Fresnel Laws Research Articles

Determination of the optical constants of thin films of regioregular poly(3-alkylthiophene) on transparent substrates

The methods of reflection and transmission are used to determine the optical constants n and k of thin films of regioregular poly (3-octylthiophene). The technique is based on the simultaneous use of Fresnel laws and the dispersion relations between n and k of the film using an iterative process. The optical and Tauc gaps are also derived.

Particules diélectriques ou absorbantes: champ electromagnétique de surface et diffusion

The exact surface field for dielectric or absorbing spheres of various sizes is first compared to the fields obtained according to three approximations: Fraunhofer diffraction, (modified) anomalous diffraction and Fresnel's laws. In particular, it is shown that for large dielectric spheres, the characteristic reinforcements observed in the surface fields according to Fresnel correspond exactly to rainbow angles. The approximate far scattered fields, calculated using the vectorial Kirchhoff integral, are then studied. For the Fresnel and anomalous diffraction approximations, they are generally satisfactory when limited to small scattering angles and to large dimensions. In that case, the method can be fruitfully extended to non-spherical particles whose radii of curvature are not too small and especially to biological particles with low refractive index. An oblate spheroid and a surface of Cassini simulating a red cell at rest are used as examples.

Iteratively derived optical constants of MoO 3 polycrystalline thin films prepared by CVD

Polycrystalline MoO 3 thin films have been prepared by oxidation at high temperature of molybdenum compound layers deposited by chemical vapour deposition (CVD) from molybdenum hexacarbonyl Mo(CO) 6. In this paper is presented the experimental procedure to prepare polycrystalline MoO 3 coatings by annealing at various temperatures and in various annealing environments of “black molybdenum” or “reflective molybdenum” thin films. From X-ray diffraction measurements the structure of the films has been determined. The optical constants n and k of films were calculated by numerical iteration, using the Fresnel laws and dispersion relations of n and k. From these results the optical gap E g has been deduced. All the samples exhibited the electrochromic effect.

Optical constants of minerals derived from emission spectroscopy: Application to quartz

The objective of this study was to develop a method for determining the optical constants (i.e., the real (n) and imaginary (k) indices of refraction) of single‐crystal, uniaxial minerals using emission, rather than reflection, observations as a step toward deriving n and k from particulate minerals. The vibrational, midinfrared, emissivity spectra of polished quartz crystals were obtained by measuring the thermal radiance from planar surfaces, parallel and perpendicular to the optic axis. From these oriented spectra the ordinary ray was directly measured, and the extraordinary ray was mathematically derived. The n and k values for quartz were obtained by application of the Fresnel laws of reflection to the ordinary‐ and extraordinary‐ray spectra of the polished surfaces. Comparison of theoretical spectra, obtained through classical Lorentz‐Lorenz dispersion theory, to experimental spectra enabled new oscillator parameters for quartz to be determined. Construction of the ordinary‐ray spectrum required seven oscillators defined by frequencies (ν, converted to wavenumbers) of 1215 cm−1, 1161 cm−1, 1067 cm−1, 795 cm−1, 694 cm−1, 449 cm−1, and 393 cm−1; strengths (4πρ) of 0.03, 0.007, 0.67, 0.11, 0.01, 0.815, and 0.4; and damping terms (γ) of 0.4, 0.007, 0.008, 0.0115, 0.01, 0.012, and 0.012, respectively. Construction of the extraordinary‐ray spectrum required six oscillators defined by frequencies (converted to wavenumbers) of 1222 cm−1, 1074 cm−1, 776 cm−1, 509 cm−1, 494 cm−1, and 364 cm−1; strengths of 0.011, 0.67, 0.10, 0.015, 0.7, and 0.68; and damping terms of 0.15, 0.008, 0.011, 0.016, 0.014, and 0.019, respectively. These results were compared to the previously published results of Spitzer and Kleinman that required an additional oscillator (seven total) to define the extraordinary‐ray spectrum. Regardless of the difference in number of required oscillators, the spectra of n and k for the two studies agree within the experimental error. The results confirm that emission spectroscopy is a viable means for determining the optical constants of uniaxial minerals using the technique described in this study.

