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Electronics and Communications in Japan (Part II Electronics)

Technique for determining the refractive indices and oscillator strengths with the angle phase‐matching conditions in optical four‐wave sum‐mixing

Kojiro Koyanagi, Teruhito Mishima, Ichiro Sakuraba

Published Jan 1, 1988• 0 citations
Publisher

Abstract

Abstract A new method is proposed for measurement of the index of refraction of gas and oscillator strength. In four‐wave sum‐mixing in such nonlinear media as metal vapor or rare gas using the third‐order nonlinear optical effect, the refractive index of a nonlinear medium at the sum frequency in the vacuum ultraviolet range is found from the angle phase‐matching condition for the maximum conversion efficiency, and the oscillator strength is determined from the measurement of refractive index by the phase matching in terms of the sum frequency. The present method in which the refractive index and the oscillator strength are determined from the incident angle of each wave satisfying the angle phase‐matching has the advantage of fewer measurement parameters compared to the conventional methods in which a phase‐matching is accomplished with a mixture of gases with ordinary and extraordinary dispersions. This is because no buffer gas is mixed. In addition, the measurement accuracy is found theoretically to improve in the region with a higher atomic density.

DOI
10.1002/ecjb.4420710603

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Abstract A new method is proposed for measurement of the index of refraction of gas and oscillator strength. In four‐wave sum‐mixing in such nonlinear media as metal vapor or rare gas using the third‐order nonlinear optical effect, the refractive index of a nonlinear medium at the sum frequency in the vacuum ultraviolet range is found from the angle phase‐matching condition for the maximum conversion efficiency, and the oscillator strength is determined from the measurement of refractive index by the phase matching in terms of the sum frequency. The present method in which the refractive index and the oscillator strength are determined from the incident angle of each wave satisfying the angle phase‐matching has the advantage of fewer measurement parameters compared to the conventional methods in which a phase‐matching is accomplished with a mixture of gases with ordinary and extraordinary dispersions. This is because no buffer gas is mixed. In addition, the measurement accuracy is found theoretically to improve in the region with a higher atomic density.
We have measured oscillator strengths for the transitions 6 1S^{1}S1S to (5${d}^{10}$6s np) n 1^{1}1,3P1{\mathrm{P}}_{1}P1​ for n=6 to 13 and to (5${d}^{9}666{s}^{2}$6p) 6p' 1P^{1}P1P for atomic Hg. Two new techniques for measuring dispersion based on nonlinear-optical sum-frequency mixing are used to achieve 10% accuracy for the stronger transitions. One method uses crossed beams in a Hg heat-pipe cell to map dispersion curves in regions of anomalous dispersion. The second method uses input beams of three separate frequencies and maps regions of normal and anomalous dispersion by tuning one of the input frequencies to the red and blue of the 6 3P1^{3}P_{1}3P1​ level. Because the dispersion of the refractive index near a resonance is determined over a large wavelength range, the oscillator strength of that resonance is determined independent of the strengths of other transitions.
We have developed new techniques based on four-wave mixing for the accurate determination of oscillator strengths and applied them to measure 61S - n1,3P and 71S - n1,3P (n = 6 - 13) matrix elements of atomic Hg. For transitions from the 61S ground state, index matching conditions were used to determine refractive indicies and thus f-values, while the frequency dependence of the nonlinear susceptibility was used to deduce matrix elements for transitions involving 71S. For all measurements, two-photon resonance with the 71S state was maintained.
Accurate modeling of optical nonlinearities is crucial to describe macroscopic laser propagation in a medium, including sum frequency generation, spectral broadening due to self-phase modulation, various ionization processes and soliton formation. For incident laser light the response of the medium is given by the induced polarization of the microscopic system. The polarization is usually expanded in a Taylor series for the electric field amplitude, which is truncated after the first non-linear term being of third order for isotropic media. A third-order nonlinearity leads to the well-known optical Kerr effect, where the refractive index of the medium becomes intensity dependent via n = n0+ n2I. This leads to an inherent problem when modeling laser propagation in two or more spatial dimensions, linked to the formal divergence (n2> 0) of the refractive index for increasing intensity.
Nonlinear optical mixing of existing laser frequencies to access portions of the spectrum where lasing action is not easily obtainable is common practice today. Although nonlinear solid-state media are available [1] for frequency conversion from just under 200 nm in the ultraviolet to about a few microns in the infrared, the generation of widely-tunable laser radiation in the mid-to-far infrared and VUV regions typically requires four-frequency mixing in atomic vapors. In the past, frequency conversion in atomic vapors suffered from poor conversion efficiencies due to the small magnitude of the third-order nonlinear susceptibility and the difficulty in phasematching. We demonstrate a method [2] for performing four-frequency mixing which overcomes both of these shortcomings, allowing efficient frequency conversion with moderate pump intensities.
Abstract In the four‐wave parametric upconverter based on isotropic alkali‐metal vapor which is considered useful as an infrared detector, the acceptance angle characteristics of the infrared ray have been studied theoretically in the case of angle phase matching (or pump phase matching) in which a phase matching is taken by way of small angular difference of two pumping light beams. It is found that various acceptance angle characteristics such as single‐peak, double‐peak, and multi‐peak characteristics can be obtained by adjustment of two pumping light angles, if the collinear phase mismatch is negative due to anomalous dispersion of the metal vapor. The collinear phase mismatch is defined as the magnitude of wave vector of the sum frequency minus the sum of the magnitudes of the wave vectors of two pumping beams and the infrared beam. A flat and broad acceptance angle is obtained in the case of tangential phase matching. It is also found that an optimum state as an image upconverter with a high conversion efficiency and a large acceptance angle exists in the four‐wave parametric upconverter of the two‐photon resonance excitation type in which a large conversion efficiency has been expected.
We report here a detailed study of the four-wave mixing process in the extreme ultraviolet region around 30 nm by using two collinear incommensurate frequency laser pulses. The experimental results reveal evidence of the coherent accumulation of the wave-mixing fields and low-order (third-order and fifth-order) nonlinear response of an argon medium. The dependence of the intensities of the mixing fields on the intensity of a weak control field, on the argon pressure, and on the interaction length is analyzed to show that the four-wave mixing fields in this spectral range are generated under the phase-matched condition.