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Quantum Electronics

Formation of optical pulses by modulating the resonant quantum transition frequency in a spectrally inhomogeneous medium

Vitaly Polovinkin, Yevgeny V. Radeonychev

Published Feb 28, 2010• 3 citations
Publisher

Abstract

We consider the conversion of monochromatic radiation in the case of resonant interaction with a quantum system under the condition of harmonic modulation of the quantum transition frequency by the action of additional nonresonant radiation due to the Stark or Zeeman effect, taking into account the inhomogeneous broadening of the quantum transition line. It is shown analytically and numerically that resonant radiation can be converted in a train of ultrashort pulses with a peak intensity exceeding manifold the incident wave intensity. The possibility of the additional compression of the produced pulses is studied by compensating the inherent frequency modulation in a medium with a quadratic or programmable dispersion. The optimal values of the radiation — matter interaction parameters are found numerically. It is shown that generation of femtosecond optical pulses of radiation quasi-resonant to the δ transition of the atomic hydrogen Balmer series is possible.

DOI
10.1070/qe2010v040n02abeh014224

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We consider the conversion of monochromatic radiation in the case of resonant interaction with a quantum system under the condition of harmonic modulation of the quantum transition frequency by the action of additional nonresonant radiation due to the Stark or Zeeman effect, taking into account the inhomogeneous broadening of the quantum transition line. It is shown analytically and numerically that resonant radiation can be converted in a train of ultrashort pulses with a peak intensity exceeding manifold the incident wave intensity. The possibility of the additional compression of the produced pulses is studied by compensating the inherent frequency modulation in a medium with a quadratic or programmable dispersion. The optimal values of the radiation — matter interaction parameters are found numerically. It is shown that generation of femtosecond optical pulses of radiation quasi-resonant to the δ transition of the atomic hydrogen Balmer series is possible.
We derive the analytical solution uncovering the origin of the ultrashort pulse formation from the resonant radiation in a hydrogenlike medium [Y. V. Radeonychev, V. A. Polovinkin, and O. Kocharovskaya, Phys. Rev. Lett. 105, 183902 (2010)], which is a quantum interference of the atomic transitions from the ground to the first excited energy level split by an intense far-off-resonant laser field due to the instantaneous Stark effect into the periodically oscillating sublevels and interference of the resonantly scattered radiation with the incident one. The analytical solution shows that the pulses are almost bandwidth limited and can be produced in a wide range of parameters in excellent agreement with the more general numerical simulation. The experimental schemes to form few-femtosecond pulses from 122-nm radiation in atomic hydrogen as well as few-hundred-attosecond pulses from 13.74-nm radiation in a Li2+{}^{2+}2+ medium are discussed.
We study a novel method to produce extremely short pulses of radiation in a resonant medium via induced transparency by means of adiabatic periodic modulation of atomic transition frequencies by far-off-resonant laser field, which causes linear Stark splitting of atomic energy levels resulting in partial transparency of an optically deep medium and drastic spectral modification of an incident resonant radiation. We find the regimes where the output spectrum corresponds to extremely short pulses and discuss several possible experimental realizations of generation of attosecond pulses in Li 2+ ions and femtosecond pulses in atomic hydrogen with commercially available facilities.
Propagation of monochromatic linearly polarized plane electromagnetic wave through resonantly absorbing anisotropic medium with frequency-modulated response is studied analytically and numerically. Frequency modulation is assumed to be provided by means of either mechanical vibration of a solid sample or modulation of quantum transition frequency by a driving low-frequency electromagnetic field. Possibility of generation of train of pulses with polarization of the incident field as well as with orthogonal polarization is shown. For each polarization, optimal combinations of values of four parameters that provide maximal ratio of peak pulse intensity to the average output intensity is found numerically. Possible realization of this resonant method of pulse shaping in laser crystal Dy 2+ :CaF 2 is discussed.
We propose a universal method to produce extremely short pulses of electromagnetic radiation in various spectral ranges. The essence of the method is a resonant interaction of radiation with atoms under the conditions of adiabatic periodic modulation of atomic transition frequencies by a far-off-resonant control laser field via dynamic Stark shift of the atomic levels and proper adjustment of the control field intensity and frequency, as well as the optical depth of the medium. The potential of the method is illustrated by an example in a hydrogenlike atomic system.
An analytic solution is obtained for the self-consistent equations describing propagation of an ultrashort pulse in a resonant two-level medium. The first approximation in respect of the dispersion is used to allow for phase modulation and for the dependence of the group velocity on the intensity and on the running value of the frequency. The conditions for the formation of a shock wave are established. It is shown that asymmetric broadening of the spectrum of a pulse results in coherent absorption, as a result of which the propagation of this pulse in such a medium leaves behind a polarization at the atomic transition frequency responsible for the radiation represented by the pulse.
An expression is obtained for the nonlinear susceptibility governing the addition of frequencies under resonance conditions. Allowance is made for the Stark shift, changes in populations, and transient response of the medium. Analysis is made of the stimulated emission of the third harmonic as a result of two-photon resonance in parallel and focused beams. It is shown that the saturation effect limits seriously the conversion coefficient of a nonlinear medium of fixed length. Optimal intensities of the fundamental-frequency radiation are found. It is shown that when a beam is focused sharply in a nonlinear medium, the saturation effect and Stark shift make it possible to add frequencies in media with normal dispersion. The relationship between four-photon parametric effects and coherent resonant processes such as self-induced transparency is established for ultrashort pulses.