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Thermal blooming effect of Hermite-Gaussianbeams propagating through the atmosphere

Zhoulin Ding, Xiaoqing Li, Jianyong Cao, and Xiaoling Ji

Doc ID: 360212 Received 15 Feb 2019; Accepted 15 May 2019; Posted 15 May 2019  View: PDF

Abstract: The thermal blooming effect of Hermite-Gaussian(H-G) beams propagating throughthe atmosphere is studied analytically and numerically. The analytical expression for thedistortion parameter of steady-state thermal blooming of H-G beams propagating theatmosphere is derived. It is shown that, under the same beam power, the higher the mode orderof H-G beams is, the weaker the thermal blooming effect is. In particular, the thermalblooming effect for a H-G beam is weaker than that for a Gaussian beam. It is found that asthe mode order increases, the beam width at the target may decrease due to the thermalblooming effect although the initial beam width increases. When the cross-wind velocity islarge enough, the symmetry of asymmetric H-G beam may be improved by the thermalblooming if the astigmatism parameter is adopted to characterize the symmetry of H-G beams.As the mode order of H-G beams increases, the shift of the beam centriod position decreases,but it takes more time to reach the steady-state thermal blooming. On the other hand, thethermal blooming effect on the multimode beam quality is also examined in this paper. It isshown that a minimum beam spot on the target can be obtained if the optimal weighting factorof multimode beams is adopted.

Eigenvalue-based depolarization metric spaces forMueller matrices

Razvigor Ossikovski and Jérémy Vizet

Doc ID: 362219 Received 12 Mar 2019; Accepted 15 May 2019; Posted 15 May 2019  View: PDF

Abstract: We present a unified formal description and a detailed study of the depolarization spaces defined by variousdepolarization metrics based on the eigenvalues of the covariance matrix associated with a given Mueller matrix.By introducing natural generalizations of the common and Lorentz depolarization metrics, we likewise advancenovel spaces appropriate for the description of extrinsic and intrinsic depolarization. We show the intimaterelation existing between the depolarization spaces and the depolarization diagrams and solve the problem of theexperimentally observed forbidden depolarization region. The theoretical developments are illustrated onnumerical, analytical and experimental examples of depolarizing Mueller matrices.

Temporal coherence modulation of pulsed, scalar lightwith a Fabry–Pérot interferometer

Henri Pesonen, Kimmo Saastamoinen, Matias Koivurova, Tero Setala, and Jari Turunen

Doc ID: 362756 Received 18 Mar 2019; Accepted 15 May 2019; Posted 15 May 2019  View: PDF

Abstract: We analyze the effect of a high-finesse Fabry–Pérot interferometer on the temporal coherence propertiesof scalar optical plane-wave pulse trains. We focus on the cases of single-peak and double-peak transmissionsof Gaussian Schell model (GSM) and supercontinuum (SC) pulses. For the GSM light we show howthe characteristics of the average intensity and the temporal degree of coherence of the transmitted pulsesdepend on the coherence parameters of the incident field. Regarding the SC light the output is found todepend specifically on the location of the transmission peak(s) within the average spectrum. The resultsdemonstrate that a Fabry–Pérot etalon can act as a simple passive element for tailoring the temporal (andspectral) coherence properties of optical pulse trains.

Combinatorial Optical ComplexWavelet-Fractional Fourier Transform

Cui-hong Lv, Fei-fei Tang, and Shi juan

Doc ID: 365300 Received 16 Apr 2019; Accepted 13 May 2019; Posted 15 May 2019  View: PDF

Abstract: By using the technique of integration within ordered product (IWOP)of operators, we put forward the combinatorial optical complex wavelet-fractional Fourier transform in the context of quantum optics. The unitaryoperator for this new transform is found and its normally ordered form isdeduced. We apply this new transform to the two-mode vacuum state andthe two-mode number state and explain that it can be used to analyzeand identify various quantum optical states.

