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Optics Express

Measuring saturable nonlinearity in atomic vapor via direct spatial mapping

Juan Wu, Pengbo Jia, Sandan Wang, Xuewen Wang, Jinpeng Yuan, Lirong Wang, Yi Hu, Zhigang Chen, Jingjun Xu

Published Oct 25, 2022• 8 citations
Publisher

Abstract

We demonstrate a scheme to measure the saturable nonlinearity of atomic vapor by mapping its nonlinear response function onto a light beam profile. Our analysis shows that a part of a nonlinear optical solution solved in a model governing the nonlinear beam dynamics in atomic vapor can be used to perform this measurement, even in the presence of large absorption. A desired beam profile is achieved by an evolution of a well-known structured beam, namely the Airy beam. Using this simple yet effective method, we retrieve the saturable nonlinear response function of rubidium (Rb) atomic vapor in experiment, and employ it in light propagation simulation that reproduces well observed nonlinear dynamics, which nevertheless cannot be fitted in a strong nonlinear regime with an ideal Kerr approximation. Our method is applicable to a broad spectrum of materials featured with saturable nonlinearities.

DOI
10.1364/oe.472652

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We demonstrate a scheme to measure the saturable nonlinearity of atomic vapor by mapping its nonlinear response function onto a light beam profile. Our analysis shows that a part of a nonlinear optical solution solved in a model governing the nonlinear beam dynamics in atomic vapor can be used to perform this measurement, even in the presence of large absorption. A desired beam profile is achieved by an evolution of a well-known structured beam, namely the Airy beam. Using this simple yet effective method, we retrieve the saturable nonlinear response function of rubidium (Rb) atomic vapor in experiment, and employ it in light propagation simulation that reproduces well observed nonlinear dynamics, which nevertheless cannot be fitted in a strong nonlinear regime with an ideal Kerr approximation. Our method is applicable to a broad spectrum of materials featured with saturable nonlinearities.
Atomic vapors make flexible and useful nonlinear optical media when light is detuned far from resonances. However, few direct measurements of their nonlinear coefficients have been performed to date. We present a measurement of the Kerr coefficient for various detunings to both the red and blue of the D2D2D2 line in hot atomic rubidium vapor. Saturation effects complicate the interpretation of the standard z-scan method, but a simple saturation model agrees well with our data. We find values of ${n}_{2}\ensuremath{\approx}\ifmmode\pm\else\textpm\fi{}{10}^{\ensuremath{-}7}{\mathrm{cm}}^{2}/\mathrm{W}$ for 1 GHz detunings from the D2D2D2 line.
We investigate the propagation properties of finite-energy Airy beams in nonlocal nonlinear atomic vapor. The nonlocality is caused by the transportation of optically excited atoms and described with a Green function. By conducting numerical simulation on Airy beams in the case of one-dimension, two-dimensions, and ring geometry, respectively, we find that the beams have a more stable shape and a longer propagation distance in the presence of nonlocality. The results show that the nonlocality can slow down the beams’ distortion induced by the self-focusing effect and contributes to a more stable propagation of Airy beams in the nonlinear media.
We present experiments of a laser with variable pulse energy and beam width saturating sodium vapor near the D1{D}_{1}D1​-line transition. At high optical depth and in a buffer gas atmosphere of argon, the effect of nonlinear radiation trapping is shown to drastically change the spatial distribution and temporal evolution of the excited-state population and of the fluorescence light trapped by the nonlinear medium. Besides observing the transient behavior of the fluorescence light, a pump-probe beam experiment enables us to gain a tomographic view inside the atomic vapor. Nitrogen as a buffer gas is used to compare with the situation where radiation trapping effects are negligible. Finally, numerical simulations based upon equations of radiative transfer for a two-level atomic system elucidate the role of nonlinear radiation trapping and support given interpretations of the experiments.
We report the measurement of the Kerr nonlinear refractive index of the rubidium vapor via the high sensitivity z-scan method by using an optical frequency comb. The novel self-focusing and self-defocusing effects of the vapor are presented with red and blue detunings of the laser frequency. The optical nonlinear characteristics of the rubidium vapor are clearly interpreted under different experimental parameters. Furthermore, the Kerr nonlinear refractive index n2 is obtained from the measured dispersion curve, and it basically occurs on the order of 10−6 cm2/W. The evolutions of the Kerr nonlinear coefficient n2 with the laser power and frequency detuning, respectively, are studied. To the best of our knowledge, the use of pulsed lasers to measure the Kerr nonlinear refractive index n2 of atomic vapor has not been reported yet. The direct measurement of the Kerr nonlinear coefficient will greatly help us understand and optimize nonlinear optical processes and find its more potential applications in quantum optics.
When an optical beam passes through a thin slice of a homogeneous material, the change of its phase and amplitude is characterized by the material's linear and nonlinear susceptibility, the latter also known as the hyperpolarizability. The standard method for measuring the nonlinear susceptibility is the ZZZ scan. This widely used method is sometimes applied outside of its range of validity, leading to systematic errors. These errors are illustrated for a two-level system with parameters taken from atomic rubidium. The present paper proposes a method called the phase retrieval of modes to determine the nonlinear susceptibility without an assumption about its functional form, in contrast to both the ZZZ-scan method and variants intended to apply in cases of saturation. In brief, a Gaussian beam passes through a thin sample and is detected on three planes in a focal scan. Phase retrieval methods are used to find coefficients of the modes which in turn determine the optical nonlinear susceptibility. Nearly exact recovery of the nonlinear susceptibility is shown numerically in the no-noise case. Additionally, two types of noise are considered: shot noise on the detector and intensity fluctuations of the input.