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Optical filter withelectromagnetically induced transparency

J. Odeurs

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

Multi-level atomic coherence induced bycoupling andprobe fields canproduce manyinteresting effects suchas electromagnetically induced transparency (EIT), lasing without inversion, electromagnetically induced absorption, slow light, stopped light, nonlinear conversion withsubstantially reduced phase matching conditions, etc. EITisobserved asanarrow holeinabroadabsorption line.Steep dispersion within theEITwindowresults ina substantial reduction ofthegroupvelocity oftheprobe pulse. Onecanexpect that theabsorption andthegroupvelocity ofthepulse aresubstantially reduced ifthecarrier frequency andthespectrum oftheinput pulse areconfined inside the EITwindow.Inthis report we showthat theEITwindowcanbeusedasatime-to-frequency filter fortheprobe pulse whosespectrum ismuchbroader thanthewidth oftheEITwindow. Wedemonstrate that thenarrowspectral part ofthe pulse, coincident withtheEITwindow, develops inalong Gaussian pulse withslowgroupvelocity. Thatpartofthe pulse spectrum, whichcoincides withthemaximumoftheabsorption line, isstrongly absorbed. Sidebands ofthepulse interacting withthewings oftheabsorption line develop ina0-tpulse. Thelatter hasanoscillatory shape andthetime integral ofitsenvelope (pulse area) isclose tozero, henceits nameof0-it pulse. Thegroupvelocity ofa0-tpulse is close tothephase velocity oflight. Inanoptically denseabsorptive medium, theslowGaussian pulse andthefast 0-it pulse arewellseparated intimeandthey donotoverlap attheoutput oftheabsorber. Timegating ofthepromptpart of thepulse allows separating thenarrowspectrum, theslowpartofthepulse attheoutput. Suchafiltering isnotsensitive tothespectrum oftheinput pulse. Theparameters ofthenarrowspectrum pulse, i.e., thewidth, theshape andthetime of arrival, depend only ontheparameters ofthefilter, i.e., theeffective length oftheabsorber andthewidth oftheEIT window.