Generalization of complex Snell–Descartes and Fresnel laws

Generalized Snell–Descartes and Fresnel laws are derived for harmonic inhomogeneous plane waves that are incident upon a static interface between two continuous absorbing dielectric media that are macroscopically characterized by their electric and magnetic permittivities and their conductivities. A coordinate-free formalism based on complex vector algebra is used to carry out all discussions. Surprisingly, the usual complex Snell–Descartes laws for reflection and refraction and Fresnel laws for polarization are recovered only in the special case in which the vector characterizing the direction of inhomogeneity is in the plane of incidence. In the more general case a new deflection angle between planes of incidence and refraction has to be introduced. An experiment is proposed to test this prediction. A generalized form of the TE and TM modes (with respect to the interface), which are elliptically polarized and which are called parallel electric and parallel magnetic modes, also emerges.

Analytic proofs of the Arago–Fresnel laws for the interference of polarized light

The four laws of Arago–Fresnel governing the interference of polarized light were determined experimentally. Analytical proofs are derived directly from first principles. The technique used for the proofs is that of the spectral representation of stationary stochastic processes in conjunction with the Jones matrix description of a polarizer.

Optical constants of electrochromic polycrystalline WO3 thin films prepared by chemical vapour deposition

Abstract Reflectance and transmittance spectra were recorded, at normal incidence, of coloured or bleached electrochromic polycrystalline WO 3 thin films prepared by chemical vapour deposition on SnO 2 -coated Pyrex substrates. The optical constants n and k were determined using Fresnel's laws and dispersion relations via an iterative process.

Effects of boundary properties on transient temperature distributions in condensed semitransparent media

An original method for the calculation of transient temperature distribution in a semi-transparent non-scattering condensed medium accounting for radiation and conduction is presented. This method was developed in order to detail the influence of interface properties on temperature distribution. Diffuse and specular reflections of the walls for three situations (contact of the vitreous boundaries with the walls on both sides, any contact on both sides and contact on one side only) are compared for a grey medium. Large differences are shown for the latter case. Concerning the situation with any contact between walls and the STCM, a comparison between vitreous interfaces governed by Fresnel laws and diffuse vitreous interfaces is given. Significant differences are pointed out. For a glass layer the differences cannot be neglected, but they are reduced because of high absorptivity in the IR range.

Determination of optical constants of thin film from reflectance spectra

We present a method of determining optical constants n and k of a thin film using only the reflectance R(omega) curve (normal incidence reflectance spectroscopy). The method is based on the simultaneous use of Fresnel laws and dispersion relations between n and k of the film, via an iterative process. To illustrate the method, optical constants in the VUV of a film grown on InP were determined. A second example with a SnO(2) film shows how the method can reduce the effect of experimental errors when two sets of spectroscopic data are available.

Optical probe for high-temperature local void fraction determination

The optical response of a high-temperature and pressure-local void fraction device was optimized using a 2-D light ray tracing computer simulation. Snell's law, Beer's law for absorption, and Fresnel laws for reflection and refraction were included to simulate the optics associated with a diamond-tipped optical void probe. Based on an optimal design obtained from the computer simulation, an actual diamond-tipped optical void fraction device was constructed and tested at low pressure in air/water flows.

Illumination of multimode optical fibresleaky ray analysis

The power transmitted within multimode circular optical fibres illuminated at one end by either coherent or incoherent light is determined. In general, a significant portion of this power is due to the radiation field even kilometres from the source. Thus an analysis in terms of bound modes alone is inadequate and so is geometric optics using Fresnel's lawS. Instead, we use a modified form of geometric optics in which the rays are appropriately weighted to account for the leakage (radiation) from the fibre not included by Fresnel's laws. Extensive numerical results are given.

Whispering-gallery rays within dielectric circles and spheres

The attenuation of rays propagating at nearly grazing incidence within lossless dielectric circles and spheres is given. There are no trapped rays, no matter how great the refractive index of the structure; however, many rays are only very weakly attenuated. These are the ‘leaky rays’ that are predicted, incorrectly, by Fresnel's laws to be trapped.

Generalised Fresnel's law for loss due to curvature

Many rays, predicted by Fresnel's laws to be totally reflected from a curved interface between two dielectric media, are only partially reflected. We derive a generalised Fresnel transmission coefficient to account for this loss. Our transmission coefficient applies to an arbitrary surface; e.g. one defined by two arbitrary radii of curvature. It can be used to determine radiation loss from bent and straight circular optical fibres.

