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Physical Review A

Proposed experiment to measure nonlinear optical susceptibilities in the saturated regime

Zachary H. Levine

Published Aug 1, 2024• 2 citations
Publisher

Abstract

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 $Z$ 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 $Z$-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.

DOI
10.1103/physreva.110.023501

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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.
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 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.
Backaction-evading measurement of an optical intensity has been observed, using a three-level system in a sodium atomic beam as a nonlinear medium. The principle of this experiment is to use the cross-phase-modulation effect, which in principle allows one to read nondestructively the quantum intensity fluctuations of the ``signal'' beam when detecting the phase fluctuations of the ``meter'' beam. Using a cavity-enhancement scheme, the quantum noise measured when recombining the signal and meter photocurrents is 0.8 dB below the shot-noise level.
Abstract Nonlinear optics plays a crucial role in science and technology, with applications ranging from spectroscopy to quantum information processing. Therefore, precise estimation of their nonlinear optical parameters is of fundamental importance. Here, we investigate quantum-enhanced sensitivity in the estimation of nonlinear absorption parameters, including saturable absorption (SA) and reverse saturable absorption (RSA). By employing the quantum Fisher information, we quantify the enhancement in sensitivity for estimating transmission ( T ), linear absorption coefficient ( α0\alpha _0α0​ ), saturable intensity ( IsI_sIs​ ), and two-photon absorption coefficient ( β\beta β ) using bright two-mode squeezed states (bTMSS) and applied it to analyze the nonlinear parameters of Pt nanoparticle samples as an example. In addition, we propose an experimental scheme based on an open-aperture Z-scan with bTMSS to realize quantum-enhanced sensitivity. Our findings establish a pathway toward quantum-enhanced estimation of nonlinear optical parameters.
The propagation of a weakly modulated light beam through a nonlinear material is treated. The optical field representing such a beam consists of a strong carrier-frequency component and two weak, symmetrically displaced sidebands that combine to form a field, which may be purely amplitude modulated (AM), frequency modulated (FM), or some combination of these two modulation forms. It is shown that, for any optical nonlinearity, two modulation forms exist that have the property that the form of modulation is invariant under propagation of the beam. If a modulation form other than one of these natural modes is injected into the nonlinear medium, the modulation form will change as the beam propagates, asymptotically approaching the natural mode that experiences the lower attenuation. Explicit expressions for these natural modes are presented for the case in which the nonlinear medium can be modeled as a collection of two-level atoms. For the special case of an on-resonance pump beam, the natural modes correspond to pure amplitude modulation and pure frequency modulation. This formalism provides a general description of saturation spectroscopy for both AM and FM fields. Formulas are derived for the rate at which a pure FM beam is converted to an AM beam owing to its interaction with a two-level atomic medium. We also consider the variation that is due to propagation of the depth of modulation of an AM wave interacting resonantly with two-level atoms. The formalism predicts the existence of spectral features whose shape depends sensitively on the internal relaxation processes of the material. Experimental spectra are presented for ruby, alexandrite, and fluorescein in glass and are interpreted.