Quantum optics. Thermal radiation.
Section of optics which studies phenomena that manifest the quantum properties of light

§1 the Thermal radiation and the luminescence

 Bodies emission of electromagnetic waves of light (a light body) may be due to different types of energy. The emission of electromagnetic waves by the internal energy bodies is called thermal radiation. All other types of glow excited by any form of energy other than the internal (thermal), is called luminescence. Depending on the nature of the radiation energy the following types of luminescence:
1) chemiluminescence - energy radiation by chemical reactions (eg, oxidation of phosphorus in the air - in hours, Christmas toys, etc.);

2) cathodoluminescence - glow solid when bombarded by electrons (CRT - cathode ray tube in oscilloscopes, CRT TV, etc.);

3) electroluminescence - glow in solids under the influence of an electric field (neon lamps, fluorescent lamps, mercury lamps, arc discharge, LED, etc.);

4) photoluminescence - glow in the absorption of the incident electromagnetic radiation on the body (road signs);

5) scintillation - glow in the absorption of ionizing radiation (scintillation detectors).

Luminescence, which immediately stops at the end of the exciter of light, called fluorescence, and last for a long time after the termination of the exciter of light - phosphorescence.
Thermal radiation is electromagnetic radiation excited by the energy of the motion of atoms and molecules (the internal energy of the bodies). Thermal radiation is characteristic of all bodies at temperatures above absolute zero. T = 0 K = 273,15 ° C.

1 - body;

2 - thermostat.

W_abs = W_rad - equilibrium thermal radiation.

Thermal radiation is in equilibrium, that is, the energy that is supplied to the body and the body is emitted, are equal. If the emitting body is not getting the energy (heat) from the off, it cools. Thermal radiation is subject to self-regulation. Assume that the body radiates more energy than it absorbs. As a result of its internal energy decreases, therefore, the body temperature decreases, respectively, the radiation intensity decreases, and it will happen as long as the equilibrium process will begin, in which W_rad = W_abs. Processes associated with the establishment of equilibrium thermal radiation explained by the dependence of the intensity of thermal radiation from the body temperature. At low temperatures the bodies emit invisible infrared radiation.

With high - red glow. Incandescent body give white glow.

Of all the types of radiation equilibrium can only be thermal radiation. By equilibrium processes apply the laws of thermodynamics, so thermal radiation can be described using the laws of equilibrium thermodynamics.

§2 the emissivity coefficient of absorption capacity.

Black body

Quantitative characteristic of the thermal radiation is a power spectral density of luminosity - emissivity ability (r_ν,T) - determines the amount of energy radiated per unit surface area of the emitting body per unit time per unit frequency range from ν to ν + dν

                                                          (1)

 [r_ν,T] = J/m²

Where r_ν,T - is a function of frequency and temperature. Used as recording r_λ,T - a function of wavelength and temperature. We find the connection between them.
From (1) that

Because λ = с/ν, therefore

Where с -  the speed of light, which is equal 3·10⁸  m/s,

The second characteristic of the thermal radiation is absorption - а_ν,Т, which is also a function of frequency and temperature. Absorption capacity а_ν,Т (or absorption coefficient) indicates how much energy per unit of time of the incident by one flat surface of the body is absorbed.

а_ν,Т ≤ 1, [а_ν,Т] = l (dimensionless).

The body, the absorption coefficient is equal to 1 is called absolutely black body (a.b.b.). A black body is able to absorb fully at any temperature all incident radiation on the body at any frequency.

Black body not exist in nature, but the black, black velvet, pupil of the eye in a certain frequency range in properties close to the absolutely black body.

The ideal model of a black body is a closed cavity with a small hole. A ray of light in the cavity as a result of multiple reflections from the walls completely absorbed. The smaller the hole, the lower the intensity of the output light, the absorption coefficient close to 1. An example of such a cavity can be pupil.

Body with a cavity - an example of a black body (а_ν,Т =1).

If а_ν,Т <  1, and with а_ν,Т = const, then the body is gray.

§3 Kirchhoff’s Law

Kirchhoff in 1855 established the law, according to which the ratio of the emissivity of the ability of the body to the absorption capacity is a quantity that does not depend on the nature of the body, is for all the bodies of the universal function of frequency (wavelength) and temperature, equal to emissivity ability of a black body.

Consequence of Kirchhoff's law:

1) Since for any body а_ν,Т < 1, from Kirchhoff's law, it follows that the ability of the emissivity of a body r_ν,Т < r_{ν,Т a.b.b.}

r_ν,Т = a_ν,Т ·r_{ν,Т a.b.b.}

2) If the body does not absorb electromagnetic radiation of a certain frequency ν, that is, a_ν,Т = 0, it is him and not radiate as r_ν,Т = a_ν,Т ·r_ν,Тa.b.b.= 0.

Kirchhoff's law describes only the thermal radiation. Radiation, which is not subject to Kirchhoff's law, not the heat - the criterion of thermal radiation.

Kirchhoff's law can be obtained by considering the equilibrium thermal radiation. Let two plates, isolated from the environment. In this case, A is the plate of a black body A and B are in thermodynamic equilibrium.

dW_abs =  a_ν,Т dW_inc

dW_inc = dW_rad , since there is a thermodynamic equilibrium

dW_{inc В} = dW_{rad А} = r_{ν,Т a.b.b.} dν ;

dW_{abs B} = a_ν,Т dW_{inc B} = a_ν,Т r_{ν,Т a.b.b.} dν= dW_{rad B} = r_ν,Т dν

r_ν,Т = a_ν,Т ·r_{ν,Т a.b.b.}, therefore, r_ν,Т /a_ν,Т  = r_{ν,Т a.b.b.}