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Annual Meeting Optical Society of America

Homogeneous hole burning in an inverted system

Stephen H. Chakmakjian, Karl W. Koch, Stephanos Papademetriou, Carlos R. Stroud

Published Jan 1, 1988• 0 citations
Publisher

Abstract

We report the observation of a spectral feature in the gain and absorption profiles of a multilevel system. The gain experienced by the sidebands of a weakly modulated laser field Is measured as a function of modulation frequency. For small modulation frequencies the sidebands experience diminished absorption or gain depending on the time-averaged inversion of the system. The width of the spectral feature depends on spontaneous as well as stimulated population transition rates. This paper Is an extension of single-field modulation experiments In collisionally broadened media.1,2 Two lasers are used in our experiment. One laser is used as an incoherent pump field that provides population for the upper level of the other optical transition. The second laser stimulates this population to the lower or ground level depending on the system configuration. In the experiment we modulate the second laser field. Using alexandrite as an active medium we are able to study both three- and four-level atomic systems.3 The stability of a single-mode laser to the growth of neighboring modes is related to the gain experienced by the sidebands. The competition between modes is strongest when their frequency separation is less than the width of this spectral feature.

DOI
10.1364/oam.1988.mc4

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Population pulsations are fluctuations in the population difference (of a two level system) due to the presence of two or more coherent waves interfering in the medium. In this work, we show that population pulsations generated by three waves, a central wave and two mode-locked sidebands, are responsible for both the multiwavelength and the single-wavelength instabilities of single-mode lasers containing homogeneously-broadened media. The role of the population pulsations in establishing these instabilities, however, diminish as the central mode is detuned away from the atomic resonance frequency. For homogeneously-broadened lasers, we find two regions of single-wavelength instability. The first is at line center, for which population pulsations are solely responsible, and the second is off line center where the unsaturated medium provides the required gain and anomalous dispersion. For the case of inhomogeneously-broadened lasers, we show that population pulsations significantly increase the instability range over that predicted by Casperson for single-mode bad-cavity lasers. Both the unidirectional ring and the standing-wave cavities are treated. The Fourier expansion technique, used in this work, for treating three-frequency operation in saturation spectroscopy is shown to be equivalent (in appropriate limits) to the linear stability analysis in laser theory and optical bistability. We also show, in single-sideband saturation spectroscopy, that for long interaction lengths propagation effects can significantly influence the absorption and dispersion coefficients of the medium. Finally, we show that under certain conditions the pronounced splittind effects of the population pulsations develop into regions of intense absorption.

