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Lecture17

# 1 n2 e n f occupancy of photons at frequency f 11

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Unformatted text preview: ( f , T ) + A ] c3 B=A 8! hf 3 8! hf 3 1 u( f , T ) = c 3 ehf /kT " 1 & Rdown # c 3 8! hf 3 1 Rate of emission per atom: =%A + A( N2 8! hf 3 c 3 ehf /kT " 1 \$ ' R Rdown 1 " % = A \$ hf /kT + 1 ' = A ( < n( f ) > +1) = spon ( < n( f ) > +1) N2 !1 & N2 #e < n( f ) > occupancy of photons at frequency f 11 Enhanced sFmulated emission Rdown Rspon = (< n( f ) > +1) N2 N2 So the transiFon rate down is ENHANCED by number of photons of energy f already present + 1 Rspon c 3 8! hf 3 1 = Bu ( f , T ) = A = A < n( f ) >= < n( f ) > 3 3 hf / kT N1 8! hf ce "1 N2 Rup c3 B=A 8! hf 3 Says transiFon rate upward per atom in ground state proporFonal to # photons and inversely proporFonal to populaFon of excited state. 12 Idea: AmpliﬁcaFon of photons The ﬁrst atom that decays with frequency f iniFates an avalanche… 1 in 2 induced This photon + sFmulated emission = 2 photons 2 becomes 3 3 becomes 4, etc….AMPLIFICATION! 2 n ! 1 incident 2 n induced 4 induced 3 in Unfortunately, this won’t work… 13 CompeFng absorpFon E2 N2 N2 ! !" / kT =e N1 E1 N1 In thermal equilibrium, there are more electrons in ground state than excited. AbsorpFon rate ∝ Ground state populaFon SFmulated emission ∝ Excited state populaFon AbsorpFon always beats sFmulated emission and kills the avalanche. Need N2 > N1: popula&on inversion 14 SFmulated/spontaneous emission E2 N2 E2 N2 E1 N1 E1 N1 Compare the raFo of sFmulated to spontaneous emission: Rstim Bu ( f , T ) 1 = = hf /kT Rspon A e !1 Spon￿Stim 5 4 SFmulated emission becomes important when kT &g...
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