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2. The following simplified mechanism captures some of the features of a 3-level laser: r= kp f(hv)[X] r= k(ICi) [I] r= kf [A] r= kị f(hv') [A] X+ hv → I pumping intersystem crossing I → A spontaneous emission lasing A → X+ hv' hv’ + A → X+ 2hv' f(hv) = flux of photons with energy = hv f(hv') = flux of photons with energy = hv' (a constant value different from f(hv)) (usually a constant value) Note that spontaneous emission (usually fluorescence) is detrimental to efficient lasing. a) Sketch a diagram of the system and identify all the states including metastable states also known as intermediates. b) Derive the steady-state concentrations for all metastable states. c) Show that population inversion ([A]s/[X] >> 1) is possible if the pumping rate constant is much larger than the sum of the rate constant of spontaneous emission plus the lasing rate constant. [A]ss = steady-state concentration of A.

2. The following simplified mechanism captures some of the features of a 3-level laser: r= kp f(hv)[X] r= k(ICi) [I] r= kf [A] r= kị f(hv') [A] X+ hv → I pumping intersystem crossing I → A spontaneous emission lasing A → X+ hv' hv’ + A → X+ 2hv' f(hv) = flux of photons with energy = hv f(hv') = flux of photons with energy = hv' (a constant value different from f(hv)) (usually a constant value) Note that spontaneous emission (usually fluorescence) is detrimental to efficient lasing. a) Sketch a diagram of the system and identify all the states including metastable states also known as intermediates. b) Derive the steady-state concentrations for all metastable states. c) Show that population inversion ([A]s/[X] >> 1) is possible if the pumping rate constant is much larger than the sum of the rate constant of spontaneous emission plus the lasing rate constant. [A]ss = steady-state concentration of A.

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2. The following simplified mechanism captures some of the features of a 3-level laser: X+ hv -→ I I → A A → X+ hv’ r= kp f(hv)[X] r = k(IC1) [I] r=kf [A] r = kị f(hv') [A] pumping intersystem crossing spontaneous emission lasing hv' + A → X+ 2hv' f(hv) = flux of photons with energy = hv f(hv') = flux of photons with energy = hv' (usually a constant value) (a constant value different from f(hv)) Note that spontaneous emission (usually fluorescence) is detrimental to efficient lasing. a) Sketch a diagram of the system and identify all the states including metastable states also known as intermediates. b) Derive the steady-state concentrations for all metastable states. c) Show that population inversion ([A]ss/[X] constant is much larger than the sum of the rate constant of spontaneous emission plus the lasing rate constant. [A]ss = steady-state concentration of A. 1) is possible if the pumping rate >>
Transcribed Image Text:2. The following simplified mechanism captures some of the features of a 3-level laser: X+ hv -→ I I → A A → X+ hv’ r= kp f(hv)[X] r = k(IC1) [I] r=kf [A] r = kị f(hv') [A] pumping intersystem crossing spontaneous emission lasing hv' + A → X+ 2hv' f(hv) = flux of photons with energy = hv f(hv') = flux of photons with energy = hv' (usually a constant value) (a constant value different from f(hv)) Note that spontaneous emission (usually fluorescence) is detrimental to efficient lasing. a) Sketch a diagram of the system and identify all the states including metastable states also known as intermediates. b) Derive the steady-state concentrations for all metastable states. c) Show that population inversion ([A]ss/[X] constant is much larger than the sum of the rate constant of spontaneous emission plus the lasing rate constant. [A]ss = steady-state concentration of A. 1) is possible if the pumping rate >>
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