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CRC Press eBooks

Transparency induced by chirped femtosecond laser pulse in a two-level medium

J Zhang

Published Jun 15, 2005• 0 citations
Publisher

Abstract

Recently, the advances in generation and characterization techniques of ultrashort laser pulses made it practical to prepare precisely defined laser pulses, these open up new possibilities for studying and controlling dynamical processes in femtosecond time scale. Hitherto, frequency-synthesized or chirped laser pulses have been widely applied to high-order harmonic generation (HHG) [3], population transfer [4], multiphoton transitions between Rydberg states [5], ect. Both the interference of two-color pulses and the nontrivial time dependence of chirped pulse laser field may lead to very interesting results. Moreover, recent studies have manifested that chirping can also have much impacts on the laser pulses as it propagates through different medium. For example, the propagation properties of chirped soliton pulses in optical nonlinear Kenmedia were investigated by Desaix et al. [6]. The result indicates that the properties of asymptotically emerging solitons depend not only on the magnitude, but also on the form of the initial chirp. In particular, the splitting of an initial pulse into separating soliton pulse pairs only occurs for certain classes of initial chirp functions. The influence of pulse shape and frequency chirp on stability of optical solitons was studied by Klaus and Shaw [7]. They found that destabilization occurs when eigenvalues of an associated Zakharov-Shabat system, which move along the positive imaginary axis with increasing chirp parameter, either are absorbed into the lower half plane or collide with a nother eigenvalue. Furthermore, the signal and group velocities for chirped pulses propagating through a GaAs cavity were measured by Centini et al. [8]. They showed that the chirp substantially modifies the group velocity of the pulse, but leaves the signal velocity unaltered.

DOI
10.1201/9781482269208-146

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Recently, the advances in generation and characterization techniques of ultrashort laser pulses made it practical to prepare precisely defined laser pulses, these open up new possibilities for studying and controlling dynamical processes in femtosecond time scale. Hitherto, frequency-synthesized or chirped laser pulses have been widely applied to high-order harmonic generation (HHG) [3], population transfer [4], multiphoton transitions between Rydberg states [5], ect. Both the interference of two-color pulses and the nontrivial time dependence of chirped pulse laser field may lead to very interesting results. Moreover, recent studies have manifested that chirping can also have much impacts on the laser pulses as it propagates through different medium. For example, the propagation properties of chirped soliton pulses in optical nonlinear Kenmedia were investigated by Desaix et al. [6]. The result indicates that the properties of asymptotically emerging solitons depend not only on the magnitude, but also on the form of the initial chirp. In particular, the splitting of an initial pulse into separating soliton pulse pairs only occurs for certain classes of initial chirp functions. The influence of pulse shape and frequency chirp on stability of optical solitons was studied by Klaus and Shaw [7]. They found that destabilization occurs when eigenvalues of an associated Zakharov-Shabat system, which move along the positive imaginary axis with increasing chirp parameter, either are absorbed into the lower half plane or collide with a nother eigenvalue. Furthermore, the signal and group velocities for chirped pulses propagating through a GaAs cavity were measured by Centini et al. [8]. They showed that the chirp substantially modifies the group velocity of the pulse, but leaves the signal velocity unaltered.
We investigate the propagation dynamics of nonlinear chirped optical laser pulses in a two-level medium.For certain chirp strength and chirp width, an incident 2π nonlinear chirped pulse will split into optical precursors and a stable self-induced transparency soliton.This is caused by the particular Fourier spectrum that includes not only central resonant frequency components but also high-frequency and low-frequency sidebands.Moreover, the effects of chirp parameters on the evolution of nonlinear chirped pulses are also discussed.
If an incident pulse is chirped, the critical parameters for self-induced transparency to occur in coherent pulse propagation can no longer be obtained from the well-known McCall-Hahn area theorem. We have been able to obtain these parameters by solving the Zakharov-Shabat eigenvalue equation for the bound-state eigenvalues. We find that critical (threshold) areas will be increased for a chirped incident pulse in almost all cases, except for a box profile or for a pulse that is approximately box-like in shape. In these latter cases, the chirped critical areas will instead decrease for the second and all higher branches. The first branch’s critical area is always increased due to chirping.
It is known that ultrashort pulse coherent propagation through the resonant absorbing medium leads to the pulse splitting and pulse train generation. First of these pulses is the input pulse and the following pulses are resonant medium response. It is also known that such a propagation mode leads to the «spectrum condensation» effect, at which broad-band input femtosecond laser emission, as it leaves opically-dense medium, centralized in the vicinity of the resonance absorption lines. It's interesting to clear up the dependence of a condensation effect on an input femtosecond pulse phase modulation value (chirp).
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.
We study the propagation of frequency-chirped laser pulses in optically thick media. We consider a medium of atoms with a $\ensuremath{\Lambda}$ level-scheme (Lambda atoms) and also, for comparison, a medium of two-level atoms. Frequency-chirped laser pulses that induce adiabatic population transfer between the atomic levels are considered. They induce transitions between the two lower (metastable) levels of the $\ensuremath{\Lambda}$-atoms and between the ground and excited states of the two-level atoms. We show that associated with this adiabatic population transfer in $\ensuremath{\Lambda}$-atoms, there is a regime of enhanced transparency of the medium---the pulses are distorted much less than in the medium of two-level atoms and retain their ability to transfer the atomic population much longer during propagation.
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.