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Physical Review A

Sum-frequency generation using strong-field coupling and induced transparency in atomic hydrogen

G. Z. Zhang, M. Katsuragawa, K. Hakuta, R. I. Thompson, Boris Peter Stoicheff

Published Aug 1, 1995• 35 citations
Publisher

Abstract

The sum-frequency generation process using strong-field coupling and quantum interference is described systematically using atomic hydrogen both in theory and experiment. It is shown that strong coupling at the 3p-2s transition creates destructive interference to reduce the linear susceptibility at the resonant 3p\ensuremath{\leftarrow}1s transition. Simultaneously, two-photon coupling of the 2s and 1s states produces constructive interference to resonantly enhance the nonlinear susceptibility for sum-frequency generation at the 3p\ensuremath{\rightarrow}1s (Lyman-\ensuremath{\beta}) transition. Experimental results clearly demonstrate the theoretical predictions. When the Rabi frequency for the 3p-2s coupling exceeds the Doppler tail of the medium, the photoion signals on resonance are suppressed significantly because of induced transparency. The generated Lyman-\ensuremath{\beta} radiation grows rapidly by a factor of 250 at an atom density of ${10}^{15}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ and interaction length of 3.5 cm, resulting in a conversion efficiency of 2\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$.

DOI
10.1103/physreva.52.1584

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•Jul 1, 1995•2 citations
The sum-frequency generation process using strong-field coupling and quantum interference is described systematically using atomic hydrogen both in theory and experiment. It is shown that strong coupling at the 3p-2s transition creates destructive interference to reduce the linear susceptibility at the resonant 3p\ensuremath{\leftarrow}1s transition. Simultaneously, two-photon coupling of the 2s and 1s states produces constructive interference to resonantly enhance the nonlinear susceptibility for sum-frequency generation at the 3p\ensuremath{\rightarrow}1s (Lyman-\ensuremath{\beta}) transition. Experimental results clearly demonstrate the theoretical predictions. When the Rabi frequency for the 3p-2s coupling exceeds the Doppler tail of the medium, the photoion signals on resonance are suppressed significantly because of induced transparency. The generated Lyman-\ensuremath{\beta} radiation grows rapidly by a factor of 250 at an atom density of 1015{10}^{15}1015 cm\ensuremath−3{\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}cm\ensuremath−3 and interaction length of 3.5 cm, resulting in a conversion efficiency of 2\ifmmode\times\else\texttimes\fi{}10\ensuremath−4{10}^{\mathrm{\ensuremath{-}}4}10\ensuremath−4.
Sum-frequency generation with electromagnetically induced transparency is investigated experimentally as the generation of coherent Lyman-(Beta) radiation (103 nm) in atomic hydrogen. We demonstrate that with the application of a strong laser field to couple the 2 s and 3 p levels, the resonant Lyman-(Beta) transition becomes transparent, and the generated wave continues to grow without suffering resonant absorption. At a density-length product NL of 3 X 1015 cm-2, a conversion efficiency of 2 X 10-4 is obtained for the coherent 103 nm radiation.
Sum-frequency generation enhanced by electromagnetically induced transparency (EIT) has been extended to the production of extreme ultraviolet (XUV) radiation in the range 97.3--92.6 nm from $np\ensuremath{-}1s$ transitions (n=4−−8)(n=4--8)(n=4−−8) in atomic hydrogen. Pulsed radiation was generated by strong coupling of the np\mathrm{np}np and 2s2s2s levels with laser radiation at Balmer wavelengths, and simultaneously (weaker) coupling of the 2s2s2s and 1s1s1s levels by two-photon resonance with 243-nm laser radiation. Investigations were carried out over a range of laser intensities and products of interaction length and atomic density (NL).(\mathrm{NL}).(NL). As the product NL\mathrm{NL}NL increased, the XUV intensities were greatly enhanced by EIT, and at high NL\mathrm{NL}NL values, the spectral distributions of some of the generated signals were found to be distorted by the presence of molecular hydrogen. Calculated profiles, modified to incorporate the effects of nearby molecular resonances, were shown to be in good agreement with the observed spectra.
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.