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Physical Review A

Interference between excitation routes in resonant sum-frequency mixing

Richard R. Moseley, Sara Shepherd, David J. Fulton, Bruce Sinclair, Malcolm H. Dunn

Published Nov 1, 1994• 12 citations
Publisher

Abstract

We present theory and observation to show that in resonant sum-frequency mixing the two pathways to the excitation of the coherence driving the output may be controlled in relative strength, and combine in antiphase on resonance. These two pathways are, first, a two-step route resulting in the creation of a real intermediate population, and second, a direct two-photon excitation resonantly enhanced by, but not populating, the intermediate level. The former route is shown to be raised over the latter by use of a stronger lower laser field. Experimental observation uses the 3S-3${\mathit{P}}_{1/2}$-3D level scheme in sodium vapor and single-frequency continuous-wave lasers for steady-state conditions and high resolution. A cancellation ratio of 94% is reported. Further, noninterfering incoherent fluorescence and an anti-Stokes Raman process are observed and contrasted.

DOI
10.1103/physreva.50.4339

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Sum frequency mixing and quantum interference in three-level atoms

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This work contains theoretical and experimental studies of the properties of three-level atoms subjected to two single-frequency, continuous-wave laser sources with special emphasis on magnetic-field-induced sum frequency mixing (SFM) and electromagnetically-induced transparency (EIT). In sodium vapour, two resonant-enhancement routes for SFM were experimentally studied. In one route (3S-3P-3D) the output is generated on a quadrupole-allowed transition and on the other (3S-3P-4P), a dipole-allowed transition. Phase matching conditions are studied in detail. On the second route, the two contributions to the phase mismatch can combine to heavily distort the spectroscopic lineshapes observed. Doubly-resonant SFM is considered and two paths for excitation of the output coherence are identified. Control of their relative strength, via the input laser strengths, is predicted, as well as interference between them. These are both experimentally observed on the 3S1/2-3P1/2-3D3/2 transition scheme in sodium. Theory is presented to show how the use of a strong upper laser in resonant SFM can, by EIT, greatly reduce the absorption on the lower transition without similarly reducing the nonlinear process. A significant increase in conversion efficiency is predicted. Theory is also presented on the inclusion of the local field correction, which is relevant for high vapour densities, in the Bloch equations for the three-level atom. Nonlinear coherence cross-coupling terms arise and the generalised equations are then used for two case studies; one concerning EIT, the other SFM. EIT is experimentally studied using continuous-wave lasers in rubidium vapour. Focusing and de-focusing were observed on the probe laser beam as it tunes through the transparency window at close, but separate, detunings. This is attributed to the radial intensity profile of the coupling laser which imposes a spatial refractive index modulation on the medium at the probe laser wavelength.

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An experimental and theoretical study of magnetic-field-induced sum-frequency mixing in sodium vapor has been carried out using two single-frequency, continuous-wave dye lasers as the sources of the fundamental radiation. In addition to the usual two-photon resonant enhancement of the three-wave-mixing nonlinear-optical process, the use of near- or on-resonant single-photon transitions for further resonant enhancement was investigated. The macroscopic phase-matching behavior of the sum-frequency mixing was examined with the intermediate states off resonance. Experimental and theoretical results are presented to illustrate the differences that occur between the coherent quadrupole emission and the incoherent cascade fluorescence when the intermediate states in the two-photon absorption are resonant. Control over the single-photon resonant enhancement and the sum-frequency-mixing phase matching was achieved to increase the power conversion efficiency to 1.2\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}5}$.

