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.);
electroluminescence - glow in solids under the influence of an electric
field (neon lamps, fluorescent lamps, mercury lamps, arc discharge,
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).
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.
Wabs = Wrad - equilibrium 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 Wrad = Wabs. 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
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.
Quantitative characteristic of the thermal radiation is a power spectral density of luminosity - emissivity ability (rν,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
[rν,T] = J/m2
Where rν,T - is a function of frequency and temperature. Used as recording rλ,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 - аν,Т, which is also a function of frequency and temperature. Absorption capacity аν,Т (or
absorption coefficient) indicates how much energy per unit of time of
the incident by one flat surface of the body is absorbed.
аν,Т ≤ 1, [аν,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.
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
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 (аν,Т =1).
If аν,Т < 1, and with аν,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 аν,Т < 1, from Kirchhoff's law, it follows that the ability of the emissivity of a body rν,Т < rν,Т a.b.b.
rν,Т = aν,Т ·rν,Т a.b.b.
2) If the body does not absorb electromagnetic radiation of a certain frequency ν, that is, aν,Т = 0, it is him and not radiate as rν,Т = aν,Т ·rν,Тa.b.b.= 0.
describes only the thermal radiation. Radiation, which is not subject
to Kirchhoff's law, not the heat - the criterion of thermal
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.
dWabs = aν,Т dWinc
dWinc = dWrad , since there is a thermodynamic equilibrium
dWinc В = dWrad А = rν,Т a.b.b. dν ;
dWabs B = aν,Т dWinc B = aν,Т rν,Т a.b.b. dν= dWrad B = rν,Т dν
rν,Т = aν,Т ·rν,Т a.b.b., therefore, rν,Т /aν,Т = rν,Т a.b.b.
Because the surface is selected in a completely arbitrary, the result will be true in the case of any surface.