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Physical Review Letters

Electric-field-induced second-harmonic generation with reduced absorption in atomic hydrogen

K. Hakuta, L. Marmet, Boris Peter Stoicheff

Published Feb 4, 1991• 349 citations
Publisher

Abstract

We show that dc-electric-field coupling of the 2s and 2p states in atomic hydrogen leads to resonantly enhanced second-order susceptibility with reduced absorption at the second-harmonic wavelength, and exact phase matching at the center of the Stark-split components.
DOI
10.1103/physrevlett.66.596

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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.
Second harmonic generation (SHG) in free atoms is one of the unsolved problems in nonlinear optics. The most probable mechanism is due to Stark mixing between nearby excited states through an electric field caused by charge separation through the process of three-photon ionization. To test the mechanism, atomic hydrogen appears to be the best candidate because of its well-known electronic structure and large dipole moments of its excited states. In this work we report on the observation of SHG in atomic hydrogen in the Lyman-α region. Pulsed dye laser radiation was doubled and tuned to 243 nm for excitation of the 2s ← 1s transition at 121.6 nm by a two-photon resonance process. A cw atomic beam was used with hydrogen atoms generated in a dc discharge of H2 gas. The laser beam was focused ~1 mm below the nozzle where the hydrogen atom density was estimated to be 1013 cm−3. The second harmonic radiation was strongly enhanced by adding an external dc field of up to 10 kV/cm. Stark splitting was clearly observed at higher fields.
We calculate the electric-field-induced second-harmonic-generation (EFISH) susceptibility of a homogeneously broadened two-level system with permanent dipole moments. This susceptibility has contributions from the second-harmonic-generation (SHG) susceptibility of the same system without the presence of a dc field and the four-wave-mixing (FWM) component of the susceptibility ${\ensuremath{\gamma}}_{\mathit{e}}$(-2\ensuremath{\omega};\ensuremath{\omega},\ensuremath{\omega},0). The magnitude and phase of the various contributions to EFISH arising from SHG and from FWM depend on the frequency of the fundamental optical field, the transition dipole moment ${\mathrm{\ensuremath{\mu}}}_{\mathit{a}\mathit{b}}$, the permanent dipole moment of the ground-state level ${\mathrm{\ensuremath{\mu}}}_{\mathit{a}\mathit{a}}$, and the difference of the ground- and excited-state dipole moments \ensuremath{\Delta}\ensuremath{\mu}. We present non-rotating-wave-approximation results for both the quasi-steady-state in systems where the dephasing time T2{\mathit{T}}_{2}T2​ is much shorter than the population decay time T1{\mathit{T}}_{1}T1​, so the polarization is in a steady state but the population is not, and for the complete steady state. Extraction of the SHG susceptibility from EFISH measurements is considered.
We have observed second-harmonic generation in atomic hydrogen in the Lyman-α region, with and without an applied dc electric field, Ea. Experiments with a continuous atomic beam were carried out by using a pulsed dye laser tuned to 243 nm for excitation of the n = 2-1 transition. The laser beam was focused 0.4 mm below the H-source nozzle, where the H-atom density was estimated to be 5 × 1013 cm-3. Measurements of second-harmonic generation (SHG) at ~122 nm were made at various electric fields up to ~27 kV/cm. It was shown that the SH signal produced at E a = 0 occurs because of a charge-separation field of ~800 V/cm that is caused by three-photon ionization. Measurements of the SHG and ion current were found to vary as I2 L and I3 L , respectively. At high fields (E a > 10 kV/cm) the SH signal at the center of the Stark-split components decreased somewhat from the peak value, but the ion current (corresponding to photon absorption) approached zero. This observation is a clear demonstration of a similar effect, predicted by Harris et al.1 of efficient nonlinear conversion with induced transparency, and it suggests the possibility of obtaining intense Lyman-a radiation.