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Weakly Diverging to Tightly Focused Gaussian Beams: a Single Set of Analytic ExpressionsContinuation: Symmetric Beams

Uri Levy and Yaron Silberberg

Doc ID: 281361 Received 22 Nov 2016; Accepted 12 Jan 2017; Posted 13 Jan 2017  View: PDF

Abstract: The always diverging-converging laser beams, more rigorously referred to as Gaussian beams, are part of many physical and electro-optical systems. Obviously, a single set of analytic expressions describing these beams in a large span of divergence-convergence angles at the focal plane, and at any distance away from the focal plane, will prove very handy.We have recently published three such analytic sets, one set for linearly polarized beams and two sets for radially polarized beams. However, our published analytic set for linearly polarized beams describes non-symmetric electric-magnetic field components. Specifically – the strong transverse magnetic field component does not become elliptic at very large divergence angles as should be, and the other transverse magnetic component, indeed very weak, is missing altogether.Here we present an analytic set of expressions symmetrically describing linearly polarized Gaussian beams. The symmetry applies to the x-electric y-magnetic components and vice versa, and to the two electric-magnetic z-components.An important property of the presented set of expressions is power conservation. That is - the electromagnetic power crossing a plane transverse to the propagation direction in a unit time is conserved. Power conservation assures beam description accuracy at any axial distance.The presented analytic expressions, although not strictly satisfying Maxwell’s equations, describe Gaussian beams with very reasonable accuracy from low divergence angles up to divergence angles as large as 0.8 radians in a medium with refractive index of 1.5, i.e. up to NA of 1.1.These expressions should then readily assist in the design of practically all laser-related systems and in the research of diverse physics and electro-optic fields.

Elimination of error induced by beam splitter substrate for dispersion compensated polarization Sagnac interferometer

Jinyu Xing, Penghao Hu, Mingyong Hu, Guo Xia, and Shiqun Jin

Doc ID: 272041 Received 21 Jul 2016; Accepted 10 Jan 2017; Posted 11 Jan 2017  View: PDF

Abstract: A wire gating beam splitter (WGBS) substrate in dispersion-compensated polarization Sagnac interferometer (DCPSI) may introduce an additional shear distance in the shear distance generated by DCPSI, thereby causing poor adaptability of DCPSI to white light. This work applies a compensation scheme of an optical flat with the same material and thickness as WGBS and parallel to the WGBS introduced in the other arm of DCPSI. Theoretically, this method can decrease the additional shear distance approaching 0. The ideal shear distance in the simulation experiment is 5.86 mm, and the shear distance before and after compensation is 5.40 and 5.86 mm, respectively. The theoretical value of the additional shear distance in this experiment is −0.6625 mm, and the average compensation value is 0.66 mm. Overall, experiment and simulation results indicate that the above method can effectively eliminate the additional shear distance.

Aberrations of Soft X-Ray and Vacuum UltravioletOptical Systems with Orthogonal Arrangement ofElements

Yiqing Cao and Lijun Lu

Doc ID: 278779 Received 17 Oct 2016; Accepted 09 Jan 2017; Posted 10 Jan 2017  View: PDF

Abstract: The wave aberration of plane-symmetric optical systems is expressed with the aperture-ray coordinates on thereference exit wave front in the paper; the defocus aberration caused by the meridional field of source is analyzedin detail. Based on the expressions of the wave aberration and the defocus, the aberrations of the soft x-ray andultraviolet (XUV) optical systems with orthogonal arrangement of elements are studied as a whole. The resultantaberration expressions are used to calculate the aberrations of two design examples; the images are compared tothe ray-tracing results with Shadow to validate the aberration expressions. The study shows that the accuracy ofthe aberration expressions is satisfactory. The analytical analysis of aberrations is helpful in the design andoptimization of the XUV optical systems with orthogonal arrangement of elements.

