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Journal of the Optical Society of America B

Interference effects in second-harmonic generation within an optical cavity

Ling-An Wu, Harry J. Kimble

Published May 1, 1985• 29 citations
Publisher

Abstract

An experiment is described that investigates certain interference effects for second-harmonic generation within a resonant cavity. By employing a noncollinear geometry, the phases of two fundamental beams from a frequency-stabilized dye laser can be controlled unrestricted by the boundary conditions imposed in an optical cavity containing a KDP crystal and resonant at the second harmonic. The fundamental beams are either traveling or standing waves and generate either one or two coherent sources of ultraviolet radiation within the cavity. The experiment demonstrates explicitly the dependence of second-harmonic phase on the fundamental phases and the dependence of coupling efficiency on the overlap of the harmonic polarization wave with the cavity-mode function. The measurements agree well with a simple theory.

DOI
10.1364/josab.2.000697

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An experiment is described that investigates certain interference effects for second-harmonic generation within a resonant cavity. By employing a noncollinear geometry, the phases of two fundamental beams from a frequency-stabilized dye laser can be controlled unrestricted by the boundary conditions imposed in an optical cavity containing a KDP crystal and resonant at the second harmonic. The fundamental beams are either traveling or standing waves and generate either one or two coherent sources of ultraviolet radiation within the cavity. The experiment demonstrates explicitly the dependence of second-harmonic phase on the fundamental phases and the dependence of coupling efficiency on the overlap of the harmonic polarization wave with the cavity-mode function. The measurements agree well with a simple theory.
The nonlinear absorption process and associated phase shift in coupled optical cavities are studied experimentally by observing optical resonance properties. In the coupled cavity configuration, two optical cavities, one for a fundamental beam and the other for a second-harmonic (SH) beam, are coupled by a nonlinear crystal for the second-harmonic generation (SHG). The cavity for the SH beam effectively extends the nonlinear crystal length so that the frequency-conversion efficiency of the SHG, which is proportional to the square of the crystal length, is enhanced. In the observation, power reduction of the fundamental beam at resonance is observed as a small dip in the resonance curve. According to a model calculation, it is found that this power reduction is caused by blue-induced infrared absorption.
We have generated squeezed states of light by the process of second harmonic conversion within an optical cavity resonant at both fundamental and harmonic frequencies. The experiment consists of a standing-wave cavity containing a crystal of lithium niobate doped with magnesium oxide and driven by the field from a frequency-stabilized Nd:YAG laser (incident power, ~10 mW). The total field reflected from the cavity illuminates a pair of high quantum efficiency photodiodes, whose individual photocurrents are summed. Observations of squeezing are made by analyzing the spectral density of fluctuations for this sum photo-current while the cavity detuning is scanned through resonance. An intensity regulator holds the reflected light intensity constant during the scan by control of the incident light level. Reductions in photocurrent fluctuations of 12% relative to the vacuum-state or shot-noise level are achieved for frequency offsets near 4 MHz. Since significantly higher degrees of squeezing are predicted by our theoretical analysis, we discuss those processes that currently limit the observed noise reduction, including phase noise produced by the intracavity crystal in the absence of nonlinear conversion.
We study the polarization of the electric field in Fabry-Perot resonators which contain at least two optically birefringent elements. One of them is a frequency-doubling crystal, the other being either a passive and/or an active crystal. Using the Jones matrix technique, we review the polarization properties of the linear Fabry-Perot cavity and extend these results to V-shaped cavities. For these configurations, we derive the rate of conversion of the fundamental frequencies into the second harmonic and the sum frequencies. These conversion rates are interpreted as intensity-dependent losses for the rate equations of the fundamental modes which are derived.
The input-output theory, originally developed for a linear coupling between cavity mode a and a bath, is extended to a coupling that is quadratic in the cavity mode operator a. We then apply this to second-harmonic generation, in a cavity that is resonant at the fundamental frequency and has an active laser medium working at the fundamental frequency. We find intensity squeezing of 50% below the shot-noise level in the output light at the second-harmonic frequency, whether or not the cavity is resonant at the second-harmonic frequency. To compare the singly resonant cavity to the doubly resonant cavity, we develop in an appendix a general technique for extracting a single mode from a continuum.
Coherent effects in the interference of overlapping laser-induced resonances in helium atoms are considered. The simultaneous action of single-mode radiation of the 294-nm second harmonic of a cw dye laser and a 1064-nm Nd:YAG laser on helium atoms provides the overlap of two resonances induced by transitions from the 1 s 2 s 1 S and 1 s 4 s 1 S helium levels. The shape of the overlapping laser-induced resonances in the rotating-wave approximation is described by analytic expressions, which depend on the laser radiation intensities and the ratio of laser frequencies.
We present experimental data on quantum interferences in resonantly enhanced frequency up-conversion towards the vacuum-ultraviolet spectral regime. The process is driven in xenon atoms by ultrashort (picosecond) laser pulses. We use two simultaneous frequency conversion pathways via an excited intermediate state, i.e., fifth harmonic generation of the fundamental wavelength and four-wave mixing of the fundamental and two photons of its second harmonic wavelength. Both conversion pathways yield radiation at 102 nm. The two pathways interfere, depending on the relative phase of the fundamental and second harmonic. By appropriate choice of the phase we get constructive interference (resulting in increased conversion efficiency) or destructive interference (resulting in reduced conversion efficiency). The total conversion yield shows very pronounced constructive and destructive quantum interference with a visibility of roughly 90%. A stable and highly accurate phase control setup enables such strong quantum interferences for more than 260 oscillation cycles. In an extension of the experiment, simultaneously to frequency conversion we also monitor laser-induced fluorescence as a measure for the excitation probability to the excited intermediate state. Also, in the excitation probability we observe strong quantum interferences. As an interesting feature, a small phase lag occurs between the quantum interference patterns of frequency conversion and population transfer. This is due to an additional atomic phase acquired during frequency conversion.