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IEEE Journal of Quantum Electronics

Large dc-electric-field-induced nonlinear optical susceptibility of hydrogen atomic vapors

Robert W. Boyd, Lian-Qin Xiang

Published Aug 1, 1982• 16 citations

Abstract

A unique set of circumstances makes the Rydberg states of atoms ideal for mediating tunable, resonantly enhanced, nonlinear optical interactions. The application of a dc electric field to a vapor of such atoms can induce a second-order or\chi^{(2)}nonlinear susceptibility, which in the absence of the applied field would be forbidden by reasons of symmetry. This paper presents an exact expression, valid within the hydrogenic approximation for field strengths that produce a linear Stark effect, for the resonant contribution to the dc-electric-field-induced\chi^{(2)}susceptibility. Numerical evaluation of this expression for field strengths of the order of 103V/cm predict\chi^{(2)}susceptibilities hundreds of times larger than those of conventional mixing crystals.

DOI: 10.1109/jqe.1982.1071679

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A unique set of circumstances makes the Rydberg states of atoms ideal for mediating tunable, resonantly enhanced, nonlinear optical interactions. The application of a dc electric field to a vapor of such atoms can induce a second-order or\chi^{(2)}nonlinear susceptibility, which in the absence of the applied field would be forbidden by reasons of symmetry. This paper presents an exact expression, valid within the hydrogenic approximation for field strengths that produce a linear Stark effect, for the resonant contribution to the dc-electric-field-induced\chi^{(2)}susceptibility. Numerical evaluation of this expression for field strengths of the order of 103V/cm predict\chi^{(2)}susceptibilities hundreds of times larger than those of conventional mixing crystals.

Broadly tunable sum-frequency generation has been observed in a vapor of atomic sodium in the presence of a dc electric field. This field induces a\chi^{(2)}nonlinearity which is resonantly enhanced when the sum frequency corresponds to the energy separation between the ground state and an atomic Rydberg state. In a vapor of number density4 \times 10^{14}cm-3, we obtain an energy conversion efficiency as large as3 \times 10^{-4}and a\chi^{(2)}as large as1.2 \times 10^{-8}ESU. We have also observed sum-frequency generation in the absence of an applied dc field, and we relate these observations to mechanisms that have been proposed to explain this effect.

It has recently been shown1 that extremely large values of the second-order nonlinear suceptibility can be obtained through use of Rydberg atomic states perturbed by an external electric field.2 In these experiments a value of χ(2) = 10-9 esu was obtained using a sodium vapor of number density ~1014 atoms cm-3 and a dc electric field of magnitude 1 kV/cm. One laser was tuned close to the sodium D2 resonance line while a second laser completed the two-photon resonance with a Rydberg state. A strong coherent UV beam at the sum frequency was generated in the forward direction. The splitting of the highly excited atomic levels induced by the external electric field created a broad region of overlapping levels, leading to continuous tunability. This technique can be applied to any system displaying a Rydberg series, and should be capable of producing coherent, tunable radiation in the extreme ultraviolet.

It has recently been shown that the dipole matrix elements between subbands in semiconductor quantum wells are extremely large.1 Third-order nonlinear susceptibilities are proportional to the fourth power of these matrix elements. Large nonlinearities have thus been predicted for these systems, in particular an intensity-dependent index of refraction suitable for use in all-optical logic elements.1 Second-order nonlinearities vanish identically in symmetric wells, suggesting the use of asymmetrically graded quantum wells for quadratic interactions.2 External bias electric fields also break the inversion symmetry, resulting in Stark shifts and large quadratic susceptibilities whose sign depends on the direction of the applied field. The magnitude of the nonlinearity depends on the carrier density, the dc bias field, and the detuning of the fundamental and second harmonic frequencies from resonances.