Homogeneous Optical Medium Research Articles

Optical simulation and experimental investigation of the crystalline silicon/black silicon/perovskite tandem structures

The use of a black silicon (b-Si) interlayer is a promising solution for improving the optical properties of crystalline Si/perovskite solar cells. Optical numerical simulation of the crystalline Si/b-Si/perovskite structures can efficiently optimize their parameters at the initial tandem solar cell design stage. In this work, the optical properties of these structures were modeled using the transfer matrix method, where an array of cone-like nanoneedles of the b-Si interlayer is approximated as a homogeneous optical medium, for which the effective complex refractive index is the weighted average of those for Si and perovskite. Analytical equations are obtained for tandem structures' reflection, transmission, and absorption. The simulated reflectance spectra of the structures were compared with those of structures without the b-Si layer, as well as with experimental data. Numerical calculations and experiments confirm that nanotexturing significantly improves the optical properties of tandem structures. In addition, the nanotextured tandem structures have a wide-angle antireflective characteristic at incidence angles less than 60°, indicating their omnidirectional light-trapping capability. The proposed simulation model satisfactorily describes the optical behavior of crystalline Si/b-Si/perovskite tandem structures and can be used to estimate their optical properties depending on various parameters. As a demonstration, a numerical analysis was performed to study the effect of the b-Si interlayer thickness on the reflection of the tandem structure.

Fine classification of the emission-line spectra of active galaxies

We refine the classification of galaxies by activity types based on a number of samples of objects having homogeneous optical medium resolution spectra from SDSS. SDSS spectra provide many spectral features and details that were not available before. Three diagnostic diagrams and eye examination have been used and the combined activity types have been derived. A fine classification scheme was developed, where QSOs have subtypes like Seyferts, Narrow Line QSOs are introduced, subclasses for Narrow Line Seyfert 1s are used and Composite spectrum objects have their subtypes. This classification scheme much better describes all fine details in the optical spectra and allows further study of active galaxies by the subtypes for better understanding the Unified model and the physical properties of AGN and Starbursts.

Angular position of singular optic axes for arbitrary dielectric tensors

We deduce formulas for the angular position of singular optic axes in homogeneous optical media. The angular position of singular optic axes for a given general (complex, nonsymmetric) dielectric tensor is the same for its transposed and complex conjugated tensors as well as for a (complex) multiple. For the case of a symmetric dielectric tensor, the four axes fulfill a connecting relation, meaning that the singular optic axes of a nonsymmetric dielectric tensor do not relate to those of any (effective) symmetric tensor. For the symmetric case, we provide analytical solutions for the angular positions of singular optic axes of triclinic, monoclinic, and orthorhombic crystals.

Optical Characterization of a Thin-Film Material Based on Light Intensity Measurements

Light interacts with materials in a variety of ways; this article focuses on determination of refraction and absorption characterized by a material’s refractive index. We discuss some of the useful models for the frequency dependence of the refractive index, and practical approaches to calculating refractive indices of thin films and thick substrates. The efficiency of manufacturing of existing and successful creation of new devices of solid-state micro- and nanoelectronics largely depends on the level of development of the technology for manufacturing layers of various materials with a thickness of several nanometers to tens of micrometers. A high degree of perfection of layered structures and particularly structures based on dielectric and/or metallic films with nanometer thickness is needed for their successful application in micro-, nano-, acousto-, microwave and optoelectronics. It is impossible to achieve high degree of perfection without the use of high-precision methods of measuring electrophysical parameters of dielectric and semiconductor materials and structures, metallic films. We have developed the program “Multilayer”, which serves both to simulate the propagation of light through multilayer thin-film layered media, and to determine the dielectric (permittivity tensor of anisotropic films) and geometric (physical and optical thicknesses of the film) parameters of various thin-film coatings. The base mathematical models applied for the description of the light wave propagation through a homogeneous optical medium and for the determination of the optical characteristics of thin layers of optical materials based on the results of light intensity measurements are described. The main mathematical formalism employed in the program is based on solving the Maxwell’s equations for propagation of light through anisotropic stratified media. The algorithm uses the Berreman matrices of order

Historical revision of the differential Stokes-Mueller formalism: discussion.

