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Journal of the Optical Society of America B

Continuous-wave amplification and light storage in optically and electrically pumped random laser media

Bin Li, Stephen Colby Rand

Published Mar 15, 2007• 2 citations
Publisher

Abstract

Gain competition is analyzed theoretically on coupled stimulated emission transitions in Λ-type configurations of excited atoms and compared with experimental observations in electrically and optically pumped random media. Under steady-state conditions, we predict and observe dramatic spectral quenching among 2F5/2 transitions in electron-beam-irradiated Nd3+:δ-Al2O3 nanopowders, identifying a simple mechanism that promotes laser action at the longest wavelength (405 nm). In optically pumped Nd3+:Y2O3 nanopowder, simultaneous laser action is observed at two previously unreported wavelengths of Nd3+ (763 and 821 nm), but spectral quenching is not observed, owing to the absence of Λ coupling among the inverted transitions. Quantitative analysis of quenching and threshold behavior in the case of Nd3+:δ-Al2O3 indicates that in wavelength-sized volumes of these light-confining media the average storage time of light may be as long as 30 ps.

DOI
10.1364/josab.24.000799

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 1, 1997•0 citations
Gain competition is analyzed theoretically on coupled stimulated emission transitions in Λ-type configurations of excited atoms and compared with experimental observations in electrically and optically pumped random media. Under steady-state conditions, we predict and observe dramatic spectral quenching among 2F5/2 transitions in electron-beam-irradiated Nd3+:δ-Al2O3 nanopowders, identifying a simple mechanism that promotes laser action at the longest wavelength (405 nm). In optically pumped Nd3+:Y2O3 nanopowder, simultaneous laser action is observed at two previously unreported wavelengths of Nd3+ (763 and 821 nm), but spectral quenching is not observed, owing to the absence of Λ coupling among the inverted transitions. Quantitative analysis of quenching and threshold behavior in the case of Nd3+:δ-Al2O3 indicates that in wavelength-sized volumes of these light-confining media the average storage time of light may be as long as 30 ps.
The spatial and spectral evolution of emission from gain media with homogeneously distributed scatterers is modeled using a Monte Carlo simulation of the random walk of pump and emitted photons. We find a sharp transition to ultrafast, narrow-linewidth emission for a 10-ps incident pump pulse and a rapid approach to steady state for longer pulses. The threshold for this transition is raised significantly when the transverse diffusion of photons out of the excited region is substantial. The quantitative agreement of the results with recent observations of emission from random gain media lends further support to the interpretation of ``random lasers'' in terms of amplified spontaneous emission within a multiply-scattering medium.
Lasing of N2+ at 428 nm is studied as a function of the delay dt between two 800 nm ultrashort pumping pulses from a Ti:sapphire laser. This lasing corresponds to a population-inverted transition between levels B2Σu+(0) and X2Σg+(1) of a singly ionized nitrogen molecule. An important erasing of laser emission is observed under pumping with two consecutive pulses separated by large delays −20 ps < dt < +20 ps. From an analysis of the quenching results, we conclude that the mechanism of lasing corresponds to a coherent two-photon amplification scheme. Our results show that a two-photon process can dominate over a population-inverted one-photon amplification.
Several parameters are proposed for describing the statistical thermodynamic component of the exchange of photons between a pump and a laser beam. They are based on the occupation probability of absorbing and emitting, pump and laser levels, and are complementary to the optical cross sections. The ldquooccupation factor,rdquof0, is appropriate for describing an optical amplifier in the small signal regime.f1is appropriate for describing an amplifier in the large signal regime, e.g., a laser. They serve to facilitate a quantitative comparison of laser gain media, operating temperatures, and choice of pump and laser wavelengths. After a simple scaling, both occupation factors have a numerical value that coincides well, in most cases, with conventional usage of the terms two-, three-, and four-level laser. They can thus serve as an unambiguous, quantitative alternative to the quasi-two-, quasi-three-, and quasi-four-level terminology. The proposed definitions are general enough to apply to many types of gain media, but are particularly useful for comparing systems with discrete levels, pumped with a narrowband source, in near-resonance with the laser wavelength. Several low-quantum-defect combinations of pump and laser wavelengths are analyzed for Er3+, Nd3+, Yb3+, and Ho3+in YAG, as a function of temperature.
In the first part of this thesis, a detailed analysis of lasing in random multiple-light-scattering media with gain is presented. Random laser emission is analyzed using a time-dependent diffusion model for light propagating in the medium containing active atoms. We demonstrate the effects of scatterers to narrow the emission spectral linewidth and to shorten the emitted pulse duration at a specific threshold pump intensity. This threshold pump intensity decreases with scatterer density and excitation spot diameter, in excellent agreement with experimental results. The coherence properties of the random laser are studied using a generalized master equation. The random laser medium is treated as a collection of low quality-factor cavities, coupled by random photon diffusion. Laser-like coherence, on average, is demonstrated above a specific pumping threshold. We demonstrate that with stronger scattering, the pumping threshold for the transition from chaotic to isotropic coherent light emission decreases and enhanced optical coherence for the emitted light is achieved above threshold. The second part of this thesis presents a study of lasing in photonic crystals (PCs). The emission from an incoherently pumped atomic system in interaction with the electro-magnetic reservoir of a PC is analyzed using a set of generalized semiclassical Maxwell-Bloch equations. We demonstrate that the photonic band edge facilitates the enhancement of stimulated emission and the reduction of internal losses, leading to an important lowering of the laser threshold. In addition, an increase of the laser output at a photonic band edge is demonstrated. We next develop a detailed quantum theory of a coherently pumped two-level atom in a photonic band gap material, coupled to both a multi-mode wave-guide channel and a high-quality micro-cavity embedded within the PC. The cavity field characteristics are highly distinct from that of a corresponding high-Q cavity in ordinary vacuum. We demonstrate enhanced, inversionless, and nearly coherent light generation when the photon density of states (DOS) jump between the Mollow spectral components of atomic resonance fluorescence is large. In the case of a vanishing photon DOS on the lower Mollow sideband and no dipolar dephasing, the emitted photon statistics is Poissonian and the cavity field exhibits quadrature coherence.
We discuss the prospects for a class of laser-like sources of atoms where the stimulated accumulation of atoms in the fundamental mode of a matter wave resonator is achieved by optical pumping. Precooled atoms in an internal state a which is not affected by the resonator trapping potential are excited into a state e by means of laser light. Once the atom is in state e it decays into the electronic ground state g by means of spontaneous emission, thereby occupying one of the resonator modes v equals 0, 1, ... Neglecting reabsorption of the spontaneously emitted photon, the probability for a transition into mode v is proportional to 1 + nv (`gain'), where nv is the number of atoms in mode v prior to the transition. Including linear losses this model shows threshold behavior in the fundamental mode v equals 0, mode competition and Poissonian atom statistics above threshold. We also analyze the `small-signal gain' including reabsorption of the spontaneously emitted photons. We demonstrate that the threshold for matter wave amplification can only be reached in small 3D resonators of linear size comparable to the wavelength of the spontaneous photon, or in resonators with effectively reduced dimensionality.