Radiation losses and dark mode at light guiding by a liner chain of nanoparticles

Mikhail Barabanenkov and Yuri Barabanenkov

Doc ID: 278825 Received 18 Oct 2016; Accepted 07 Jan 2017; Posted 09 Jan 2017  View: PDF

Abstract: A new general formula is presented for a collective extinction cross–section of a dielectric or a metallic nanoparticle ensemble in terms of incident electric field work on currents excited inside particles. The derived formula is applied to the problem of radiation losses at electromagnetic excitation transfer along a straight chain of particles. Our general formula predicts a zero collective extinction cross section for an infinite straight chain of nonabsorbing dielectric particles providing that the projection on the chain axis of wave vector of the incident electromagnetic wave does not coincide with its counterpart of the Bloch wave vector of propagating excitation. In another case of a finite chain of particles, with only the first particle of the chain being irradiated by the incident narrow electromagnetic wave beam, the derived formula shows that only the irradiated particle contributes directly into the collective extinction cross-section despite the fact how large the total number of particles can be, which makes a direct summing contribution of all other particles in wave scattering as if they were unviewed (dark mode). Using a recently developed quasi-separable T-scattering operator approach that leads to the equation system for self-consistent currents excited inside particles by an incident electromagnetic wave field and restricting ourselves to the electric dipole single scattering and neighbour coupling approximation, we revealed a few gigahertz transparency band in the terahertz frequency range (orange color) in the spectra of a straight chain of closely spaced gold nanospheres with a certain radius and the length of a few millimeters. Because we also found a resonant mechanism of filtering the dark mode from radiation losses, we revealed a few fold more narrow pass band in the spectra of a longer gold particle chain with the full length of a few centimeters.

Generalized ray tracing formulas

Hassan Elagha

Doc ID: 276083 Received 19 Sep 2016; Accepted 06 Jan 2017; Posted 06 Jan 2017  View: PDF

Abstract: In this work, we generalize the Gaussian ray tracing formulas to include non-paraxial rays. For a refracting (reflecting) spherical surface, a new single meridional formula is derived. This formula can be easily reduced to a paraxial formula. It can also be applied to any aspheric surface with a known equation. Also, a new exact ray tracing procedure for a centered system of spherical surfaces is derived. In this procedure, we apply just two simple equations for each surface of the system which makes it the shortest ray tracing technique ever. This procedure can be applied in some other applications. For example, it can be reduced to a new single paraxial formula that can be easily used to trace a paraxial ray propagating through a system of spherical surfaces. Also, it is applied to derive an exact meridional formula for both thick and thin lenses that can be also reduced to a new paraxial formula different from the Gaussian one. These results led us to easily derive an exact formula for the longitudinal spherical aberration for both thick and thin lenses and also for a single refracting (reflecting) spherical surface. Numerical examples are provided and discussed.

Propagation dynamics of generalized and symmetric Airy beams

Yixian Qian, Li hui, and hongxing mao

Doc ID: 279073 Received 20 Oct 2016; Accepted 04 Jan 2017; Posted 05 Jan 2017  View: PDF

Abstract: We present theoretically and experimentally a generalized and symmetric Airy beams, where the two sidelobes are not mutually perpendicular by introducing two rotary angle factors. The symmetric Airy beam is induced by a binary phase pattern. We demonstrate that the intensity distributions of generalized Airy beams are apparently different from those of normal Airy beams. Moreover, they can propagate along arbitrary trajectories. Numerical results show that the generalized and symmetric Airy beams still have the ability of self-healing and non-diffraction. The experimental results are in complete accord with numerical results. Some possible applications are also discussed, and these interesting properties will also likely have potential applications.

Structural color analysis of the photoresist gratinginfluenced by the light source and its parameters

SIWEI ZENG, liu zhengkun, Keqiang Qiu, Xiangdong Xu, Ying Liu (NSRL, USTC), and Shaojun Fu

Doc ID: 278288 Received 17 Oct 2016; Accepted 02 Jan 2017; Posted 06 Jan 2017  View: PDF

Abstract: The basic principle and method in generating structural color from the photoresist grating of the multilayerdielectric diffraction grating are introduced. Rigorous coupled-wave analysis is used for the computationthrough the open software rcwa-1d. The relation between the characteristics of the photoresistand its structural color is explained. This article discussed the effect of light source characteristics withthe duty cycle color resolution, indicating that TE polarization is better than TM polarization, the FWHMshould be sufficiently large with an optimized value for incident angle.

Electromagnetic induction holography imaging forstroke detection

Lulu Wang

Doc ID: 272383 Received 26 Jul 2016; Accepted 31 Dec 2016; Posted 05 Jan 2017  View: PDF

Abstract: This paper presents the application of electromagnetic induction holography (EMIH) approach to imagingelectromagnetic activity of the brain with particular focus on stroke detection. An integral equation formulation ispresented to describe the scattered magnetic field from distribution of optically small dielectric and magneticobjects of arbitrarily shaped adsorbed onto a planar electromagnetic substrate. A numerical computer model wasdeveloped under MATLAB environment to validate the theory. Several realistic human head models weredeveloped to investigate the detectability of stroke with the multi-channel EMIH system. Small stroke can be clearlyidentified with correct location and size in the reconstructed head images. The simulation results demonstratedthe feasibility of detecting and imaging small stroke using the approach.

