Explicit determination of the complex refractive index of an absorbing medium from reflectance measurements at and near normal incidence

Azzam, R. M. A.

doi:10.1364/josa.72.001439

Cited by 13 publications

(4 citation statements)

References 18 publications

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“…[Note that a = -p/2 and b = q', where p and q' are given by Eqs. (9) and (11).] Equation (29) allows the determination of the maximum possible value of Ei that is consistent with a specified or measured kpB (or u).…”

Section: The Results Ismentioning

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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Section: The Results Ismentioning

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 measured irradiances at two different liquid path lengths were expressed as Ii(yi) = Ioexp', (2) I2(y2) = Ioexp'2. (3) Irradiances Ii and '2 are known values at known path lengths y and y and from Equations 2 and 3, 1 (Ii a = ln-j, (4) y2-yl \12J the relation between a and k is 4irk a = -:- (5) Where ) is the wavelength of the laser. From Equations 4 and 5, ) k = ln(-j.…”

Section: Imaginary Part Of the Index Of Refractionmentioning

confidence: 99%

<title>Real and imaginary index-of-refraction measurements for RP-1 rocket fuel</title>

Alexander¹,

Kubik²,

Kalwala³

et al. 1994

SPIE Proceedings

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Complex index of refraction values of RP-1 liquid rocket fuel is reported at laser wavelengths of 0.193 1um (ArF excimer), 0.5145 pm (argon-ion), 0.532 ,am (Nd-YAG, frequency doubled), 1.064 ,um (Nd-YAG), and 10.5915 m (C02). The imaginary part of the index of refraction (k) was determined by the traditional transmission method. The real part (nr) 5 determined by reflectance measurements, critical angle, Mueller matrix, and Michelson interferometer techniques. Reflectance measurements are used to obtain nr at a wavelength of 0.193 1am. Critical angle method is used to determine n at 0.5145 um and 0.532 m. The real part of the refractive index is obtained from Snell's law by measuring the critical angle. The real part of the refractive index at 1.064 ,am is derived based on elements of the Mueller matrix. Specular measurements were performed using a TMA scatterometer to obtain the Mueller matrix. A Michelson interferometer is used to determine r at 10.5915 ,m.

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“…Reflectance measurements are also used to find optical properties such as optic axis, complex refractive index, optical constants etc. [16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Uniform Plane Wave Reflection From Pec Plane Embedded in a Nonlinear Medium

Hussnain¹,

Mughal²

2011

PIER M

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Abstract-Reflection from a perfect electric conductor (PEC) plane of infinite dimensions embedded in a second order nonlinear medium is studied. The reflected wave has two parts, one due to linear behavior, the other due to nonlinear behavior of the medium. The expressions of the reflection coefficients for parallel and perpendicular polarization cases are obtained. The reduction of reflection coefficient to a linear medium case is also reported. Dependence of the said coefficients on incident electric field intensity and the angle of incidence is also plotted.

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Explicit determination of the complex refractive index of an absorbing medium from reflectance measurements at and near normal incidence

Cited by 13 publications

References 18 publications

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

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

<title>Real and imaginary index-of-refraction measurements for RP-1 rocket fuel</title>

Uniform Plane Wave Reflection From Pec Plane Embedded in a Nonlinear Medium

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