Multiply subtractive Kramers–Kronig analysis of optical data

Abstract

We describe a new, multiply subtractive Kramers-Kronig (MSKK)method to find the optical constants of a material from a singletransmittance or reflectance spectrum covering a small frequencydomain. The MSKK method incorporates independent measurements ofn and k at one or more reference wave-numbervalues to minimize errors due to extrapolations of the data. Anunexpected connection between the MSKK equations and the interpolationtheory allows us to derive the equations from an interpolationtheorem. We found that the locations of the reference points affectthe accuracy of the values determined for the optical constants andthat the optimal spacing of N reference data points isrelated to the zeros of a suitably transformed Chebychev polynomial oforder N. We discuss our efforts to optimize both the numberand the spacing of these reference points and apply our method to sometest spectra.

Evidence of Dispersion Relations for the Nonlinear Response of the Lorenz 63 System

“…24 require in principle an infinite domain of integration. Whereas more efficient integration schemes and data manipulation could be envisaged and implemented, such as those described in [15,27,28], or, more simply, the consideration of the asymptotic behavior, we simply truncate the dispersion integrals shown in Eqs. 24 at the maximum frequency considered in our simulations ω cutof f ∼ 100.…”

Fast generation of nonresonant and resonant optical rotatory dispersion curves with the help of circular dichroism calculations and Kramers‐Kronig transformations

“…A second known value can then be subtracted from the SSKK equation to give a doubly-subtractive equation (DSKK), and so forth. This has been proposed to eliminate the cut-off errors when the integration is truncated at low frequencies 50 since the transform can be ''anchored'' to the exact values. Applications to computed molecular properties were not tested in Ref.…”

Testing the validity of terahertz reflection spectra by dispersion relations

“…A singly subtractive K-K (SSKK) relation for the phase retrieval from the logarithm of reflectance was first employed by Ahrenkiel [6], and the concept was generalized by Palmer et al [7]. We apply this technique for the powers of the complex reflection coefficient r n (ω), and obtain the relations as follows:…”