Laser new, Thesis of Accelerator Physics

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LASER

Holography

Laser Light

• “LASER” = Light Amplification by Stimulated

Emission of Radiation

Properties of Laser

• (^) Monochromatic Concentrate in a narrow range of wavelengths (one specific colour).
• (^) Coherent All the emitted photons bear a constant phase relationship with each other in both time and phase
• (^) Directional A very tight beam which is very strong and concentrated.

Basic concepts for a laser

• (^) Absorption
• (^) Spontaneous Emission
• (^) Stimulated Emission
• (^) Population inversion

Absorption

E  E  h 

2 1

• The probability of this absorption from state 1 to state 2 is proportional to the energy density u(v) of the radiation ( ) 12 1 12 P  N B u v where the proportionality constant is known as the Einstein’s coefficient of absorption of radiation. 12

B

Spontaneous Emission

• (^) The atom decays from level 2 to level 1 through the emission of a photon with the energy hv. It is a completely random process.

Stimulated Emission

Stimulated Emission

atoms in an upper energy level can be triggered or stimulated in phase by an incoming photon of a specific energy. 2 1

h    E  E  E

E 1 E 2 h  (a) Absorption h  (b) Spontaneous emission h  (c) Stimulated emission In h  Out h  E 2 E 2 E 1 E 1 Absorption, spontaneous (random photon) emission and stimulated emission. © 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

Stimulated emission leads to a chain reaction and laser emission Excited medium If a medium has many excited molecules or atoms, one photon can become many. This is the essence of the laser.

Relation between Einstein’s Coefficients

Let N 1 and N 2 be the number of atoms at any instant in the state 1 and 2, respectively. The probability of absorption transition for atoms from state 1 to 2 per unit time is ( ) 12 1 12 P  N B u v The probability of transition of atoms from state 2 to 1,either by spontaneously or by stimulated emission per unit time is [ ( )] 21 2 21 21

P  N A  B u 

12 21

P  P

In thermal equilibrium at temperature t, the emission and absorption probabilities are equal and thus

( ) [ ( )]

1 12 2 21 21

N B u   N A  B u 

1 12 2 21 2 21 ( ) N B N B

N A

u 

1 21 2 21 2 21 ( ) N B N B

N A

u 

But Einstein proved thermodynamically that probability of (stimulated) absorption is equal to the probability of stimulated emission, So 12 21

B  B

21 1 2 21 

B N N

A

u 

3 / 3 

h kT e e h u 

Planck’s radiation formula gives the energy density of radiation u(v) as (2) from equation (1) and (2) 3 3 21 21

e h B

A  

This equation gives the relation between the probabilities of spontaneous and stimulated emission.

Condition for the laser operation If N 1

N 2

• (^) radiation is mostly absorbed
• (^) spontaneous radiation dominates.
• most atoms occupy level E 2 , weak absorption
• (^) stimulated emission prevails
• (^) light is amplified if N 2 >> N 1 - population inversion Necessary condition: population inversion