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Physical Review

Quantum Mechanical Effects in Stimulated Optical Emission

Roscoe C. Williams

Published May 1, 1962• 6 citations
Publisher

Abstract

An analysis of a three-level system using time-dependent perturbation theory shows that two distinct photon-emission processes take place within such a system when stimulated optical emission occurs: one-and two-photon transitions. The two-photon transition consists of the emission of a stimulated photon followed by the absorption of a coherent pump photon.In three-level systems which possess a narrow pump level, two-photon transitions are dominant at high pump powers while the maser line is split into two lines due to the modulation of the wave function at an angular frequency determined by the rate of pumping. This might lead to the possibility of frequency-modulating the maser line. These results are extended qualitatively to include optical masers which possess broad pump-bands.

DOI
10.1103/physrev.126.1011

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Quantum Mechanical Effects in Stimulated Optical Emission

Roscoe C. Williams

An analysis of a three-level system using time-dependent perturbation theory shows that two distinct photon-emission processes take place within such a system when stimulated optical emission occurs: one-and two-photon transitions. The two-photon transition consists of the emission of a stimulated photon followed by the absorption of a coherent pump photon. In three-level systems which possess a narrow pump level, two-photon transitions are dominant at high pump powers while the maser line is split into two lines due to the modulation of the wave function at an angular frequency determined by the rate of pumping. This might lead to the possibility of frequency-modulating the maser line. These results are extended qualitatively to include optical masers which possess broad pump-bands.

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Quantum Mechanical Effects in Stimulated Optical Emission

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An analysis of a three-level system using time-dependent perturbation theory shows that two distinct photon-emission processes take place within such a system when stimulated optical emission occurs: one-and two-photon transitions. The two-photon transition consists of the emission of a stimulated photon followed by the absorption of a coherent pump photon. In three-level systems which possess a narrow pump level, two-photon transitions are dominant at high pump powers while the maser line is split into two lines due to the modulation of the wave function at an angular frequency determined by the rate of pumping. This might lead to the possibility of frequency-modulating the maser line. These results are extended qualitatively to include optical masers which possess broad pump-bands.

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Quantum-Mechanical Effects in Stimulated Optical Emission. II

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The existence of multiple-quantum transitions in optically pumped lasers, along with splitting of the laser line due to the modulation of the wave function at an angular frequency determined by the rate of pumping, is demonstrated for a certain class of incoherent broad-band sources pumping large pump bands in crystals. The source consists of a large number of stationary elements emitting wave fields continuously at various arbitrary frequencies and arbitrary phases. The distribution of frequencies and phases among the various elements is random. The pump band belongs to the class found in laser crystals of the ionic type. The analysis shows that such sources pumping such bands act like narrow-line sources pumping narrow lines. The effective linewidth is directly related to the pump rate.

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Radiative transitions When a system changes its energy as the result of the emission or the absorption of a photon, it is said to undergo radiative transition. There are three kinds of radiative transition. In the presence of an electromagnetic field the system can absorb a photon, so that its energy is raised to a higher level. If the system is initially in a state other than the ground state, it can emit a photon and so shed energy. This can happen without the presence of any external electromagnetic field, in which case a spontaneous emission is said to occur. On the other hand, if the excited system is placed in an electromagnetic field that varies in time with the appropriate frequency, the probability that it will emit a photon can be greatly enhanced. In this case the emission process is known as stimulated emission . Stimulated emission is the basis of maser and laser action, which we describe in this chapter. First, we construct a simple model that allows us to investigate how the internal structure of a quantum system changes as the result of a radiative transition. Although the model is very simple, it will allow us to understand the main features of the proper, more exact treatment. We shall deal mainly with absorption and stimulated emission, the two types of radiative transition where there is an external electromagnetic field.

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The quantum mechanical behavior of the three-level maser was experimentally studied using the rotational spectrum of HCOOH molecule at microwave frequencies. By using the 2 11 ←1 10 line at the frequency of 46581 Mc as the pumping, the induced emission of the 2 11 →2 12 line at the frequency of 4916 Mc was obtained. For a strong pumping, the splitting of emission line due to resonant modulation effect was observed. The line-shape of emission signal under off-resonant pumping was studied in detail. The emission spectrum due to simultaneous emission and absorption of two photons corresponding to the signal and the pumping was observed for the condition of far off-resonant pumping. The results were compared with the theory described in the previous paper, and was found to be in good agreement in many respects. Some discrepancies concerning emission intensity are also discussed. An application of the multiple quantum transition to a four-level system of HC·OOH is described.

