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Accepted papers to appear in an upcoming issue

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Spectrum of classes of point emitters ofelectromagnetic wave fields

Roman Castaneda

Doc ID: 268131 Received 09 Jun 2016; Accepted 28 Jul 2016; Posted 29 Jul 2016  View: PDF

Abstract: The spectrum of classes of point emitters has been introduced as a numerical tool suitable for the design, analysisand synthesis of non–paraxial optical fields in arbitrary states of spatial coherence. In this paper, the polarizationstate of planar electromagnetic wave fields is included in the spectrum of classes, thus increasing its modelingcapabilities. In this context, optical processing is realized as a filtering on the spectrum of classes of point emitters,performed by the complex degree of spatial coherence and the two–point correlation of polarization, which couldbe implemented dynamically by using programmable optical devices.

Corrigenda to “Angular spectral framework to test fullcorrections of paraxial solutions”

Raúl Mahillo-Isla and María-Jesús González-Morales

Doc ID: 264521 Received 13 May 2016; Accepted 26 Jul 2016; Posted 26 Jul 2016  View: PDF

Abstract: In our previous article (Journal of the Optical Societyof America A, Vol. 32, No. 7, pp. 1 6–1242) thereis an issue concerning the comparison of plane wavespectrum solutions of paraxial and Helmholtz equations.We compared the angular plane wave spectrumof Helmholtz solutions with plane wave spectrum ofthe paraxial solutions in terms of normalized projectionsof paraxial wavevectors. We show that the propercomparison of plane wave spectra must be done interms of angles. The results presented in our previouswork are corrected accordingly. The most importantchange is that Wünsche’s T2 operator leads to a validmethod.

Effects of urban microcellular environments on ray-tracing-based coverage predictions

Zhongyu Liu, Lixin Guo, Xiaowei Guan, and Jiejing Sun

Doc ID: 264846 Received 10 May 2016; Accepted 26 Jul 2016; Posted 26 Jul 2016  View: PDF

Abstract: The ray tracing (RT) algorithm, which is based on geometrical optics and the uniform theory of diffraction, has become a typical deterministic approach of studying wave propagation characteristics. Under urban microcellular environments, the RT method highly depends on detailed environmental information. The aim of this paper is to provide help in selecting the appropriate level of accuracy required in building databases to achieve good trade-offs between database costs and prediction accuracy. After familiarization with the operating procedures of the RT-based prediction model, this study focuses on the effect of errors in environmental information on prediction results. The environmental information consists of two parts, namely, geometric and electrical parameters. The geometric information can be obtained from a digital map of a city. To study the effects of inaccuracies in geometry information (building layout) on RT-based coverage prediction, two different artificial erroneous maps are generated based on the original digital map, and systematic analysis is performed by comparing the predictions with the erroneous maps and measurements or the predictions with the original digital map. To make the conclusion more persuasive, the influence of random errors in RMS delay spread results is investigated. Furthermore, given the electrical parameters’ effect on the accuracy of the predicted results of the RT model, the dielectric constant and conductivity of building materials are set with different values. The path loss and RMS delay spread under the same circumstances are simulated by the RT prediction model.

Curvatures of the refracted wavefronts andronchigrams for a plano arbitrary lens

Omar Cabrera Rosas, Gilberto Silva-Ortigoza, Paula Ortega Vidals, and Salvador Juárez-Reyes

Doc ID: 266753 Received 27 May 2016; Accepted 26 Jul 2016; Posted 26 Jul 2016  View: PDF

Abstract: In this work we obtain the equations for the curvatures of the refracted wavefronts for a plano arbitrarylens. The functions H0, H1 and H2 that determine the caustic, also determine the curvature of these wave-fronts. The analysis performed in these calculations allows us to study the behavior of the ronchigramsfor the case of plane incident wavefronts. We apply this procedure for a plano spherical lens and we findout that it is possible to describe the behavior of the rochigrams based on the t function, the function thatlabels the refracted wavefronts of the optical system

GEOMETRICAL CONNECTION BETWEEN CATACAUSTICS AND KINEMATICS OF PLANAR MOTION OF A RIGID SOLID

Consuelo Cebreros and Marcelo Rodríguez-Danta

Doc ID: 267463 Received 01 Jun 2016; Accepted 26 Jul 2016; Posted 26 Jul 2016  View: PDF

Abstract: Unnoticed and hidden opto-mechanical analogies between kinematics of planar motion of a rigid solid and catacaustics generated by mirror reflection on smooth profiles in geometrical optics are discussed. A concise and self-consistent theory is developed, which intends to explain and clarify many partial aspects covered by the literature.

