Determination of molecular contributions to the nonlinear refractive index of air for mid-infrared femtosecond laser-pulse excitation

Abstract

Numerical simulations of the rotational contribution of oxygen and nitrogen molecules to the Kerr refractive index change in air are performed for ultrashort laser pulses in the near and mid-infrared wavelength region. The calculated molecular response is parametrized by means of a damped harmonic oscillator model that is easily tractable in numerical simulations of long-distance propagation of ultrashort laser pulses. Our simulations show that pulses from available mid-infrared laser systems are long enough to be dramatically affected by the molecular response of air during propagation.

Powerful terahertz waves from long-wavelength infrared laser filaments

“…( 5 ), we find that the peak of the response function R ( t ) occurs at time . According to the values of Γ and Λ calculated by Langevin et al 61 , t p lies in the range between 75 and 90 fs, which roughly indicates the pulse durations above which the Raman contribution will have a significant impact on the refractive index change. Therefore, taking into account the above values of f R , we can conclude that for laser pulses with durations above approximately 75 fs, the molecular Raman contribution prevails over the electronic Kerr response for all wavelengths from the near-infrared to the mid-infrared region.…”

“…Here, χ (3) is the total (Kerr plus Raman) third-order susceptibility, and is the fraction of the Raman contribution. For subpicosecond laser pulses, the response function R ( t ) can be calculated based on the damped harmonic oscillator model 60 , 61 : where is a normalization factor and Γ and Λ are the damping and oscillation frequencies, respectively.…”

“…b Values of frequencies Γ and Λ determining the Raman response function R ( t ) (arrows indicate the associated scale), and c the fraction of the Raman contribution f R in air as a function of the pulse duration for wavelengths of 0.8–4 μm. Figures b and c are reprinted from 61 with permission from the American Physical Society …”

“…In parallel, Langevin et al 61 numerically studied the molecular Raman contribution in air at mid-infrared wavelengths. By solving the time-dependent Schrödinger equation, they calculated the rotational molecular response of air for laser pulses with wavelengths from 0.8 to 4 μ m, pulse durations from 10 to 500 fs, and intensities from 0.2 to 20 TW/cm.…”

“…( 5 ) can be safely extended to mid-infrared wavelengths. Figure 5b shows the two frequencies, Γ and Λ, calculated by Langevin et al 61 for air in the range of different wavelengths and pulse durations. According to this figure, the values of Γ and Λ are almost independent of the wavelength but exhibit a moderate dependence on the pulse duration.…”