = = = ∫∫ ∫∫∫    Differential Integral Form Form © 2009 Henry Zmuda

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Set 1 - Essentials of Electromagnetic Field Theory 4 Field Quantities ( ) ( ) ( ) ( ) 22 Electric Field Vector Volts/meter V/m Magnetic Field Vector Amps/meter A/m Electric Flux Density Coulombs/meter C/m Magnetic Flux Density Webers/meter Wb/m Current Density Amps/ Symbol Meaning Units E H D B J ( ) ( ) ( ) 33 meter A/m Volume Charge Density Coulombs/meter C/m Charge Coulombs C Q ρ © 2009 Henry Zmuda
Set 1 - Essentials of Electromagnetic Field Theory 5 Constitutive Relations: Free Space Permeability: 7 4 10 o µπ = × (Henrys/meter) DE BH ε µ = =  Free Space Permittivity: 9 12 10 8.854 10 36 o π = = (Farads/meter) Ohm’s Law: JE σ = ( ) ( ) dielectric permittivity Farads/meter dielectric permeability Henrys/meter f f can be tensors, i.e., , , depend on field orientation Both are generally a function of frequenc , , y f εµ © 2009 Henry Zmuda

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Set 1 - Essentials of Electromagnetic Field Theory 6 Constitutive Relations: r o ε = Dielectric Constant: Usually for optics, or n µµ = ⇒= oo n µε = Index of Refraction: © 2009 Henry Zmuda
Set 1 - Essentials of Electromagnetic Field Theory 7 The Wave Equation © 2009 Henry Zmuda

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Set 1 - Essentials of Electromagnetic Field Theory 8 The Wave Equation For linear media and a source free region of space: ( ) 2 2 , BD EH tt BH t DE E t µ µε ∂∂ ∇× = − = ∇×∇× = −∇×  0, 0 J ρ ≡≡ © 2009 Henry Zmuda
Set 1 - Essentials of Electromagnetic Field Theory 9 Identity: ( ) ( ) ( ) 2 2 2 0, , 0 E E EE t D DE r D E µε ρ ε εε ∇×∇× = ∇ ∇ −∇ = − ∇= = = = = = +∇ =   ( ) 2 E ( ) 2 2 2 0 E t r ∂∇  = −∇   =  © 2009 Henry Zmuda

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Set 1 - Essentials of Electromagnetic Field Theory 10 0 ε ∇= Single Mode Optical Fiber Multi Mode Graded Index Optical Fiber Core Cladding Buffer Air r 0 ∇≠ Core Cladding Air r Not to scale! 0 © 2009 Henry Zmuda
Set 1 - Essentials of Electromagnetic Field Theory 11 The Wave Equation For Source-Free, Linear, (Piecewise) Homogeneous Media: 2 2 2 0 E E t µε ∇− = 2 2 2 0 H H t = 0 ε ∇= © 2009 Henry Zmuda

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Set 1 - Essentials of Electromagnetic Field Theory 12 In Rectangular Coordinates: 2 2
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Note Set 1 - EM Review-1 - Essentials of Electromagnetic...

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