LASER

4.1 INTRODUCTION
The word Laser is an abbreviation for ‘Light Amplification by Stimulated Emission of Radiation’. It is
one of the most important discovery of 20th century. The word Laser is also used for a device that emits
a narrow intense beam of light which differs from ordinary light and has very special applications.
Output of a laser can either be a continuous beam of low to medium power or pulses of intense radiation.
The first laser was built in 1960 by Theodore Maiman and other scientists in California (U.S.A.),
although the essential ingredients for lasers were provided by Einstein in 1917. At present various types
of lasers have been developed using liquids and solids. Before describing the operation of a particular
laser, it is important to discuss the following three transition phenomenon given by Einstein.
4.2 SPONTANEOUS EMISSION
It is well known that there are various energy levels in an atom. Ground state of the atom is the minimum
energy state and it is the most stable state. When the atom gets suitable thermal energy, its valence
electron (say of energy E1) jumps to higher energy level (say to energy E2) called excited level. Electrons
in this level are also called atoms in its excited state. Life time of electron in the excited state is very
small, of the order of 10–8 sec, hence the electron within this time falls back to lower energy level E1 by
emitting a radiation. This process is called spontaneous emission. The frequency, ? of the emitted radiation
is given by
? =
E E
h
2 ? 1
...(4.1)
where h is the Planck constant. We also say that in this transition a photon of energy h? is emitted. If
there are large number of atoms in the upper energy level then the emitted radiations will have randomly
different initial phases and directions and the emitted radiations will be incoherent.
LASER 4
LASER 87
CHAPTER 4
E2
E1
E2
E1
(a) (b)
h
Fig. 4.1. (a) Initial state, (b) Final state
4.3 STIMULATED EMISSION
If an atom is in an excited state of energy E2 and an incident photon of suitable energy (h? = E2 – E1)
may cause the atom (electron) to jump to lower energy state (? E1) emitting an additional photon of
same frequency, same phase and in the same direction. Thus now two photons each of energy equal to
E2 – E1 are present. This kind of transition is called stimulated emission of radiation. This is shown in
Fig. 4.2.
E2
E1
E2
E1
(a) (b)
h h
h
Fig. 4.2. (a) Initial state (b) Final state
4.4 ABSORPTION OF RADIATION
If an atom in its ground state of energy E1 and radiation of suitable energy (h? = E2 – E1) is given such
that the atom goes to excited state E2 i.e., its electron jumps from E1 level to higher energy state E2 by
absorbing a quantum of radiation or photon. This kind of transition is called the absorption of radiation.
This is shown in Fig. 4.3.
E2
E1
E2
E1
(a) (b)
h h = E – E 2 1
Fig. 4.3. (a) Initial state (b) Final state
88 PHYSICS FOR ENGINEERS
4.5 RELATION BETWEEN EINSTEIN’S A AND B COEFFICIENTS
Let us consider an enclosure containing atoms which are in thermal equilibrium or in steady state. Let
N1 and N2 are the number of atoms per unit volume called population in energy levels E1 and E2,
respectively. Here E2 is greater than E1. In thermal equilibrium three processes of transition described
above will take place.
1. Spontaneous Emission: According to Einstein the probability of spontaneous emission from
energy level E2 to energy level E1 per unit time is denoted by
(P21)spontaneous = A21 ...(4.2)
A21 is called the Einstein’s A coefficient of spontaneous emission of radiation. Thus the number of
photons of energy E2 – E1 emitted per second by spontaneous emission in the system is equal to N2A21.
2. Induced Emission: According to Einstein the probability of induced emission from energy
level E2 to energy level E1 per unit time can be written as
(P21)induced emission = B21 u(?) ...(4.3)
Here B21 is called the Einstein’s B coefficient of induced emission of radiation and u(?) is the energy
density of the radiation of frequency ?. Then the number of photons of energy h? emitted per second by
induced emission in the system is equal to N2 B21 u(?).
3. Absorption of Radiation: According to Einstein the probability of absorption of energy for
transition from energy level E1 to energy level E2 per unit time can be written as
(P12)absorption = B12 u(?) ...(4.4)
Here B12 is called the Einstein’s B coefficient of absorption of radiation and u(?) is the energy density of
the radiation of frequency ?. Then the number of photons of energy h? absorbed per second in the
system is equal to N1B12 u(?).
In the thermal equilibrium state (i.e., steady state) total number of photons