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Acta Physica Sinica

Enhancement of nonlinear-optical signals in a cascade three-level system

Dan Du, Xiangming Hu, (1)华中师范大学物理科学与技术学院,武汉 430079; (2)华中师范大学物理科学与技术学院,武汉 430079;南华大学数理学院,衡阳 421001

Published Jan 1, 2006• 3 citations
Publisher

Abstract

In this paper we show that non-maximal coherence can lead to more efficient nonlinear frequency conversion than maximal coherence does. For this purpose we exemplify with the three-level cascade system (with no maximal coherence) to calculate the intensity of nonlinear-optical signal. A comparison is made between the Ξ system and the Λ system (with maximal coherence). The generated intensity is calculated by employing a nonperturbative approach. It is shown that under the conditions of the two-photon resonance and the same parameters, the largest intensity from the Ξ system is about twice as large as that from Λ system. The difference is analyzed in terms of dressed states. It is shown that both the spontaneous emission on the coupling transition and the spontaneous emission mediated three photon process play a contrary role for the two systems. These two processes enhance the generation of nonlinear signals for Ξ system but act contrarily for the Λ systems.

DOI
10.7498/aps.55.5232

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Journal of Physics B Atomic Molecular and Optical Physics•Oct 20, 2006•15 citations
In this paper we show that non-maximal coherence can lead to more efficient nonlinear frequency conversion than maximal coherence does. For this purpose we exemplify with the three-level cascade system (with no maximal coherence) to calculate the intensity of nonlinear-optical signal. A comparison is made between the Ξ system and the Λ system (with maximal coherence). The generated intensity is calculated by employing a nonperturbative approach. It is shown that under the conditions of the two-photon resonance and the same parameters, the largest intensity from the Ξ system is about twice as large as that from Λ system. The difference is analyzed in terms of dressed states. It is shown that both the spontaneous emission on the coupling transition and the spontaneous emission mediated three photon process play a contrary role for the two systems. These two processes enhance the generation of nonlinear signals for Ξ system but act contrarily for the Λ systems.
This paper reveals that spontaneous-emission-mediated emissive multiphoton progress can efficiently enhance nonlinear-optical signal in the cascade system:1) under the same parameters,the strongest nonlinear-optical signal takes place in the cascade system nearly double than it in the Λ system at coherent-population-trapping;2)within a certain range,the pump-atoms detuning controlled in the cascade system,we can get an increase in the generated nonlinear-optical signal efficiently,which is relaxed restrictions on the resonance between pump fields and atoms,and it is easy to operate.
We derive and compare the optical fluorescence spectra for all three transitions for three-level systems coherently coupled with two fields in a cascade or lambda configuration. It is shown that the total intensity of fluorescence at the combinational frequency (the sum or difference of the driving field frequencies in the ladder and lambda systems, respectively) may essentially exceed the fluorescence intensity at the driven transitions under the condition of two-photon resonance. The influence of additional homogeneous and inhomogeneous line broadening on the distribution of intensities between different fluorescence channels is studied. In particular, Doppler broadening is found to suppress fluorescence from the driven transitions but in some cases not from the combinational transition.
The nonlinear interaction of two intense optical waves with three energy levels of an atomic system is analyzed theoretically. The frequencies of the applied fields are assumed to be on or near two of the resonances involving the three levels. Particular attention is given to the generation of power at the difference frequency of the two applied fields where their frequency separation lies in the far-infrared range of the spectrum. In the limit of large input fields where atomic transitions are driven to saturation, the generated difference-frequency power is no longer proportional to the product of the two input powers. It is shown that, in this limit, the total rate of emission of photons at the difference frequency may, in principle, approach a value given by rNT\frac{\mathrm{rN}}{T}TrN​, where NNN is the total number of atoms, TTT is the average time of coherent interaction of atoms and the radiation field, and rrr is a factor which in favorable cases approaches unity at low temperatures. Also, a number of additional effects are encountered due to coherent double-quantum transitions among various levels which may be ignored only for weak input powers. These effects are highly dependent on the modes of relaxations of atomic levels and the details of the line shape. The results are applied to several cases, in which the resonance condition yields large efficiency in nonlinear frequency mixing.
Abstract We theoretically investigate the self-nonlinear and cross-nonlinear responses of the Λ-type, V-type, and ladder-type three-level atomic systems. The analytical solutions of the cross-nonlinearity are obtained by using an iterative method. These analytical expressions reveal that the atomic decay rates and two-photon resonance are closely related to the cross-nonlinear response. For the Λ-type system, the relaxation rate between the ground-state sublevels determines the amplitude and linewidth of the cross-nonlinearity. For the ladder-type system, the lifetime of the upper excited state governs the amplitude and linewidth of the cross-nonlinearity. In both systems, the amplitude of the cross-nonlinearity is significantly enhanced, and the linewidth is greatly compressed simultaneously. In contrast, for the V-type three-level system, the amplitude and linewidth of the cross-nonlinearity are related to the spontaneous emission rate of the excited states, where neither the amplitude enhancement nor the linewidth compression is observed. We conclude that the cross-nonlinear response can reach or even exceed the linear response in the Λ-type system when the relaxation rate between the ground states is sufficiently small, or in the ladder-type system when the spontaneous emission rate of the upper excited state is sufficiently small. Compared with the crossnonlinearity, the self-nonlinearity is related to the Rabi frequency and detuning of the coupling field. Its amplitude decreases with the increase of the coupling Rabi frequency, while it can be increased to a certain extent with the increase of the coupling detuning. Our results provide a theoretical basis for the optimization and application of strong nonlinear effects in three-level atomic systems.
Abstract We theoretically study the two- and three-photon coherence in a Ξ−Λ type four-level system for stationary as well moving atoms at the room temperature using density matrix formalism. We discuss the role of dressed states to elucidate the electromagnetically induced transparency and electromagnetically induced absorption phenomena. The presence of the third field induces absorption at the line centre. A negative dispersion slope owing to the enhanced absorption results in super-luminal light propagation and the group index variation with the coupling field is switched from sub- to super-luminal. Group index with probe detuning shows super-luminal light propagation behaviour at the dressed state positions. The three optical fields trigger four-wave mixing as a result of the third order nonlinearity. The transient evolution is also discussed for optimum strengths of the coupling and drive fields to realize the optical switching in the system.
In a three-level closed Λ system with incoherent pumping, both the dynamically induced coherence (DIC) and the spontaneously generated coherence (SGC) play a significant role in inducing different nonlinear processes like amplification without population inversion (AWI), electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA). These two coherences can interfere destructively and constructively giving rise to different nonlinear processes (EIT, EIA, AWI) when the strength of these two coherences is comparable. Therefore the system can switch over from one nonlinear process to the other and the desired response of the system can be achieved by controlling the system parameters. It has been shown that this switching can occur by changing the relative strength of Rabi frequencies for the coherent and probe fields and the mode of incoherent pumping (unidirectional and bidirectional) for a chosen SGC parameter. Further control over the response can be achieved by changing the phase between two radiation fields. But the dependence on phase is different when both the coherences contribute than that obtained only from SGC. Exact analytical expressions for the coherences and populations in the steady state limit have been derived (keeping all orders of system parameters) to generalize the analysis and any restrictions over the system parameters (e.g. spontaneous decay widths on probe and coherent transitions are equal) have been avoided to make it applicable to various atomic and molecular systems. However the approximate expressions can be derived from these exact values. Numerical values obtained by solving the density matrix equations agreed well with these exact analytical values.