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Journal of the Optical Society of America B

Subharmonic instabilities in resonant interactions with bichromatic fields

Karl W. Koch, Lloyd W. Hillman, Brian J. Oliver, Stephen H. Chakmakjian, Carlos R. Stroud

Published Jan 1, 1989• 12 citations
Publisher

Abstract

We consider the interaction of two 100% amplitude-modulated fields with a two-level system. The analysis includes a discussion of the stability of an amplitude-modulated laser field to the growth of subharmonic amplitude-modulated fields.
DOI
10.1364/josab.6.000058

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Subharmonic instabilities in resonant interactions with bichromatic fields

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The behavior of a two-level system interacting with a bichromatic classical field is studied. Analytic expressions are found for the Green's-function operator for the system if the field is weak and near resonance, and a systematic procedure is developed to obtain the Green's-function operator in a more general case. The results are used to calculate the probability of a transition from the lower to the upper state; resonance conditions occur when the level spacing of the system, ${\ensuremath{\omega}}_{ba}$, is near $n{\ensuremath{\omega}}_{\ensuremath{\lambda}}\ensuremath{-}(n\ensuremath{-}1){\ensuremath{\omega}}_{\ensuremath{\mu}}$, where nnn is a positive or negative integer, and ${\ensuremath{\omega}}_{\ensuremath{\lambda}}$ and ${\ensuremath{\omega}}_{\ensuremath{\mu}}$ are the frequencies of the components of the field. The resonance frequency depends on the intensity of the field components. In addition, the cross section for scattering photons out of the field has been calculated. It is found that the spectrum of the scattered radiation consists of lines at frequency ${\ensuremath{\omega}}_{k}={\ensuremath{\omega}}_{\ensuremath{\mu}},{\ensuremath{\omega}}_{\ensuremath{\lambda}}$, and odd harmonics of these, combinations of the fundamental and the harmonics with $\ensuremath{\Delta}={\ensuremath{\omega}}_{\ensuremath{\lambda}}\ensuremath{-}{\ensuremath{\omega}}_{\ensuremath{\mu}}$, and satellites shifted from all of these features by an amount which depends on the intensity of the field and ${\ensuremath{\omega}}_{ba}$. The cross section is intensity dependent particularly insofar as the location of resonance peaks is concerned. It is suggested that this effect may be exploited in transferring intensity modulation of one component of the field to phase modulation in the other component.
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 response of a two-level atom interacting with a 100% amplitude modulated field is known.1 In this work we investigate the stability of this stationary state solution to the growth of probe fields. Specifically we consider the gain of a 100% AM probe field, both in phase and in quadrature to the strong field, at the one-third subharmonic of the strong AM field. This case is of particular interest because the beat frequencies generated by all the field components with the nearest other field component are degenerate. We use Floquet's theorem in solving for the stationary-state response of the atoms. The solution is obtained using matrix-continued fractions. The effects of strong AM field intensity and of relative damping times on the gain and dispersion of the probe fields are presented.
The interaction of a strong bichromatic field with a two-level atom has been the subject of numerous experimental and theoretical investigations. We performed an experimental study of the Interaction of an intense 100% amplitude-modulated (AM) field with an ensemble of homogeneously broadened two-level atoms. An optically pumped sodium atomic beam is used as the atomic medium. The field is created by interfering two intense frequency-stabilized laser fields. The frequency of one field is held fixed while another field of equal amplitude is scanned in frequency. The beat frequency produced by interfering the two laser fields is equal to twice the modulation frequency of a 100% AM field. We monitor the time-averaged fluorescent intensity of the atoms as the frequency separation between the two fields is varied. A similar experiment was done in the past in the rf regime.1 For the first time, we report the observation of multiple, well-resolved resonances in the absorption spectrum of the field in the optical regime. We present data and theory for several values of detuning between the fixed field and atomic resonance. The experimental results are in good agreement with theory.