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Electronics and Communications in Japan (Part II Electronics)

Nonlinear susceptibility of cesium and sodium atoms for frequency upconversion from 10‐μm atmospheric window to the visible

Teruhito Mishima, Kenji Hisadome, Ichiro Sakuraba, Members

Published Jan 1, 1988• 0 citations

Abstract

Abstract This paper presents a calculation of the third‐order nonlinear susceptibility for the frequency upconversion of 10‐μm atmospheric window to the visible band. The following cases are compared. Two‐photon resonance 1 at 6 d 2D3/2, and 2 at 6 d 2D5/2 of cesium to generate difference frequency. 3 Two‐photon resonance at 7 s 2S1/2 of cesium to generate sum frequency. 4 Two‐photon resonance at 3 d 2D5/2 of sodium to generate sum frequency. Density matrix is used in the calculation, and the spinorbit coupling and the Doppler effect are considered. The major results are the following. In 1, a large nonlinear susceptibility and large number density is obtained at relatively low temperature. The nonlinear susceptibility has the maximum at the wavelength of 12.1 μm. In 2, a large nonlinear susceptibility and large number density are obtained at relatively low temperature. The nonlinear susceptibility increases with the increase of infrared wavelength. In 3, a system free from polarization property can be constructed, but the temperature must be raised by more than 100°C, compared with the forementioned two cases. In 4 the largest nonlinear susceptibility is obtained for the wavelength of 9.1 μm. However, the temperature must be raised by several hundreds degree compared with the cases of 1 and 2.

DOI: 10.1002/ecjb.4420710101

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Abstract This paper presents a calculation of the third‐order nonlinear susceptibility for the frequency upconversion of 10‐μm atmospheric window to the visible band. The following cases are compared. Two‐photon resonance 1 at 6 d 2D3/2, and 2 at 6 d 2D5/2 of cesium to generate difference frequency. 3 Two‐photon resonance at 7 s 2S1/2 of cesium to generate sum frequency. 4 Two‐photon resonance at 3 d 2D5/2 of sodium to generate sum frequency. Density matrix is used in the calculation, and the spinorbit coupling and the Doppler effect are considered. The major results are the following. In 1, a large nonlinear susceptibility and large number density is obtained at relatively low temperature. The nonlinear susceptibility has the maximum at the wavelength of 12.1 μm. In 2, a large nonlinear susceptibility and large number density are obtained at relatively low temperature. The nonlinear susceptibility increases with the increase of infrared wavelength. In 3, a system free from polarization property can be constructed, but the temperature must be raised by more than 100°C, compared with the forementioned two cases. In 4 the largest nonlinear susceptibility is obtained for the wavelength of 9.1 μm. However, the temperature must be raised by several hundreds degree compared with the cases of 1 and 2.

A study was made of the dependences of the efficiency of resonant parametric frequency conversion in sodium vapor on the infrared radiation wavelength, vapor density, and detuning from two-photon pump resonance. It was found in this conversion system that for each infrared wave the conversion efficiency had three maxima on tuning the frequency of two-photon pumping over the region of a forbidden transition. The principal maximum was realized for accurate two-photon resonance, and the two other maxima resulted from a rise in the cubic susceptibility close to single-photon sum-frequency resonances. A quantum efficiency of 35% was achieved for a 9.26 μ infrared wave.

We show that second-order nonlinear optical processes such as sum and difference generation can be observed in isotropic media, despite the fact that such processes are forbidden in the electric-dipole approximation. A theoretical treatment of quadrupole sum- and difference-frequency generation is given, which includes the effects of spin-orbit and Zeeman splittings. The quadrupole nonlinear susceptibility is evaluated and expressions for phase matching and output power are found. We have generally confirmed the theoretical predictions by observing quadrupole sum-frequency generation of ultraviolet light in sodium vapor. Deviations of the data from the simple theory can be satisfactorily accounted for by the effects of two-photon saturation, induced index of refraction changes, and single- and multi-photon absorption. Generalization of the dipole forbidden susceptibilities to the case of quadrupole-pumped processes is discussed, with difference-frequency generation in Cs vapor considered as an example.

A study was made of the influence of autoionization-like resonances in the continuum, induced by strong optical radiation, on the nonlinear susceptibilities governing third harmonic generation and the optical activity of sodium vapor. It was demonstrated experimentally for the first time that it should be possible to study high-lying states of atoms and molecules by the method of nonlinear polarization spectroscopy of the fifth-order optical nonlinearity. The experimental results were compared with the theory. An analysis was made of the feasibility of using this effect for spectroscopy of the states in the continuum and for generation of short-wavelength radiation in gaseous media.

A theoretical analysis is made of the influence of the pump intensity on the nonlinear susceptibility of the third harmonic excited under conditions of two-photon resonance between the pump wave and the Doppler-broadened transition. Pumping by both traveling and standing waves is considered. For traveling wave pumping, an expression for the nonlinear harmonic susceptibility in an arbitrary field is derived and analyzed. The optimal detunings of twice the pump frequency relative to the two-photon transition frequency are determined. For standing wave pumping an expression for the nonlinear harmonic susceptibility is obtained from perturbation theory up to and including the third order. It is shown that an important factor in the reduction of the harmonic susceptibility is the saturation of the transition due to Doppler-free two-photon absorption of opposite traveling waves.

We have investigated three resonant nonlinear processes in atomic cesium vapor. They are third harmonic generation, two photon absorption, and parametric frequency conversion. Resonant enhancement of each is provided by tuning the ruby laser half the 6S - 9D transition frequency of 28828.90 cm. The parametric process involves, in addition, a resonance with one of the P states. We have studied the variation of each of the three processes with laser intensity and frequency. At exact resonance the THG is found to be proportional to the square of the laser intensity and the TPA is proportional to laser intensity over a large power range. The resonance lineshape for both processes is found to be power dependent. A detailed analysis of these two processes based on steady state density matrix calculations and including A. C. Stark shifts, photoionization, and beam geometry is shown to accurately describe most of our observations.