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Journal of Modern Optics

Transparent propagation of few-cycle laser pulses with arbitrary intensity in double-lambda atomic systems

Li Deng, Yueping Niu, Shangqing Gong

Published Oct 11, 2012• 0 citations
Publisher

Abstract

A numerical study is reported of the transparent propagation of few-cycle laser pulses with arbitrary intensity. The phenomenon is based on the preparation of steady maximum coherent superposition state of the lower two levels in double-lambda atomic systems. The transparency of the few-cycle pulse is sensitive to its parameters such as the arriving time and relative phase. The advantages of the method are discussed.

DOI
10.1080/09500340.2012.728254

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Journal of Experimental and Theoretical Physics Letters•Jun 1, 1998•1 citation
A numerical study is reported of the transparent propagation of few-cycle laser pulses with arbitrary intensity. The phenomenon is based on the preparation of steady maximum coherent superposition state of the lower two levels in double-lambda atomic systems. The transparency of the few-cycle pulse is sensitive to its parameters such as the arriving time and relative phase. The advantages of the method are discussed.
Quantum coherence and interference in atomic systems can lead to interesting optical phenomena such as nonabsorbing resonances, lasing without inversion, generating an ultrahigh index of refraction without absorption, propagation of light pulses without losses. In the last-named is given the title transparency. Up to now it is known some types of transparency in multi-level resonant media. One of them is electromagnetically induced transparency (EIT). The phenomenon of EIT in the propagation of laser radiation through an absorbing medium has been recently investigated and explained in terms of quantum coherence and interference for multi-level atomic system. For instance in the (Lambda) -system, if the atomic medium is prepared in a quantum superposition of states, matched pulses, i.e., a pair of optical pulses whose amplitude and phase have a well defined relation, propagate without absorption. The mechanism of coherent population trapping is responsible for EIT in a (Lambda) -system. There is another, well known mechanism for creating transparency in a two-state atom: self-induced transparency, or SIT. Here, a single pulse whose area (the integral of its Rabi frequency over time) is 2(pi) is applied to the medium. Such a pulse causes the atoms to cycle smoothly from the ground to the excited state and then back again. In principle, such a pulse can propagate over long distances. SIT can be generalized to multi-level systems and multiple quasi-monochromatic fields. Generalization of SIT in a (Lambda) -system was obtained in reference 2. In this report we present a new type of transparency (combined transparency). This type describes propagation of laser pulse through a (Lambda) -type medium where the initial atomic state is prepared in the form of spatially varying coherent superposition of low-energetic states (initial coherency gradient). The common envelope behaves as usual 2(pi) hyperbolic secant pulse, but the ratio between the components of frequencies transitions 1> yields 3> and 2> yields 3> changes due to coherent Raman scattering so (phi) equals atan(E1/E2) equals (pi) /2-Gz, where z is the coordinate, G is the constant determined by both the incident pulse parameters and the initial coherence between the atomic states. Our solution demonstrates a direct connection of EIT in adiabatic regime to the SIT effects. This type of a transparency is given the title screw-type transparency, because for the given form of incident pulse (pitch of screw) medium is transparent, if medium's the initial coherence gradient is correspondingly prepared (thread on a engine nut). Besides a transparency, this phenomenon contains a transformation of the incident pulse frequency during the process of the propagation. This property of the phenomena can be result in a complete conversion of the frequency.
The quantum dynamics of a two-level system illuminated by a few-cycle pulse with an adjustable carrier-envelope (C-E) phase is investigated theoretically. We consider the weak-field regime where tunneling processes and multiphoton ionization are negligible. It is shown that the upper state population exhibits a strong dependence on the C-E phase and on the time of arrival of the few-cycle pulse if the system is initially prepared in a coherent superposition state. We demonstrate that this effect can be employed to probe the coherence properties of the superposition state and allows one to determine the phase of the laser that prepares this state.
Propagation of single- and two-color hyperbolic secant femtosecond laser pulses in a three-level $\ensuremath{\Lambda}$-type quantum system is investigated by solving the Maxwell and density matrix equations with the finite-difference time-domain and Runge-Kutta methods. As a first study of our modeling, we simulate pulse self-induced transparency (SIT) in two-level systems and see how this phenomenon can be controlled by manipulating the initial relative phase between the SIT pulse and a second control pulse, provided the ratio between both pulse frequencies obeys the relation ${\ensuremath{\omega}}_{1}∕{\ensuremath{\omega}}_{2}=3$. We then examine frequency down-conversion processes that are observed with single- and two-color pulses the envelope area of which is equal to or a multiple of $2\ensuremath{\pi}$, for pulse frequencies close to resonance with the transitions of a three-level $\ensuremath{\Lambda}$ medium. Also, phase-sensitive phenomena are discussed in the case of two-color $\ensuremath{\omega}\text{\ensuremath{-}}3\ensuremath{\omega}$ pulses propagating resonantly in the three-level system. In particular, possibilities for such coherent control are found for frequency down-conversion processes when the ratio of the frequencies of optical transitions is ${\ensuremath{\omega}}_{13}∕{\ensuremath{\omega}}_{12}=3$. The conditions for quantum control of four-wave mixing processes are also examined when the pulse frequencies of two-color $\ensuremath{\omega}\text{\ensuremath{-}}3\ensuremath{\omega}$ pulses are far from any resonance of the three-level system. We demonstrate the possibility to cancel the phase sensitivity of the four-wave coupling in a $\ensuremath{\Lambda}$-type system by competition effects between optical transitions.
The spectrum evolution of a few-cycle optical pulse in a resonant two-level atom medium is studied theoretically by using the full Maxwell-Bloch equations. On the propagating pulse, significantly much faster oscillation components separated with the main pulse appear due to strong self-phase modulation and pulse reshaping. In this case, ideal self-induced transparency cannot occur for a 2π pulse. The spectrum of the 4π pulse shows an evident oscillatory feature because of the continuum interference of the separate pulses. For larger pulse areas, continuum generation from near ultraviolet to infrared occurs.
The phase-dependent feature of few-cycle pulsed laser propagation in a resonant two-level atom medium is demonstrated by solving the full Maxwell-Bloch equations. Even in the perturbative region, the propagating carrier field and the corresponding spectra of the few-cycle pulsed laser are sensitive to the initial phase due to self-phase modulation. For the larger pulse area, the fact that the carrier-wave reshaping comes from the carrier-wave Rabi flopping is also responsible for this sensitivity, and the phase-dependent feature is more evident.
A solution is obtained for the system of Maxwell-Schrödinger equations describing the propagation of a laser pulse through a three-level Λ medium in which the initial atomic populations are in a specially prepared coherent superposition of low-energy states. This solution describes a new type of transparency which is characterized by the presence of conversion of the frequency of the incident pulse and can be used, specifically, to produce “optical keys” and frequency converters for laser radiation.