Terahertz Vortices Generation Methods in Rippledand Vortex Plasmas

Hassan Sobhani and Elham Dadar

Doc ID: 359368 Received 04 Feb 2019; Accepted 13 May 2019; Posted 20 May 2019  View: PDF

Abstract: Terahertz vortices have strong potential for many applications such as imaging and sensingin medicine, biomedical engineering, rotations of molecules, quantum condensation, opticaltweezers, manipulation of electron beams, and communications. However, owing to recent developments,there are less researches about the vortices generation in the terahertz domain. Dueto the damaging limit and low conversion efficiency, recently a few schemes to generate terahetzvortices based on plasma have been reported. Generally, to excite the helicity of the terahertzvortices, two scenarios have been reported; one is transferring the orbital angular momentumfrom the plasma vortex to the emitted terahertz radiation, the other is exciting the helicity of theterahertz vortices by employing the twisted input lasers. This paper is a review on recent studieson the terahertz vortices generation based on the rippled and vortex plasma substratums.

Ray-tracing in monocentric and ball lenses by ageneral exact formula

Hassan Elagha

Doc ID: 357224 Received 10 Jan 2019; Accepted 13 May 2019; Posted 13 May 2019  View: PDF

Abstract: In this work, we derive a general ray tracing formula for mono-centric lenses based on a linear form of Snell's law. From thisformula, we can directly get the meridional formula for a single symmetric (or asymmetric) mono-centric lens. All of these formulascan be reduced to their corresponding paraxial forms and also their spherical aberration exact formulas can be easily derived. Alsowe easily apply this general formula to get the position of the final image formed by a system of monocentric lenses having acommon optical axis. The successive lenses of this system can be a mixture of different mono-centric lenses of any kind havingknown separation distances between their centers. We have no need to apply Snell's law in its trigonometric form and no need todetermine the angles of incidence or refraction and no need to know the height of the ray at any point along its path. If the raybetween any two lenses crosses the optical axis, the procedure will continue without any change and without adding any specialequations. We also provide an exact procedure to trace a skew ray through a system of monocentric lenses that can be centered ordecentered. In this procedure, we have no need to determine the points of incidence or the normal to the surface. The contribution ofthe procedure in this work is that we can apply our equations, lens by lens, and not surface by surface, as in classical ray-tracingmethods. This greatly reduces effort and mathematical complexity.

Supernumerary bows: interference theorywith the zero wavefront as basic element

Paul Etienne Ouellette

Doc ID: 358190 Received 21 Jan 2019; Accepted 13 May 2019; Posted 13 May 2019  View: PDF

Abstract: This study relates to the prediction of the angular positions of the supernumerary screenbows and rainbows,in the case of a refractive sphere illuminated by a point source placed at a distance h from its center;for h ! ¥ the incident light beam becomes parallel. The screenbow appears on a spherical screen whosecenter is that of the sphere and which intercepts the tangential caustic surface. The rainbow, specific tothe water drop but here generalized to any refractive sphere, corresponds to a screenbow produced on a“screen” placed at an infinite distance.This paper uses exact graphical representations of the wavefronts associated with rainbows resulting fromk internal reflections to illustrate how to calculate the angular positions of the supernumerary rainbowsand the positions of the corresponding supernumerary bows on screens.All considerations are made within the framework of geometrical optics being, on the one hand, the limitof the electromagnetic theory as the wavelength goes to 0, and, on the other hand, complemented by theGouy phase shift theory.

Robust edge spread function constructionmethods to counter poor sample spacinguniformity in the slanted-edge method

Frans van den Bergh

Doc ID: 360056 Received 12 Feb 2019; Accepted 13 May 2019; Posted 14 May 2019  View: PDF

Abstract: The slanted-edge method describes an algorithm for measuring the spatial frequencyresponse (SFR) of digital imaging systems. The method can be applied to edges oriented at nearlyany angle, but there are some angles that cause simplistic implementations of the algorithm tofail, or produce inaccurate measurements. These angle-dependent phenomena are demonstratedto stem from a lack of uniformity in supersample spacing in the edge spread function (ESF).Two well-known slanted-edge implementation variants are adapted to minimize edge orientationdependent errors. These robust slanted-edge implementations are demonstrated yield accuratemeasurements, regardless of edge orientation angle or moderate image noise.

Tunable two-dimensional optical filter based on guided-moderesonance

Atefe Taheri and Mehrdad Shokooh-Saremi

Doc ID: 351898 Received 14 Nov 2018; Accepted 08 May 2019; Posted 09 May 2019  View: PDF

Abstract: In this paper, a tunable, two-dimensional periodic structure based on guided-mode resonance (GMR) is proposed.This element can be employed as a tunable optical filter or a display pixel. Resonance tuning in this device is accomplishedthrough perturbation in refractive index profile and element's thickness, conceptually by a MEMS mechanism. Simulationresults show that resonance wavelength tuning of ~48 nm (522-570 nm) and ~17 nm (526-543 nm) are achieved by physicalmovement of 166 nm horizontally and 300 nm vertically, respectively. The proposed device is insensitive to the incident lightpolarization and can fairly maintain its tunability under ±5° deviations in the angle of incidence.

