A Short Introduction to Laser Physics
To study the influence of light on the dynamics of an atom or a molecule experimentally, laser light sources are used most frequently. This is due to the fact that lasers have well-defined properties. The theory of the laser dates back to the 1950s and 19
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To study the influence of light on the dynamics of an atom or a molecule experimentally, laser light sources are used most frequently. This is due to the fact that lasers have well-defined properties. The theory of the laser dates back to the 1950s and 1960s of the twentieth century and by now, 50 years later is textbook material. In this introductory chapter, we start by recapitulating some basic notions of laser theory, which will be needed to understand later chapters. More recently, experimentalists have been focusing on pulsed mode operation of lasers with pulse lengths of the order of femtoseconds, allowing for time-resolved measurements. At the end of this chapter, we therefore put together some aspects of pulsed lasers that are important for their application to atomic and molecular systems.
1.1 The Einstein Coefficients Laser activity may occur in the case of nonequilibrium, as we will see later. Before dealing with this situation, let us start by considering the case of equilibrium between the radiation field and an ensemble of atoms in the walls of a cavity. This will lead to the Einstein derivation of Planck’s radiation law. The atoms will be described in the framework of Bohr’s model of the atom, allowing the electron to occupy only discrete energy levels. For the derivation of the radiation law, the consideration of just two of those levels is sufficient. They shall be indexed by 1 and 2 and shall be populated such that for the total number of atoms N = N1 + N2
(1.1)
holds. This means that N2 of the atoms are in the excited state with energy E2 and N1 atoms are in the ground state with energy E1 . Transitions between the states shall be possible by emission or absorption of photons of the appropriate energy. The following processes can be distinguished:
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1 A Short Introduction to Laser Physics
Absorption of light leading to a transition rate dN2 = ρN1 B12 dt abs
(1.2)
from the ground to the excited state. • Induced (or stimulated) emission of light leading to a transition rate dN1 = ρN2 B21 (1.3) dt emin for the population change of the ground state. • Spontaneous emission of light leading to a rate dN1 = N2 A dt emsp
(1.4)
which amounts to a further increase of the ground state population. The first two processes are proportional to the energy density ρ of the radiation field with the constants B12 , respectively, B21 . The process of spontaneous emission does not depend on the external field and is proportional to A. These coefficients are called Einstein’s A- and B-coefficients. In thermal equilibrium, the rate of transition from level 1 to 2 has to equal that from 2 to 1, leading to the stationarity condition N1 B12 ρ = N2 B21 ρ + N2 A.
(1.5)
This equation can be resolved for the energy density ρ leading to ρ = (N1 B12 /(N2 B21 ) − 1)−1 A/B21 .
(1.6)
Furthermore, in thermal equilibrium, the ratio of populations is given by the Boltzmann factor according to E1 − E2 (1.7) N1 /N2 = exp − kT with the temperature T and the Boltzmann constant k. As T → ∞ also ρ → ∞, and we can
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