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Optics Express

Sensitivity enhancement of nonlinear refractive index measurement by Gaussian-Bessel beam assisted z-scan method

Wei Gao, Sandan Wang, Jinpeng Yuan, Lirong Wang, Liantuan Xiao, Suotang Jia

Published Feb 9, 2022• 7 citations
Publisher

Abstract

Characterizing the nonlinear optical properties of numerous materials plays a prerequisite role in nonlinear imaging and quantum sensing. Here, we present the evaluation of the nonlinear optical properties of Rb vapor by the Gaussian-Bessel beam assisted z-scan method. Owed to the concentrated energy in the central waist spot and the constant intensity of the beam distribution, the Gaussian-Bessel beam enables enhanced sensitivity for nonlinear refractive index measurement. The nonlinear self-focusing and self-defocusing effects of the Rb vapor are illustrated in the case of blue and red frequency detunings from 5S1/2 − 5P3/2 transition, respectively. The complete images of the evolution of nonlinear optical properties with laser power and frequency detuning are acquired. Furthermore, the nonlinear refractive index n2 with a large scale of 10−6 cm2/W is determined from the measured transmittance peak-to-valley difference of z-scan curves, which is enhanced by a factor of ∼ 1.73 compared to the result of a equivalent Gaussian beam. Our research provides an effective method for measuring nonlinear refractive index, which will considerably enrich the application range of nonlinear material.

DOI
10.1364/oe.451038

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Characterizing the nonlinear optical properties of numerous materials plays a prerequisite role in nonlinear imaging and quantum sensing. Here, we present the evaluation of the nonlinear optical properties of Rb vapor by the Gaussian-Bessel beam assisted z-scan method. Owed to the concentrated energy in the central waist spot and the constant intensity of the beam distribution, the Gaussian-Bessel beam enables enhanced sensitivity for nonlinear refractive index measurement. The nonlinear self-focusing and self-defocusing effects of the Rb vapor are illustrated in the case of blue and red frequency detunings from 5S1/2 − 5P3/2 transition, respectively. The complete images of the evolution of nonlinear optical properties with laser power and frequency detuning are acquired. Furthermore, the nonlinear refractive index n2 with a large scale of 10−6 cm2/W is determined from the measured transmittance peak-to-valley difference of z-scan curves, which is enhanced by a factor of ∼ 1.73 compared to the result of a equivalent Gaussian beam. Our research provides an effective method for measuring nonlinear refractive index, which will considerably enrich the application range of nonlinear material.
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.
The potential to precisely control both the linear and nonlinear index of refraction through optical manipulation of the atomic states has recently pushed warm alkali vapors to the forefront of research in the field of quantum sensors, quantum memories, and quantum fluids of light. Rubidium (Rb) vapor in centimeter-scale glass cells or millimeter-scale micro-electro-mechanical system (MEMS) cells has proven to be a very promising platform for these applications, yet only a handful of research works have been dedicated to the investigation of the (non)linear refractive index of Rb vapor. We present results of theoretical calculations of the (non)linear refractive index of warm Rb vapor, based on the optical Bloch equations for 6-level Rb atoms interacting with a probe laser. They are compared to the experimental results obtained using an interferometric technique, showing very good quantitative agreement. A Kerr nonlinear refractive index n2 of up to −1.2×10−4 cm2/W is obtained. Python scripts for all theoretical calculations presented in this work are provided, including the refractive index calculation, that can readily be used in practical implementations for simulating the (non)linear refractive index of Rb vapor including the effects of Doppler broadening, transit time broadening, pressure broadening, saturation, optical pumping, and spin-exchange collisions.
The potential to precisely control both the linear and nonlinear index of refraction through optical manipulation of the atomic states has recently pushed warm alkali vapors to the forefront of research in the field of quantum sensors, quantum memories, and quantum fluids of light. Rubidium (Rb) vapor in centimeter-scale glass cells or millimeter-scale MEMS cells has proven to be a very promising platform for these applications, yet only a handful of research works have been dedicated to the investigation of the (non)linear refractive index of Rb vapor. We present results of theoretical calculations of the (non)linear refractive index of warm Rb vapor, based on the optical Bloch equations for 6-level Rb atoms interacting with a probe laser. They are compared to the experimental results obtained using an interferometric technique, showing excellent quantitative agreement. A Kerr nonlinear refractive index n2n_2n2​ of up to 10−410^{-4}10−4 cm2^22/W is obtained. Python scripts for all theoretical calculations presented in this work are provided, including the refractive index calculation, that can readily be used in practical implementations for simulating the (non)linear refractive index of Rb vapor including the effects of Doppler broadening, transit time broadening, pressure broadening, saturation, optical pumping, and spin-exchange collisions.
We present measurements of the nonlinear refraction coefficients for the D1 line of cesium vapor. A variant of the z-scan technique is applied for which we scan the laser frequency across resonance for different sample positions and detect the transmission after an aperture in the far field. From the spectra for different positions we reconstruct the position-dependent transmission z-scan curve for a given laser detuning. This technique allows obtaining the vapor Kerr coefficient over a large and continuous range of frequencies. From the saturation of the Kerr coefficient, n2, with beam power we obtain n4, the next term in the refraction index expansion. A theoretical model is used to calculate n2 and n4 giving values consistent with experimental ones.
We report on the enhancement of phase conjugation degenerate four-wave mixing (DFWM) in hot atomic Rb vapor by using a Bessel beam as the probe beam. The Bessel beam was generated using cross-phase modulation based on the thermal nonlinear optical effect. Our results demonstrated that the DFWM signal generated by the Bessel beam is about twice as large as that generated by the Gaussian beam, which can be attributed to the extended depth and tight focusing features of the Bessel beam. We also found that a DFWM signal with reasonable intensity can be detected even when the Bessel beam encounters an obstruction on its way, thanks to the self-healing property of the Bessel beam. This work not only indicates that DFWM using a Bessel beam would be of great potential in the fields of high-fidelity communication, adaptive optics, and so on, but also suggests that a Bessel beam would be of significance to enhance the nonlinear process, especially in thick and scattering media.
Nonlinear atomic media are promising substitutes for spatial light modulators (SLMs) owing to the high tunability and fast response. We demonstrate the generation of high-order Bessel-like beam based on cross-phase modulation in 85 Rb atoms. The atomic medium, whose refractive index is spatially modulated by the focused Gaussian pump beam, acts as a nonlinear focusing lens for the Laguerre-Gaussian probe beam. As a result, the probe beam carries the nonlinear phase shift and is converted into a Bessel-like mode in far-field diffraction. The superior self-healing ability of the generated high-order Bessel-like beam is verified by inserting an obstruction in the beam path, and its high tunability is investigated in terms of the pump beam power and vapor temperature. Furthermore, this novel beam is used in an obstruction-immune rotation sensor to measure the angular velocity. Nonlinear atomic medium as a novel SLM promises considerable application prospects in modulating the light field structure.