Transient Analysis of Electromagnetic Wave Interactions on Plasmonic Nanostructures using a Surface Integral Equation Solver

Ismail Uysal, Huseyin Ulku, and Hakan Bagci

Doc ID: 262644 Received 07 Apr 2016; Accepted 24 Jul 2016; Posted 26 Jul 2016  View: PDF

Abstract: Transient electromagnetic interactions on plasmonic nanostructures are analyzed by solving the Poggio-Miller-Chan-Harrington-Wu-Tsai (PMCHWT) surface integral equation (SIE). Equivalent (unknown) electric and magnetic current densities, which are introduced on the surfaces of the nanostructures, are expanded using Rao-Wilton-Glisson (RWG) and polynomial basis functions in space and time, respectively. Inserting this expansion into the PMCHWT-SIE and Galerkin-testing the resulting equation at discrete times yield a system of equations that is solved for the current expansion coefficients by a marching on-in-time (MOT) scheme. The resulting MOT-PMCHWT-SIE solver calls for computation of additional convolutions between the temporal basis function and the plasmonic medium's permittivity and Green function. This computation is carried out with almost no additional cost and without changing the computational complexity of the solver. Time domain samples of the permittivity and the Green function required by these convolutions are obtained from their frequency domain samples using a fast relaxed vector fitting algorithm. Numerical results demonstrate the accuracy and applicability of the proposed MOT-PMCHWT solver.

Reverse propagation and negative angular momentum density flux of an optical nondiffracting nonparaxial fractional Bessel vortex beam of progressive waves

Farid Mitri

Doc ID: 265133 Received 16 May 2016; Accepted 19 Jul 2016; Posted 19 Jul 2016  View: PDF

Abstract: Energy and angular momentum flux density characteristics of an optical nondiffracting nonparaxial vector Bessel vortex beam of fractional order are examined based on the dual field method for the generation of symmetric electric and magnetic fields. Should some conditions determined by the polarization state, the half-cone angle as well as the beam-order (or topological charge) be met, the axial energy and angular momentum flux densities vanish (representing Poynting singularities), before they become negative. These negative counter-intuitive properties suggest retrograde (negative) propagation as well as a rotation reversal of the angular momentum with respect to the beam handedness. These characteristics of nondiffracting nonparaxial Bessel fractional vortex beams of progressive waves open new capabilities in optical tractor beam tweezers, optical spanners, invisibility cloaks, optically-engineered metamaterials and other applications.

Polynomial modal analysis of lamellar diffraction gratings in conical mounting

Gérard Granet, Manjakavola Randriamihaja, Edee Senyo, and Karyl Raniriharinosy

Doc ID: 264132 Received 29 Apr 2016; Accepted 19 Jul 2016; Posted 19 Jul 2016  View: PDF

Abstract: An efficient numerical modal method for modelling lamellar grating in conical mounting is presented. Within each region of the grating, the electromagnetic field is expanded onto Legendre polynomials which allows to enforce in an exact manner the boundary conditions which determine the eigen-solutions. Our code is successfully validated by comparison with results obtained with the analytical modal method.

Numerical generation of polarization singularities array with modulated amplitude and phase

Dong Ye, Xinyu Peng, Qi Zhao, and yanru chen

Doc ID: 264631 Received 05 May 2016; Accepted 19 Jul 2016; Posted 19 Jul 2016  View: PDF

Abstract: The point having no defined polarized ellipse azimuthal angle (circularly polarized) in a space-variant vector fields are called polarization singularity, and it has three types: Lemon, Monstar and Star. Recently the connection of polarization singularities has been performed. Inspired by this, we conduct numerical generation of polarization singularities array. Our method is based on two orthogonal linearly polarized light beams with modulated amplitudes and phases. With appropriate distribution functions of amplitudes and phases we can control the polarized states of polarization singularities, which offer a possibility to simulate polarization singularities array.

Interaction of axial and oblique astigmatism intheoretical and physical eye models

Tao Liu and Larry Thibos

Doc ID: 264296 Received 02 May 2016; Accepted 18 Jul 2016; Posted 20 Jul 2016  View: PDF

Abstract: The interaction between oblique and axial astigmatism was investigated analytically (generalized Coddington’sequations) and numerically (ray tracing) for a theoretical eye model with a single refracting surface. A linearvector-summation rule for power vector descriptions of axial and oblique astigmatism was found to account fortheir interaction over the central 90° diameter of visual field. This linear summation rule was further validatedexperimentally using a physical eye model measured with a laboratory scanning aberrometer. We then used thelinear summation rule to evaluate the relative contributions of axial and oblique astigmatism to the totalastigmatism measured across the central visual field. In the central visual field, axial astigmatism dominatesbecause the oblique astigmatism is negligible near the optical axis. At intermediate eccentricities, axial and obliqueastigmatism may have equal magnitude but orthogonal axes, which nullifies total astigmatism at two locations inthe visual field. At more peripheral locations, oblique astigmatism dominates axial astigmatism and the axes oftotal astigmatism become radially oriented, which is a trait of oblique astigmatism. When eccentricity is specifiedrelative to a foveal line-of-sight that is displaced from the eye’s optical axis, asymmetries in the visual field map oftotal astigmatism can be used to locate the optical axis empirically and to estimate the relative contributions ofaxial and oblique astigmatism at any retinal location, including the fovea. We anticipate the linear summation rulewill benefit many topics in vision science (e.g. peripheral correction, emmetropization, meridional amblyopia) byproviding improved understanding of how axial and oblique astigmatism interact to produce net astigmatism.

