Файл: Weber H., Herziger G., Poprawe R. (eds.) Laser Fundamentals. Part 1 (Springer 2005)(263s) PEo .pdf

1.1.6.1 Normalized shape functions

Normalized line shapes are introduced, which determine the relative strength of interaction.

The line shape depends on the specific interaction process. Two standard line shapes, easy to handle, are the Lorentzian and the Gaussian profiles [92Koe], shown in Fig. 1.1.12. They can be normalized di erently.

I ω

∆ω *DXVVLDQ /RUHQW]LDQ

Landolt-B¨ornstein

New Series VIII/1A1

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:

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

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].

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