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Suppression of a four-photon resonance by four-wave mixing near an intermediate three-photon resonance

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We use resonance ionization involving two colors in single-pass and retroreflected geometries to study the suppression of excitation of a four-photon resonance by an interference involving four-wave sum-frequency generation occurring near an intermediate three-photon resonance. The 6p[1/2](J=0) state of xenon is excited by three blue photons plus one infrared photon. One beam, focused to ${\mathit{I}}_{1}$\ensuremath{\simeq}7\ifmmode\times\else\texttimes\fi{}${10}^{9}$ W/${\mathrm{cm}}^{2}$, is nearly three-photon resonant with the 6s[3/2](J=1) resonance; the second, unfocused beam (${\mathit{I}}_{2}$\ensuremath{\simeq}2\ifmmode\times\else\texttimes\fi{}${10}^{7}$ W/${\mathrm{cm}}^{2}$) is tuned to maintain exact four-photon resonance with the 6p[1/2](J=1) state. One additional blue photon ionizes from the four-photon level. Third-harmonic light is generated by the first, nearly three-photon-resonant beam by four-wave sum-frequency mixing. One third-harmonic photon plus one photon from the second laser form a second excitation pathway to the four-photon level; destructive interference between the two pathways results in a reduction in the observed ionization. The degree of reduction depends on the xenon density and the detuning (both positive and negative) from three-photon resonance. This interference may be overcome by retroreflecting the nearly three-photon-resonant beam to provide an additional excitation pathway which generates no third harmonic.The study provides detailed information on the pressure-dependent range from exact resonance over which the familiar three-photon cancellation effect is operative; it shows that the interference occurs in high- and low-energy regions about three-photon resonance; and it establishes that interference is produced for large values of the phase mismatch even if the absorption of the interfering field is low. We compare our measurements of the reduction in ionization with predictions published by us elsewhere [M. G. Payne, J. C. Miller, R. C. Hart, and W. R. Garrett, Phys. Rev. A 44, 7684 (1991)]; excellent agreement is observed. We also report the observation of suppression of pressure-induced wing absorption into the three-photon state observed in a classic ``hybrid'' resonance mode of excitation.

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Evolution of four-wave mixing by controlling Raman coherence in a multi-dressed atomic system

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The evolution of enhanced four-wave mixing based on Raman coherence as the probe intensity increases is observed experimentally in an 85 R b atomic vapor system. We propose that for a Doppler-broadened Λ -type level system, the generated anti-Stokes field from one-photon resonance will be suppressed by the dressed-states resonance and can be controlled by the probe intensity, which influences the effective transverse relaxation rate of Raman coherence. When the probe field is not so weak, the double resonance for dressed states will greatly suppress the anti-Stokes emission at the central frequency, and the signal peak will be split. We show that this phenomenon is a result of the destructive polarization interference between atoms with different velocities from the two types of resonance. Based on our model, we present a new, to the best of our knowledge, interpretation of four-wave mixing enhancement in the conventional Λ -type electromagnetically induced transparency system.

Journal of the Optical Society of America B•Mar 23, 2021•0 citations

Competition between coherent and incoherent nonlinear optical processes

Daniel J. Gauthier, Michelle S. Malcuit, Robert W. Boyd

Competition has been observed between amplified spontaneous emission (ASE) and four-wave mixing (FWM). Previously, competition between an incoherent and coherent process was observed in the form of suppression of multiphoton ionization by third harmonic generation.1,2 In our experiment, an input laser was tuned precisely to the 3s → 3d two-photon allowed transition in atomic sodium vapor and the emission was observed in both the forward and backward directions. In these conditions, either FWM or ASE can occur. Ignoring the possibility of competition between these two processes, the calculated gain for ASE is much larger than that for FWM. However, we have observed experimentally that FWM and not ASE occur. To determine that it is the presence of efficient FWM that suppresses ASE, we have excited the atomic vapor instead with counterpropagating pump waves of different frequency. In this case, FWM, being a phase-matched process, cannot occur and strong ASE is observed. The nature of this competition is explained by solving the coupled Maxwell and density matrix equations for a three-level system. It is found that the suppression is due to the destructive interference between two different pathways of excitation of the 3d level which results in trapping of the population in the ground state.