The Presence of Ice in the Venus Atmosphere as Inferred from a Halo Effect

view Abstract Citations (9) References (8) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Presence of Ice in the Venus Atmosphere as Inferred from a Halo Effect O'Leary, Brian T. Abstract The most common terrestrial halo phenomenon is a luminous ring located 22 from the Sun or Moon, and is due to the presence of hexagonal ice crystals in the atmosphere. Photometric profiles of halos show a brightness maximum and minimum at certain scattering angles which can be predicted by refraction theory. Photometry of the integrated light of Venus was performed at Kitt Peak National Observatory in three colors (B, V, and R) between phase angles 153 and 165 before and after inferior conjunction of 1966. These results along with an interpretive study of the photometric, colorimetric, and polarimetric characteristics of Venus as it passes through these phase angles suggest a halo effect of brightness dispersions of about 0.05 mag. brighter than the background phase-curve at predicted halo maximum and about 0.04 mag. fainter than the background phase-curve at predicted halo minimum. The corresponding polarizations of Venus observed near the halo maximum and minimum agree both in quantity and in direction with the predictions of Fresnel's laws of reflection as applied to the 22 halo. No photometric or polarimetric observations to date are inconsistent with the presence of a Venus halo effect. But since all observations are fairly close to error scatter, the existence of a Venus halo effect cannot now be definitely established. A halo effect would indicate definite proof of ice as a constituent of the Venus cloud layer because of the uniqueness of the angle and the curves of brightness, color, and polarization corresponding to an index of refraction of 1.31 and a hexagonal shape. The findings then tentatively indicate confirmation of H2O in the Venus atmosphere and a temperature and pressure environment at the cloud tops conducive to the formation of ice. The amplitude of the effect shows that, at most, a small fraction (a few per cent) of the tops of the Venus clouds would consist of these halo-producing crystals, i.e., hexagonal ice with sizes somewhat greater than a wavelength of light. There is also slight evidence of the secondary halo in the Venus atmosphere; this would be due to right-angle interfaces in ice crystals. It is suggested that the Venus halo eflect should be sought again at the next opportunity in summer, 1967, with as much accuracy as possible. The Kitt Peak observations also indicated that Venus was a tenth of a magnitude redder in B - R color index after inferior conjunction than before inferior conjunction at phase angles around 160 . The interpretation of this phenomenon might depend on a change in the scattering properties of the cloud tops from the Venus morning to afternoon or on local differences between the clouds near each limb during the times of observation. Venus was found to become redder at phase angles greater than 1560, contrary to the trend of previous observations. Publication: The Astrophysical Journal Pub Date: December 1966 DOI: 10.1086/148954 Bibcode: 1966ApJ...146..754O full text sources ADS |

Measurements of the Refractive Index of Films

The refractive index of a film of transparent or translucent material may be determined by immersing the film in a suitable liquid mixture and observing the intensity of light reflected from the surface of the specimen. The composition of the immersion liquid is varied, and a record is made of its refractive index (measured on a refractometer) and of the reflected light intensity. The refractive index of the film is the same as that of the immersion liquid giving the lowest reflected intensity. This has been confirmed by experiments with a glass plate, whose refractive index was known. According to Fresnel's laws of reflection, the experimental data should fit a parabola with its minimum at the refractive index of the film. On fitting the data by the method of least squares, the minimum is obtained with a standard deviation of the order of 0.002 refractive index units. The method has been applied to several plastic materials.

A note on the polarization of a plane polarized wave after transmission through a system of centred refracting surfaces, and some effects at the focus

It is the purpose of this note to consider the state of polarization of a wave emerging from a lens system in the light of Fresnel's Laws, when the incident wave is plane-polarized and proceeds from a point on the axis at a great distance from the system. Three special cases can be distinguished: the one in which 6, the semi-angular aperture of the system, is small, whereas the angles of incidence within the system are large; the second, in which θ is comparatively large, whereas the transmission of energy along marginal ray-paths can be regarded as complete; the third, in which both θ and the angles of incidence are small. In the course of the discussion an assumption concerning the planes containing the light vectors made in a previous communication is shown to be not strictly valid. The approximation, however, is shown to be very close.

Note on a Departure from Fresnel's Laws of Reflection

Note on a Departure from Fresnel's Laws of Reflection

On a Simple Way of Obtaining the Half-Shade Field in Polarimeters

SummaryThe half-shade effect in polarimeters is usually obtained, either by the well-known, method of Laurent, or else by the more recent method of Lippich. In the former a quartz plate is employed to give the necessary rotation to one-half of the beam of polarised light propagated through the instrument; in the latter, a Nicol prism additional to the polariser serves the same end.It occurred to the author that the required effect might be obtained very simply by merely interposing a glass plate in the beam of light, so that half the beam traversed it, in an oblique direction. It follows at once, from Fresnel's laws of the intensity of refracted light, that this will produce a slight rotation of the vibration-direction in the traversing half of the beam.In practice the method is found to give very good results.