Choosing a Parameterization

Chavent, Guy

doi:10.1007/978-90-481-2785-6_3

Cited by 12 publications

(3 citation statements)

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“…Such application of an appropriate model represents a case of parametrization; the constraints in this case are the many frequency-resolved values of reflectance, and the degrees of freedom are the few parameters of the KK-consistent model. Ill-posed problems can thus be regularized by parametrization . Here, we apply parametrization to the analysis of nano-FTIR spectra, which has important advantages.…”

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“…On the other hand, one might believe that only one parameter can be extracted per independent experiment, potentially missing exclusive information. The question of exactly how many parameters are retrievable from parametrized inverse problems has been studied extensively, ,, but this understanding is often overlooked by practitioners of optical characterization.…”

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“…On the other hand, if the singular values are about equal, then all the parameters are necessary to explain the variance. Because experimental spectra have finite noise (SI, Section S3), the number of practically identifiable (sometimes called retrievable) parameters n r equals the number of singular values μ j , j ∈ {1,..,4}, whose singular vectors explain a fraction of the variance above the noise level where SNR, the “signal-to-noise ratio,” is defined as the norm of predicted values ∥ z nom ∥ 2 for a nominal parameter set divided by the uncertainty level on the data Δ z .…”

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Quantitative Nanoinfrared Spectroscopy of Anisotropic van der Waals Materials

et al. 2020

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Anisotropic dielectric tensors of uniaxial van der Waals (vdW) materials are difficult to investigate at infrared frequencies. The small dimensions of high-quality exfoliated crystals prevent the use of diffraction-limited spectroscopies. Near-field microscopes coupled to broadband lasers can function as Fourier transform infrared spectrometers with nanometric spatial resolution (nano-FTIR). Although dielectric functions of isotropic materials can be readily extracted from nano-FTIR spectra, the inand out-of-plane permittivities of anisotropic vdW crystals cannot be easily distinguished. For thin vdW crystals residing on a substrate, nano-FTIR spectroscopy probes a combination of sample and substrate responses. We exploit the information in the screening of substrate resonances by vdW crystals to demonstrate that both the in-and out-of-plane dielectric permittivities are identifiable for realistic spectra. This novel method for the quantitative nanoresolved characterization of optical anisotropy was used to determine the dielectric tensor of a bulk 2H-WSe 2 microcrystal in the mid-infrared.

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