Vortex avalanche in the perturbed singular beams

Alexander Volyar, BRETSKO Mihail, Akimova Yana, and Egorov Yuriy

Doc ID: 363422 Received 29 Mar 2019; Accepted 07 May 2019; Posted 07 May 2019  View: PDF

Abstract: We have theoretically and experimentally considered transforming a single optical vortex beam into the vortexavalanche caused by weak local perturbations of the holographic grating responsible for the beam shaping. Thevortex avalanche is accompanied by a sharp change of the orbital angular momentum (OAM) so that itsdependence on the holographic grating perturbations forms the OAM spectrum. We revealed that the restoredvortex beam has anomalous regions of the OAM spectrum in a form of sharp dips and bursts (resonances) thatoccur when the integer perturbation parameter coincides with a topological charge of one of the vortex mode. Wefound also that the intensity of the perturbed beam is non-uniformly distributed among the vortex modes withpositive and negative topological charges. They form two groups of satellites with clearly marked intensitymaxima. As the grating perturbation increases, the initial beam intensity is almost completely pumped over intothe vortex avalanche with nearly the same energy redistribution among the satellites.

Circulant preconditioning in thevolume integral equation method forsilicon photonics

Samuel Groth, Athanasios Polimeridis, Alexandra Tambova, and Jacob White

Doc ID: 362853 Received 19 Mar 2019; Accepted 06 May 2019; Posted 07 May 2019  View: PDF

Abstract: Recently, the volume integral equation (VIE) approach has been proposed as an efficient simulation toolfor silicon photonics applications [J. Lightw. Technol. 36 (2018)]. However, for the high-frequency andstrong contrast problems arising in photonics, the convergence of iterative solvers for the solution of thelinear system can be extremely slow. The uniform discretization of the volume integral operator leads toa three-level Toeplitz matrix, which is well suited to preconditioning via its circulant approximation. Inthis paper, we describe an effective circulant preconditioning strategy based on the multi-level circulantpreconditioner of Chan and Olkin [Numer. Algorithms 6, 89 (1994)]. We show that this approach provesideal in the canonical photonics problem of propagation within a uniform waveguide, in which the flowis unidirectional. For more complex photonics structures, such as Bragg gratings, directional couplers,and disk resonators, we generalize our preconditioning strategy via geometrical partitioning (leading toa block-diagonal circulant preconditioner) and homogenization (for inhomogeneous structures). Finally,we introduce a novel memory reduction technique enabling the preconditioner’s memory footprint to remainmanageable, even for extremely long structures. The range of numerical results we present demonstratesthat the preconditioned VIE is fast and has great utility for the numerical exploration of prototypephotonics devices.

Multi-level Weighted Enhancement forUnderwater Image Dehazing

Kuldeep Purohit, Srimanta Mandal, and Ambasamudram Rajagopalan

Doc ID: 359053 Received 31 Jan 2019; Accepted 01 May 2019; Posted 01 May 2019  View: PDF

Abstract: Attenuation and scattering of light are responsible for haziness in images of underwaterscenes. To reduce this effect, we propose an approach for single image dehazing by multi-levelweighted enhancement of the image. The underlying principle is that enhancement at differentlevels of detail can undo the degradation caused by underwater haze. The depth information iscaptured implicitly while going through different levels of details due to depth-variant nature ofhaze. Hence, we judiciously assign weights to different levels of image details and reveal thattheir linear combination along with the coarsest information can successfully restore the image.Results demonstrate the efficacy of our approach as compared to state-of-the-art underwaterdehazing methods.

Multiple-twisted spiral beams

Evgeniya Razueva and Eugeny Abramochkin

Doc ID: 359871 Received 13 Feb 2019; Accepted 29 Apr 2019; Posted 29 Apr 2019  View: PDF

Abstract: We propose a method to construct paraxial light fields whose transverse intensity rotates during the field propagation (spiral beams) and the total rotation angle is an integer multiple of π/2 (multiple-twisted beams). We derive analytical expressions for the field complex amplitude by utilizing integral description of Laguerre-Gaussian beams. This method provides a straightforward way to obtain multiple-twisted spiral beams of various intensity shapes and rotation rates.

