What is a wave? The one-dimensional wave equation

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2/3/14The relativephase ofemitted lightwith respect tothe input lightdepends on thefrequency.The emitted light is90° phase-shiftedwith respect to theatom’s motion.Belowresonanceω > ω 0Electric fieldat atomElectroncloudEmittedfieldWeakemission.90° out ofphase.Strongemission.180° outof phase.Weakemission.-90° outof phase.Courtesy Prof. Rick Trebino, Georgia TechRefractive index (n) – the dispersion equationn = 1+q 2e2ε 0m∑kq e = charge on an electronε 0 = electric constantm = mass of an electronN k € = number of charges (oscillators) of type k per unit volumeω = angular frequency of the EM radiationω k = resonant frequency of an electron bound in an atomγ = ‘damping coefficient’ for oscillator k (oscillation cannot be permanent)What is the refractive index of visible light in air?What happens as the frequency of EM radiation increases at constant ω k ?What happens if the resonant frequency is in the visible range?What happens if ω > ω k ? e.g., shine x-rays on glass, or radio waves on freeelectrons.N kω k2− ω 2 + iγ kω16
2/3/14Refractive index (n) of water and icePenetration depth of water and ice(also called absorption depth or skin depth)17
Page 1 and 2: 2/3/14Mathematical description ofEM
Page 3 and 4: 2/3/14What about a harmonic wave?E
Page 5 and 6: 2/3/14Dispersion: phase/group veloc
Page 7 and 8: 2/3/14Waves as rotating vectorsWave
Page 9 and 10: 2/3/14Waves using complex amplitude
Page 11 and 12: 2/3/14EM propagation in homogeneous
Page 13 and 14: 2/3/14Absorption of EM radiationThe
Page 15: 2/3/14The Forced Oscillator:The rel
Page 19: 2/3/14Complex refractive index of v

What is a wave? The one-dimensional wave equation

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