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Physical Review Letters

Observation of Higher Order Dynamical States of a Homogeneously Broadened Laser

Lloyd W. Hillman, Jerzy S. Krasiński, Robert W. Boyd, Carlos R. Stroud

Published Apr 30, 1984• 88 citations
Publisher

Abstract

A series of new stable operating states of a homogeneously broadened laser have been observed. As the pump power is varied, thresholds are reached where the power and spectrum of the laser change discontinuously. In these states the laser simultaneously oscillates at two frequencies whose separation is given by the Rabi frequency or one of its subharmonics. A theoretical explanation is given which includes field-induced structure within the homogeneous line.

DOI
10.1103/physrevlett.52.1605

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When a pump field and probe field simultaneously drive an electronic-state atomic transition, the probe field absorption spectrum can consist of an absorption peak centered near \ensuremath{\Delta}'=0 and amplification peak centered near \ensuremath{\Delta}'=2\ensuremath{\Delta} (\ensuremath{\Delta} and \ensuremath{\Delta}' are the pump and probe field detunings from the atomic transition frequency, respectively). This type of spectrum is seen in the limit \ensuremath{\Vert}\ensuremath{\Delta}\ensuremath{\Vert}\ensuremath{\gg}\ensuremath{\chi}\ensuremath{\gg}\ensuremath{\Gamma}, where \ensuremath{\chi} is the Rabi frequency associated with the pump field and 2\ensuremath{\Gamma} is the homogeneous width associated with the atomic transition. For atoms cooled below the recoil limit of laser cooling, the qualitative nature of the probe absorption spectrum can undergo a dramatic change. Provided that the recoil splitting ${\mathrm{\ensuremath{\omega}}}_{\mathit{k}}$ is larger than the homogeneous decay rate (as might occur in the case of a forbidden transition), the absorption and amplification features each split into an absorption-amplification doublet. In addition, structure is found in the probe absorption spectrum near \ensuremath{\Delta}'=\ensuremath{\Delta}; this structure consists of two absorption-amplification doublets. Both doublets can be resolved if ${\mathrm{\ensuremath{\omega}}}_{\mathit{k}}$>\ensuremath{\Gamma}. If ${\mathrm{\ensuremath{\omega}}}_{\mathit{k}}$, one of the doublets can be resolved provided that ${\mathrm{\ensuremath{\omega}}}_{\mathit{k}}$>${\mathrm{\ensuremath{\Gamma}}}_{\mathit{A}}$, where ${\mathrm{\ensuremath{\Gamma}}}_{\mathit{A}}$ is some effective atomic ground state width in the problem. The positions, widths, and relative weights of all the components are readily predicted using a dressed-atom theory in which quantization of the center-of-mass momentum is included. An analytical expression for the probe field spectrum is obtained for a simple case in which spontaneous decay to the lower level is neglected. Validity criteria for the results are discussed.