The differential Stokes-Mueller matrix formalism expresses the local evolution of the Mueller matrix or the Stokes parameters for light propagating through a homogeneous optical medium. This paper presents a historical revision of the development of the differential Stokes-Mueller matrix formalism and highlights several important early contributions that have been overlooked. Particularly relevant is that this formalism was pioneered as early as 1929 by Paul Soleillet, almost 50 years earlier than it has been usually assumed. This historical revision demonstrates that several different authors independently formulated the differential Stokes-Mueller formalism during the 20th century and they found equivalent results studying the propagation problem from different approaches.

Stabilization of vortex beams in Kerr media by nonlinear absorption

We elaborate a new solution for the problem of stable propagation of transversely localized vortex beams in homogeneous optical media with self-focusing Kerr nonlinearity. Stationary nonlinear Bessel-vortex states are stabilized against azimuthal breakup and collapse by multiphoton absorption, while the respective power loss is offset by the radial influx of the power from an intrinsic reservoir. A linear stability analysis and direct numerical simulations reveal a region of stability of these vortices. Beams with multiple vorticities have their stability regions too. These beams can then form robust tubular filaments in transparent dielectrics as common as air, water and optical glasses at sufficiently high intensities. We also show that the tubular, rotating and speckle-like filamentation regimes, previously observed in experiments with axicon-generated Bessel beams, can be explained as manifestations of the stability or instability of a specific nonlinear Bessel-vortex state, which is fully identified.

Kinds of optically induced force derived from laws of conservation of the momentum and energy

Optically induced forces (OIF) applied to a transparent optical medium are analyzed. We deliberately do not use any assumptions about a nature of optically induced force and analyze thought experiments where only notions and laws of conservation are used. Two unambiguous but contradictory thought experiments are used as a ground of an analysis. It is shown that only two kinds of well-known OIF is sufficient to match contradictory results of the experiments. This is the kind of density force known in electrostatics that is responsible for the density force arising in an inhomogeneous dielectric located in an electrical field. This is the Abraham density force arising at propagation of a light pulse in an optical medium. The force is located in the regions of the optical medium where leading and trailing edges of a light pulse are propagating. OIF in a homogeneous optical medium located in an inhomogeneous electrical field is equal to zero at a steady-state. This result contradicts to that obtained by means of the widely used approach based on the Lorentz density force.

Sagnac effect in ring lasers and ring resonators. How does the refractive index of the optical medium influence the sensitivity to rotation?

The Sagnac effect in a ring laser (RL) results in a frequency difference of counterpropagating waves that is proportional to the RL angular rotation rate. We address the question of how an optical medium filling the whole RL or a part of it influences the frequency difference of counterpropagating waves. While the formulas for this difference in a rotating RL abound in the literature, there is no agreement among them as to whether the medium increases or decreases this difference or indeed leaves it unchanged. Nor do the available (and often contradictory) experimental data fully clarify the situation. Because the Sagnac effect is a special relativity effect, the relativistic velocity addition law is used here to calculate the frequency difference of counterpropagating waves in an RL. When a homogeneous optical medium fills the entire perimeter of the resonator of a rotating RL, we show that the frequency difference of counterpropagating waves is inversely proportional to the refractive index of the medium. The results obtained can also be used to calculate the difference between the resonant frequencies of counterpropagating waves in rotating ring resonators in the presence of an optical medium.

Compensation of the optically induced Lorentz force in a homogeneous optical medium

It is shown on the basis of different approaches that the density of optically induced forces applied to a homogeneous optical medium embedded in a simplest 1D structure in a form of a plane optical resonator is equal to zero. In particular, the density forces calculated on the base of the energetic approach, where no assumptions about physical nature of optically induced forces are used, are also equal to zero. At the same time the same forces calculated by means of the approach based on the Lorentz force are different from zero. A conclusion is derived that there is an additional type of optically induced force which compensates the Lorentz density forces. Thus, the Lorentz force approach used for calculation of the density of optically induced force is inconsistent.

