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Annual Meeting Optical Society of America

Broadband atomic response to incommensurate modulation frequencies

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

Published Jan 1, 1987• 0 citations
Publisher

Abstract

Pomeau et al.1 have shown that a two-level atom strongly driven by a single 100% amplitude modulated (AM) field can show broadband spectral behavior when the two-frequency components of the field are incommensurate. The equations describing the atomic response to a monochromatic field without making the rotating wave approximation (RWA) are identical to form to the equations describing a 100% amplitude modulated field within the RWA. This fact makes the observation of the predictions of Pomeau et al. experimentally realizable in an optical resonance experiment. We present theoretical and numerical results of a pair of 100% AM fields interacting with a single atomic resonance. The effects on the atomic response of commensurate and incommensurate modulation frequencies are discussed as are the experimental implications.

DOI
10.1364/oam.1987.wf6

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Pomeau et al.1 have shown that a two-level atom strongly driven by a single 100% amplitude modulated (AM) field can show broadband spectral behavior when the two-frequency components of the field are incommensurate. The equations describing the atomic response to a monochromatic field without making the rotating wave approximation (RWA) are identical to form to the equations describing a 100% amplitude modulated field within the RWA. This fact makes the observation of the predictions of Pomeau et al. experimentally realizable in an optical resonance experiment. We present theoretical and numerical results of a pair of 100% AM fields interacting with a single atomic resonance. The effects on the atomic response of commensurate and incommensurate modulation frequencies are discussed as are the experimental implications.
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.
We have investigated the interaction between bichromatic optical fields and atomic transitions. We have considered both the interaction of a saturating bichromatic field in the form of a 100% amplitude-modulated field resonantly interacting with a single atomic transition as well as the interaction of a pair of 100% amplitude-modulated fields with two coupled atomic transitions. In our studies of a single atomic transition resonantly excited by a 100% amplitude-modulated field we have used a fully quantum-electrodynamical analysis to model the Autler-Townes effect induced by a bichromatic optical field. We find that the effect induced by a bichromatic field is markedly different from the effect produced by a monochromatic exciting field. We have derived analytic expressions for the bichromatic Autler-Townes absorption spectrum. The absorption spectrum consists of equally spaced lines spaced by the modulation frequency. The linewidths of neighboring lines alternate as functions of the field strength. Experimentally, we observed this spectrum for both resonant and detuned 100% amplitude-modulated driving fields by monitoring the absorption of a weak monochromatic field as it was tuned about the resonance frequency of the 3²P₃/₂(F = 3, mF = 3) ↔ 4²D₅/₂(F = 4, mF = 4) transition while driving the 3²S₁/₂(F = 2, mF = 2) ↔ 3²P₃/₂(F = 3, mF = 3) transition with a saturating 100% amplitude-modulated field. We found excellent agreement between our predicted and measured spectra. We then investigated the resonant interaction between a pair of 100% amplitude-modulated fields and two atomic transitions sharing a common atomic level. We considered both a three-level atomic cascade system and a three-level atomic lambda system. We examined the effect that the relative phase between the two modulations has on the rate at which the modulated fields are absorbed. We find that the saturated time-averaged field absorption exhibits parametric resonances in both the cascade and lambda systems. The time-averaged absorption is strongly dependent upon the relative phase of modulation between the two fields and for certain phase differences the time-averaged absorption can be enhanced over the maximum saturated absorption experienced by cw fields of the same time-averaged intensities. We also find that the stationary atomic response exhibits periodic oscillations and for the cascade system periodic two-photon inversions of up to 40% can be achieved. We further find dark absorption resonances as a function of phase in the lambda system. We analyze the results from the point of view of semi-classical adiabatic dressed states.
The spectral distribution of light scattered by a two-level atom in a laser beam with phase modulation has been calculated. The spectrum has been obtained via numerical solution of the optical Bloch equations using the algorithm of Wilkens and Rza\ifmmode \mbox{\c{}}\else \c{}\fi{}\ifmmode \dot{z}\else \.{z}\fi{}ewski [Phys. Rev. A 40, 3164 (1989)]. The modulation produces additional sidebands in both coherent and incoherent parts of the spectrum; the location of the added components depends on the modulation depth. In the case of two-frequency phase modulation with incommensurate frequencies, wild, ``chaotic'' behavior of the spectrum has been observed, similar to the case of bichromatic amplitude modulation. The intensity distribution is practically insensitive to the chosen constant value of the phase of modulation.
The propagation of a weakly modulated light beam through a nonlinear material is treated. The optical field representing such a beam consists of a strong carrier-frequency component and two weak, symmetrically displaced sidebands that combine to form a field, which may be purely amplitude modulated (AM), frequency modulated (FM), or some combination of these two modulation forms. It is shown that, for any optical nonlinearity, two modulation forms exist that have the property that the form of modulation is invariant under propagation of the beam. If a modulation form other than one of these natural modes is injected into the nonlinear medium, the modulation form will change as the beam propagates, asymptotically approaching the natural mode that experiences the lower attenuation. Explicit expressions for these natural modes are presented for the case in which the nonlinear medium can be modeled as a collection of two-level atoms. For the special case of an on-resonance pump beam, the natural modes correspond to pure amplitude modulation and pure frequency modulation. This formalism provides a general description of saturation spectroscopy for both AM and FM fields. Formulas are derived for the rate at which a pure FM beam is converted to an AM beam owing to its interaction with a two-level atomic medium. We also consider the variation that is due to propagation of the depth of modulation of an AM wave interacting resonantly with two-level atoms. The formalism predicts the existence of spectral features whose shape depends sensitively on the internal relaxation processes of the material. Experimental spectra are presented for ruby, alexandrite, and fluorescein in glass and are interpreted.
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.
We present a detailed theoretical treatment of the response of a two-level atom to a fully-amplitude-modulated, narrow-band optical field. Specifically, we calculate the resonance behavior of modulated fluorescence and susceptibility components from the scalar continued-fraction solution of the optical Bloch equations. In the limit of vanishing damping the resonances are generally doubly branched: One set of branches reproduces the resonances of the time-averaged fluorescence, while the second set is different for each harmonic component. However, each branch is uniquely associated with an odd multiple quantum resonance. In analogy with magnetic resonance work, we derive analytical expressions for the generalized Bloch-Siegert shifts of the additional resonances. We discuss also the possibility of experimental verification of the theory.