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Journal of Modern Optics

Resonant enhancement of refractive index in transition element doped crystals via coherent control of excited state absorption

Chris O’Brien, Olga A. Kocharovskaya

Published Aug 14, 2009• 8 citations
Publisher

Abstract

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.

DOI
10.1080/09500340903157432

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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.
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.
We show the possibility to periodically modulate the refractive index in a homogeneous resonant atomic medium in space or/and time while simultaneously keeping vanishing absorption or gain. Such modulation is based on periodic resonant enhancement of the refractive index, controlled by an external optical field, and opens the way to produce coherently controllable photonic structures. We suggest the possible implementation of the proposed scheme in rare-earth doped crystals with excited state absorption.
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.
A method of suppression of losses due to excited-state absorption (ESA) in laser crystals is proposed, based on the well-known phenomenon of electromagnetically induced transparency. Typical situations in which ESA prevents lasing are considered. Theoretical analysis shows that by using an additional driving laser field one can inhibit ESA and make lasing possible. On the basis of available spectroscopic information estimates for rare-earth-ion-doped laser materials are presented. They show the feasibility of obtaining optical gain at parity-allowed $4{f}^{n}\ensuremath{\leftrightarrow}4{f}^{n\ensuremath{-}1}5d$ transitions of rare-earth ions in the ultraviolet spectral region after suppression of ESA at an emission wavelength into the conduction band of a host material.
We propose coherent control and enhancement of the refractive index with zero absorption in an n-type asymmetric double quantum well using intersubband transitions. These effects are caused by quantum coherence and interference whereby a strong infrared laser mixes upper conduction subbands of an intersubband transition with an auxiliary subband. In the ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ system considered here, an approximately 10% enhancement of the refractive index accompanied with zero absorption occurs at 10.5 \ensuremath{\mu}m, when the system is driven by a 6.2-\ensuremath{\mu}m laser field with an intensity of \ensuremath{\sim}1 MW/cm2{\mathrm{M}\mathrm{W}/\mathrm{c}\mathrm{m}}^{2}MW/cm2. The interplay between quantum coherence and electron population dynamics not only causes an enhancement of refractive index similar to that in atomic systems, but can also induce both low positive and negative group velocities.
A simple three-level system is proposed to produce high index of refraction with zero absorption in an Er 3+ -doped yttrium aluminium garnet (YAG) crystal, which is achieved for a probe field between the excited state 4 I 13/2 and ground state 4 I 15/2 by adjusting a strong coherent driving field between the upper excited state 4 I 11/2 and 4 I 15/2 . It is found that the changes of the frequency of the coherent driving field and the concentration of Er 3+ ions in the YAG crystal can maximize the index of refraction accompanied by vanishing absorption. This result could be useful for the dispersion compensation in fibre communication, laser particle acceleration, high precision magnetometry and so on.