Journal of the Physical Society of Japan•Sep 1, 1961•11 citations
An analysis of a three-level system using time-dependent perturbation theory shows that two distinct photon-emission processes take place within such a system when stimulated optical emission occurs: one-and two-photon transitions. The two-photon transition consists of the emission of a stimulated photon followed by the absorption of a coherent pump photon.In three-level systems which possess a narrow pump level, two-photon transitions are dominant at high pump powers while the maser line is split into two lines due to the modulation of the wave function at an angular frequency determined by the rate of pumping. This might lead to the possibility of frequency-modulating the maser line. These results are extended qualitatively to include optical masers which possess broad pump-bands.
An analysis of a three-level system using time-dependent perturbation theory shows that two distinct photon-emission processes take place within such a system when stimulated optical emission occurs: one-and two-photon transitions. The two-photon transition consists of the emission of a stimulated photon followed by the absorption of a coherent pump photon. In three-level systems which possess a narrow pump level, two-photon transitions are dominant at high pump powers while the maser line is split into two lines due to the modulation of the wave function at an angular frequency determined by the rate of pumping. This might lead to the possibility of frequency-modulating the maser line. These results are extended qualitatively to include optical masers which possess broad pump-bands.
An analysis of a three-level system using time-dependent perturbation theory shows that two distinct photon-emission processes take place within such a system when stimulated optical emission occurs: one-and two-photon transitions. The two-photon transition consists of the emission of a stimulated photon followed by the absorption of a coherent pump photon. In three-level systems which possess a narrow pump level, two-photon transitions are dominant at high pump powers while the maser line is split into two lines due to the modulation of the wave function at an angular frequency determined by the rate of pumping. This might lead to the possibility of frequency-modulating the maser line. These results are extended qualitatively to include optical masers which possess broad pump-bands.
The existence of multiple-quantum transitions in optically pumped lasers, along with splitting of the laser line due to the modulation of the wave function at an angular frequency determined by the rate of pumping, is demonstrated for a certain class of incoherent broad-band sources pumping large pump bands in crystals. The source consists of a large number of stationary elements emitting wave fields continuously at various arbitrary frequencies and arbitrary phases. The distribution of frequencies and phases among the various elements is random. The pump band belongs to the class found in laser crystals of the ionic type. The analysis shows that such sources pumping such bands act like narrow-line sources pumping narrow lines. The effective linewidth is directly related to the pump rate.
Radiative transitions When a system changes its energy as the result of the emission or the absorption of a photon, it is said to undergo radiative transition. There are three kinds of radiative transition. In the presence of an electromagnetic field the system can absorb a photon, so that its energy is raised to a higher level. If the system is initially in a state other than the ground state, it can emit a photon and so shed energy. This can happen without the presence of any external electromagnetic field, in which case a spontaneous emission is said to occur. On the other hand, if the excited system is placed in an electromagnetic field that varies in time with the appropriate frequency, the probability that it will emit a photon can be greatly enhanced. In this case the emission process is known as stimulated emission . Stimulated emission is the basis of maser and laser action, which we describe in this chapter. First, we construct a simple model that allows us to investigate how the internal structure of a quantum system changes as the result of a radiative transition. Although the model is very simple, it will allow us to understand the main features of the proper, more exact treatment. We shall deal mainly with absorption and stimulated emission, the two types of radiative transition where there is an external electromagnetic field.
The multiple quantum process in the off-resonant condition of the three-level gas maser is discussed. The intensity of the emission produced by this process is calculated by a perturbation theory and also by a more general treatment which is the application of Javan's theory to the off-resonant case. Some graphical representations of the signal line under off-resonant pumping are given for the purpose of comparison with experiment. The Doppler effect in three-level maser action is analyzed from both semiclassical and quantum mechanical points of view under the presence of collision relaxation. It was shown that in a saturation process between two levels, Doppler effect behaves as to contribute to both line-width and relaxation time for the transition, and that under strong pumping, Doppler effect in pumping transition has a marked influence on both intensity and shape of the signal line through the effect of multiple quantum transition.
The quantum mechanical behavior of the three-level maser was experimentally studied using the rotational spectrum of HCOOH molecule at microwave frequencies. By using the 2 11 ←1 10 line at the frequency of 46581 Mc as the pumping, the induced emission of the 2 11 →2 12 line at the frequency of 4916 Mc was obtained. For a strong pumping, the splitting of emission line due to resonant modulation effect was observed. The line-shape of emission signal under off-resonant pumping was studied in detail. The emission spectrum due to simultaneous emission and absorption of two photons corresponding to the signal and the pumping was observed for the condition of far off-resonant pumping. The results were compared with the theory described in the previous paper, and was found to be in good agreement in many respects. Some discrepancies concerning emission intensity are also discussed. An application of the multiple quantum transition to a four-level system of HC·OOH is described.