Online Multi-Object Tracking with Efficient Track Drift and Fragmentation Handling

Hanseok Ko, Jaeyong Ju, Daehun Kim, Bonhwa Ku, and David Han

Doc ID: 272906 Received 01 Aug 2016; Accepted 23 Dec 2016; Posted 05 Jan 2017  View: PDF

Abstract: This paper addresses the problem of multi-object tracking in complex scenes by a single, static, un-calibrated camera. Tracking-by-detection is a widely used approach for multi-object tracking. Challenges still remain in complex scenes, however, when this approach has to deal with occlusions, unreliable detections (e.g., inaccurate position/size, missing detections, or false positives), and sudden object motion/appearance changes, among other issues. To handle these problems, this paper presents a novel online multi-object tracking method, which can be fully applied to real-time applications. First, an object tracking process based on frame-by-frame association with a novel affinity model and an appearance update that does not rely on online learning is proposed to effectively and rapidly assign detections to tracks. Second, a two-stage drift handling method with novel track confidence is proposed to correct drifting tracks caused by the abrupt motion change of objects under occlusion and prolonged inaccurate detections. In addition, a fragmentation handling method based on a track-to-track association is proposed to solve the problem in which an object trajectory is broken into several tracks due to long-term occlusions. Based on experimental results derived from challenging public datasets, the proposed method delivers an impressive performance compared with other state-of-the-art methods. Furthermore, additional performance analysis demonstrates the effect and usefulness of each component of the proposed method.

CP Tensor Based Compression of Hyperspectral Images

Hui Lin, Leyuan Fang, and Nanjun He

Doc ID: 279066 Received 20 Oct 2016; Accepted 19 Dec 2016; Posted 19 Dec 2016  View: PDF

Abstract: In this paper, an effective CANDECOMP/PARAFAC tensor based compression (CPTBC) approach is proposed for ongroundhyperspectral images (HSIs). By considering the observed HSI cube as a whole three-order tensor, the proposed CPTBCmethod utilizes the CANDECOMP/PARAFAC tensor decomposition to decompose the original HSI data into the sum of R rank-1 tensors which can simultaneously exploit both the spatial and spectral information of HSIs. Specifically, compared with theoriginal HSI data, the R rank-1 tensors have fewer non-zero entries. In addition, non-zero entries of the R rank-1 tensors aresparse and follow a regular distribution. Therefore, the HSI can be efficiently compressed into R rank-1 tensors with theproposed CPTBC method. Our experimental results on real three HSIs demonstrate the superiority of the proposed CPTBCmethod over several well-known compression approaches and the average PSNR improvements of the proposed method overthe six compared methods (i.e., MPEG4, band-wise JPEG2000, TD, 3D-SPECK, 3D-TCE, 3D-TARP) are more than 13dB, 10dB,6dB, 4dB, 3dB, 3dB, respectively.

The expression of degree of polarization based on geometrical optics pBRDF model

Jingping Zhu, Kai Wang, and Liu Hong

Doc ID: 274177 Received 26 Aug 2016; Accepted 19 Dec 2016; Posted 20 Dec 2016  View: PDF

Abstract: An expression of degree of polarization (DOP) based on the geometrical optics polarimetric bidirectional reflectance distribution function (pBRDF) model is presented. This DOP expression considers diffuse reflection that makes DOP both related with the surface roughness and decreased at different reflected angles as measurement. In addition, shadowing/masking function is added to specular reflection which makes DOP values decreased as the angle of incidence or observation approaches grazing. Different kinds of materials were measured to validate the expression. Test results show that errors are reduced significantly and it can decribe the polarized reflection characteristics more reasonably and accurately.