Optically induced force in a curve waveguide

We show that optically induced force (OIF) that arises in a curve waveguide due to a change of the momentum of light wave because of a change of its direction is not a special kind of OIF. A conventional approach based on an analysis of OIF that arises in a homogeneous optical medium immersed in an alternate electrical field of light wave as well as an energetic approach can be used also.

Interrelation between various types of optically induced forces

Optically induced forces applied to a transparent optical medium are analyzed. It is shown on the basis of various approaches that the density of optically induced forces applied to a homogeneous optical medium located in an inhomogeneous electrical field is equal to zero at a steady-state. This result contradicts that obtained by means of an approach based on the Lorentz density force. An explanation is presented that the Lorentz density force is compensated at a steady-state by other kind of optically induced force. Thus, a calculation of optically induced force based on the approach using the Lorentz force is inconsistent.

The point-characteristic function, wavefronts, and caustic of a spherical wave refracted by an arbitrary smooth surface

The aim of this paper is to obtain expressions for the k-function, the wavefront train, and the caustic associated with the light rays refracted by an arbitrary smooth surface after being emitted by a point light source located at an arbitrary position in a three-dimensional homogeneous optical medium. The general results are applied to a parabolic refracting surface. For this case, we find that when the point light source is off the optical axis, the caustic locally has singularities of the hyperbolic umbilic type, while the refracted wavefront, at the caustic region, locally has singularities of the cusp ridge and swallowtail types.

Absolute Motion Determined from Michelson-Type Experiments in Optical Media

The symmetry of vacuum is characterized by the Lorentz group with the parameter c. Physical space inside the homogeneous optical medium should be described by the Lorentz group with the parameter c/n, where n is the refractive index of the medium. Violation of a one-parameter phenomenological symmetry in the discrete medium, such as gas, creates the opportunity for the experimental detecting of the motion of the optical medium relative to luminiferous aether.

A planar circular detector based on multiple point chemi- or bio-luminescent source within a coaxial cylindrical reactor

An analytical method was proposed for calculating radiative fluxes incident on a planar circular detector from a volume multiple point chemi- or bio-luminescent source inside a coaxial cylindrical reactor. The method was designed for a cylindrical reactor when the surface reflections were neglected and when chemi- or bio-luminescence reaches a detector embedded in the same homogeneous optical medium as the point emitters of the volume multiple point source model. The radiative fluxes from arbitrarily distributed point emitters were expressed by one generalized quadruple-integral formula. Then some double- and single-integral formulas were obtained for calculating radiative fluxes from identically radiating point emitters uniformly distributed within the reactor. Selected results were computed and illustrated graphically. The obtained formulas are suitable for optimizing and/or calibrating the considered source-detectors systems (optical radiometers or luminometers) and determining radiative fluxes generated by chemical, biological, and physical processes leading to chemi-, bio-, radio-, and sono-luminescence for example.

Determination of toric intraocular lenses

In the last decades, toric posterior chamber lenses (TPCLs) for cataract surgery and phakic toric lenses (PTLs) for refractive surgery have become more and more popular for correcting high or excessive corneal astigmatism. The purpose of this article is to present a vergence-based calculation scheme for TPCLs and PTLs. In Gaussian optics (in the paraxial space), spherocylindrical optical surfaces can be described in a mathematically equivalent formulation as vergences. There are dual notations: The standard notation is used for transforming vergences through a homogeneous optical medium, and the component notation is applied to add up the power of a refractive surface to the vergence. Both notations can be used interchangeably. For calculating TPCLs, the vergences in front of and behind the predicted pseudophakic lens position are determined and subtracted. For calculating PTLs, the anterior vergence at the predicted lens position is estimated for the preoperative and postoperative states, and the difference between the two yields the desired lens power. WORKING EXAMPLES: In the 1(st) example, the power of a thin TPCL is determined step by step by applying the presented calculation scheme, which was designed to be transferred directly to a simple computer program (e.g., Microsoft Excel). In the 2(nd) example, the postoperative refraction is estimated for a simulation in which a TPCL similar to that in example 1 is implanted in a slightly misaligned orientation. In a 3(rd) example, the power of a PTL is determined step by step using the above-mentioned calculation scheme. The presented calculation scheme allows determination of"thin" TPCLs or PTLs to achieve spherocylindrical target refraction with a cylinder axis at random or to predict the postoperative refraction for any toric lens implanted in any axis. The concept can be easily generalized to"thick" toric intraocular lenses if the geometric data and refraction index of the material are known.

