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Physical Review A

Effects of different phase-matching conditions in sum-frequency-mixing systems in vapors

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

Published Apr 1, 1994• 3 citations
Publisher

Abstract

We have examined the effect of various phase-matching conditions on sum frequency generation in vapors. Using sodium vapor two resonant-enhancement routes for sum-frequency mixing (SFM) via a second-order magnetic-field-induced nonlinearity were explored. On one route the output is resonant with a quadrupole-allowed transition and the other a dipole-allowed resonance. We will show that the first route is preferential for SFM as phase matching on this route is easier to control and we present results detailing the important parameters and their effect in focused and unfocused cases. A second-order nonlinearity of 0.5--1 ${\mathrm{pmV}}^{\mathrm{\ensuremath{-}}1}$ is observed under optimum conditions. In the second route, variations in phase matching as one tunes across the transition may lead to a significant distortion of the spectroscopic line shapes. We show how the combination of different refractive-index sources can account for the different features seen.

DOI
10.1103/physreva.49.3002

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Physical Review A•Nov 1, 1994•12 citations
We have examined the effect of various phase-matching conditions on sum frequency generation in vapors. Using sodium vapor two resonant-enhancement routes for sum-frequency mixing (SFM) via a second-order magnetic-field-induced nonlinearity were explored. On one route the output is resonant with a quadrupole-allowed transition and the other a dipole-allowed resonance. We will show that the first route is preferential for SFM as phase matching on this route is easier to control and we present results detailing the important parameters and their effect in focused and unfocused cases. A second-order nonlinearity of 0.5--1 pmV\ensuremath−1{\mathrm{pmV}}^{\mathrm{\ensuremath{-}}1}pmV\ensuremath−1 is observed under optimum conditions. In the second route, variations in phase matching as one tunes across the transition may lead to a significant distortion of the spectroscopic line shapes. We show how the combination of different refractive-index sources can account for the different features seen.
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 show that second-order nonlinear optical processes such as sum and difference generation can be observed in isotropic media, despite the fact that such processes are forbidden in the electric-dipole approximation. A theoretical treatment of quadrupole sum- and difference-frequency generation is given, which includes the effects of spin-orbit and Zeeman splittings. The quadrupole nonlinear susceptibility is evaluated and expressions for phase matching and output power are found. We have generally confirmed the theoretical predictions by observing quadrupole sum-frequency generation of ultraviolet light in sodium vapor. Deviations of the data from the simple theory can be satisfactorily accounted for by the effects of two-photon saturation, induced index of refraction changes, and single- and multi-photon absorption. Generalization of the dipole forbidden susceptibilities to the case of quadrupole-pumped processes is discussed, with difference-frequency generation in Cs vapor considered as an example.
A high-resolution study of magnetic-field-induced second-harmonic generation in sodium vapor has been carried out with use of a single-frequency continuous-wave dye laser. Resonant enhancement was obtained by tuning the laser to the frequency of the 3S\ensuremath{\rightarrow}4D two-photon transition of the sodium atom. Experimental and theoretical results are presented showing the variation of the power and polarization properties of the second-harmonic radiation as the laser is tuned across the two-photon resonance, and as the transverse magnetic field is varied.
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.