Physical Review A•May 1, 1995•13 citations
A series of new stable operating states of a homogeneously broadened laser have been observed. As the pump power is varied, thresholds are reached where the power and spectrum of the laser change discontinuously. In these states the laser simultaneously oscillates at two frequencies whose separation is given by the Rabi frequency or one of its subharmonics. A theoretical explanation is given which includes field-induced structure within the homogeneous line.
A theory is presented that describes a series of bichromatic states of an ideal homogeneously broadened laser. These states are produced when the laser is pumped far above threshold so that the intracavity field is strong enough to overcome damping and produce Rabi oscillations of the atomic inversion. The two-frequency laser field is amplitude modulated at a frequency that may be either the Rabi frequency or a subharmonic of it. The theoretical predictions are compared qualitatively with recent experimental results.
Abstract : This thesis describes theoretical and experimental studies of a homogeneously broadened ring dye laser; particularly the two frequency instability in which a bichromatic field emerges from the laser above the instability threshold. The interaction of a bichromatic field with an isolated atomic resonance is examined. The time averaged inversion and the saturated gain exhibit structure in the form of a series of subharmonic resonances. The stability of a strong bichromatic laser field to the growth of a subharmonic probe field is examined. The gain of the subharmonic bichromatic probe field in the presence of the strong bichromatic laser field is calculated. The strong bichromatic field is stable to the growth of the subharmonic fields when the modulation frequency of the strong field coincides with the Rabi frequency of the lasing transition. The existence of chaos in a strongly driven nonlinear system is experimentally investigated in a multimode ring dye laser. A dye laser is pumped with a modulated pump source. The response of the dye laser to commensurate and incommensurate modulations is reported. For commensurate modulations, the dye laser responds in a periodic fashion and the rf spectrum of the dye is composed of a series of harmonics. For incommensurate modulations, the dye laser responds in a quasiperiodic fashion with a broadband rf spectrum.
The emission linewidth in active medium emerges due to homogeneous and inhomogeneous broadening. We demonstrate that in lasers with inhomogeneous broadening there is a critical pump rate, above which the special mode forms. This mode consists of locked-in oscillations of cavity mode and of the active atoms with different transition frequencies. Below the critical value of the pump rate, the radiation spectrum of the laser has a Gaussian profile, provided that inhomogeneous broadening is dominant. Above the critical value of pump rate, the special mode mostly determines the laser radiation spectrum. As a result, the spectrum attains Lorentz shape characteristic for homogeneous broadening. The formation of the special mode precedes lasing and that the critical pump rate plays the role of lasing prethreshold. We suggest a system where such a transition could be experimentally observed separately from lasing. We obtain expressions for the threshold and generation frequency of a single-mode laser where both homogeneous and inhomogeneous broadening are present.
We investigate the laser equations in the mean-field limit for a homogeneously broadened two-level system, taking into account the local-field correction arising from dipole-dipole interactions. Our analysis concentrates on the dynamical properties of the laser versus the pumping parameter. The effect of detuning between atomic and cavity frequencies is also studied. We first show that the local-field correction reduces the range of the chaotic regime when the frequency detuning is set for minimum instability threshold operation. For a fixed local-field correction, we demonstrate that the symmetry of the dynamical scenario versus the frequency detuning is broken. In addition, we point out generalized bistability between the chaotic regime and the off state of the laser. This bistability results from the smallness of the basins of attraction of the off state.
We report the observation of the first six subharmonic resonances of the Rabi frequency in the absorption of a 100% amplitude-modulated laser beam by a two-level atom. The amplitude-modulated field is formed by combining two separate cw lasers; one is held fixed in frequency, and the other, of equal amplitude, is scanned in frequency. We present data and theory for several values of the detuning between the fixed field and the atomic resonance. The experimental results are in good agreement with theory.
When a pump field and probe field simultaneously drive an electronic-state atomic transition, the probe field absorption spectrum can consist of an absorption peak centered near \ensuremath{\Delta}'=0 and amplification peak centered near \ensuremath{\Delta}'=2\ensuremath{\Delta} (\ensuremath{\Delta} and \ensuremath{\Delta}' are the pump and probe field detunings from the atomic transition frequency, respectively). This type of spectrum is seen in the limit \ensuremath{\Vert}\ensuremath{\Delta}\ensuremath{\Vert}\ensuremath{\gg}\ensuremath{\chi}\ensuremath{\gg}\ensuremath{\Gamma}, where \ensuremath{\chi} is the Rabi frequency associated with the pump field and 2\ensuremath{\Gamma} is the homogeneous width associated with the atomic transition. For atoms cooled below the recoil limit of laser cooling, the qualitative nature of the probe absorption spectrum can undergo a dramatic change. Provided that the recoil splitting ${\mathrm{\ensuremath{\omega}}}_{\mathit{k}}$ is larger than the homogeneous decay rate (as might occur in the case of a forbidden transition), the absorption and amplification features each split into an absorption-amplification doublet. In addition, structure is found in the probe absorption spectrum near \ensuremath{\Delta}'=\ensuremath{\Delta}; this structure consists of two absorption-amplification doublets. Both doublets can be resolved if ${\mathrm{\ensuremath{\omega}}}_{\mathit{k}}$>\ensuremath{\Gamma}. If ${\mathrm{\ensuremath{\omega}}}_{\mathit{k}}$, one of the doublets can be resolved provided that ${\mathrm{\ensuremath{\omega}}}_{\mathit{k}}$>${\mathrm{\ensuremath{\Gamma}}}_{\mathit{A}}$, where ${\mathrm{\ensuremath{\Gamma}}}_{\mathit{A}}$ is some effective atomic ground state width in the problem. The positions, widths, and relative weights of all the components are readily predicted using a dressed-atom theory in which quantization of the center-of-mass momentum is included. An analytical expression for the probe field spectrum is obtained for a simple case in which spontaneous decay to the lower level is neglected. Validity criteria for the results are discussed.