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Optics Letters

Control of spectral interference patterns in broad Rabi sidebands toward quasi-comb structures

Dmitri Romanov, A. I. Filin, Robert J. Levis

Published Feb 13, 2015• 2 citations

Abstract

The pattern of spectral interference fringes in broad dynamic Rabi sidebands allows for a considerable degree of control by shaping the picosecond driving pulse. We demonstrate experimental evidence of such control and report an analytic and numerical investigation of possibilities to control the fringe pattern to produce a comb-like optical structure. The temporal phase and amplitude shaping of a picosecond driving pulse influence the spectrum envelope, fringe contrast, and fringe spacing variation in the sideband spectra. The sideband spectrum envelope depends on the sharpness of the driving pulse, that is, on the rate at which the temporal distance between the leading and trailing edges grows away from the pulse maximum. Increasing this parameter reduces the variation of the envelope amplitude across the sideband. The fringe contrast, defined by the maximum-to-minimum difference, depends strongly on the asymmetry of the driving pulse. The imbalance between the leading and trailing edges leads to a decrease of the contrast. The variation of interpeak distance within a sideband was controlled using the temporal shape of the driving pulse. In the particular case of a blue-shifted sideband emitted by excited oxygen atoms driven by a picosecond pulse of 800 nm carrier wavelength and ∼5×10¹⁰ W cm⁻² intensity, a Gaussian pulse shape results in an interpeak distance increasing almost five times over the interval from 1.60 to 1.66 eV, whereas a super-Gaussian shape leads to almost equidistant fringes producing a comb-like spectrum.

DOI: 10.1364/ol.40.000717

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The pattern of spectral interference fringes in broad dynamic Rabi sidebands allows for a considerable degree of control by shaping the picosecond driving pulse. We demonstrate experimental evidence of such control and report an analytic and numerical investigation of possibilities to control the fringe pattern to produce a comb-like optical structure. The temporal phase and amplitude shaping of a picosecond driving pulse influence the spectrum envelope, fringe contrast, and fringe spacing variation in the sideband spectra. The sideband spectrum envelope depends on the sharpness of the driving pulse, that is, on the rate at which the temporal distance between the leading and trailing edges grows away from the pulse maximum. Increasing this parameter reduces the variation of the envelope amplitude across the sideband. The fringe contrast, defined by the maximum-to-minimum difference, depends strongly on the asymmetry of the driving pulse. The imbalance between the leading and trailing edges leads to a decrease of the contrast. The variation of interpeak distance within a sideband was controlled using the temporal shape of the driving pulse. In the particular case of a blue-shifted sideband emitted by excited oxygen atoms driven by a picosecond pulse of 800 nm carrier wavelength and ∼5×10¹⁰ W cm⁻² intensity, a Gaussian pulse shape results in an interpeak distance increasing almost five times over the interval from 1.60 to 1.66 eV, whereas a super-Gaussian shape leads to almost equidistant fringes producing a comb-like spectrum.

Characteristic fringe patterns of spectral interference in dynamic Rabi sidebands are used as a means to investigate decoherence phenomena in a highly nonequilibrium underdense microplasma formed in atmospheric-pressure oxygen gas in the wake of a strong-field (\ensuremath{\sim}10

{}^{13}

W/cm

{}^{2}

) femtosecond pump pulse. The same transient processes in the nonequilibrium plasma work both to create the effective two-level systems producing coherent sidebands and to destroy the coherence and smear the sideband spectral structure; the observed spectral fringe pattern is a result of the trade-off of these two effects. The sidebands generated on a moderately intense (\ensuremath{\sim}10

{}^{10}

W/cm

{}^{2}

) picosecond laser pulse reveal the decoherence rate as a function of the pump-pulse intensity and the pump-probe delay time. The rate increases with the pump laser intensity and decreases with the delay with corresponding decoherence times in the range of 750 fs to 3 ps, in good agreement with theory revealing that electron scattering dominates the dynamics for the subnanosecond relaxation processes.

