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Quantum Electronics and Laser Science Conference

Local-field enhancement of the nonlinear-optical susceptibility

Jeffery J. Maki, Robert W. Boyd, Michelle S. Malcuit, John E. Sipe

Published May 12, 1991• 0 citations
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Abstract

We have quantitatively studied the effects of Lorentz local fields on the linear and nonlinear optical properties of an atomic potassium vapor. In the linear regime, the effects of local fields are treated theoretically by the Lorentz-Lorenz equation. The Lorentz-Lorenz equation predicts that the linear dielectric constant e for an isolated optical resonance should have a density-dependent frequency shift from that of the single-atom response toward the red end of the spectrum.

Related papers

Linear and nonlinear optical measurements of the Lorentz local field

Jeffery J. Maki, Michelle S. Malcuit, John E. Sipe +1 more

We have studied the resonant optical response of a dense atomic potassium vapor under conditions such that the response is strongly influenced by local-field effects. Our experimental results are in good agreement with the predictions of theory. We have also discovered a collision-induced shift of the potassium resonance lines given by \ensuremath{\Delta}${\mathrm{\ensuremath{\omega}}}_{\mathrm{c}\mathrm{o}\mathrm{l}=}$\ensuremath{\beta}N, where \ensuremath{\beta}=-5.0\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}8}$ ${\mathrm{sec}}^{\mathrm{\ensuremath{-}}1}$ ${\mathrm{cm}}^{3}$ for the 4 $^{2}$${\mathit{S}}_{1/2}$\ensuremath{\leftrightarrows}4 $^{2}$${\mathit{P}}_{1/2}$ transition and where \ensuremath{\beta}=-3.0\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}8}$ ${\mathrm{sec}}^{\mathrm{\ensuremath{-}}1}$ ${\mathrm{cm}}^{3}$ for the 4 $^{2}$${\mathit{S}}_{1/2}$\ensuremath{\leftrightarrows}4 $^{2}$${\mathit{S}}_{1/2}$\ensuremath{\leftrightarrows}4 $^{2}$${\mathit{P}}_{3/2}$ transition.

Physical Review Letters•Aug 19, 1991•219 citations

Measurement of the excitation dependence of the Lorentz local-field shift

H. van Kampen, Vladimir A. Sautenkov, C. J. C. Smeets +2 more

We have experimentally investigated the resonant optical response of a partially excited high-density atomic potassium vapor under conditions where local-field effects strongly influence the response. We have measured the excitation dependence of the Lorentz local-field shift, and found it to be in excellent agreement with theoretical predictions.

Physical Review A•Jan 1, 1999•39 citations

Observation of the Lorentz local-field in a dense atomic vapor using transient four-wave-mixing

Steven T. Cundiff, Justin M. Shacklette

The Lorentz local-field modifies the properties of a dense medium, compared to isolated atoms. It results in the Lorentz-Lorenz shift, and a negative delay signal in transient-four- wave mixing, which we have observed in potassium vapor.

International Conference on Ultrafast Phenomena•Jan 1, 2000•0 citations

Lorentz red shift and self-broadening of atomic potassium vapor

Jeffery J. Maki, Robert W. Boyd, Michelle S. Malcuit +1 more

The Lorentz-Lorenz equation predicts that the dispersion feature of an isolated optical resonance should have a density-dependent frequency shift toward the red end of the spectrum. We have investigated the dispersion feature experimentally by observing the frequency dependence of the Fresnel reflection (selective reflection) from the boundary between a dense atomic potassium vapor and the window of the vessel containing the vapor. We find that the selective-reflection features of both the S1/2-P1/2 (770.1 nm) and S1/2-P3/2 (766.7 nm) lines of potassium shift increasingly toward the red and broaden as the number density of the vapor is increased to 2 × 1017 atoms/cm3. We compare the results of the experiment to theoretical predictions for the selective reflection. The broadening is well described by conventional binary collision theory; however, the observed red shift of both of the lines is somewhat larger than that predicted by the Lorentz-Lorenz equation. It is possible that other mechanisms that lead to frequency shifts are occurring.

Annual Meeting Optical Society of America•Jan 1, 1990•0 citations

Local-field effects in lasing without inversion: An enhancement of gain and absorptionless index of refraction

Jonathan P. Dowling, Charles M. Bowden

It is well known that, for static fields, the local microscopic electric field EL, that couples to the atomic dipole moment p, is related to the macroscopic field E and volume polarization P, in a dense dielectric medium, by the Lorentz-Lorenz (LL) relation.1 For dense media, this relation implies a nonlinear relationship between the microscopic molecular polarizability α and the macroscopic susceptibility χ, for a material volume density N. The LL relation also holds for arbitrary time-dependent fields in a nonlinear medium.2 What this implies is that all of quantum optics that uses an external electric field rather than the local field is internally inconsistent and will yield only approximate results for an optically dense medium. We consider the effect of the local field interaction on a simple three-level A system predicted to exhibit lasing without inversion and a high index of refraction at zero absorption.3 A threshold transition allows us to choose a value of this parameter that enhances inversionless gain and absorptionless dispersion by at least two orders of magnitude over that foundin usual lasing without inversion.4

