Laser Types Two main types depending on time operation Continuous Wave (CW) Pulsed operation Pulsed is easier, CW more useful

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1 Main Requirements of the Laser Optical Resonator Cavity Laser Gain Medium of 2, 3 or 4 level types in the Cavity Sufficient means of Excitation (called pumping) eg. light, current, chemical reaction Population Inversion in the Gain Medium due to pumping Laser Types Two main types depending on time operation Continuous Wave (CW) Pulsed operation Pulsed is easier, CW more useful

2 Optical Resonator Cavity In laser want to confine light: have it bounce back an forth Then it will gain most energy from gain medium Need several passes to obtain maximum energy from gain medium Confine light between two mirrors (Resonator Cavity) Also called Fabry Perot Etalon Have mirror (M ) at back end highly reflective Front end (M 2 ) not fully transparent Place pumped medium between two mirrors: resonator Curved mirror will focus beam approximately at radius However is the resonator stable? Stability given by g parameters: g back mirror, g 2 front mirror: g i = For two mirrors resonator stable if unstable if 0 < g g2 L r i < g g2 < 0 gg2 > at the boundary (g g 2 = 0 or ) marginally stable

3 Stability of Different Resonators

4 Polarization and Lasers Lasers often need output windows on gain medium in cavity Output windows often produce polarized light Polarized means light's electric and magnetic vectors at a particular angle Normal windows lose light to reflection Least loss for windows if light hits glass at Brewster Angle Perpendicular polarization reflected Parallel polarization transmitted with no loss (laser more efficient) Called a Brewster Window & the Brewster Angle is n2 θ b = tan n n = index of refraction of air n 2 = index of refraction of glass Example: What is Brewster for Glass of n 2 =.5 θ = n.5 2 o b tan = tan = n

5 Laser Threshold With good Gain Medium in optical cavity can get lasing but only if gain medium is excited enough Low pumping levels: mostly spontaneous emission At some pumping get population inversion in gain medium Beyond inversion get Threshold pumping for lasing set by the losses in cavity Very sensitive to laser cavity condition eg slight misalignment of mirrors threshold rises significantly At threshold gain in one pass = losses in cavity

6 Round Trip Power Gain Within medium light intensity I gained in one pass [( g ) L] I( L ) = I0 exp α where g = small signal gain coefficient α = the absorption coefficient L = length of cavity Thus calculate Round Trip Power Gain G r Each mirror has a reflectivity R i R= for perfect reflection off a mirror I( 2L ) Gr = = RR2 I(0 ) exp At threshold G r = Thus threshold gain required for lasing is g = α + th 2L Some of the loss = laser emission ln [( g α ) 2L] R R 2

7 Transition Lineshape Distribution of energy levels creates width of emission Usually Gaussian shape Width broadened by many mechanisms Most more important in gases Doppler Broadening (movement of molecules) Collision Broadening (atomic/molecular collisions) Radiative Lifetime Broadening (finite lifetime of transitions)

8 Axial Modes of laser Proper phase relationship only signal in phase in cavity Thus cavity must be integer number of half wavelengths pλ L = 2 where p = integer Results in frequency separation of peaks ν = Emission from the atomic transitions is a wider Gaussian Result is axial modes imposed on Gaussian Transition spread c 2L

9 Axial modes within Transition Gaussian Each axial mode is Gaussian shape narrower than transition peak eg for L= m Argon laser at 54 nm 8 8 c 3.00x0 c 3.00x0 4 ν = = = 50 MHz ν = = = 5.83x0 Hz 7 2L 2 λ 5.4x0 Thus emission much smaller than % of frequency Much narrower than other light sources.

10 Transverse Modes Comes from microwave cavities Some waves travel off axis, but within cavity Result is Phase changes in repeating paths These can change shape of output Get local minimums (nulls) in the output beam shape Reduce these by narrowing the beam Called Transverse ElectroMagnetic, TEM

11 Transverse Modes Transverse ElectroMagnetic, TEM depend on cavity type In cylindrical geometry two possible phase reversal orientations horizontal (q) and vertical (r) Show these as TEM qr q and r give number of null's in output beam Horizontal (q) gives number of vertical running nulls Vertical (r) gives number of horizontal running nulls Thus TEM 2 has 2 vertical, horizontal nulls Special mode TEM 0* or donut mode comes from rapid switching from TEM 0 to TEM 0

12 General Laser Types Solid State Laser (solid rods): eg ruby Gas laser: eg He-Ne Dye Lasers Semiconductor Laser: GaAs laser diode Chemical Lasers Free Electron Lasers

13 Gas Lasers Gas sealed within a tube with brewster windows electric arc in tube causes glowing of gas glow indication of pumping Commonest type He-Ne

14 He-Ne Laser Energy levels One type of 3 level laser

15 Einstein Coefficients and Lasers Recall the Einstein Emission/Absorption Coefficients Consider again a 2 level system being pumped by light A 2 is the Einstein spontaneous emission Coefficient B 2 is the Einstein spontaneous absorption coefficient B 2 is the Einstein stimulated emission coefficient At equilibrium the absorption from pumping equals the spontaneous and stimulated emission. N ρ B2 = N2A2 + N2ρB2 Now recall the Boltzman distribution N N 0 = exp ν = the frequency of the light hν = energy in photon Thus [ E E ] KT 0 hν = exp KT hν ρ B + KT 2 exp = A2 ρb2

16 Einstein Coefficients relationships Solving for the emitted photon energy density ρ = B 2 A2 hν exp KT From Planck's law the photons emitted at a given temperature are: ρ = c 3 3 8π hν hν exp KT From these two can solve noting B 2 = B 2 A 8π hν c 8π h λ B = B 3 2 = B 3 2 Note absorption to emission increases rapidly with wavelength

17 Under Lasing Conditions Spontaneous emission is nil so total emission/unite area is di dx = ( N N ) B ρhν For a linear beam I = ρ c (energy density times speed) thus Thus the gain is di dx g = = 2 ( N N ) 2 c ( N N ) 2 c B B hνi hν Or substituting for the spontaneous coefficient g = 2 ( N N ) A c ( N N ) = 2 8πν 8πτ 2 λ Three important implications because we need g>g th to lase () For gain N 2 >N (i.e. population inversion) (2) Shorter wavelength the lower the gain Hence much harder to make UV than IR lasers (3) Want short lifetime τ 2 for higher gain But want metastable long τ 2 to get population inversion! Hence tradeoff: τ 2 must be short enough for threshold g but long enough for population inversion More difficult to achieve for CW (continuous) lasers 2

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