Laser, Induced Absorption, Spontaneous and Stimulated emission, Population Invertion

Introduction:

The term LASER stands for "Light Amplification By Stimulated Emission Of Radiation". Laser is a light of highly intense, monochromatic, coherent and unidirectional beam of light. Or it is a device which produces a highly concentrated monochromatic, coherent, and unidirectional beam of light. The typical operating frequency in visible region for LASER is \(10^{15}\) Hz, and hence LASER produces a coherence and extreme purity line spectrum. The first successful LASER was built by T.H Maiman in the summer of 1960.

The basic principle of LASER is the quantum theory of radiation, for two energy level \(E_1\) and \(E_2\) , the equation is given by $$E_2-E_1=hf$$ ; where, h- the Planck's constant and f- the frequency of radiation incident on the specimen.

There are three kinds of transitions are possible involving electromagnetic radiation between two energy level \(E_1\) and \(E_2\) (i.e. according to quantum theory of radiation three types of absorption or emission are possible between the two energy level \(E_1\) and \(E_2\) for given that \(E_2\) > \(E_1\).)

Induced Absorbtion:

When a beam of photon ( having energy \(E_2-E_1\)=hf ) is incident on a group of atom in the ground state ( i.e. \(E_1\) ), it absorbs energy and moves to the excited state. This phenomenon is called induced absorption.

According to Einstein's, the rate of induced absorption is directly proportional to the number of atom in the ground state and the energy density of incident photons. So

$$\frac{N_{12}}{dt}=B_{12} N_1\rho$$

Where, \(B_{12}\) = Einstein's proportionality constant

\(N_1\) = Number of atoms in the ground state and

\(\rho\) = Energy density

Spontaneous Emission:

When an atoms in the excited state ( \(E_2\) ) goes to the ground state ( \(E_1\) ) by emitting energy in the form of radiation , this process is called spontaneous emission. The dictionary meaning of spontaneous emission is "The emission of photon by an atom as it makes a transition from an excited state to a ground state. "The process of spontaneous emission, which can not be described by non-relativistic quantum mechanics as given by formulation such an excited state of an atom such as the Schrodinger Equation , is responsible for the limited lifetime before it emits a photon.

The energy difference of ground state of ground state and excited state is given by, $$E_2-E_1=hf$$

Which implies that; f = \(\frac{E_2-E_1}{h}\) , Where, f = frequency of radiation

According to Einstein's, the rate of spontaneous emission is directly proportional to the number of atoms in the excited state i.e. $$\frac{N_{21}}{dt}=A_{21} N_2\rho$$

Where \(N_2\) = number of atoms with electrons in the excited state and \(A_{21}\) = Einstein's coefficient for spontaneous emission.

Stimulated Emission Or Induced Emission:

When a photons of suitable frequency is incident on a group of atoms in the excited state, the atoms jumps towards the ground state by emitting energy having the frequency equal to that of incident photons. The process of emitting radiation is called Stimulated or induced emission. The phenomenon is essential for the production of laser light. Stimulated emission occurs if the number of atoms in the excited state will be greater.

The energy in which the number of atoms becomes greater with relatively greater time ( > 3x\(10^-3\) sec ) is called metastable state. According to Einstein the rate of stimulated or induced emission is directly proportional to the number of atoms in the excited state and energy density of incident photon;

$$\frac{N_{21}}{dt}=B_{21} N_2\rho$$

Population Invertion:

The condition of being greater number of atoms in the excited state is called population inversion. Laser light is produced under the stimulated or induced condition and emission occurs only when the excited state contains more number of atoms then in the ground state.

According to Bose Einstein's statistics, at thermal equilibrium and ordinary condition, the number of atoms in the lower energy state is always greater than that in the higher energy state or excited state which is given by

$$N_2=N_1 e^{\epsilon_2-\epsilon_1}{k_B T}$$

i.e. \(N_2<N_1\)

Pumping:

The method of producing population invertion is called pumping. There are four types of pumping, which are given below:

(i) Optical Pumping: In this method, the energy in the form of light energy is used which may be obtained from gaseous discharge flash tube. This method is used in Ruby Laser.

Nearly all atoms in solid, liquid or gases at near absolute zero are in their ground state. As the temperature is raised by some form of energy input, more and more electrons are bumped into excited state. The population of electrons in hte higher energy level increses.

If a metastable state exists, the situation is different. As atoms are excited to higher level, more and more of them get caught in hte metastable level and relatively few of them get out except through mechanical collision with other atoms. A steady state can exists and just a many will be leaving per second as they are arriving there. The average populations of atoms in the metastable levels may be thousands and even millions of times that of any other, except the ground state. If they exceeds the number in the ground state, it is called populatin inversion.

(ii) Electrical Pumping: This method is generally used in gaseous active medium. When electric discharge is passed through the gas , it converts into plasma sttae. At this state, atoms collides in elastically with free electron and the atom moves to excited state.

(iii) Chemical Pumping: In this method, the active medium is activated by exothermic chemical reaction.

(iv) Heat Pumping: In this method, the acive medium isheated at high temperature and cooled rapidly.

Conditions for Laser Action:

In order to produce laser, one must collimate the stimulated emission, and this is done by properly designing a cavity in which the waves can be used over and over again. Here, in optics the principle of the Fabry-Perot Inerferometer is appilied, i.e. multiple reflections taking place between two mirrors several times. Suppose we retain the high reflecting power of the two end mirrors of the etalon and increase the distance between them. Into this cavtity, we then introduce an appropriate solid, liquid or gas having metastable states in the atoms or molecules of its structure.

References:

Adhikari, P.B, Daya Nidhi Chhatkuli and Iswar Prasad Koirala. A Textbook of Physics. Vol. II. Kathmandu: Sukunda Pustak Bhawan, 2012.

Jenkins, F.A and H.E White. Fundamental of optics. New York (USA): McGraw-Hill Book Co, 1976.

wood, R.W. Physical Optics. New York (USA): Dover Publication , 1934.