Wavefront propagation based on ray transfermatrix and numerical orthogonal Zernikegradient polynomials

Huimin Yin, Zhishan Gao, Qun Yuan, Lu Chen, Jinci Bi, Xin Cao, and Jialing Huang

Doc ID: 359525 Received 07 Feb 2019; Accepted 24 Apr 2019; Posted 25 Apr 2019  View: PDF

Abstract: The aberrated wavefront propagates along its normal. Both magnitude andboundary change after the propagation. Wavefront characterized by Zernike coefficients andnormalized pupil radius, can also be represented by a bundle of feature rays normal to thelocal surface. A ray transfer matrix parameterized by the pupil radius and propagationdistance is proposed to transfer these feature rays to obtain the slope and position data of thepropagated feature rays. Numerical orthogonal Zernike gradient polynomials are derived toreconstruct the wavefront from the discrete data by using a numerical method. Two aberratedwavefronts are performed as examples to validate the accuracy and flexibility of the proposednumerical method.

Dynamic focal shift and extending depth offocus based on the masking of theilluminating beam and using an adjustableaxicon

Svetlana Khonina, Andrey Ustinov, and Alexey Porfirev

Doc ID: 360962 Received 26 Feb 2019; Accepted 23 Apr 2019; Posted 25 Apr 2019  View: PDF

Abstract: We investigate several methods of focus shift and focus extension in detail. Thesemethods are divided into two groups: 1) changing the radius of the illuminating beam and/orlimiting diaphragm; and 2) adding an optical system with an adjustable element (lens oraxicon). In the cases of a planar and Gaussian illuminating beam, values of the focus positionand depth of focus (DOF) were calculated theoretically and numerically, depending on thebeam radius. In addition, theoretical and numerical evaluations of displacement and DOFincrease for the focusing system with the adjustable lens or axicon were obtained. We haveshown that these methods for changing the parameters of the focal area provide flexibility andefficiency in the control of its characteristics. Recommendations about possible applicationsin which such control is important are formulated on the basis of the results obtained.

Generating dark and antidark beams using thegenuine cross-spectral density functioncriterion

Milo Hyde and Svetlana Avramov-Zamurovic

Doc ID: 360930 Received 06 Mar 2019; Accepted 20 Apr 2019; Posted 29 Apr 2019  View: PDF

Abstract: In this work, we demonstrate how to generate dark and antidark beams—diffractionfreepartially coherent sources—using the genuine cross-spectral density function criterion.These beams have been realized in prior work using the source’s coherent-mode representationand by transforming a J0-Bessel correlated partially coherent source using a wavefront-foldinginterferometer. We generalize the traditional dark and antidark beams to produce higher-ordersources, which have not been realized. We simulate the generation of these beams and comparethe results to the corresponding theoretical predictions. The simulated results are found to be inexcellent agreement with theory, thus validating our analysis. We discuss the pros and cons ofour synthesis approach vis-à-vis the prior coherent modes work. Lastly, we conclude this paperwith a brief summary, and a discussion of how to physically realize these beams and potentialapplications.

Sharp-edge diffraction under Gaussianillumination: a paraxial revisitation ofMiyamoto-Wolf’s theory

Riccardo Borghi

Doc ID: 361996 Received 11 Mar 2019; Accepted 16 Apr 2019; Posted 24 Apr 2019  View: PDF

Abstract: A “genuinely” paraxial version of Miyamoto-Wolf’s theory aimed at dealing withsharp-edge diffraction under Gaussian beam illumination is presented. The theoretical analysisis carried out in such a way the Young-Maggi-Rubinowicz boundary diffraction wave theorycan be extended to deal with Gaussian beams in an apparently straightforward way. The keyfor achieving such an extension is the introduction of suitable “complex angles” within theintegral representations of the geometrical and BDWcomponents of the total diffracted wavefield.Surprisingly enough, such a simple (although not rigorously justified) mathematical generalizationseems to work well within the Gaussian realm. The resulting integrals provide meaningfulquantities that, once suitably combined, give rise to predictions which are in perfect agreementwith results already obtained in the past. An interesting and still open theoretical questionabout how to evaluate “Gaussian geometrical shadows” for arbitrarily shaped apertures is alsodiscussed.

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