Laser theory:[/

Laser theory:
[align=left]The word "LASER" is an acronym for "Light Amplification by Stimulated Emission of Radiation.
An atom is the smallest particle of an element that retains the characteristics of the element. An atom consists of a positive nucleus surrounded by a "cloud" of negative electrons. All neutral atoms of a given element have the same number of positive charges (protons) in the nucleus and negative charges (electrons) in the cloud. The energy content of atoms of a particular type may vary, however, depending on the energies contained by the electrons within the cloud.
If a light incident on a matter, it either passes through it without any interaction, or it interacts with it and it may be absorbed totally or partially, and in this case the photon energy transfer to the molecules by absorption.
According to the quantum theory, the absorbed energy is given by:
E= hγ = hc/λ ……………………………………………….(1)[/align]
[align=left]Where[/align]:
[align=left]h is plank’s constant.
c is the speed of the light.
λ is the incident light wavelength.
γ is the incident light frequency.
Each type of atom can contain only certain amounts of energy. When an atom contains the lowest amount of energy that is available to it, the atom is said to be in its "atomic ground state." If the atom contains additional energy over and above its ground state, it is said to be in an "excited atomic state."
It can be noticed that the last interaction can takes place with one of the three following processes[/align]:
[align=left] Absorption:[/align]
[If an electromagnetic wave of frequency γ_21 travels through an atomic system consisting of two levels 1 & 2 with energies E1 &E2 since E2>E1 and the difference between them is h γ_21 ( see fig. 1). So the atom in the lower level 1 rise to the upper level 2 with a rate proportional to radiation density ρ(γ) and number of atoms of lower level N1, i.e.[/align][align=left]
((dN_1)/(d t))ab= - B12 ρ(γ) N1 ………………………………………..(2)[/align][/size]
[align=left]B12 represents the proportionality constant and it is called also Einstein coefficient, it units is Cm3/Sec2.Joule.
It also can be written as[/align]:
[align=left][B]B12 =σ12 F ………………………………………………(3)[/B][/align][align=left]Where[/align]:
[align=left]σ12 is the absorption cross- section and it depends on the single transition only.
F is the incident photon flux. [/align]


[align=center]http://www.iraqup.com/uploads/VWmf5-8A6f13113.JPG[/align][align=center]fig. 1[/align]

[align=left]Spontaneous emission:[/align] [align=left]Since a number of lower level atoms 1 rise to the upper level 2 in the previous atomic system by absorption, so the upper level atoms will decay spontaneously to level 1 (fig.2) which the atoms in the excited state are unstable with rate proportional to the number of atoms occupying level 2, i.e.[/align]
[B][align=left]((dN_1)/(d t))sp.em. =A21 N2 …………………………………………………(4]
Where
[align=left]A21 is the proportionality constant and also called Einstein coefficient, its units is 1/S (S-1 ,Hz) also it is called spontaneous emission may be defined as the life time of the electron in the excited state which is after a time interval will go to the difference between energies of levels 1 & 2 and with a frequency γ given by:[/align][B]γ= (E2 – E1)/h[/B]
[]The relation between the life time and Einstein coefficient A21 is]
[align=left]T21 =1/A21 ……………………………………………………….(5)[/align]
[This energy release may occur in a single transition or in a series of transitions that involve intermediate energy levels.
In ordinary light sources, individual atoms release photons at random. Neither the direction nor the phase of the resulting photons is controlled in any way, and many wavelengths usually are present. This process is referred to as "spontaneous emission" because the atoms emit light spontaneously, quite independent of any external influence.


[align=center]http://www.jojokw.net/up-pic/uploads/8e084b1bfe.jpg[/align]
[align=center]Fig.2[/align]
[align=left] Stimulated emission:[/align][The emission occurs not only spontaneously, it can occur by stimulation of electromagnetic radiation with certain frequency, so if this radiation incident on an excited atom existing in level 2 of the atomic system to go to lower level giving an electromagnetic radiation having the same phase, frequency and direction (the condition of coherency) of the incident radiation (i.e. the two waves are coherence) according to the following relation:[/align] ](
(dN_2)/(d t))st.em.= B21 ρ(γ_21) N2 ………………………………………………….(6)[/align]]
[align=left]Where[/align]:
[align=left]B21 is the proportionality constant and is called Einstein coefficient, and it is called also stimulated emission probability and it depends on the transition from level 2 to level 1 and on the strength of the incident electromagnetic radiation. So:[/align]B21=σ21 F

Where]
[σ21 is the stimulated emission cross section (units of area) and depends on the characteristics of the given transition only.
F is the incident photon flux.
The coherent light of the laser is produced by a "stimulated-emission" process (fig. 3).In this case, the excited atom is stimulated by an outside influence to emit its energy (photon) in a particular way.

[align=center]http://www.jojokw.net/up-pic/uploads/5c00e61db4.jpg[/align]
[align=center]Fig.3[/align]
[If we sum the absorption, spontaneous emission and stimulated emission as given by equations 2, 4, 6, so we can write the change in the total number of atoms in level 1, 2 in the atomic system as follows:
[B][align=left]((dN_total)/(d t)) = B21 ρ(γ) N2 - B12 ρ(γ) N1 + A21 N2 ……………………………]
And so
[align=left]Ntot =N1 +N2 …………………………………………….…………………..(9)[/align]
Thene]
]((dN_1)/(d t)) + ((dN_2)/(d t)) = B21 ρ(γ) N2 - B12 ρ(γ) N1 + A21 N2 ……………….……….(10]
[]In thermal equilibrium, the number of transitions per unit time from 1 to 2 must be equal to that 2 to 1, i.e]
[]((dN_1)/(d t)) = ((dN_2)/(d t)) =0 …………………………………………………………..(11]
So]:
[B21 ρ(γ) N2 + A21 N2 = B12 ρ(γ) N1 ……………………………………………(12[=2][align=left]This means the probability of the stimulated emission and the absorption equal to each other. So:[/align]
[]B21 = B12]
[align=left]POPULATION INVERSION:[/align]
In order for a laser to produce an output, more light must be produced by stimulated emission than is lost through absorption. For this process to occur, more atoms must be in energy level E3 than in level E2, which does not occur under normal circumstances. In any large collection of atoms in matter at any temperature T, most of the atoms will be in the ground state at a particular instant, and the population of each higher energy state will be lower than that of any of the lower energy states. This is called a "normal population distribution." ."
Under "normal" circumstances, each energy level contains many more atoms than the energy level just above it, and so on up the energy lever ladder. Thus, in any large collection of atoms in matter at any temperature T, most of the atoms will be in the ground state at a particular instant, and the population of each higher energy state will be lower than that of any of the lower energy states. This is called a "normal population distribution."
A population inversion exists whenever more atoms are in an excited atomic state than in some lower energy state. The lower state may be the ground state, but in most cases it is an excited state of lower energy. Lasers can produce coherent light by stimulated emission only if a population inversion is present. And a population inversion can be achieved only through external excitation of the atomic population