What are Lasers? Light Amplification by Stimulated Emission of Radiation LASER Light emitted at very narrow wavelength bands (monochromatic) Light

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1 What are Lasers?

2 What are Lasers? Light Amplification by Stimulated Emission of Radiation LASER Light emitted at very narrow wavelength bands (monochromatic) Light emitted in a directed beam Light is coherenent (in phase) Light often Polarized Diode lasers much smaller but operate on similar principals

3 Why Study Lasers: Market & Applications Market $6.0 billion (2006) (just lasers) Major areas: Market Divided in laser Diodes (56%) & Non diode lasers (44%) Traditional Non Diode Laser Materials Processing (30%) Medicine (8%) Diode Lasers Entertainment/CD/DVD/Printers (~21%) Telecommunications (21%)

4 Why Study Lasers: Laser Types Traditional Lasers Solid State laser (Infra Red to Visible) CO 2 Gas laser (Far Infra Red) Eximer Lasers (UV light) These mostly used in material processing Diode Lasers Near Infra Red diodes dominate Mostly used in telecommunications and CD s Visible diode use is increasing DVD s driving this

5 History of the Laser 1917: Einstein's paper showing "Stimulated Emission" 1957: MASER discovered: Townes & Schawlow 1960: First laser using Ruby rods: Maiman first solid state laser 1961: gas laser 1962: GaAs semiconductor laser 1964: CO 2 laser 1972: Fiber optics really take off 1983: Laser CD introduced 1997: DVD laser video disks

6 World s First Laser: Ruby Laser Dr. Maiman: Inventor of the World s First Laser (on left)

7 Electromagnetic Spectrum

8 Light and Atoms Light: created by the transition between quantized energy states c =νλ hc E = hν = λ c = speed of light ν = frequency hc = 1.24 x 10-6 ev m Energy is measured in electron volts 1 ev = x J Atomic Energy levels have a variety of letter names (complicated) Energy levels also in molecules: Bending, stretching, rotation

9 Black Body Emitters Most normal light emitted by hot "Black bodies" Classical radiation follows Plank's Law E( λ,t ) = 2π hc 5 λ 2 1 hc exp λ KT 1 h = Plank's constant = 6.63 x J s c = speed of light (m/s) λ = wavelength (m) T = Temperature ( o K) K = Boltzman constant 1.38 x J/K = 8.62 x 10-5 ev/k W m 3

10 Black Body Emitters: Peak Emission Peak of emission Wien's Law T = degrees K λ = max 2897 T Total Radiation Stefan-Boltzman Law E(T ) = σ T 4 W m 2 μ m σ = Stefan-Boltzman constant = 5.67 x 10-8 W m -2 K -4

11 Example of the Sun Sun has a surface temperature of 6100 o K What is its peak wavelength? How much power is radiated from its surface λ max = = = 0.475μ m T 6100 or Blue green colour E ( T ) = σ T = 5.67x10 x 6100 = 7.85x10 W m ie 78 MW/m 2 from the sun's surface

12 Black Body, Gray Body and Emissivity Real materials are not perfectly Black they reflect some light Called a Gray body Impact of this is to reduce the energy emitted Reason is reflection at the surface reduces the energy emitted Measure this as the Emissivity ε of a material ε = fraction energy emitted relative to prefect black body Ematerial ε = Eblack body Thus for real materials energy radiated becomes E 4 2 ( T ) = εσ T W m Emissivity is highly sensitive to material characteristics & T Ideal material has ε = 1 (perfect Black Body) Highly reflective materials are very poor emitters

13 Electro-Magnetic Nature of Light Classic light in vacuum has Electric field and magnetic field at 90 o Obtained from Maxwell s Equations Electric wave E y x c ( x t) = E cos ω t = E exp( i [ ω t kx ]) = E exp i ω t x, Where k = Wave vector c = velocity of light t = time (sec) λ = wavelength k = 2π λ ω= angular frequency (radians/sec) ω = 2 πf = E x = c c 0 Magnetic wave ( x, t) cos ω t B z 2π τ Photons are quantized wave packets with energy Coherent light: all the photons have waves aligned Photons waves are behaving as sections of the continuous wave Phase and E field direction are aligned but are discrete packets = hc λ 2π λ

14 Irradiance or Light Intensity What we see is the time averaged energy S, not E or B field S t + T () t = t T / 2 S( t) dt Where T is the period of the wave Called the irradiance I in Watts/unit area/unit time For sin waves this results in I I / 2 == ε = = S c 2 2 0c E B μ0 c E 2 = ε 0 = cε E Not true in absorbing materials because E & B have different relationship & phase there If just a black body light expands in all directions Thus intensity falls with inverse square of distance Consider a sphere radius r 0 with intensity I 0 at surface Then at distance r from the center of the sphere get I0 I ( r) = 2 r Laser sources, or sources with optics behave differently

