What are Lasers?
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
Why Study Lasers: Laser Applications Market $4.3 billion (2002) (just lasers) Major areas: Market Divided in laser Diodes (56%) & Non diode lasers (44%) Materials Processing (28%) Medicine (10%) Entertainment/CD/DVD/Printers (~50%) Communications
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
World s First Laser: Ruby Laser Dr. Maiman: Inventor of the World s First Laser (on left)
Electromagnetic Spectrum
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 = 1.602 x 10-19 J Atomic Energy levels have a variety of letter names (complicated) Energy levels also in molecules: Bending, stretching, rotation
Black Body Emitters Most normal light emitted by hot "Black bodies" Radiation follows Plank's Law E( λ,t ) = 2π hc 5 λ 2 1 hc exp λ KT h = Plank's constant = 6.63 x 10-34 J s c = speed of light (m/s) λ = wavelength (m) T = Temperature ( o K) 1 W m 3
Black Body Emitters: Peak Emission Peak of emission Wien's Law T = degrees K λ = 2897 T max µ Total Radiation Stefan-Boltzman Law E(T ) = σ T 4 W m 2 σ = Stefan-Boltzman constant = 5.67 x 10-8 W m -2 K -4 m
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 2897 2897 λ max = = = 0.475µ m T 6100 or Blue green colour E 4-8 4 7 2 ( T ) T 5.67x10 x 6100 7.85x10 W m = σ = ie 78 MW/m 2 from the sun's surface =
Equilibrium Energy Populations 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 N = exp [ E E ] i i 0 0 KT T = degrees K K = Boltzman constant 1.38 x 10-23 J/K = 8.62 x 10-5 ev/k
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
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 1 2 2 = 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 dt ( ) 2 = N2B ν 21ρ 21 emissions 3 m s
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" 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
Absorption in Homogeneous Mediums Monochromatic beam passing through absorbing homogeneous medium Change in light intensity I is I = I ( x + x) I(x) I = α xi(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)
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
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
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