Annual Meeting Optical Society of America•Jan 1, 1985•0 citations
We present theory and observation to show that in resonant sum-frequency mixing the two pathways to the excitation of the coherence driving the output may be controlled in relative strength, and combine in antiphase on resonance. These two pathways are, first, a two-step route resulting in the creation of a real intermediate population, and second, a direct two-photon excitation resonantly enhanced by, but not populating, the intermediate level. The former route is shown to be raised over the latter by use of a stronger lower laser field. Experimental observation uses the 3S-3P1/2{\mathit{P}}_{1/2}P1/2​-3D level scheme in sodium vapor and single-frequency continuous-wave lasers for steady-state conditions and high resolution. A cancellation ratio of 94% is reported. Further, noninterfering incoherent fluorescence and an anti-Stokes Raman process are observed and contrasted.
This work contains theoretical and experimental studies of the properties of three-level atoms subjected to two single-frequency, continuous-wave laser sources with special emphasis on magnetic-field-induced sum frequency mixing (SFM) and electromagnetically-induced transparency (EIT). In sodium vapour, two resonant-enhancement routes for SFM were experimentally studied. In one route (3S-3P-3D) the output is generated on a quadrupole-allowed transition and on the other (3S-3P-4P), a dipole-allowed transition. Phase matching conditions are studied in detail. On the second route, the two contributions to the phase mismatch can combine to heavily distort the spectroscopic lineshapes observed. Doubly-resonant SFM is considered and two paths for excitation of the output coherence are identified. Control of their relative strength, via the input laser strengths, is predicted, as well as interference between them. These are both experimentally observed on the 3S1/2-3P1/2-3D3/2 transition scheme in sodium. Theory is presented to show how the use of a strong upper laser in resonant SFM can, by EIT, greatly reduce the absorption on the lower transition without similarly reducing the nonlinear process. A significant increase in conversion efficiency is predicted. Theory is also presented on the inclusion of the local field correction, which is relevant for high vapour densities, in the Bloch equations for the three-level atom. Nonlinear coherence cross-coupling terms arise and the generalised equations are then used for two case studies; one concerning EIT, the other SFM. EIT is experimentally studied using continuous-wave lasers in rubidium vapour. Focusing and de-focusing were observed on the probe laser beam as it tunes through the transparency window at close, but separate, detunings. This is attributed to the radial intensity profile of the coupling laser which imposes a spatial refractive index modulation on the medium at the probe laser wavelength.
An experimental and theoretical study of magnetic-field-induced sum-frequency mixing in sodium vapor has been carried out using two single-frequency, continuous-wave dye lasers as the sources of the fundamental radiation. In addition to the usual two-photon resonant enhancement of the three-wave-mixing nonlinear-optical process, the use of near- or on-resonant single-photon transitions for further resonant enhancement was investigated. The macroscopic phase-matching behavior of the sum-frequency mixing was examined with the intermediate states off resonance. Experimental and theoretical results are presented to illustrate the differences that occur between the coherent quadrupole emission and the incoherent cascade fluorescence when the intermediate states in the two-photon absorption are resonant. Control over the single-photon resonant enhancement and the sum-frequency-mixing phase matching was achieved to increase the power conversion efficiency to 1.2\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}5}$.
We use resonance ionization involving two colors in single-pass and retroreflected geometries to study the suppression of excitation of a four-photon resonance by an interference involving four-wave sum-frequency generation occurring near an intermediate three-photon resonance. The 6p[1/2](J=0) state of xenon is excited by three blue photons plus one infrared photon. One beam, focused to I1{\mathit{I}}_{1}I1​\ensuremath{\simeq}7\ifmmode\times\else\texttimes\fi{}109{10}^{9}109 W/cm2{\mathrm{cm}}^{2}cm2, is nearly three-photon resonant with the 6s[3/2](J=1) resonance; the second, unfocused beam (I2{\mathit{I}}_{2}I2​\ensuremath{\simeq}2\ifmmode\times\else\texttimes\fi{}107{10}^{7}107 W/cm2{\mathrm{cm}}^{2}cm2) is tuned to maintain exact four-photon resonance with the 6p[1/2](J=1) state. One additional blue photon ionizes from the four-photon level. Third-harmonic light is generated by the