LASER

LASER

* Usefulness of Einstein’s coefficients in construction of laser : 

(1) The rate of stimulated emission must be as large as 

 possible compared to the rate of spontaneous emission. 

 i.e 

(𝑹𝟐𝟏)𝒔𝒑

(𝑹𝟐𝟏)𝒔𝒕

< < 1 

 Now , 

(𝑹𝟐𝟏)𝒔𝒑

(𝑹𝟐𝟏)𝒔𝒕

=

𝑨𝟐𝟏 𝑵𝟐

𝑩𝟐𝟏 𝑵𝟐 𝝆 ( 𝝂 )

=

𝒄

𝟑

𝟖 𝝅 𝒉 𝒇

𝟑

[ 𝒆

𝒉 𝒇

𝑲 𝑻 − 𝟏]

𝟖 𝝅 𝒉 𝒇

𝟑

𝒄

𝟑

 

 ∴ 

(𝑹𝟐𝟏)𝒔𝒑

(𝑹𝟐𝟏)𝒔𝒕

= 𝒆

𝒉 𝒇

𝑲 𝑻 − 𝟏

 Thus, from the above eqn. we can see that at normal 

 temperature the value of frequency ( f ) must be small . 

(2) The ratio of the rate of stimulated emission to the rate of 

 absorption should be as large as possible . i.e (𝑹𝟐𝟏)𝒔𝒕

(𝑹𝟏𝟐)𝒂𝒃

≥ 𝟏 

 ∴ 

(𝑹𝟐𝟏)𝒔𝒕

(𝑹𝟏𝟐)𝒂𝒃

=

𝑩𝟐𝟏 𝑵𝟐 𝝆 ( 𝝂 )

𝑩𝟏𝟐 𝑵𝟏 𝝆 ( 𝝂 )

=

𝑵𝟐

𝑵𝟏

 ( 𝑩𝟐𝟏

𝑩𝟏𝟐

= 𝟏 )

∴ 

(𝑹𝟐𝟏)𝒔𝒕

(𝑹𝟏𝟐)𝒂𝒃

= 𝒆

−

𝒉 𝒇

𝑲 𝑻 

 From the above equation we can conclude that , to get 

 𝒆

−

𝒉 𝒇

𝑲 𝑻 grater then 1 , then value of f should be small and 

 Value of 𝑵𝟐 should not be much smaller that 𝑵𝟏 . 

(3) The excited state must be metastable state . 

(4) The lifetime of excited atoms should be as large as possible. 

* Thermal equilibrium : 

 A material medium is composed of identical atoms which 

 are characterized by specific energy level. 

 The no. of atoms per unit volume that occupy a given 

 energy level is called the population of that energy level. 

 If energy of the ground state and excited state is 𝑬𝟏 and 

 𝑬𝟐 resp. Let the population in these energy level is 𝑵𝟏 and

 𝑵𝟐 then , 

 𝑵𝟏 = 𝑵𝟎 𝒆

−

𝑬𝟏

𝑲 𝑻 and 𝑵𝟐 = 𝑵𝟎 𝒆

−

𝑬𝟐

𝑲 𝑻

∴ in thermal equilibrium relative population is 

 

𝑵𝟐

𝑵𝟏

= 𝒆

−

( 𝑬𝟐− 𝑬𝟏

)

𝑲𝑻 

 This relative population 𝑵𝟐

𝑵𝟏

 depends on 

 (1) temperature T and (2) the energy difference 𝑬𝟐 − 𝑬𝟏 . 

* Important parameters for laser device :

(1) Population inversion : 

 The condition in which number of atoms in the excited 

 state is more than that of the ground state is called 

 population inversion. 

 In order to produce laser , this condition is essential. 

(2) Optical pumping : 

 The process during which ground state atoms are taken to 

 the excited state by giving appropriate amount of energy 

 from the external source is called the optical pumping.

 Different optical pumping scheme ( method ) : 

* Three levels pumping scheme :

 

 In this method , first atoms of the ground state 𝑬𝟏 are taken 

 to the excited state of energy 𝑬𝟑 with the help of 

 appropriate form and amount of energy as shown in fig . 

 Atoms remain in the 𝑬𝟑 level for 10-8

sec and then they 

 come to the metastable state 𝑬𝟐 through non radiative 

 transition. 

 As a result of continuous optical pumping , the population 

 inversion is achieved in metastable state 𝑬𝟐

 Finally in presence of external photons, atoms of level 𝑬𝟐 

 comes to the ground state 𝑬𝟏 by stimulated emission of 

 photons . 

 Thus, in this scheme we have overall three energy levels , so

 it is known as three level pumping scheme . 

 This scheme is generally observed in solid –state laser . 

* Four level pumping scheme ( method ) : 

 

 In this scheme , first atoms of the ground state 𝑬𝟏 are taken

o the excited level 𝑬𝟒 with help of proper form and 

 amount of energy .

 Atoms stay in this level 𝑬𝟒 for 10-8

 sec and quickly drop 

 down to the metastable state 𝑬𝟑 ( upper lasing level ) through

 spontaneous emission and population inversion is achieved .

 These populated atoms of level 𝑬𝟑 comes to the level 𝑬𝟐

 ( lower lasing level ) by stimulated emission of photons. 

 and finally atoms come to the ground state 𝑬𝟏 by again 

 spontaneous emission of photons. 

 Thus, in this scheme we get four energy levels so, it is 

 known as four level pumping scheme. 

 generally this scheme can be observed in gas laser . 

* The electrical discharge method : 

 In this method , an electric field causes passage of electric 

 current through gaseous medium which causes discharge of 

 gas molecules i.e gas molecules go to the excited state.

* Direct conversion method : 

 This method is generally used to produced semiconductor 

 laser . 

* Optical resonant cavity : 

 In production of laser , chain of the photon should be formed. 

 In order to achieve this chain , an active medium should be 

 used. 

 A medium in which large number of atoms can be obtained

 in the metastable state is called active medium and the 

 atoms in metastable state are called the active centres . 

 The fig. shows the schematic construction of the optical 

 resonant cavity . 

 As shown in fig. , active medium is enclosed by a pair of 

 optically plane mirrors which are exactly parallel to eachother which is known as Febry – Perot resonator . The rear 

 mirror is complete reflective ( 100 % ) while front mirror is

 made partially reflective ( about 90 % ) such that when light 

 is incident on it , a small fraction of light gets transmitted 

 through it . 

* Lasing action : 

 Initially , the active centres of medium are taken into the 

 excited state through proper pumping scheme so that 

 population inversion is achieved .

 Some of the excited atoms emit photons spontaneously in 

 various directions. Many of these emitted photons get lost 

 without producing chain of photons. 

 Out of the emitted photons , only those photons moving 

 along the axial direction are reflected back by the mirrors.

In their return journey they interact with another excited 

 atoms and causes stimulated emission of another photons. 

 This process takes place repeatedly due to which number 

 of photons having same frequency and phase get increased.

 Finally all these photons get superposed and forms a beam 

 of laser with very high intensity. 

 From the above discussion we can conclude that any laser 

 device should have following parameters. 

 (1) Proper pumping source . 

 (2) Active medium with large number of active centres , so 

 population inversion can be achieved . 

 (3) The proper optical resonant cavity should be used.