Pseudophake und phake torische Linsen zur Korrektur des kornealen Astigmatismus - Theorie und klinische Aspekte

In the last decades the implantation of pseudophakic and phakic toric lenses has become wide-spread for the correction of corneal astigmatism in cases of classical cataract surgery with implantation of a posterior chamber lens or in cases of refractive surgery with implantation of a piggyback lens. The purpose of this review article is to present an en bloc mathematical strategy for calculating pseudophakic and phakic toric lenses and for deriving the spectacle refraction after implantation of an arbitrary lens. We restrict ourselves to a centred coaxial optical system containing spherocylindrical surfaces and interspaces with a homogeneous optical medium. All calculations are done in the paraxial space according to linear Gaussian optics. We define an optical model for the pseudophakic and phakic eye and characterise all known refractive surfaces and interspaces between the surfaces with 4 x 4 refraction and translation matrices, respectively. The entire optical system is described with a 4 x 4 system matrix, which relates the impinging beam (slope angle and height, both in x and y directions) with the exiting beam (slope angle and height, both in x and y directions) and extract the required parameters from the matrix representation. In example 1, we describe step-by-step how to derive a pseudophakic toric lens implant from the biometric parameters and in example 2 we estimate the residual refraction at spectacle plane after implantation of a pseudophakic lens. In example 3, we describe step-by-step how to derive a phakic toric lens implant from the initial refraction and biometric measurements and in example 4 we estimate the residual refraction at spectacle plane after implantation of a phakic lens. The calculation scheme presents a strategy for calculating toric lenses and residual refractions based on a thin lens model of the spectacle correction, the cornea and the lens implant. This model can be generalised easily to a thick lens model, if the appropriate geometric parameters of both lens surfaces are known. The phakic lens calculation can directly be transferred to the case of pseudophakic piggyback lenses.

Aberration of light in a uniformly moving optical medium

The transverse Fresnel–Fizeau light drag in the presence of a nondispersive homogeneous optical medium in uniform rectilinear motion is explained by using a simple Huygens’ construction. As a consequence of the motion of the medium, the wavefront of every individual secondary wavelet is an ellipse partially dragged by the moving medium. The resulting formula agrees with the experiment by Jones in the early 1970s and with Fresnel’s formula for transverse light drag.

Rotating optical soliton clusters.

We introduce the concept of soliton clusters--multisoliton bound states in a homogeneous bulk optical medium--and reveal a key physical mechanism for their stabilization associated with a staircaselike phase distribution that induces a net angular momentum and leads to cluster rotation. The ringlike soliton clusters provide a nontrivial generalization of the concepts of two-soliton spiraling, optical vortex solitons, and necklace-type optical beams.

Scheme for the calculation of ocular components in a four-surfaced eye without need for measurement of the anterior crystalline lens surface Purkinje images

The computing scheme described in this paper allows calculation of the internal radii of the human eye on the assumption that it possesses four (two corneal and two lenticular) axially aligned spherical surfaces separated by homogeneous optical media. It involves measurement of Purkinje images I, II and IV. This approach is novel in that it accounts for the contribution of the posterior corneal surface and does not require measurement of the Purkinje images arising from the anterior crystalline lens surface which are notoriously poor in quality.

Scheme for the calculation of ocular components in a four‐surfaced eye without need for measurement of the anterior crystalline lens surface Purkinje images

The computing scheme described in this paper allows calculation of the internal radii of the human eye on the assumption that it possesses four (two corneal and two lenticular) axially aligned spherical surfaces separated by homogeneous optical media. It involves measurement of Purkinje images I, II and IV. This approach is novel in that it accounts for the contribution of the posterior corneal surface and does not require measurement of the Purkinje images arising from the anterior crystalline lens surface which are notoriously poor in quality.