•Jan 1, 1982•0 citations
We report the observation of a spectral feature in the gain and absorption profiles of a multilevel system. The gain experienced by the sidebands of a weakly modulated laser field Is measured as a function of modulation frequency. For small modulation frequencies the sidebands experience diminished absorption or gain depending on the time-averaged inversion of the system. The width of the spectral feature depends on spontaneous as well as stimulated population transition rates. This paper Is an extension of single-field modulation experiments In collisionally broadened media.1,2 Two lasers are used in our experiment. One laser is used as an incoherent pump field that provides population for the upper level of the other optical transition. The second laser stimulates this population to the lower or ground level depending on the system configuration. In the experiment we modulate the second laser field. Using alexandrite as an active medium we are able to study both three- and four-level atomic systems.3 The stability of a single-mode laser to the growth of neighboring modes is related to the gain experienced by the sidebands. The competition between modes is strongest when their frequency separation is less than the width of this spectral feature.
The response of three- and four-level homogeneous laser systems to an amplitude modulated field in the presence of an incoherent pump is treated using a rate equation model. A spectral hole due to the finite bandwidth of the population oscillations is observed with a modulated field at either the pump or the laser frequency. The spectral width of the hole broadens at a rate proportional to the sum of the dimensionless intensities of the pump and laser fields. The power levels required to broaden the 1/T1 hole in various laser systems is presented. The experimental implications of this result are discussed.
This chapter begins with a heuristic derivation of atomic population rate equations which include changes to level populations due to stimulated transitions as well as level relaxations and pump. These equations are used to study the saturation of population inversion with increasing light intensity and its dependence on the type of gain medium (three-level gain media vs. four-level gain media), lineshape and nature of line broadening (homogeneous vs inhomogeneous broadening). How saturation affects lineshape and thus gain and absorption giving rise to phenomena like power broadening and spectral hole burning is also discussed. The chapter summarizes the equations of motion for atomic polarization, inversion and the cavity field describing their nonlinear dynamical coupling. These equations, known as the Maxwell-Bloch equations, provide a complete description of atom-field interaction in a laser. Approximations of these equations, including the rate equation approximation, to deal with different laser classes are briefly described. These will be used in the next few chapters to explore and understand the rich and varied behavior of lasers. The chapter ends with a summary of select gain media for different types of commonly used lasers.
Through the use of modulation spectroscopy we have measured the absorption spectrum experienced by a weak probe beam in the presence of a saturating pump beam at two different wavelengths within the broad homogeneous absorption band of alexandrite. At 584 nm the absorption saturates at high pump intensities, and a hole (of width 612 Hz) appears at frequencies near that of the pump laser. However, at 457 nm the absorption demonstrates the inverse of normal saturation because of strong excited-state absorption, and an antihole appears at the pump frequency. These results are in good quantitative agreement with the predictions of a model that ascribes the origin of these spectral features to the temporal modulation of the ground-state population at the beat frequency between the pump and the probe beams. These population oscillations are treated properly within a rate-equation approximation in which the amplitude modulation of the total optical intensity caused by the beating of the pump and the probe beams is taken into account.
A theory is developed to describe the way in which modulations in the pump intensity produce modulations in the gain of a four-level, homogeneously broadened laser amplifier. The theory is tested by carrying out an experiment using an alexandrite crystal pumped by a cw dye laser. A second dye laser is used to measure the gain in the inverted laser transition. The dependence of the magnitude and the bandwidth of the gain on the pumping rate is determined. Agreement between theory and experiment is good.
When a two-level system interacts resonantly with a saturating pump laser, the absorption profile of a probe wave in the Rabi sidebands resembles two separate dispersion profiles. At sufficiently high probe intensity this effect is accompanied by a dispersive profile in the pump-wave absorption, considered as a function of the probe-wave frequency, and also by a dip in the population of the upper state of the two-level system. The relative stabilization of the ground state is interpreted in terms of two-laser-photon processes where absorption of a pump (probe) photon is followed by stimulated emission of a probe (pump) photon. The dispersive absorption profile is attributed to the competition between three- and four-photon scattering processes.
Population pulsations are fluctuations in the population difference (of a two level system) due to the presence of two or more coherent waves interfering in the medium. In this work, we show that population pulsations generated by three waves, a central wave and two mode-locked sidebands, are responsible for both the multiwavelength and the single-wavelength instabilities of single-mode lasers containing homogeneously-broadened media. The role of the population pulsations in establishing these instabilities, however, diminish as the central mode is detuned away from the atomic resonance frequency. For homogeneously-broadened lasers, we find two regions of single-wavelength instability. The first is at line center, for which population pulsations are solely responsible, and the second is off line center where the unsaturated medium provides the required gain and anomalous dispersion. For the case of inhomogeneously-broadened lasers, we show that population pulsations significantly increase the instability range over that predicted by Casperson for single-mode bad-cavity lasers. Both the unidirectional ring and the standing-wave cavities are treated. The Fourier expansion technique, used in this work, for treating three-frequency operation in saturation spectroscopy is shown to be equivalent (in appropriate limits) to the linear stability analysis in laser theory and optical bistability. We also show, in single-sideband saturation spectroscopy, that for long interaction lengths propagation effects can significantly influence the absorption and dispersion coefficients of the medium. Finally, we show that under certain conditions the pronounced splittind effects of the population pulsations develop into regions of intense absorption.