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

Size: px

Start display at page:

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

Randall Casey
6 years ago
Views:

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

laser Diodes (56%) & Non diode lasers (44%) Materials

3 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

4 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

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

6 Electromagnetic Spectrum

7 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

8 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 J s c = speed of light (m/s) λ = wavelength (m) T = Temperature ( o K) 1 W m 3

9 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

10 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 ) T 5.67x10 x x10 W m = σ = ie 78 MW/m 2 from the sun's surface =

11 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 J/K = 8.62 x 10-5 ev/k

12 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

13 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 dt ( ) 2 = N2B ν 21ρ 21 emissions 3 m s

14 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

15 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)

16 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

17 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

18 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

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

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