Model a nitrogen-like gas as having two independent classes of bound electron

PHYSICS · Subjective · Fermi University Physics · Optics & Photonics · Wave propagation and light in media · Wave propagation and light in media

Optics and Photonics, Ch Light as an electromagnetic wave in matter

Problem

Model a nitrogen-like gas as having two independent classes of bound electron. A fraction

f_1

of the electrons behave as Lorentz oscillators with resonance frequency

\omega_{01}

and negligible damping; the remaining fraction

f_2 = 1-f_1

behave as a second, independent set of oscillators with resonance frequency

\omega_{02}

, also with negligible damping. The total number density of active electrons is

N

. (a) Starting from the equation of motion of one electron of each class driven by the field

E = E_0 e^{-i\omega t}

(complex representation, CV3), derive the dilute-gas refractive index

n - 1 \approx \frac{Ne^2}{2\epsilon_0 m_e}\left[\frac{f_1}{\omega_{01}^2-\omega^2} + \frac{f_2}{\omega_{02}^2-\omega^2}\right].

(b) Show that this reduces to the single-resonance dilute formula of the chapter when

f_2 \to 0

. (c) Evaluate

n-1

for this gas at a wavelength of 550 nm, given

N = 2.5\times10^{25}

^{-3}

f_1 = 0.80

\omega_{01} = 2.0\times10^{16}

rad s

^{-1}

f_2 = 0.20

\omega_{02} = 3.5\times10^{16}

rad s

^{-1}