# Stimulated emissionSpontaneous emission Light Amplification by Stimulated Emission of Radiation.

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Stimulated emissionSpontaneous emission Light Amplification by Stimulated Emission of Radiation

Energy level diagram The possible energies which electrons in the atom can have is depicted in an energy level diagram.

In 1958, Charles Townes and Arthur Schawlow theorized about a visible laser, an invention that would use infrared and/or visible spectrum light. Light Amplification by Stimulated Emission of Radiation- (LASER). Properties of Lasers –Produce monochromatic light of extremely high intensity. The operation of the Laser

absorption

The operation of the Laser Spontaneous emission

The operation of the Laser Spontaneous emission 1.Incoherent light 2.Accidental direction

The operation of the Laser

Stimulated emission

The operation of the Laser Light: Coherent, polarized The stimulating and emitted photons have the same: frequency phase direction

Two level system absorption Spontaneous emission Stimulated emission h h h E1E1 E2E2 E1E1 E2E2 h  =E 2 -E 1

E1E1 E2E2 n 1 - the number of electrons of energy E 1 n 2 - the number of electrons of energy E 2 Boltzmann’s equation example: T=3000 K E 2 -E 1 =2.0 eV

Einstein’s coefficients Probability of stimulated absorption R 1-2 R 1-2 =  ( ) B 1-2 Probability of stimulated and spontaneous emission : R 2-1 =  ( ) B 2-1 + A 2-1 assumption: n 1 atoms of energy  1 and n 2 atoms of energy  2 are in thermal equilibrium at temperature T with the radiation of spectral density  ( ): n 1 R 1-2 = n 2 R 2-1 n 1  ( ) B 1-2 = n 2 (  ( ) B 2-1 + A 2-1 ) E1E1 E2E2

B 1-2 /B 2-1 = 1 According to Boltzman statistics:   ( ) = = Planck’s law

The probability of spontaneous emission A 2-1 /the probability of stimulated emission B 2-1  (  : 1.Visible photons, energy: 1.6eV – 3.1eV. 2.kT at 300K ~ 0.025eV. 3.stimulated emission dominates solely when h  /kT <<1! (for microwaves: h <0.0015eV) The frequency of emission acts to the absorption: if h  /kT <<1. x~ n 2 /n 1

Condition for the laser operation If n 1 > n 2 radiation is mostly absorbed absorbowane spontaneous radiation dominates. most atoms occupy level E2, weak absorption stimulated emission prevails light is amplified if n 2 >> n 1 - population inversion Necessary condition: population inversion E1E1 E2E2

How to realize the population inversion? Thermal excitation: Optically, electrically. impossible. The system has to be „pumped” E1E1 E2E2

Measurement disturbes the system The Uncertainty Principle

Classical physics –Measurement uncertainty is due to limitations of the measurement apparatus –There is no limit in principle to how accurate a measurement can be made Quantum Mechanics –There is a fundamental limit to the accuracy of a measurement determined by the Heisenberg uncertainty principle –If a measurement of position is made with precision  x and a simultaneous measurement of linear momentum is made with precision  p, then the product of the two uncertainties can never be less than h/2 

The Uncertainty Principle Virtual particles: created due to the UP

Three level laser The laser operation E1E1 E3E3 E2E2 Fast transition Laser action 1  3 pumping spontaneous emission 3  2. state 2 is a metastable state population inversion between states 2 and 1. stimulated emission between 2 i 1.

E1E1 E3E3 E2E2 szybkie przejścia akcja laserowa - optical pumping - occupation of E3 of a short life time, 10-8s. It is a band, the metastable and ground states are narrow : - electrons are collected on E2: population inversion - stimulated emission (one photon emitted spontaneously starts the stimulated radiation ) - Beam of photons moves normally to the mirrors – standing wave. The laser operation

ruby laser discovered in 60-ies of the XX century. ruby (Al 2 O 3 ) monocrystal, Cr doped.

Akcja laserowa z jonów Cr 3+, zawartych w rubinie. Laser trzypoziomowy. Energy 4A24A2 4T24T2 4T14T1 2T22T2 2E2E LASING optical pumping: 510-600nm and 360- 450nm. fast transition on 2 E. lasing: 2 E on 4 A 2, 694nm rapid decay Ruby laser Al 2 O 3 Cr +

Ruby laser First laser: Ted Maiman Hughes Research Labs 1960

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