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Physical Review X

Competing Inversion-Based Lasing and Raman Lasing in Doped Silicon

S. G. Pavlov, Nils Dessmann, Britta Redlich, Alexander F. G. van der Meer, Nikolay V. Abrosimov, Helge P. Riemann, Roman Kh. Zhukavin, V. N. Shastin, Heinz‐Wilhelm Hübers

Published Oct 5, 2018• 4 citations
Publisher

Abstract

We report on an optically pumped laser where photons are simultaneously generated by population inversion and by stimulated Raman scattering in the same active medium, namely crystalline silicon doped by bismuth (Si∶Bi).The medium utilizes three electronic levels: ground state [j1i: 1sðA 1 Þ in Si∶Bi], upper [j3i: 2p Æ ] and lower [j2i: 1sðEÞ] laser levels.The j1i ↔ j3i and j2i ↔ j3i transitions are optically allowed and the j1i ↔ j2i transition is Raman active.Lasing based on population inversion occurs between the states j3i and j2i, while Raman scattering benefits from the Raman-active transition.At high pump power the inversion-based stimulated emission j3i → j2i disappears, because electronic scattering from j1i to j2i via a virtual state dominates and the electrons are excited into j2i rather than into j3i.Starting as population inversion-based lasing, it ends as stimulated Raman scattering.Our model shows that such a competition occurs on the timescale of the 10-ps-long pump pulse.

DOI
10.1103/physrevx.8.041003

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Annual Meeting Optical Society of America•Jan 1, 1993•0 citations
We report on an optically pumped laser where photons are simultaneously generated by population inversion and by stimulated Raman scattering in the same active medium, namely crystalline silicon doped by bismuth (Si∶Bi).The medium utilizes three electronic levels: ground state [j1i: 1sðA 1 Þ in Si∶Bi], upper [j3i: 2p Æ ] and lower [j2i: 1sðEÞ] laser levels.The j1i ↔ j3i and j2i ↔ j3i transitions are optically allowed and the j1i ↔ j2i transition is Raman active.Lasing based on population inversion occurs between the states j3i and j2i, while Raman scattering benefits from the Raman-active transition.At high pump power the inversion-based stimulated emission j3i → j2i disappears, because electronic scattering from j1i to j2i via a virtual state dominates and the electrons are excited into j2i rather than into j3i.Starting as population inversion-based lasing, it ends as stimulated Raman scattering.Our model shows that such a competition occurs on the timescale of the 10-ps-long pump pulse.
A mechanism for the generation of population inversion and far-infrared emission in Si with shallow donors is investigated. By optically pumping a phosphorus doped Si crystal with a CO2 laser it was possible to achieve population inversion between the metastable 2p0 state and the 1s(E) and 1s(T) states. Spontaneous emission from these transitions was detected. Frequency measurements of this emission are in agreement with the expected transition frequency. Absorption measurements with a far-infrared probe laser confirm the existence of population inversion between the 2p0 state and the 1s(E) and 1s(T) states.
This paper describes a model and provides the mathematical formulation for describing the spike pulsing phenomenon observed in optically pumped three-level lasers. The model is based on the pumping of electrons from a ground state to an excited pump band from which they relax very rapidly to the excited laser level. With population inversion then achieved, laser action starts and repetitive pulses with decreasing amplitude are generated; the pulses then damp out and the laser output reaches a steady state as long as sufficient pump radiation energy is available. The equations describing the system in terms of the population inversion and photon density are nonlinear. However, approximations are made which permit the required relations between the transition rates to be established for such action to progress. The time variation of the population inversion and the photon density at the laser frequency are obtained for both the pumping time interval and the stimulated emission laser region.
The nonlinear regime of stimulated Raman scattering (SRS) may be reached in two ways. The best known is that of depletion of the pump laser as a large number of photons are scattered into the Stokes field. There is, however, another way in which gain saturation can occur, that is, by depletion of the atomic population while the laser remains undepleted. The equations which describe SRS, including damping and population inversion,1 are remarkably similar to those of well-known theories of two-level superfluorescence, and it is possible by analogy to define a delay time τ D for cooperative Raman scattering (CRS). This delay time is inversely proportional to the spontaneous scattering rate, which depends on the pump laser intensity. A sufficient condition for CRS is that the spontaneous Stokes linewidth Γ is very much greater than τ D − 1 . The only other requirement is that there be more laser photons than scatterers, so that τ D is independent of the number of scatterers. The S(1) transition in molecular hydrogen, when excited by a short (≅ 100-ps) laser pulse, provides a possible system for observing pure CRS. Similar studies have been carried out previously2 for Γ ≅ τ D − 1 .
Considerable attention has been directed recently to the study of lasing without the need of population inversion. The optical coherence and quantum interference associated with the light amplification may lead to interesting statistical properties in inversionless lasers. Here we analyze a laser model that consists of an ensemble of closed multi-level (three or four levels) atoms driven by a single coherent field. Unlike conventional lasers where population inversion is maintained and kept at the threshold value for arbitrary laser output, the multi-level laser analyzed here can start lasing from population inversion and evolves from population inversion into non-inversion with the increasing atomic pumping. In other words, the system makes transition from light amplification by population inversion into light amplification by coherence. On the other hand, the system can be also made to start lasing without population inversion in any state basis. In both cases, initial inversion and non-inversion, which are controlled by the ratio of spontaneous decay rates, the laser well above threshold is always maintained by lasing without inversion (light amplification by coherence), and the laser intensity fluctuations may drop below the shot noise limit. Two factors contribute to the noise reduction: first, the disappearance of the population inversion leads to the depleted atomic population in the upper lasing state, which reduces the spontaneous emission noises; second, the fast coherent cycling of electrons between excited states leads to the highly regulated absorption and emission processes. We found that the combination of these two mechanisms can lead to the noise reduction in the laser output more than 50% below the shot-noise limit.