28	1.1.6 Line shape and line broadening	[Ref. p. 40

1.1.6.2 Mechanisms of line broadening

1.1.6.2.1 Spontaneous emission

The spontaneous emission decay time Tsp of quantum dot lasers can be influenced by the geometry [97Scu], but for all macroscopic laser systems it is equal to the free-atom decay and related to the dipole moment (see Sect. 1.1.5.2). The line width of the power spectrum is ∆ ω = 1/Tsp . The line shape is Lorentzian for undisturbed systems.

1.1.6.2.2 Doppler broadening

In thermal equilibrium the particles in a gas have a Maxwellian velocity distribution of the velocity v:

						mAv2/2
h(v) =		mA		exp	−			(1.1.95)
		2π κT				κT

with

mA : atomic mass,

κT : thermal energy of the particles.

The resonance frequency of a transition is shifted by the Doppler e ect

∆ ω = ωAv/c0 .

Replacing the velocity in (1.1.76) by the frequency, delivers for the resulting spectral distribution a Gaussian line shape (1.1.74) with the width

ωA				mAc02
∆ ωD	=			8 κT ln 2	.		(1.1.96)

Some numbers are compiled in Table 1.1.5.

Table 1.1.5. Doppler and collision broadening for a thermal energy of κT = 1 eV. The Doppler broadening refers to ωA = 1015 s−1, the collision broadening holds for a pressure of p = 133 Pa (1 torr) [81Ver, 01Men].

Gas	Doppler broadening	Collision broadening
	∆ ωD [1010 s−1]	∆ ωC [107 s−1]
H2	5.6	2.8
He	4	1.3
Ne	1.8	0.8
CO2	1.2	1.2
Ar	1.5	9

1.1.6.2.3 Collision or pressure broadening

Elastic collisions between radiating atoms imply no energy loss, but a discontinuous jump in the phase of the emitted field. The average temporal length of the wave trains, in the undisturbed case

Landolt-B¨ornstein

New Series VIII/1A1