Broadband, coherent radiation in the optical-frequency range is generated using microplasma channels in atmospheric gases in a pump-probe experiment. A microplasma medium is created in a gas by a focused intense femtosecond pump pulse. A picosecond probe pulse then interacts with this microplasma channel, producing broad, coherent sidebands that are associated with luminescence lines and are redshifted and blueshifted with respect to the laser carrier frequency. These sidebands originate from the induced Rabi oscillations between pairs of excited states that are coupled by the probe pulse. Thus the sideband radiation intensity tracks the microplasma evolution. The sidebands arise from broad and tunable Rabi shifts corresponding to varying values of the electric-field magnitude in the probe pulse. The \ensuremath{\sim}10

{}^{10}

W cm${}^{\ensuremath{-}2}$ probe beam creates a maximum sideband shift of >90 meV from the carrier frequency, resulting in an effective bandwidth of 200 meV. The sidebands can be tuned and controlled by the intensity and temporal profile of the probe pulse. The fact that the coherence is observed in a microplasma demonstrates that Rabi cycling is possible at high temperature with moderately high laser intensities as long as transitions close to the driving frequency ($\ensuremath{\Delta}$\ensuremath{\sim}2% ${\ensuremath{\omega}}_{c}$) are available. Plasma excitation combined with Rabi-shifting measurements also serves as a means to simultaneously extract quantitative ratios for the transition-dipole moments between multiple sets of highly excited states with transitions in the optical regime.

We report observation and control of the spatial-spectral distributions of coherent, dynamic Rabi sideband radiation. The Rabi sidebands result from the interaction of a shaped picosecond probe laser of intensity 10(10) W cm(-2), with neutral excited atomic oxygen generated in a laser-induced microplasma. The spatial-spectral distribution is measured and compared for picosecond laser pulses having either an asymmetric temporal shape or a Gaussian temporal shape. The resulting spatial-spectral distributions are in quantitative agreement with theoretical predictions that account for the radial intensity distribution of the picosecond probe pulse.

Broadband, coherent radiation in the optical frequency range is generated using micro-plasma channels in atmospheric gases in a pump-probe experiment. A micro-plasma medium is created in a gas by a focused intense femtosecond pump pulse. A picosecond probe pulse then interacts with this micro-plasma channel, producing broad, coherent sidebands that are associated with luminescence lines and are red- and blue-shifted with respect to the laser carrier frequency. These sidebands originate from the induced Rabi oscillations between pairs of excited states that are coupled by the probe pulse. These excited states become populated in the process of plasma cooling. Thus, the sideband radiation intensity tracks the micro-plasma evolution. The sidebands incorporate Rabi shifts corresponding to varying value of the electric field magnitude in the probe pulse: this makes them broad and malleable to tuning. The intensity of the probe beam ~ 1010 W cm-2, creates a maximum sideband shift of> 90 meV from the carrier frequency, resulting in an effective bandwidth of 200 meV. The sidebands may be effectively controlled by the intensity and temporal profile of the probe pulse. The giant Rabi shift is both tunable and coherent over a wide range of frequencies and over a wide range of atomic transitions. The fact that the coherence is observed in a micro plasma demonstrates that Rabi cycling is possible at high temperature with moderately high laser intensities (1010 W cm-2) as long as transitions close to the driving frequency ( ~ 2 % c) are available.

Previous work has shown that a new light source consisting of mutually coherent spectral sidebands ranging from 2.94 μm to 195 nm can be obtained by adiabatic preparation of a molecular ensemble in a single vibrational superposition state. Molecular motion modulated the refractive index and thus led to the frequency modulation of the driving beat-note. The resulting sidebands were equidistant and separated by a frequency equal to the modulation frequency. In the present work we extend this idea by applying more input fields to the molecular ensemble. We take two input fields separated by one half of the modulation frequency, such that their second harmonics drive the molecular ensemble. The proposed approach results in generating an equidistant comb of frequencies separated by a fraction (1/4) of the modulation frequency. Moreover, the intensity of the generated train of pulses increases by the inverse of the same factor. An important feature of the generated comb is that it reaches zero frequency, and as a consequence allows for control of the absolute phase, or the phase of the carrier with respect to the envelope. Since many physical processes, for example photoionization of molecules by intense laser pulses, are influenced by the time dependence of the electric field (and not the envelope), control of absolute phase will become an important issue for few-cycle pulses.