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Physical Review A•Jan 28, 2005•20 citations
Multi-level atomic coherence induced bycoupling andprobe fields canproduce manyinteresting effects suchas electromagnetically induced transparency (EIT), lasing without inversion, electromagnetically induced absorption, slow light, stopped light, nonlinear conversion withsubstantially reduced phase matching conditions, etc. EITisobserved asanarrow holeinabroadabsorption line.Steep dispersion within theEITwindowresults ina substantial reduction ofthegroupvelocity oftheprobe pulse. Onecanexpect that theabsorption andthegroupvelocity ofthepulse aresubstantially reduced ifthecarrier frequency andthespectrum oftheinput pulse areconfined inside the EITwindow.Inthis report we showthat theEITwindowcanbeusedasatime-to-frequency filter fortheprobe pulse whosespectrum ismuchbroader thanthewidth oftheEITwindow. Wedemonstrate that thenarrowspectral part ofthe pulse, coincident withtheEITwindow, develops inalong Gaussian pulse withslowgroupvelocity. Thatpartofthe pulse spectrum, whichcoincides withthemaximumoftheabsorption line, isstrongly absorbed. Sidebands ofthepulse interacting withthewings oftheabsorption line develop ina0-tpulse. Thelatter hasanoscillatory shape andthetime integral ofitsenvelope (pulse area) isclose tozero, henceits nameof0-it pulse. Thegroupvelocity ofa0-tpulse is close tothephase velocity oflight. Inanoptically denseabsorptive medium, theslowGaussian pulse andthefast 0-it pulse arewellseparated intimeandthey donotoverlap attheoutput oftheabsorber. Timegating ofthepromptpart of thepulse allows separating thenarrowspectrum, theslowpartofthepulse attheoutput. Suchafiltering isnotsensitive tothespectrum oftheinput pulse. Theparameters ofthenarrowspectrum pulse, i.e., thewidth, theshape andthetime of arrival, depend only ontheparameters ofthefilter, i.e., theeffective length oftheabsorber andthewidth oftheEIT window.
This report shows that the electromagnetically-induced transparency (EIT) window can be used as a time-to-frequency filter for the probe pulse whose spectrum is much broader than the width of the EIT window. This study demonstrates that the narrow spectral region of the pulse, coincident with the EIT window, develops in a long Gaussian pulse with slow group velocity. An analytical theory is developed describing the propagation of a small amplitude pulse through an optically dense absorptive medium with a narrow EIT window.
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.
Electromagnetically Induced Transparency (EIT) is one of the most remarkable phenomenain quantum optics. Under conventional interpretation, a coupling laser prepares a coherentatomic state in which destructive interference suppresses absorption of a resonant probebeam while producing an exceptionally steep dispersion profile responsible for slow-lightpropagation. The present paper accepts these experimental observations while proposingan alternative physical interpretation within the Space-Phase (SP3) framework. Theprincipal observational clue is the strict wavelength selectivity of EIT. Transparency occursonly when the probe wavelength closely matches a naturally absorbing atomic transition.This paper proposes that the resonance condition may characterize not only the atomictransition but also the coherence-joining behavior of the coupled atom-space-phasesystem. Under this interpretation, the coupling laser conditions both the atomic ensembleand its adjacent space-phase environment. Probe radiation subsequently propagatesthrough sequential coherence joining rather than repeated absorption and spontaneous reemission. The resulting interpretation naturally links resonant transparency, slow light,halted light, Bose-Einstein condensates, process-time, and medium conditioning within asingle physical framework while generating experimentally testable predictions.
Summary form only given. The recent observation of slow light propagation by Harris and Hau (1999) motivates the study of nonlinear optical processes under conditions where slow group velocity, or equivalently large nonlinearity, is the dominant feature of the problem. By combining electromagnetically induced transparency (EIT) and cold atom technology, a sharp resonance is created with a transmission linewidth much less than the natural linewidth of the atoms. A pulse of light propagating in this medium has a phase velocity of c and a group velocity that can be less than 10/sup -7/ c. As a light pulse of sufficiently wide bandwidth enters a cold-atom, EIT medium, the pulse shape, electric field strength, and power density remain nominally unchanged. Concurrently, because the group velocity is decreased, the stored energy per volume must increase. This increase occurs by spatial compression of the travelling pulse. A pulse measuring 300 m in free space compresses to 30 /spl mu/m within the cold-atom medium.
Recently, there has been increasing interest on the idea of controlling optical responses using atomic-coherence or quantum-interferences. Typical example may be the concept of electomagnetically-induced transparency (EIT) [1]. The key idea of EIT is to apply a strong-coupling field between a metastable and upper states to dress them equivalently as two states decaying to a common level or continuum, and to induce the transparency at the split-center of Autler-Townes components. This idea of EIT may open new possibilities to various coherent processes, such as lasing without population inversion, enhanced refractive index without absorption], slow group velocity without absorption, enhanced nonlinearity without absorption, etc.
A simple analytical solution for the propagation of a weak Gaussian pulse in a dense absorptive medium with electromagnetically induced transparency is found. This solution is applied to the analysis of three regimes: (1) and (2) the pulse spectrum is narrower than the transparency window [which is narrow (1) or wide (2) with respect to the width of the absorption line] and (3) the pulse spectrum is broader than the transparency window. It is shown that the pulse maintains its area in all three regimes and maintains its Gaussian shape but narrows in spectrum in regime 1. In regime 2, the pulse begins to distort after a certain distance. In regime 3, the pulse is split into two parts. One part is an adiabatic part with a spectrum defined by the effective width of the transparency window for a thick medium and the other is an oscillating nonadiabatic part of short duration. The adiabatic part propagates slowly and the nonadiabatic part propagates with a velocity close to the speed of light. Thus in regime 3, the medium acts as a time-frequency filter, separating the narrow and wide spectrum components of the pulse in time at the output of the absorber.