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Journal of Modern Optics

Resonant enhancement of refractive index in a cascade scheme

Alexander S. Zibrov, Andrey B. Matsko, Leo W. Hollberg, Vladimir L Velichansky

Published Mar 1, 2002• 9 citations
Publisher

Abstract

The refractive index of coherently driven rubidium vapour is experimentally investigated in a three-level cascade con® guration using a selective reection technique. The maximum measured resonant change in the refractive index is ¢n ' 0:1. The selective reection is accompanied by a four-wave-mixing process that can reach π90% eA ciency.

DOI
10.1080/09500340110088588

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The refractive index of coherently driven rubidium vapour is experimentally investigated in a three-level cascade con® guration using a selective reection technique. The maximum measured resonant change in the refractive index is ¢n ' 0:1. The selective reection is accompanied by a four-wave-mixing process that can reach π90% eA ciency.
Refractive index enhancement accompanied by vanishing absorption in a four-level atomic system interacting with two control and two probe fields in a regime of four-wave mixing (FWM) has been predicted and studied in the present work. We analyzed the maximal index enhancement in the four-level FWM system and gave index estimates for a real atomic gas of 40{}^{40}40K, taking into account its multilevel structure and collisional and Doppler broadenings at large atomic densities. We also discussed how vanishing absorption with no nearby amplification can be realized in a two species system, consisting of a four-level FWM and a two-level system, where the latter provides additional absorption for one of the probe fields. We numerically estimated the index change in a system composed of 40{}^{40}40K and 39{}^{39}39K gases.
The Kerr nonlinear index of refraction for rubidium atoms is measured by using an optical ring cavity with and without electromagnetically induced transparency (EIT). Significant enhancement and inhibition of the Kerr nonlinear index is observed near resonance with EIT. The nonlinear index of refraction is measured as functions of probe and coupling frequency detunings, respectively, with and without the presence of EIT. A simple theoretical calculation including Doppler broadening is presented and is found to be in good qualitative agreement with the experimentally measured results.
Enhancement and control of the index of refraction in a mixture of two three-level atomic species that form a pair of far-detuned $\ensuremath{\Lambda}$ schemes under two-photon resonance has been studied. We employ the density-matrix approach to properly take population relaxation into account and to describe the interaction of each $\ensuremath{\Lambda}$ system with the electromagnetic fields. Both $\ensuremath{\Lambda}$ systems are driven by a corresponding far-detuned coherent field at one atomic transition and are probed by the same weak field. In the dressed-state basis, it represents a superposition of effective two-level subsystems with the positions, widths, and amplitudes of the resonances controlled by the driving fields and allows for efficient control of the susceptibility of the total system; leading to refractive index (RI) enhancement with vanishing absorption in the absence of amplification. We analyze the experimental implementation of such a system in a cell of Rb atoms with a natural abundance of isotopes. An upper limit estimate of the RI enhancement is obtained.
We demonstrate a scheme for coherently induced grating based on a mixture of two three-level atomic species interacting with two standing-wave fields. As a result of interaction between the absorptive and amplified Raman resonances, the refractive index of the medium can be enhanced and modulated periodically. Then a sinusoidal grating, which can diffract the probe field into high-order directions, is coherently formed in the medium. The proposed scheme is theoretically investigated in a mixture of atomic isotopes of rubidium. The results show that the diffraction efficiency depends strongly on the two two-photon detunings of the two Raman transitions and the intensities of the two driving standing-wave fields. The proposed electromagnetically induced grating scheme may be applied to the all-optical switching and beam splitting in optical networking and communication.
The resonant absorption, emission, and scattering of light are the fundamental optical processes that have been used both to probe matter and to manipulate light itself. In the last decade there has been essential progress in coherent control of both linear and nonlinear optical responses based on resonant excitation of atomic coherence in multilevel quantum systems. Some interesting and useful phenomena, resulting from coherent control of absorption and the group index, such as electromagnetically induced transparency, lasing without inversion, and ultra-slow group velocity of light have been widely studied. This work is focused on coherent control of refractive index and resonant fluorescence in multilevel medium. \n \nWe suggest two promising schemes for resonant enhancement of the refractive index with eliminated absorption and propose their implementation in transition element doped crystals with excited state absorption and in a cell of Rb atoms at natural abundance. We show how to use one of these schemes for spatial variation of the refractive index via its periodic resonant increase/decrease, remarkably keeping at the same time zero absorption/gain. It opens the way to production of transparent photonic structures (such as distributed Bragg reflectors, holey fibers, or photonic crystals) in a homogeneous resonant atomic media such as dielectrics with homogeneously distributed impurities, atomic, or molecular gases. These optically produced photonic structures could easily be controlled (including switching on/off, changing amplitude and period of modulation) and would be highly selective in frequency, naturally limited by the width of the optical resonance. \n \nWe also derive the optical fluorescence spectra of a three-level medium driven by two coherent fields at the adjacent transitions in a general case when all three transitions are allowed. We show that coherent driving can efficiently control the distribution of intensities between the fluorescent channels. In particular, the total intensity of fluorescence at the transition which is not driven by the optical fields may essentially exceed the fluorescence intensity at the driven transitions under the condition of two-photon resonance. This counter-intuitive effect is due to depletion of the intermediate state via atomic interference.
Index of refraction characterizes the linear response of a medium and hence it is strongly enhanced near atomic resonance. However, it is accompanied by either resonant absorption or gain preventing the use of high index. We show that these problems may be overcome using coherent control of excited state absorption (ESA), i.e. absorption from the populated excited electronic state. The idea is to compensate gain at the lower operating transition via partially suppressed ESA at the frequency of the probe field tuned to the maximum refractive index of the ESA transition. It results in resonant enhancement of refractive index without absorption in the absence of any neighboring amplification regions.