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Symposium on Photonics and Optoelectronics

The Modulation Properties of Local-Field Effect on a Dense Two-Level System

Xiangyang Yu, Cheng Li

Published Jun 1, 2010• 0 citations
Publisher

Abstract

In this paper we investigate the evolutions of Bloch vector in a dense two-level system with near-dipole-dipole (NDD) interactions driven by ultrafast incident pulses, whose duration is far less than the relaxation times. The results show that the evolutionary relationships between dispersion (absorption) and inversion, as function of NDD parameter, are reciprocal. And the pulse width and pulse area effect on the final state of inversion (FSI) are sensitive and obvious for nonzero NDD parameter. Furthermore, we demonstrate a way to eliminate the NDD interactions effect on the FSI by adding an appropriate detuning.

DOI
10.1109/sopo.2010.5504293

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Jisuan wuli•Jan 1, 2009•0 citations
In this paper we investigate the evolutions of Bloch vector in a dense two-level system with near-dipole-dipole (NDD) interactions driven by ultrafast incident pulses, whose duration is far less than the relaxation times. The results show that the evolutionary relationships between dispersion (absorption) and inversion, as function of NDD parameter, are reciprocal. And the pulse width and pulse area effect on the final state of inversion (FSI) are sensitive and obvious for nonzero NDD parameter. Furthermore, we demonstrate a way to eliminate the NDD interactions effect on the FSI by adding an appropriate detuning.
We performed a numerical investigation of the dynamics of the optical Bloch equations, extended for near dipole-dipole (NDD) interactions in dense collections of two-level systems. As a function of peak field strength, the inversion that remains in the medium following excitation by an ultrashort optical pulse has step-like transitions between the ground state and the excited state. The medium is left fully inverted if the peak Rabi frequency (peak field strength written in units of frequency) is equal to the NDD interaction strength. Remarkably, this result is independent of pulse area. About this point is a region of peak field strength for which the dense medium is left fully, or nearly fully, inverted. On the weak side of this region, the dense medium is left in the ground state. On the strong side of this region, the medium alternates between absorbing (ground state) and amplifying (inverted) as a function of peak field strength. This response can be used to measure the strength of the NDD interaction, for coherent optical pumping, and also constitutes a new and unique intrinsic optical switch, which, unlike optical bistability, does not have hysteresis and is independent of dissipation from incoherent effects.
The propagation behaviors, which include the carrier-envelope phase, the area evolution and the solitary pulse number of few-cycle pulses in a dense two-level medium, are investigated based on full-wave Maxwell-Bloch equations by taking Lorentz local field correction (LFC) into account. Several novel features are found: the difference of the carrier-envelope phase between the cases with and without LFC can go up to pi at some location; although the area of ultrashort solitary pulses is lager than 2pi, the area of the effective Rabi frequency, which equals to that the Rabi frequency pluses the product of the strength of the near dipole-dipole (NDD) interaction and the polarization, is consistent with the standard area theorem and keeps 2pi; the large area pulse penetrating into the medium produces several solitary pulses as usual, but the number of solitary pulses changes at certain condition.
According to the semi-classical theory of light-matter interaction,the Bloch equations with chirped terms were established in a dense two-level medium,and an accurate and efficient fourth-order Runge-Kutta method was applied for solving the equations.After numerical simulation,the interactions between a chirped ultra-short pulse and dense resonant two-level medium were investigated,and the influences of local-field effects and chirp on Bloch vectors were gained.The numerical results show that,the evolutions of Bloch vectors and the final state of inversion are strongly modulated by the local-field effects correction coefficient and chirp parameter,which provides a method to achieve stable population inversion of control by adjusting the linear chirp parameter and local-field correction coefficient.
Propagation of a few-cycle laser pulses in a dense V-type three-level atomic medium is investigated based on full-wave Maxwell-Bloch equations by taking the near dipole-dipole (NDD) interaction into account.We find that the ratio, γ, of the transition dipole moments has strong influence on the time evolution and split of the pulse: when γ ≤ 1, the NDD interaction delays propagation and split of the pulse, and this phenomenon is more obvious when the value of γ is smaller; when γ = √ 2, the NDD interaction accelerates propagation and split of the pulse.
In this work the authors will present analytical results that explain the numerical simulations of M. E. Crenshaw et al.1 on the extended optical Bloch equations that include near dipole–dipole interactions. These simulations have shown the possibility of an ultrafast switch, caused by an incident unaltered pulse in a thin dense medium of two-level atoms. The switching parameter, defined as Ω 0 ε , is a ratio of the Rabi frequency to the strength of the near dipole–dipole interaction Our analysis will show an exact solution for the first switching condition, Ω 0 ε ≈ 1 . Furthermore, an asymptotic analysis will show that to leading order in the asymptotic expansion, only three possible final states of the medium occur. These states, if characterized by the population inversion w, are total inversion (w f = 1), no inversion (w f = -1), or half inversion (w f = 0). For the case w f = 0, a reduced system in a phase plane is derived. This reduced system will help us understand this self-transparent behavior. We will conclude by presenting the results on the stability analysis in parameter space.
Full Maxwell-Bloch equations are solved with PC-FDTD method to investigate population evolution of dense V-type three-level medium in few-cycle laser pulses.It is shown that the ratio of transition dipole moments(γ) has strong influence on appearing time and oscillation frequency of population inversion.As γ=1 population inversion with LFC appears later than that without LFC and near dipole-dipole(NDD) interaction delays population inversion.As γ1,appearing with LFC is earlier than that without LFC and NDD interaction accelerates the population inversion.The number of population inversion with unequal transition dipole moments is more than that with equal transition dipole moments.Moreover,evolution of populations in a dense medium is quite different from that in a dilute medium.At input surface,in a dilute medium,population inversion appears with time evolution.With increasing of medium density,populations show quasi-periodicity oscillation and oscillation frequencies of populations with LFC are less than that without LFC.