15 Equilibrium Energy Populations Laser are quantum devices Assume gas in thermal equilibrium at temperature T Some atoms in a Gas are in an excited state Quantization means discrete energy levels Atoms N i (atoms/m -3 ) at a given energy level E i E 0 is the ground state (unexcited) Fraction at a given energy follows a Boltzmann distribution N = exp [ E E ] N i i 0 0 KT T = degrees K K = Boltzman constant 1.38 x J/K = 8.62 x 10-5 ev/k

16 Spontaneous and Stimulated Emission Consider 2 energy levels E 0 (ground state) and E 1 (excited state) Photon can cause Stimulated Absorption E 0 to E 1 Excited state has some finite lifetime, τ 10 (average time to change from state 1 to state 0) Spontaneous Emission of photon when transition occurs Randomly emitted photons when change back to level 0 Passing photon of same λ can cause "Stimulated Emission" Stimulated photon is emitted in phase with causal photon Stimulated emission the foundation of laser operation

17 Einstein's Rate Equations Between energy levels 2 and 1 the rate of change from 2 to 1 is dn21 = A21N2 dt where A 21 is the Einstein Coefficient (s -1 ) After long time energy follows a Boltzmann distribution [ E E ] N = exp N1 KT If (E 2 - E 1 ) >> KT then over a long time ( A t) N2( t ) = N2( 0 ) exp 21 Thus in terms of the lifetime of the level τ 21 sec, 1 A 21 = τ 21 illuminated by light of energy density ρ = nhν (J/m 3 ) (n= number of photons/m 3 ) of frequency ν 12 the absorption is At frequency ν 12 the absorption is dn 1 = N B ( ) emissions 1 12ρ 12 3 dt ν m s B 12 is the Einstein absorption coefficient (from 1 to 2) Similarly stimulated emission rate (with B 21 =B 12 ) is dn 2 = N2B21ρ dt ν ( ) 21 emissions 3 m s

18 Two level system: Population Inversion In thermal equilibrium lower level always greater population N 1 >> N 2 Can suddenly inject energy into system - pumping Now not a equilibrium condition If pumped hard enough get "Population Inversion" Upper level greater than lower level: N 2 >> N 1 Population Inversion is the foundation of laser operation Creates the condition for high stimulated emission In practice difficult to get 2 level population inversion Best pumping with light gives is equal levels Reason is Einstein s rate equations dn 2 = N 2B21ρ ( ν 21 ) = N1B12ρ( ν 21 ) = dt dn dt Since B 21 =B 12 then N 1 =N 2 with light pumping Need more levels to get population inversion 1 emissions m 3 s

19 Three level systems Pump to E 0 level E 2, but require E 2 to have short lifetime Rapid decay to E 1 E 1 must have very long lifetime: called Metastable Now population inversion readily obtained with enough pumping Always small amount of spontaneous emission (E 1 to E 0 ) Spontaneous create additional stimulated emission to E 0 If population inversion: stimulated emission dominates: Lasing Common example Nd:Yag laser Problem: E 0 often very full

20 Four Level Systems Pump to level E 3, but require E 3 to have short lifetime Rapid decay to E 2 E 2 must have very long lifetime: metastable Also require E 1 short lifetime for decay to E 0 Now always have E 1 empty relative to E 2 Always small amount of spontaneous emission (E 2 to E 1 ) Spontaneous photons create additional stimulated emission to E 1 If population inversion: stimulated emission dominates: Lasing In principal easier to get population inversion Problem: energy losses at E 3 to E 2 and E 1 to E 0

21 Absorption in Homogeneous Mediums Monochromatic beam passing through absorbing medium homogeneous medium Change in light intensity I is Δ I = I ( x + Δx) I(x) ΔI = α ΔxI(x) where α = the absorption coefficient (cm -1 ) In differential form di( x) = αi ( x) dx This differential equation solves as I( x) = I0 exp( αx)

22 Gain in Homogeneous Mediums If we have a population inversion increase I Stimulated emission adds to light: gain I ( x) = I0 exp( gx) g = small signal gain coefficient (cm -1 ) In practice get both absorption and gain I( x) = I0 exp([ g a] x) Gain is related directly to the population inversion g = g ( N ) 0 1 N0 g 0 = a constant for a given system This seen in the Einstein B Coefficients Thus laser needs gain medium to amplify signal

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