What is a wave? The one-dimensional wave equation

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2/3/14EM propagation in homogeneous materialsRelationships between the wave vector and the refractive index (theseare derived from Maxwell’s Equations):k ʹ′ = ω n rc= 2π λReal part of wave vector€€k ʹ′ ʹ′ = ω n ic= 2πνn icImaginary part of wave vectorThese are the so-called ‘dispersion relations’ relating wavelength,frequency, velocity and refractive index.Absorption of EM radiationRecall the expression for the flux density of an EM wave (Poyntingvector):F = 1 2 cε 0 E 2When absorption occurs, the flux density of the absorbed frequencies isreduced.€12
2/3/14Absorption of EM radiationThe scalar amplitude of an EM wave at locationFrom the expression for the flux density we have:xF = F 0 [ exp(−k "⋅x )] 2 = F€ 0exp(−2k "⋅x )€is:E 0exp(−k "⋅x )€Absorption of EM radiationNow substitute the expression for :And we have:k ʹ′ ʹ′For a plane wave propagating in the x-direction.€F = F 0exp(− 4πνn ix)c€€k ʹ′ ʹ′ = ω n ic= 2πνn ic13
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What is a wave? The one-dimensional wave equation

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