p- and s-polarized FTIR reflectance spectroscopy at oblique incidence by Kramers-Kronig transformation

Hopfe, V.; Bussemer, P.; Richter, E.; Klobes, P.

doi:10.1088/0022-3727/25/2/024

Cited by 15 publications

(8 citation statements)

References 11 publications

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“…It appears that the Blashke factor contributes to the global phase by the term -π in the Drude model, in agreement with the data given in [13], case 3.1 of the Table 1.…”

Section: Blashke Factor B(ω 0 θ) In the Drude Modelsupporting

confidence: 89%

On the Kramers–Kronig transform with logarithmic kernel for the reflection phase in the Drude model

André

Guen

Jonnard

et al. 2010

Journal of Modern Optics

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We consider the Kramers-Kronig transform (KKT) with logarithmic kernel to obtain the reflection phase and subsequently the complex refractive index of a bulk mirror from reflectance. However, it remains some confusion on the formulation for this analysis.Assuming the damped Drude model for the dielectric constant and the oblique incidence case, we calculate the additional terms: phase at zero frequency and Blashke factor and we propose a reformulated KKT within this model. Absolute reflectance in the s-polarization case of a gold film is measured between 40 and 350 eV for various glancing angles using synchrotron radiation and its complex refractive index is deduced using the reformulated KKT that we propose. The results are discussed with respect to the data available in the literature.2

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“…It appears that the Blashke factor contributes to the global phase by the term -π in the Drude model, in agreement with the data given in [13], case 3.1 of the Table 1.…”

Section: Blashke Factor B(ω 0 θ) In the Drude Modelsupporting

confidence: 89%

On the Kramers–Kronig transform with logarithmic kernel for the reflection phase in the Drude model

André

Guen

Jonnard

et al. 2010

Journal of Modern Optics

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“…The software used was developed by us in a MatLab ͑The Math Works͒ environment based on previously reported investigations. 19,20 The amorphous TiO 2 used in this work was obtained through the hydrolysis of TTIP in the air, a process which is well described in the literature since it is the basis of the sol-gel deposition. No crystalline structure was observed for this solid by x-ray diffraction.…”

Section: Determination Of the Optical Constants Of Tio 2 Standardsmentioning

confidence: 99%

“…However, the validity of each expression seems to be still unknown. 20 Our intention here is not an exhaustive study of EMTs' validity, but we focus on the results they generated for our specific problem.…”

Section: A To and Lo Energy-loss Functionsmentioning

confidence: 99%

“…Since in nonmagnetic materials, ⑀ is related to the complex refractive index through ⑀ ϭñ 2 , it can be determined from experimental reflectance data by Kramers-Krönig analysis ͑KKA͒. 19,20 Such a method has been widely used to determine ñ of materials in the IR region because it needs only a specular reflectance spectrum observed at some known angle of incidence. A specular reflection spectrum of these powders can be regarded as a superposition of the two polarized single crystal's reflectance spectra attenuated by the fact that the density of the pellet is smaller than that of the single crystal.…”

Section: A To and Lo Energy-loss Functionsmentioning

confidence: 99%

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Berreman effect applied to phase characterization of thin films supported on metallic substrates: The case ofTiO2

et al. 2001

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Infrared reflection-absorption spectra of TiO 2 thin films deposited by plasma-enhanced chemical vapor deposition onto aluminum and by a sol-gel process onto platinum were obtained using s-and p-polarized light and oblique incidence angles. Prominent bands with variable reflection minima position and line shapes, which were shown to be phase dependent, were observed for all samples in the 800Ϫ900 cm Ϫ1 wave number range when p-polarized light and oblique incidence were used. Such bands were attributed to an LO mode of TiO 2 and their enhancement with the incidence angle is a good example of Berreman effect. Such spectra were analyzed by means of spectral simulation based on the Fresnel equation for a three-layered system. The films' optical constants used in the simulations were obtained through the Kramers-Krönig analysis ͑KKA͒ of the reflectance spectra of pellets of powdered amorphous TiO 2 , anatase and rutile. Optical constants for hypothetical polycrystalline TiO 2 systems were also calculated from the dielectric functions of single crystals by means of effective medium theories ͑EMTs͒, such as those of Bruggeman, Maxwell-Garnett, and Hunderi. These optical constants were used both for spectral simulation and for understanding the bands observed. However, the optical constants for the powdered standards determined through KKA reproduced experimental results more accurately than those determined through the EMTs. In both experimental and simulated spectra, Berreman effect was very clear-cut and a reliable phase characterization could be carried out.

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“…The same problem appears, when the sample is a thin film on a substrate and in many other cases. A number of analytical and numerical algorithms were put forward to extend the KK method to off-normal reflection 9,10,11,12,13,14,15 , transmission 16,17,18,19 , attenuated total reflection (ATR) spectra 13,20,21,22 as well as to optical data on layered samples 14,17,23,24,25,26,27 and lowsymmetry crystals 28,29 and other 'non-standard' situations. Although the proposed techniques, taken together, certainly cover a substantial scope of applications, it is desirable, from the practical point of view, to have a single universal approach, which can be used in most of the currently used and future optical experiments without major readaptation.…”

Section: Introductionmentioning

confidence: 99%

Kramers–Kronig constrained variational analysis of optical spectra

Kuzmenko

2005

Review of Scientific Instruments

676

478

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A universal method of extraction of the complex dielectric function ǫ(ω) = ǫ1(ω) + iǫ2(ω) from experimentally accessible optical quantities is developed. The central idea is that ǫ2(ω) is parameterized independently at each node of a properly chosen anchor frequency mesh, while ǫ1(ω) is dynamically coupled to ǫ2(ω) by the Kramers-Kronig (KK) transformation. This approach can be regarded as a limiting case of the multi-oscillator fitting of spectra, when the number of oscillators is of the order of the number of experimental points. In the case of the normal-incidence reflectivity from a semi-infinite isotropic sample the new method gives essentially the same result as the conventional KK transformation of reflectivity. In contrast to the conventional approaches, the proposed technique is applicable, without readaptation, to virtually all types of linear-response optical measurements, or arbitrary combinations of measurements, such as reflectivity, transmission, ellipsometry etc., done on different types of samples, including thin films and anisotropic crystals.

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p- and s-polarized FTIR reflectance spectroscopy at oblique incidence by Kramers-Kronig transformation

Cited by 15 publications

References 11 publications

On the Kramers–Kronig transform with logarithmic kernel for the reflection phase in the Drude model

On the Kramers–Kronig transform with logarithmic kernel for the reflection phase in the Drude model

Berreman effect applied to phase characterization of thin films supported on metallic substrates: The case ofTiO2

Kramers–Kronig constrained variational analysis of optical spectra

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