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Stimulated emissionSpontaneous emission Light Amplification by Stimulated Emission of Radiation

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

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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

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absorption

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The operation of the Laser Spontaneous emission

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

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The operation of the Laser

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Stimulated emission

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

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

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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

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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 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 A 2-1 ) E1E1 E2E2

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

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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

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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

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

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Measurement disturbes the system The Uncertainty Principle

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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

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The Uncertainty Principle Virtual particles: created due to the UP

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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.

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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

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

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

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Ruby laser First laser: Ted Maiman Hughes Research Labs 1960

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