Dispersion theory of effective meromorphic nonlinear susceptibilities of nanocomposites

Kramers-Kronig (K-K) relations have constituted one of the principal tools in the optical spectroscopy for the assessment of the optical properties of media from measured spectra. The underlying principle for the existence of the K-K relations is causality. Thanks to the K-K relations we have achieved a better understanding of both macroscopic and microscopic properties of media.Recently, various kinds of modified K-K relations have been presented in the literature. Such relations have been applied, e.g. to the nonlinear optical properties of polymers. A typical advantage of these generalized K-K relations is that the measured data do not need to be manipulated as in the case of the traditional K-K relations. Hence, the accuracy of the inverted data on linear or nonlinear optical properties of media becomes higher.A novel way to utilize generalized K-K relations is related to the measurement and correction of terahertz spectra in the time-domain reflection spectroscopy. Terahertz spectroscopy is nowadays one of the most rapidly developing fields in modern physics with applications being related to, e.g. security at the airports or inspection of pharmaceutical tablets. While recording THz spectra it is also possible to perform a chemical mapping of species. Therefore, correctness of the spectrum is of crucial importance for the identification of different species. This is possible by the generalized K-K relations. In this review paper we consider advances of K-K relations both in nonlinear optical and THz spectroscopy.

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“…Fortunately, MEM can be used to resolve the phase from the modulus of a meromorphic degenerate nonlinear susceptibility [113][114][115].…”

Section: Degenerate Nonlinear Susceptibilitymentioning

confidence: 99%

Generalized Kramers–Kronig relations in nonlinear optical- and THz-spectroscopy

Peiponen

Saarinen

2009

Rep. Prog. Phys.

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“…MEM has been successfully applied for phase retrieval in linear optical spectroscopy, [47][48][49][50][51][52] in nonlinear spectroscopy of holomorphic susceptibilities, 53,54 and also for phase retrieval of meromorphic nonlinear susceptibility of homogenous media 55 and nanostructures. 46,56 It should be noted that there is no causality breaking with meromorphic nonlinear susceptibilities. Merely causality is necessary, but not a sufficient condition for the existence of conventional K-K relations, as pointed out by Kircheva and Hadjichristov.…”

Section: Holomorphic Nonlinear Susceptibilitiesmentioning

confidence: 99%

Kramers—Kronig Relations and Sum Rules in Nonlinear Optical Spectroscopy

et al. 2004

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The full potential of the Kramers-Kronig relations and sum rules for nonlinear susceptibilities has unfortunately drawn relatively little attention in nonlinear optical spectra analysis. In this feature article a simple treatment of an anharmonic oscillator model in description of the nonlinear susceptibility of media and holomorphic properties of the nonlinear susceptibility were utilized. Using such concepts, conventional Kramers-Kronig, multiply-subtractive Kramers-Kronig, and generalized Kramers-Kronig dispersion relations can be derived. We demonstrate how in practice the variety of different Kramers-Kronig relations mentioned above, as well as various sum rules, can be applied in nonlinear optical spectra analysis. As an example we treat the third-harmonic wave generation spectrum from a polymer.

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“…Recently, a phase-retrieval procedure based on the maximum-entropy principle has been proposed by Vartiainen et al [1][2][3][4] and Peiponen. 5,6 The maximumentropy phase-retrieval procedure (MEPRP) is superior to that based on the Kramers-Kronig relations 7,8 in two aspects. First, the MEPRP is applicable to degenerate cases 3 such as second-harmonic generation and degenerate four-wave mixing, for which the Kramers-Kronig relations do not hold.…”

Section: Introductionmentioning

confidence: 99%

Model-independent maximum-entropy method for the analysis of sum-frequency vibrational spectroscopy

Yang

Huang

2000

J. Opt. Soc. Am. B

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We have developed and applied a maximum-entropy phase-retrieval procedure to analyze sum-frequency vibrational spectra from a CCl 4 /octadecyl tricholosilane/silica interface and a hydrogen-terminated diamond C(111) surface. Some a priori knowledge of a nonlinear optical spectrum was employed for determining the phase of nonlinear optical susceptibility, and therefore the requirement for experimental phase measurement can be avoided. The results agree well with those from the Lorentzian line-shape model and justify the applicability of the a priori constraints employed in our phase-retrieval procedure.

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Dispersion theory of effective meromorphic nonlinear susceptibilities of nanocomposites

Cited by 5 publications

References 21 publications

Generalized Kramers–Kronig relations in nonlinear optical- and THz-spectroscopy

Generalized Kramers–Kronig relations in nonlinear optical- and THz-spectroscopy

Kramers—Kronig Relations and Sum Rules in Nonlinear Optical Spectroscopy

Model-independent maximum-entropy method for the analysis of sum-frequency vibrational spectroscopy

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