Infrared refractive index dispersion of PMMA spheres from synchrotron extinction spectra

Reinhold Blumel, Achim Kohler, Murat Bagcioglu, and Rozalia Lukacs

Doc ID: 266688 Received 20 May 2016; Accepted 17 Jul 2016; Posted 19 Jul 2016  View: PDF

Abstract: We performed high-resolution Fourier-transform infrared (FTIR) spectroscopy of a polymethyl methacrylate (PMMA) sphere of unknown size in the Mie scattering region. Apart from a slow, oscillatory structure (wiggles), which is due to an interference effect, the measured FTIR extinction spectrum exhibits a ripple structure, which is due to electromagnetic resonances. We fully characterize the underlying electromagnetic mode structure of the spectrum by assigning two mode numbers to each of the ripples in the measured spectrum. We show that analyzing the ripple structure in the spectrum in the wavenumber region from about $3000\,$cm$^{-1}$ to $8000\,$cm$^{-1}$ allows us to both determine the unknown radius of the sphere and the PMMA index of refraction, which shows a strong frequency dependence in this near-infrared spectral region. While in this paper we focus on examining a PMMA sphere as an example, our method of determining the refractive index and its dispersion from synchrotron infrared extinction spectra is generally applicable for the determination of the index of refraction of any transparent substance that can be shaped into micron-sized spheres.

A 3-Dimensional Inverse Problem of Geometrical Optics: a Mathematical Comparison Between Fermat’s Principle and the Eikonal Equation

Francesco Demontis and Francesco Borghero

Doc ID: 264793 Received 16 May 2016; Accepted 17 Jul 2016; Posted 19 Jul 2016  View: PDF

Abstract: In the framework of Geometrical Optics we consider the following inverse problem: given a two-parameter family of curves (congruence) (i.e., f (x, y, z) = c 1 , g(x, y, z) = c 2 ), construct the refractive-index distribution function n = n(x, y, z) of a 3-dimensional continuous transparent inhomogeneous isotropic medium allowing for the creation of the given congruence as a family of monochromatic light rays. We solve this problem by following two different procedures:i) by applying Fermat’s principle: We establish a system of two first order linear non-homogeneous PDEs in the unique unknown function n = n(x, y, z) relating the assigned congruence of rays with all possible refractive-index profiles compatible with this family. Moreover, we furnish an analytical proof that the family of rays must be a normal congruence.ii) by applying the eikonal equation: We establish a second system of two first order linear homogeneous PDEs whose solutions give the equation S(x, y, z) = const. of the geometric wave-fronts and, consequently, all pertinent refractive-index distribution functions n = n(x, y, z).Finally, we make a comparison between the two procedures described above discussing some appropriate examples having exact solutions.

Exponential Filtering of Singular Values Improves Photoacoustic Image Reconstruction

Phaneendra Yalavarthy, Manish Bhatt, and Sreedevi Gutta

Doc ID: 263273 Received 15 Apr 2016; Accepted 17 Jul 2016; Posted 19 Jul 2016  View: PDF

Abstract: Model based image reconstruction techniques yield better quantitative accuracy in photoacoustic imagereconstruction. In this work, an exponential filtering of singular values was proposed for carrying outthe image reconstruction in photoacoustic tomography. The results were compared with widely popularTikhonov regularization, time reversal, and the state of the art least-squares QR based reconstructionalgorithms for three digital phantom cases with varying signal-to-noise ratios of data. It was shown thatexponential filtering provides superior photoacoustic images of better quantitative accuracy. Moreover,the proposed filtering approach was observed to be less biased towards regularization parameter and didnot come with any additional computational burden as it was implemented within the Tikhonov filteringframework. It was also shown that the standard Tikhonov filtering becomes an approximation to theproposed exponential filtering.

Low reflection region within the stop band of an absorbing periodic multilayer

John Lekner

Doc ID: 261605 Received 24 Mar 2016; Accepted 11 Jul 2016; Posted 12 Jul 2016  View: PDF

Abstract: Non-absorbing periodic multilayers reflect both the s (TE) and p (TM) polarizations strongly within the respective stop bands. We find that weakly absorbing layers, for which the reflection is usually strong within the stop bands, can have very weak reflection of the p polarization near the middle of the stop band, close to glancing incidence. Approximate expressions are derived for the location (in angle of incidence and frequency) of the reflection minimum, and compared with calculated reflectances for specific multilayers.

