Transient mid-IR nonlinear refraction in air

Abstract

We use the polarization-sensitive, time-resolved Beam-Deflection technique to measure the nonlinear refraction of air, exciting in both the near and mid-IR and probing in the mid-IR. This gives us the first measurements for air using both excitation and probe in the mid-IR, and we find no dispersion of the bound-electronic nonlinear refractive index, n2,el(λ p ;λ e ), assuming, as has been shown earlier, that the nuclear rotational nonlinear refraction is nearly dispersionless. From these data, we can model the pulsewidth dependence of the effective nonlinear refractive index, n2,eff, i.e., as would be measured by a single beam. Interestingly, n2,eff is maximized for a pulsewidth of approximately 0.5 ps. The position of this maximum is nearly independent of pressure while its magnitude decreases with increasing pressure and temperature. From the measurements and modeling, we predict the nonlinear refraction in the atmosphere at different altitudes.

Using machine learning to predict dinitrogen molecule density by analyzing transient-dependent nonlinear pulse propagation in an air-filled hollow core photonic crystal fiber

“…The effective nonlinear refractive index of air can be written as n 2,air = n 2,el + n 2,mol , where n 2,el is the electronic contribution (Tofighi et al 2021) (n 2,el = 10 × 10 −20 cm 2 W −1 ), and n 2,mol is the molecular response. The total Raman response function R(t) includes both contributions, with the instantaneous response coming from bound electrons and the noninstantaneous response coming from molecular-nuclei.…”

“…Energy term E J = 2π chBJ(J + 1) is the rotational energy and T the temperature. The air's nonlinear refractive index corresponding to the molecular response can be calculated using the equation given in Tofighi et al (2021):…”

“…The density composition N of each component alters the total non-instantaneous response function h rot (t), leading to weighted contributions to the total molecular nonlinear refractive index n 2,mol . We have initially considered a total air density of molecules N = 2.5 × 10 25 m −3 that corresponds to the normalized temperature and pressure conditions (NTP, 20 • C, 1 atm) (Tofighi et al 2021). Although, for NTP conditions in lower atmospheric layers and up to the upper-stratosphere (30 km of altitude), the compositions of the primary constituents N 2 and O 2 are roughly constant (about 78.8% and 21.2% respectively (Emmert et al 2021, Tofighi et al 2021), some slight variation of this concentration is found in the mesosphere layer when the altitude reaches around 100 km, changing from 78.8% to 81.1% for N 2 and from 21.2 to 18.4% for O 2 (Zheltikov 2007, Emmert et al 2021.…”

“…Recently, it has been experimentally demonstrated that the effective nonlinear refractive index of air is dependent on the pulsewidth of the input optical pulse (Tofighi et al 2021). Motivated by this finding, this paper aims to study the pulsefeatures along the fiber when these pulsewidth dependencies modify the typical nonlinear effects reported previously where air-nonlinearities are excited (Bhagwat and Gaeta 2008, Li et al 2014, Mousavi et al 2018, and when the transientdependency and pulse-shape are taken into account during the propagation modeling.…”

“…Motivated by this finding, this paper aims to study the pulsefeatures along the fiber when these pulsewidth dependencies modify the typical nonlinear effects reported previously where air-nonlinearities are excited (Bhagwat and Gaeta 2008, Li et al 2014, Mousavi et al 2018, and when the transientdependency and pulse-shape are taken into account during the propagation modeling. The pulse propagation in air-filled HC-PCF is modeled using the Generalized Nonlinear Schrödinger equation, incorporating the recently reported transient nonlinear refractive index features (Tofighi et al 2021).…”