Light and general radiation laws. Coherence and incoherence. Emission, absorption and amplification of radiation. Units and physical constants

Table 1.1. Numerical values of wavelengths, frequencies, wave numbers and photon energy.

Wavelength	Frequency	Wave number	Quantum energy
4000	7,49	25 000	4,965
5000	6,00	20 000	3,972
6000	5,00	16 667	3,310
7000	4,28	14 286	2,837
8000	3,75	12 500	2,482
9000	3,33	11 111	2,207
Micrones
1,0	3,00	10 000	1,986
2,0	1,50	5 000	0,993
3,0	1,00	3 333	0,662

Sometimes it is desirable to relate the radiation flux density to the amplitudes of electric and magnetic fields. For a plane wave propagating in a medium with dielectric permeability and magnetic permeability , we have

(1.9)
Consequently, the quantities in question are related by
(1.10)
where E is the amplitude of the electric field.
2.1. Negative absorption

The principle of the operation of the quantum oscillator, for the sake of determinateness of reasoning, we shall consider using the example of a laser, although the basic assumptions remain for a maser. In the most general formulation, the principle of laser operation consists in the forced emission of directed coherent light radiation by an active medium transferred from an external energy source to an inverted state and having a positive feedback at the resonant frequency. This formulation is indeed quite general, since it is suitable for any design laser, but it certainly does not give an elementary idea of ​​the operation of the laser. Therefore, below we try to disclose its main provisions more popular.

Before getting acquainted with the device and the principle of laser action, let us consider some aspects of the interaction of light with matter. Let a plane monochromatic light wave with intensity and frequency fall on a layer of a homogeneous substance (Figure 2.1). When light passes through a layer of thickness dx, with a cross-sectional area of ​​unity, the intensity attenuation will be proportional to the intensity of the incident light on the surface of the layer and its thickness:
(2.1)
where is the linear absorption coefficient of the substance. Integrating (2.1) from zero to l, we obtain
(2.2)
where is the intensity of light emerging from a layer of thickness l . The formula (2.2) is the Bouguer-Lambert law.

As follows from (2.2), with a positive absorption coefficient ( > 0), the passage of light through the medium leads to a weakening of the intensity. In classical linear optics, always > 0 and, consequently, there is always a light absorption.

.

Fig. 2.1. The passage of light through a layer of thickness dx.
The dependence of I on x for > 0, according to formula (2.2), is shown in Fig. 2.2. In the same place an analogous dependence is given for = 0 and <0. This dependence gives rise to a very interesting fact: for <0, as the light flux passes through the medium, its amplification takes place, ie, absorption is negative. Is there any negative absorption in real environments? It turns out that such an absorption can be realized.

We will clarify the conditions under which the absorption coefficient of the medium becomes negative. We will consider the idealized case: we will assume that the energy levels of atoms are lines (Fig. 2.3). This means that in each state the atom has a definite energy and, under optical transitions between them, strictly monochromatic light is emitted or absorbed.

In the interaction of atoms with electromagnetic radiation, as is well known, two counterpropagating processes can occur:

1. Atoms in the ground state E₁, swallowing external radiation with energy , pass from the ground state to the excited state. The probability of such a process will be proportional to the Einstein coefficient B₁₂.

Fig. 2.2. Dependence of the intensity of radiation on the thickness of matter.


Fig. 2.3. Optical transitions between energy levels of atoms.
2. Atoms in the excited state E₂, under the influence of external radiation with energy , are forcedly transferred to the ground state, emitting a quantum with energy . The probability of such a process will be proportional to the Einstein coefficient B₂₁. This process is a forced process. The discovery of stimulated emission by Einstein in 1916 is the physical basis of lasers created in 1960. Experimental facts indicate that the radiation arising during the induced transitions is identical to the radiation created by these radiation: the frequency, directivity, polarization of both radiations are identical. This means that both the radiation, stimulated and the radiation that creates this radiation are mutually coherent.

In contrast to these two processes, there is another process, the transition of atoms spontaneously (spontaneously) from the upper E₂ state to the lower E₁ state. This process is called spontaneous. Spontaneous transitions do not have any effect on laser radiation.

Suppose that the number of atoms per unit volume at the energy levels E₁ and E₂ is equal to n₁ and n₂, respectively. In thermodynamic equilibrium, n₁ and n₂ are determined from the Boltzmann distribution:
(2.3)
(2.4)
where n₀ is the number of atoms per unit volume.

Taking into account (2.3) and (2.4)

(2.5)
Since E₂> E₁, as follows from (2.5), for thermodynamic equilibrium, always n₁> n₂ and only at an infinitely high temperature ( ) n₁ = n₂. Consequently, in a system in a thermodynamic equilibrium state, negative absorption-amplification of light-is impossible. For negative absorption to take place, there must be n₂> n₁, i.e. the number of atoms in the excited state is greater than the corresponding number in the ground state, in other words, there should be an "inverse" (inverted) distribution of atoms over the energy states.