Annual Meeting Optical Society of America•Jan 1, 1993•0 citations

Introduction

Charles M. Bowden, Mark J. Bloemer

Local field effects that occur due to dipole-dipole interactions have been vigorously investigated since the initial works of Lorentz[1] and Lorenz[2]. Linear interactions of light in condensed matter and dense gases are manifest in the Clausius-Mossotti relations[3], and nonlinear effects have been known for some time[4]. Generalized Maxwell-Bloch formulation incorporating local field effects[5, 6] has stimulated considerable theoretical development and predictions, but to date few experiments have been performed. Several experiments, however, have addressed key issues stemming from various theoretical developments. Boyd and coworkers have observed local field induced spectral red shifts in rubidium vapor[7], and Rand and coworkers have observed intrinsic bistability due to local field effects in a crystal lattice highly doped with rare earth ions[8]. Most recently, Eliel and coworkers have studied local field effects in very high density metal vapors[9], and find novel cooperative effects and excitation dependent line narrowing. The papers presented in this Focus Issue are indicative of the currently increasing interest and activity in this field.

Optics Express•Sep 15, 1997•1 citation
We have quantitatively studied the effects of Lorentz local fields on the linear and nonlinear optical properties of an atomic potassium vapor. In the linear regime, the effects of local fields are treated theoretically by the Lorentz-Lorenz equation. The Lorentz-Lorenz equation predicts that the linear dielectric constant e for an isolated optical resonance should have a density-dependent frequency shift from that of the single-atom response toward the red end of the spectrum.
We have studied the resonant optical response of a dense atomic potassium vapor under conditions such that the response is strongly influenced by local-field effects. Our experimental results are in good agreement with the predictions of theory. We have also discovered a collision-induced shift of the potassium resonance lines given by \ensuremath{\Delta}${\mathrm{\ensuremath{\omega}}}_{\mathrm{c}\mathrm{o}\mathrm{l}=}$\ensuremath{\beta}N, where \ensuremath{\beta}=-5.0\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}8}$ ${\mathrm{sec}}^{\mathrm{\ensuremath{-}}1}$ cm3{\mathrm{cm}}^{3}cm3 for the 4 2^{2}2S1/2{\mathit{S}}_{1/2}S1/2​\ensuremath{\leftrightarrows}4 2^{2}2P1/2{\mathit{P}}_{1/2}P1/2​ transition and where \ensuremath{\beta}=-3.0\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}8}$ ${\mathrm{sec}}^{\mathrm{\ensuremath{-}}1}$ cm3{\mathrm{cm}}^{3}cm3 for the 4 2^{2}2S1/2{\mathit{S}}_{1/2}S1/2​\ensuremath{\leftrightarrows}4 2^{2}2S1/2{\mathit{S}}_{1/2}S1/2​\ensuremath{\leftrightarrows}4 2^{2}2P3/2{\mathit{P}}_{3/2}P3/2​ transition.
The Lorentz-Lorenz equation predicts that the dispersion feature of an isolated optical resonance should have a density-dependent frequency shift toward the red end of the spectrum. We have investigated the dispersion feature experimentally by observing the frequency dependence of the Fresnel reflection (selective reflection) from the boundary between a dense atomic potassium vapor and the window of the vessel containing the vapor. We find that the selective-reflection features of both the S1/2-P1/2 (770.1 nm) and S1/2-P3/2 (766.7 nm) lines of potassium shift increasingly toward the red and broaden as the number density of the vapor is increased to 2 × 1017 atoms/cm3. We compare the results of the experiment to theoretical predictions for the selective reflection. The broadening is well described by conventional binary collision theory; however, the observed red shift of both of the lines is somewhat larger than that predicted by the Lorentz-Lorenz equation. It is possible that other mechanisms that lead to frequency shifts are occurring.
It is well known that, for static fields, the local microscopic electric field EL, that couples to the atomic dipole moment p, is related to the macroscopic field E and volume polarization P, in a dense dielectric medium, by the Lorentz-Lorenz (LL) relation.1 For dense media, this relation implies a nonlinear relationship between the microscopic molecular polarizability α and the macroscopic susceptibility χ, for a material volume density N. The LL relation also holds for arbitrary time-dependent fields in a nonlinear medium.2 What this implies is that all of quantum optics that uses an external electric field rather than the local field is internally inconsistent and will yield only approximate results for an optically dense medium. We consider the effect of the local field interaction on a simple three-level A system predicted to exhibit lasing without inversion and a high index of refraction at zero absorption.3 A threshold transition allows us to choose a value of this parameter that enhances inversionless gain and absorptionless dispersion by at least two orders of magnitude over that foundin usual lasing without inversion.4
Local field effects that occur due to dipole-dipole interactions have been vigorously investigated since the initial works of Lorentz[1] and Lorenz[2]. Linear interactions of light in condensed matter and dense gases are manifest in the Clausius-Mossotti relations[3], and nonlinear effects have been known for some time[4]. Generalized Maxwell-Bloch formulation incorporating local field effects[5, 6] has stimulated considerable theoretical development and predictions, but to date few experiments have been performed. Several experiments, however, have addressed key issues stemming from various theoretical developments. Boyd and coworkers have observed local field induced spectral red shifts in rubidium vapor[7], and Rand and coworkers have observed intrinsic bistability due to local field effects in a crystal lattice highly doped with rare earth ions[8]. Most recently, Eliel and coworkers have studied local field effects in very high density metal vapors[9], and find novel cooperative effects and excitation dependent line narrowing. The papers presented in this Focus Issue are indicative of the currently increasing interest and activity in this field.