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Atomic model Semi-classical view of atom excitations Energy Atom in ground state Energy Atom in excited state MIT 2.71/2.710 Optics 10/20/04 wk7-b-21 Absorption Spontaneous emission Stimulated emission Boltzmann’s equation E2 n2 ( E2 E1 ) exp n1 kT • n1 - the number of electrons of energy E1 • n2 - the number of electrons of energy E2 E1 example: T=3000 K E2-E1=2.0 eV n2 4.4 104 n1 Einstein’s theory of spontaneous and stimulated emission Einstein’s coefficients Probability of stimulated absorption R1-2 R1-2 = r (n) B1-2 E2 E1 Probability of stimulated and spontaneous emission : R2-1 = r (n) B2-1 + A2-1 assumption: n1 atoms of energy e 1 and n2 atoms of energy e 2 are in thermal equilibrium at temperature T with the radiation of spectral density r (n): n1 R1-2 = n2 R2-1 n1r (n) B1-2 = n2 (r (n) B2-1 + A2-1) A21 / B21 r n = n1 B1 2 1 n2 B21 According to Boltzman statistics: r (n) = n1 exp( E2 E1 ) / kT exp(hn / kT ) n2 A21 / B21 B1 2 hn exp( ) 1 B21 kT = 8hn 3 / c 3 exp( hn / kT ) 1 Planck’s law B1-2/B2-1 = 1 A21 8hn 3 B21 c3 The probability of spontaneous emission A2-1 /the probability of stimulated emission B2-1r(n : A21 exp(hn / kT ) 1 B21r (n ) 1. Visible photons, energy: 1.6eV – 3.1eV. 2. kT at 300K ~ 0.025eV. 3. stimulated emission dominates solely when hn/kT <<1! (for microwaves: hn <0.0015eV) The frequency of emission acts to the absorption: n A n B r (n ) A21 n2 n2 x 2 21 2 21 [1 ] n1B12 r (n ) B21r (n ) n1 n1 if hn /kT <<1. x~ n2/n1 Population inversion For lasing action • Active medium • Pumping mechanism – Optical – Electrical discharge – Chemical pumping • Optical resonator Resonator Laser characteristics Carbon Di Oxide LASER Principle The transition between the rotational and vibrational energy levels lends to the construction of a molecular gas laser. Nitrogen atoms are raised to the excited state which in turn deliver energy to the CO2 atoms whose energy levels are close to it. Transition takes place between the energy levels of CO2 atoms and the laser beam is emitted. Type : Molecular gas laser Active Medium : Mixture of CO2, N2, He or H2O vapour Active Centre : CO2 Pumping Method : Electric Discharge Method Optical Resonator : Gold mirror or Si mirror coated with Al Power Output : 10 kW Nature of Output : Continuous or pulsed Wavelength Emitted : 9.6 μm or 10.6 μm Symmetric 100 C - stationary O - vibrates simultaneously along molecular axis Bending 010, C & O vibrate 020 perpendicular to molecular axis Asymmetric 001, C & O atoms Stretching 002 vibrate in opposite directions along molecular axis Applications • Bloodless surgery • Open air communication • Military field Nd (Neodymium) – YAG (Yttrium Aluminium Garnet) LASER Principle Doped Insulator laser refers to yttrium aluminium garnet doped with neodymium. The Nd ion has many energy levels and due to optical pumping these ions are raised to excited levels. During the transition from the metastable state to E1, the laser beam of wavelength 1.064μm is emitted Characteristics Type : Doped Insulator Laser Active Medium : Yttrium Aluminium Garnet Active Centre : Neodymium Pumping Method : Optical Pumping Pumping Source : Xenon Flash Pump Optical Resonator : Ends of rods silver coated Two mirrors partially and totally reflecting Power Output : 20 kWatts Nature of Output : Pulsed Wavelength Emitted : 1.064 μm Nd (Neodymium) – YAG (Yttrium Aluminium Garnet) LASER M1– 100% reflector mirror M2 – partial reflector mirror Laser Rod Flash Tube Capacitor Resistor Power Supply Energy Level Diagram of Nd– YAG LASER E3 Non radiative decay E2 E4 E1 Laser 1.064μm Non radiative decay Nd E0 E1, E2, E3 – Energy levels of Nd E4 – Meta Stable State E0 – ground State Energy Level Applications Transmission of signals over large distances Long haul communication system Endoscopic applications Remaote sensing HOMOJUNCTION SEMICONDUCTOR LASER (Ga-As Laser) Principle • The electron in the conduction band combines with a hole in the valence band and the recombination produces radiant energy. This photon induces another electron in the CB to combine with a hole in the VB and thereby stimulate the emission of another photon. Type : Homojunction Semiconductor laser Active Medium : P – N junction Active Centre : Recombination of electrons and holes Pumping Method : Direct Pumping Optical Resonator : Polished junction of diode Power Output : 1 mW Nature of Output : Continuous or pulsed Wavelength Emitted : 8400 – 8600 Angstrom Units P- and N-type Semiconductors • In the compound GaAs, each gallium atom has three electrons in its outermost shell of electrons and each arsenic atom has five. When a trace of an impurity element with two outer electrons, such as zinc, is added to the crystal. The result is the shortage of one electron from one of the pairs, causing an imbalance in which there is a “hole” for an electron but there is no electron available. This forms a p-type semiconductor. • When a trace of an impurity element with six outer electrons, such as selenium, is added to a crystal of GaAs, it provides on additional electron which is not needed for the bonding. This electron can be free to move through the crystal. Thus, it provides a mechanism for electrical conductivity. This type is called an ntype semiconductor. Reverse-biased pn Junction A reverse bias widens the depletion region, but allows minority carriers to move freely with the applied field. Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000 Forward-biased pn Junction Lowering the barrier potential with a forward bias allows majority carriers to diffuse across the junction. Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000 Applications • Compact & used in fibre optic communications • CD writer • Relieves pain • Laser printers Excimer LASER • Excited dimer Excimer Function Chemicals Characteristic applications Organic Dye Chemicals Function Characteristic applications – Short lived molecule formed from one or two species, at least one of which is in an electronically excited state – May not be stable in ground state • Excimer LASER: – Electron pumped LASER – Dimer (excimer)/complex (exciplex) formation – LASER radiation: relaxation from excited state dimer to ground state Excimer Excimer Function Chemicals Characteristic applications Organic Dye Chemicals Function Characteristic applications e- + A → A* A* + B → AB* → AB + hν Immediately AB → A + B Two important facts: 1. The lower state does not exist! 2. No rotational/vibrational bands Excimer LASER Energy states of an excimer Excimer Function Chemicals Characteristic applications Organic Dye Chemicals Function Characteristic applications Excimer Excimer Function Chemicals Characteristic applications Organic Dye Chemicals Function Characteristic applications • Excited Dimers – F2, Xe2 ect. • Excited Complexes (Exciplex) – Combination of rare gas atoms and halogen atoms – Ar, Kr, Xe – F, Cl, Br Excimer LASER Excimer Function Chemicals Characteristic applications Organic Dye Chemicals Function Characteristic applications Excimer Wavelength Ar2 126 nm Kr2 146 nm F2 157 nm Xe2 172 and 175 ArF 193 nm CaF2 193 nm KrCl 222 nm KrF 248 nm Cl2 259 nm XeBr 282 nm XeCl 309 nm N2 337 nm XeF 351 nm •Many wavelength possibilities •Depends upon the excited dimer •Repetition rate from 0.05 Hz to 20 kHz •High power: •several 10-200 W Excimer LASER • Micromaching Excimer Function Chemicals Characteristic applications Organic Dye Chemicals Function Characteristic applications – Ink jet cartidges (drilling the nozzles) • Radiation for changing the structure and properties of materials – Active matrix LCD monitors – Fiber bragg gratings – High temperature superconducting films • “Short wavelength light bulb” in optical litography – Computer chips 1. Introduction The Free Electron Laser (FEL) consists of a relativistic beam of electrons (v≈c) moving through a spatially periodic magnetic field (wiggler). S N S N S Relativistic EM radiation N S N S N electron l lw /g2<< lw Magnetostatic “wiggler” field beam (wavelength lw) Principal attraction of the FEL is tunability : - FELs currently produce coherent light from microwaves through visible to UV - X-ray production via Self- Amplified Spontaneous Emission (SASE) (LCLS – 1.5Å) Principle Two beams (object beam and reference beam) are superimposed on a holographic plate to form an image called a hologram. Principle A beam of light (reading beam) having the same wavelength as that of the reference beam used for constructing the hologram, is made to fall over the hologram, which in turn gives rise to a 3-D image in the field of view. Extra slides Review of Semiconductor Physics kB 1.381023 JK -1 a) Energy level diagrams showing the excitation of an electron from the valence band to the conduction band. The resultant free electron can freely move under the application of electric field. b) Equal electron & hole concentrations in an intrinsic semiconductor created by the thermal excitation of electrons across the band gap Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000 n-Type Semiconductor a) b) Donor level in an n-type semiconductor. The ionization of donor impurities creates an increased electron concentration distribution. Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000 p-Type Semiconductor a) Acceptor level in an p-type semiconductor. b) The ionization of acceptor impurities creates an increased hole concentration distribution Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000 The pn Junction Electron diffusion across a pn junction creates a barrier potential (electric field) in the depletion region. Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000