first, nearly three-photon-resonant beam by four-wave sum-frequency mixing. One third-harmonic photon plus one photon from the second laser form a second excitation pathway to the four-photon level; destructive interference between the two pathways results in a reduction in the observed ionization. The degree of reduction depends on the xenon density and the detuning (both positive and negative) from three-photon resonance. This interference may be overcome by retroreflecting the nearly three-photon-resonant beam to provide an additional excitation pathway which generates no third harmonic.The study provides detailed information on the pressure-dependent range from exact resonance over which the familiar three-photon cancellation effect is operative; it shows that the interference occurs in high- and low-energy regions about three-photon resonance; and it establishes that interference is produced for large values of the phase mismatch even if the absorption of the interfering field is low. We compare our measurements of the reduction in ionization with predictions published by us elsewhere [M. G. Payne, J. C. Miller, R. C. Hart, and W. R. Garrett, Phys. Rev. A 44, 7684 (1991)]; excellent agreement is observed. We also report the observation of suppression of pressure-induced wing absorption into the three-photon state observed in a classic ``hybrid'' resonance mode of excitation.
Two-color excitation by spatially coherent and incoherent laser beams has been used to study three-photon-resonant excitation and subsequent ionization of xenon in conditions, when internally generated sum-frequency field plays an important role in excitation of atomic resonances through interfering one-photon excitation pathway. We show that the incoherence in one of the pumping fields reduces the efficiency of generated sum-frequency field, and thus suppresses the interference between the three- and the one-photon excitation channels. The degree of suppression is controlled by varying the crossing angle between coherent and incoherent laser beams. We show that ionization profiles can be analyzed on the basis of the well-studied interference of one- and three-photon transition amplitudes, but with pumping field decomposed into multiple small-scale uncorrelated domains where coherent process of four-wave mixing occurs. The gain length for a coherent process in these domains depends on the coherence degree and excitation geometry. It gives a possibility of controlling the contribution of coherent processes to the excitation of multiphoton resonances.
The evolution of enhanced four-wave mixing based on Raman coherence as the probe intensity increases is observed experimentally in an 85 R b atomic vapor system. We propose that for a Doppler-broadened Λ -type level system, the generated anti-Stokes field from one-photon resonance will be suppressed by the dressed-states resonance and can be controlled by the probe intensity, which influences the effective transverse relaxation rate of Raman coherence. When the probe field is not so weak, the double resonance for dressed states will greatly suppress the anti-Stokes emission at the central frequency, and the signal peak will be split. We show that this phenomenon is a result of the destructive polarization interference between atoms with different velocities from the two types of resonance. Based on our model, we present a new, to the best of our knowledge, interpretation of four-wave mixing enhancement in the conventional Λ -type electromagnetically induced transparency system.
Competition has been observed between amplified spontaneous emission (ASE) and four-wave mixing (FWM). Previously, competition between an incoherent and coherent process was observed in the form of suppression of multiphoton ionization by third harmonic generation.1,2 In our experiment, an input laser was tuned precisely to the 3s → 3d two-photon allowed transition in atomic sodium vapor and the emission was observed in both the forward and backward directions. In these conditions, either FWM or ASE can occur. Ignoring the possibility of competition between these two processes, the calculated gain for ASE is much larger than that for FWM. However, we have observed experimentally that FWM and not ASE occur. To determine that it is the presence of efficient FWM that suppresses ASE, we have excited the atomic vapor instead with counterpropagating pump waves of different frequency. In this case, FWM, being a phase-matched process, cannot occur and strong ASE is observed. The nature of this competition is explained by solving the coupled Maxwell and density matrix equations for a three-level system. It is found that the suppression is due to the destructive interference between two different pathways of excitation of the 3d level which results in trapping of the population in the ground state.