Question

49. A normalized Lorentzian function may be written Its maximum value of 1/(π7) occurs at x-0. The half-width at half maximum is y. The area under the peak is unity (a) Prove the preceding statements. (b) Consider a dilute system of N oscillators per unit volume embedded in a dielectric medium. The oscillators have charge q, mass m, natural frequency ω oscillator strength fand damping time τ, where ωοτ > 1. The medium itself has no absorption near to, so that its index of refraction n may be treated as a real constant number for ω near coo. Show that for ω near 000, the absorption coefficient is well approximated by 2mceo _ 9n Change variables fy (a)-(00); to 1/λ-co/2nc (c) (wave- numbers). Show that where i, = 2x/a, represents the vacuum wavelength of light at the plasma frequency The integral is to be taken over the wavenumber range about the resonance peak where K is nonzero.

Answer 1

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