Characteristics of surface plasmon-polariton waves excited on 2D periodically patterned columnar thin films of silver

Jhuma Dutta, Akhlesh Lakhtakia, and S. Anantha Ramakrishna

Doc ID: 264134 Received 27 Apr 2016; Accepted 11 Jul 2016; Posted 12 Jul 2016  View: PDF

Abstract: Periodically patterned thin films of slanted silver nanocolumns were deposited by directing a collimated vapor flux of silver towards square and hexagonal gratings of photoresist on glass substrates. Angle-resolved specular-transmittance measurements in the visible and near-infrared wavelength bands on these periodically patterned columnar thin films (CTFs) were carried to investigate the excitation of surface plasmon-polariton (SPP) waves bound tightly to either the air/CTF or the photoresist/CTF interfaces. The orientation of the propagation vector of the incident p-polarized plane wave with respect to the morphologically significant plane of the CTFs was varied to reveal asymmetric (unidirectional) coupling of Floquet modes to SPP waves. The asymmetric coupling is maximal when the propagation vector of the incident planewave lies wholly in the morphologically significant plane. Theoretical understanding based on the Bruggeman formalism to homogenize the silver CTFs into hyperbolic biaxial continua is able to explain the experi-mental observations very well.

Determination of the complex refractive index of a subwavelength-diameter Pt- or Au-pipe by light scattering

Fumiaki Tajima and Yoshio Nishiyama

Doc ID: 264117 Received 05 May 2016; Accepted 05 Jul 2016; Posted 06 Jul 2016  View: PDF

Abstract: The complex refractive indices of a Pt- or Au-pipe of a subwavelength in diameter have been found to be different from those of metal thin films for the first time. The metal pipe is made by cladding the metal around a spider silk of a half wavelength in diameter and illuminated by a plane polarized laser of wavelength 660 nm at normal incidence. Angular distribution of light intensity scattered by the pipe is measured and fitted by theoretical calculations based on the corresponding model. The fitting results have lead to the optimum values and uncertainty ranges of the indices and diameter of the pipe. A field emission electron microscope confirms the diameter of the optical estimation and reveals an image of the surface of the pipe.

Wideband Image Demodulation Via Bi-dimensional Multirate Frequency Transformations

Wenjing Liu and Balu Santhanam

Doc ID: 259217 Received 15 Feb 2016; Accepted 27 Jun 2016; Posted 30 Jun 2016  View: PDF

Abstract: Existing image demodulation approaches based on the 2D multicomponent AM-FM model assume narrowband components that can be demodulated using either the analytical signal or energy operator. However, if the FM components are wideband then these demodulation approaches incur significant error. Recent work by the authors extended wideband FM demodulation in 1D to accommodate large conversion factors using multirate frequency transformations. In this paper, we extend the multirate frequency transformations technique developed for 1D signals to 2D and images in conjunction with a recently proposed 2D higher-order energy demodulation approach. This extension is applied to both synthetic and real images to demonstrate the efficacy of the approach.

Losing focus: how lens position and viewing angleaffect the function of multifocal lenses in fishes

Yakir Gagnon, David Wilby, and Shelby Temple

Doc ID: 259077 Received 12 Feb 2016; Accepted 12 Jun 2016; Posted 14 Jun 2016  View: PDF

Abstract: Light rays of different wavelengths are focused at different distances when they pass through a lens (longitudinal chromatic aberration; LCA). For animals with colour vision this can pose a serious problem, because in order to perceive a sharp image the rays must be focused at the shallow plane of the photoreceptor outer segments in the retina. A variety of fish and tetrapods have been found to possess multifocal lenses, which correct for LCA by assigning concentric zones to correctly focus specific wavelengths. Each zone receives light from a specific beam entrance position (BEP) – the lateral distance between incoming light and the centre of the lens. Any occlusion of incoming light at specific BEPs changes the composition of the wavelengths that are correctly focused on the retina. Here, we calculated the effect of: lens position relative to the plane of the iris; and light entering the eye at oblique angles on how much of the lens was involved in focusing the image on the retina (measured as the availability of BEPs). We used rotational photography of fish eyes and mathematical modelling, to quantify the degree of lens occlusion. We found that at most lens positions and viewing angles there was a decrease of BEP availability, and in some cases complete absence of some BEPs. Given the implications of these effects on image quality, we postulate that three morphological features (aphakic spaces, curvature of the iris and intraretinal variability in spectral sensitivity) may, in part, be adaptations to mitigate the loss of spectral image quality in the periphery of the eyes of fishes.

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