Abstract
The main geometrical and quantum relationships between light and a substance are derived by characterizing the laser’s light generation, threshold, resonances, stability, multimode locking and selection, polarization and stimulated Raman phase matching towards achieving the best energy gain, intensities, and optical information on the involved states either of light or of the substance that is investigated.
Top4.2. A Laser’S Threshold Condition
Consider an EM wave that travels in the 0z direction trough a medium of molecules with energy levels 
and with the frequency 
; then, the intensity 
is given by (Demtröder 2008; Born & Wolf 1999)
(4.1) with the frequency–dependent absorption coefficient
(4.2) where
are the population densities,
are the statistical weights, and
is the cross section for the transition
. If
(4.3) then it is said that light is amplified. This process is the source of lasers; other features can come from the geometrical arrangement of an active medium, such as the following (Figure 1):
Figure 1. A laser cavity and optical principle (on the left) and physical processes inside (on the right): A) scattered light, B) transmitted light, C) emitted light, and D) absorbed light; adapted and redrawn from Demtröder (2008).
- •
The partial reflectivity of mirrors;
- •
Absorption in the windows of the cell that contains the active medium;
- •
Diffraction by apertures; and
- •
Scattering due to dust particles in the beam path or by imperfect surfaces