Complete femtosecond linear free induction decay, Fourier algorithm for dispersion relations, and accuracy of the rotating wave approximation

Abstract

A complete (both amplitude and phase) measurement of the femtosecond linear free induction decay on a Raman active dye in solution (IR144 in methanol) is demonstrated. For weak femtosecond pulses passing through a homogeneous material, Beer’s Law can be used to predict the spectral amplitude changes, and dispersion relations can be used to calculate the spectral phase change. A modified fast Fourier transform algorithm calculates the phase change by applying dispersion relations to a symmetrical absorption spectrum spanning positive and negative frequencies. A reformulation of the rotating wave approximation in the frequency domain shows that related limits on the accuracy of the rotating wave approximation in nonlinear optics arise from the width of the linear spectrum relative to the center frequency, and not from the excitation pulses.

Solvatochromism and Solvation Dynamics of Structurally Related Cyanine Dyes

“…This difference between IR144 and other cyanines explains why echo measurements on most cyanines 32,33 could be modeled exclusively in terms of vibrational wave packet spreading while IR144 experiments were interpreted in term of polar solvation. , The solvatochromic fit results suggest that one-third to one-half of the IR144 solvation energy arises from self-consistent feedback between the solvent reaction field and the polarizable solute. Although such large solute polarizability effects have been questioned, significant feedback is supported by the IR144 refractive index calculated from the free induction decay phase shift . The large refractive index at zero frequency is caused by the strong IR144 charge resonance transition in the visible.…”

Assessing the dephasing dynamics of water from linear field-resolved pulse propagation experiments and simulations in highly absorbing solutions

“…Note that the relationship between FID phase change and the absorption spectrum, as calculated in Ref. 46, is valid in the limit where the material bandwidth is much larger than the laser bandwidth. This assumption does not hold for ultrashort midIR pulses propagating through HDO / D 2 O.…”

Pulse Propagation Effects in Optical 2D Fourier-Transform Spectroscopy: Theory

“…The effects of this approximation are even smaller than the effects of neglecting the directional filtering distortions discussed previously. Over the frequency range shown, the maximum fractional error in the linear susceptibility from the rotating-wave approximation is less than 10 –4 , so rotating-wave errors in the 2DFT spectrum are expected to be negligible. The expressions for testing the applicability of the 3DFT approach developed by Yetzbacher et al indicate that the conditions of the experiment by Li et al satisfy the essential assumptions implicit in the 3DFT theory with one exception: significant error arises from the assumption that excitation beams have complete transverse overlap, as will be discussed below.…”

“…Measurement of the free-induction decay of each of the excitation pulses can check linear propagation of the excitation fields, which is a requirement of the theory underlying these calculations. Linearity of absorption, however, does not guarantee linear propagation. ,, Well-resolved linear absorption spectra are also critical to this check. As with free-induction decay measurements, absorption spectra indicate the optical density of the sample and, for the homogeneous Bloch model, determine the line shape function.…”

“…For sufficiently weak excitation fields, propagation distortions in nonlinear optics result from linear reshaping of the excitation pulses and emitted signal field as they propagate through an optically thick medium. ,,, For weak, resonant pulses shorter than the polarization decay time of a low optical density medium, each input field propagates almost without distortion, but is trailed by a reradiated field that is π out of phase with the input field and decays with the polarization decay time (the trailing linear free-induction decay or FID). , As the optical density increases, multiple absorption–reradiation cycles increasingly distort the input field and FID. In some work, this effect on the signal has been termed cascaded free-induction decay four-wave mixing because it arises from linear cascading of the input fields; such cascading is fully included in the treatment of propagation distortions here.…”