Long period fiber gratings with off-resonance spectral response based on mechanical oscillations

Moti Fridman, shir shahal, avi Klein, Gilad Masri, and Hamootal Duadi

Doc ID: 279505 Received 26 Oct 2016; Accepted 16 Dec 2016; Posted 16 Dec 2016  View: PDF

Abstract: We present long period fiber gratings with off-resonance spectral response. Our long period fiber gratings are composed of periodic structure of large perturbations in the fiber diameter which results in unique spectral response even in off-resonance frequencies. Writing these long period fiber grating is based on utilizing the mechanical vibrations of tapered fibers during the tapering process. This writing method is simple, robust with high efficiency, high reproducibility and low polarization dependency. It also enables real-time tunability of the periodicity, efficiency and length of the grating. We also demonstrate complex grating by writing multiple gratings one on top of the other. Finally, We utilized the formation of the gratings in different fiber diameters to investigate the Young's modulus of tapered fibers.

Correction of turbulence-degraded underwater images using shift map analysis

Kalyan Halder, Manoranjan Paul, Murat Tahtali, Sreenatha Anavatti, and Manzur Murshed

Doc ID: 278065 Received 03 Oct 2016; Accepted 12 Dec 2016; Posted 13 Dec 2016  View: PDF

Abstract: In underwater imaging, the water waves cause severe geometric distortions and blurring of the acquiredshort-exposure images. Corrections for these distortions have been tackled reasonably well by previousefforts, but still need improvement in the estimation of pixel shift maps to increase the restoration accuracy.This paper presents a new algorithm that efficiently estimates the shift maps from the geometricallydistorted video sequences and uses those maps to restore the sequences. A non-rigid image registrationmethod is employed to estimate the shift maps of the distorted frames against a reference frame. Thesharpest frame of the sequence, determined using a sharpness metric, is chosen as the reference frame.A k-means clustering technique is employed to discard too blurry frames that could result in inaccuracyin the shift maps’ estimation. The estimated pixel shift maps are processed to generate the accurate shiftmap that is used to dewarp the input frames into their non-distorted forms. The proposed method isapplied on several synthetic and real-world video sequences and the obtained results exhibit significantimprovements over the state-of-the-art methods.

Time-domain electromagnetic scattering by a sphere in uniform translational motion

Timothy Garner, Akhlesh Lakhtakia, James Breakall, and Craig Bohren

Doc ID: 279885 Received 01 Nov 2016; Accepted 11 Dec 2016; Posted 12 Dec 2016  View: PDF

Abstract: Scattering by a uniformly translating sphere of a pulse that modulates the amplitude of a linearly polarized plane wave was formulated using the frame-hopping method involving a laboratory inertial reference frame and the sphere’s co-moving inertial reference frame. The incident signal was defined in the laboratory frame and transformed to the co-moving frame with the Lorentz transformation, thereby altering the incident signal’s spectrum, direction of propagation of the carrier plane wave, and the direction of the incident electric field, depending on the sphere’s velocity. In the co-moving frame, the incident signal was Fourier transformed to the frequency domain and the scattered field phasors were computed in all directions using the constitutive parameters of the material of the sphere at rest. The scattered signal in the co-moving frame was obtained using the inverse Fourier transform. Finally, the scattered signal in the laboratory frame was obtained by inverting the original Lorentz transformation. The backscattered signal was found to depend strongly on the sphere’s velocity. The change in the backscattered signal compared with the backscattered signal from a stationary sphere is the greatest when the sphere’s velocity is either parallel or antiparallel to the direction of propagation of the incident signal. The backscattered signal is also affected by motion transverse to the incident signal’s direction of propagation; then, the backscattered signal depends on whether or not the motion is aligned with the direction of the incident electric field.

A Vision-based Technique for Circle Detection and Measurement Using Look-up Table and Bitwise Center Accumulator

Hancheng Yu and Tuo Wang

Doc ID: 267297 Received 02 Jun 2016; Accepted 09 Dec 2016; Posted 12 Dec 2016  View: PDF

Abstract: In this paper, a fast algorithm for circle detection and measurement is proposed, which uses look-up table and bitwise center accumulator (LUT-BCA). The LUT-BCA is a two stage procedure. The first stage determines the candidate circle centers with normal lines produced by the look-up table and recorded by the bitwise center accumulator. The second stage computes the radius of each candidate circle centers and validates these centers, which eliminates the false detections. The proposed LUT-BCA can also be easily implemented on massively parallel high-performance graphics hardware using the Compute Unified Device Architecture (CUDA). Experimental results indicate that LUT-BCA can locate circle centers and measure their radii accurately and is very suitable for real-time circle detection and measurement.

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