In order to achieve lasing, the energy loss due to absorption in each round trip in the laser cavity must be less than the gain obtained in each trip. We quantified this condition using a relative efficiency of the laser 8<l, which represents the energy loss due to absorption by the laser cavity We saw that in order to achieve lasing, it must be that Consider the plot of ay as a function of frequency. ay has a maximum at the center of the laser bandwidth, v=h. The lasing threshold describes a horizontal line at the value of a Id. Lasing is only possible for values of ay above this line. The possible lasing frequencies are equidistant in frequency space at intervals of id 1. 3 Hole burning Recall that ay was involved in the solution to the differential equation that gave the irradiance of a beam as a function of distance traveled in the lasing medium I(2)=I(0)e2 If ay is above the lasing threshold, this equation appears to predict that I(a) will increase without bound. In practice, the irradiance is limited by the number of atoms in the lasing medium available to undergo spontaneous emission. As atoms are emitted from the excited state by stimulated emis- sion, there are fewer atoms in the excited state near the lasing frequencies These depopulations appear as dips in the absorption spectrum of the lasing medium near the lasing frequencies. This depopulation effect is known as hole burning Note. The "hole"being burned is in frequency space only, and does not refer to any tangible hole The finite time for repopulation of the pumped state leads to some natural frequency width in output of the laser E2-E1 where At is the lifetime of the excited stateIn order to achieve lasing, the energy loss due to absorption in each round trip in the laser cavity must be less than the gain obtained in each trip. We quantified this condition using a relative efficiency of the laser, δ, where δ ≤ 1, which represents the energy loss due to absorption by the laser cavity. We saw that in order to achieve lasing, it must be that, e 2ανd > 1 δν Consider the plot of αν as a function of frequency. αν has a maximum at the center of the laser bandwidth, ν = E2−E1 h . The lasing threshold describes a horizontal line at the value of αν = − ln δν 2d . Lasing is only possible for values of αν above this line. The possible lasing frequencies are equidistant in frequency space at intervals of c 2d . 1.3 Hole burning Recall that αν was involved in the solution to the differential equation that gave the irradiance of a beam as a function of distance traveled in the lasing medium, I(z) = I(0)e ανz If αν is above the lasing threshold, this equation appears to predict that I(z) will increase without bound. In practice, the irradiance is limited by the number of atoms in the lasing medium available to undergo spontaneous emission. As atoms are emitted from the excited state by stimulated emis￾sion, there are fewer atoms in the excited state near the lasing frequencies. These depopulations appear as dips in the absorption spectrum of the lasing medium near the lasing frequencies. This depopulation effect is known as hole burning. Note. The “hole” being burned is in frequency space only, and does not refer to any tangible hole. The finite time for repopulation of the pumped state leads to some natural frequency width in output of the laser, ∆νnat = E2 − E1 ∆t where ∆t is the lifetime of the excited state. 2