Determination of optical constants using pseudo-Brewster angle and normal incidence reflectance measurements

Darcie, T.E.; Whalen, M. S.

doi:10.1364/ao.23.001130

Cited by 17 publications

(8 citation statements)

References 3 publications

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“…Therefore, in almost all of the region characteristic of a metal, the sensitivity of the method in the determination of the absorption coefficient k is the same as or better than the experimental precision in measurements of ␣ and R. Since measurements of the normal-incidence reflection coefficient R may be performed very exactly, 9 this gives a simple practical method for determining of the complex refractive index of a metal and absorbing media. The only exception is the region 1 Ϫ R Ӷ 1 (in terms of n and k this relates to the materials with n Ӷ 1 and k Ͼ 1, i.e., for example, a metal in the vacuum ultraviolet spectral region) and the vicinity of the dielectric boundary A, i.e., materials with k Ӷ 1.…”

Section: A Unambiguity Of the Methodsmentioning

confidence: 99%

“…Bearing this in mind, we can proceed in a different way and choose, instead of R s Ј , any other experimental parameter. To be exact, by reasoning similar to the Darcie-Whalen approach in the case of the pseudo-Brewster-angle measurements, 9 one can suggest an idea for combining the grazing-angle parameter ␣ with the normal-incidence reflectance R(0).…”

Section: Imaginary Part [mentioning

confidence: 99%

“…3,4,7,8 A particular case of this category consists of measuring of the pseudo-Brewster angle and the reflectivity at normal incidence. 9 The variety of the proposed methods stems from the need to improve sensitivity and overcome ambiguities in the solutions. Such ambiguities arise when the experimentally measured values are compatible with several physically reasonable pairs of the optical constants.…”

Section: Introductionmentioning

confidence: 99%

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Combined grazing-angle and normal-incidence reflectometry of absorbing media

1999

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We have studied the grazing-incidence differential-reflectance method for obtaining the dielectric function of absorbing media in terms of the derivatives R p Ј and R s Ј of the polarized light reflectances and found that it does not guarantee adequate accuracy for almost any values of the optical parameters. Therefore we modify that approach and describe what we believe is a novel method for the unambiguous determination of the optical constants n and k of a metal and other absorbing materials in terms of the ratio of the derivatives ␣ ϭ R p Ј/R s Ј at the grazing incidence and the normal incidence reflection coefficient R. Moreover, it is possible to express ␣ through the logarithmic derivatives (1/R)RЈ in the vicinity of the grazing angle. The possibility of performing measurements at the unspecified angle without knowledge of the explicit value of this angle is an evident advantage of this technique. For the great majority of metals and semiconductors the relative errors in the optical constants are comparable to or less than the relative errors in the experimentally measured parameters.

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Section: A Unambiguity Of the Methodsmentioning

confidence: 99%

Section: Imaginary Part [mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Combined grazing-angle and normal-incidence reflectometry of absorbing media

1999

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“…Because the refractive index n is dependent on the wavelength () (or color) of light, i.e., n ϭ n͑͒, dispersion can be measured by determining the relation between the refractive index n and the wavelength . Many techniques have been proposed for measuring the refractive index, including the reflectance method, [1][2][3] Abbe refractometers, 4 the critical angle, 5,6 Brewster's angle, 7,8 the pseudo-Brewster's angle, 9,10 prism couplers, [11][12][13] total internal reflection (TIR), 14 ellipsometry, [15][16][17][18][19][20] interference, [21][22][23][24][25][26] holograms, 27 and the moiré method. 28 However, most of these methods are related to light intensity or interference fringe variation measurements.…”

Section: Introductionmentioning

confidence: 99%

Phase geographical map for determining the material type of a right-angle prism

Chiu

Lai

Wang³

et al. 2006

Appl. Opt.

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A phase geographical map for determining a right-angle prism is presented. The proposed method is based on total-internal-reflection effects and chromatic dispersion. Under the total-internal-reflection condition, the phase difference between the S and P polarizations, as a function of the wavelength and refractive index, can be extracted and measured using heterodyne interferometry. Various wavelengths correspond to various refractive index values. The proposed map is convenient in ensuring the prism material using a specific V number. The method has the following merits: high stability, ease of operation, and rapid measurement.

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“…When the medium of refraction is also transparent, e is real, and (kpB reverts to the exact Brewster angle, OB = tan_'(el"2), (3) at which Irpimin = O. u = sin 2pB. (6) In this paper we consider the nature of the contours of constant qOpB in the complex e (and N) plane both analytically and graphically. Previously, Holl 5 presented a family of constant-(pB contours in the nk plane but without giving any accompanying formula that would permit others to create fresh and accurate sets of those contours.…”

Section: Introductionmentioning

confidence: 99%

Contours of constant pseudo-Brewster angle in the complex ∊ plane and an analytical method for the determination of optical constants

Azzam

Ugbo

1989

Appl. Opt.

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The locus of all points in the complex plane of the dielectric function ?[?(r) + j?(i) = |?| exp(jtheta)], that represent all possible interfaces characterized by the same pseudo-Brewster angle theta(p)B of minimum p reflectance, is derived in the polar form: |?| = l cos(zeta/3), where l = 2(tan(2)Phi(p)B)k, zeta = arccos(- costheta cos(2)Phi(p)B/k(3)), and k = (1 - 2/3 sin(2)Phi(p)B)(1/2). Families of iso-Phi(p)B contours for (I) 0 degrees 80 degrees ) is the iso-Phi(p)B contour accurately approximated as a circle. We find that |?| < 1 for Phi(p)B < 37.23 degrees , and |?| > 1 for Phi(p)B > 45 degrees . The optical constants n,k (where n + jk = ?((1/2)) is the complex refractive index) are determined from the normal incidence reflectance R(0) and Phi(p)B graphically and analytically. Nomograms that consist of iso-R(0) and iso-Phi(p)B families of contours in the nk plane are presented. Equations that permit the reader to produce his own version of the same nomogram are also given. Valid multiple solutions (n,k) for a given measurement set (R(0),phi(p)B) are possible in the domain of fractional optical constants. An analytical solution of the (R(0),Phi(p)B) ? (n,k) inversion problem is developed that involves an exact (noniterative) solution of a quartic equation in |?|. Finally, a graphic representation is developed for the determination of complex ? from two pseudo-Brewster angles measured in two different media of incidence.

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Determination of optical constants using pseudo-Brewster angle and normal incidence reflectance measurements

Cited by 17 publications

References 3 publications

Combined grazing-angle and normal-incidence reflectometry of absorbing media

Combined grazing-angle and normal-incidence reflectometry of absorbing media

Phase geographical map for determining the material type of a right-angle prism

Contours of constant pseudo-Brewster angle in the complex ∊ plane and an analytical method for the determination of optical constants

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