Search

Self-healing optical beams are a class of propagation modes that can recover their beam shapes after distortion or partial blockage. This self-healing property makes them attractive for use in applications involving turbid media as they can—in theory—penetrate further into these materials than standard Gaussian beams. In this paper, we characterize the propagation of two different self-healing beams (Bessel and Airy) through a solid scattering material with different scatterer concentrations and find that both beams do recover after scattering for samples below a threshold scatterer concentration. Additionally, we test the applicability of both beam shapes for improved sub-surface spectroscopy in heterogeneous materials using fluorescent particles and find that there is an average fluorescence intensity enhancement of 1.3× using self-healing beams versus a standard Gaussian beam.

Self-healing optical beams are a class of propagation modes that can recover their beam shapes after distortion or partial blockage. This self-healing property makes them attractive for use in applications involving turbid media as they can—in theory—penetrate further into these materials than standard Gaussian beams. In this paper, we characterize the propagation of two different self-healing beams (Bessel and Airy) through a solid scattering material with different scatterer concentrations and find that both beams do recover after scattering for samples below a threshold scatterer concentration. Additionally, we test the applicability of both beam shapes for improved sub-surface spectroscopy in heterogeneous materials using fluorescent particles and find that there is an average fluorescence intensity enhancement of 1.3× using self-healing beams versus a standard Gaussian beam. [ABSTRACT FROM AUTHOR]

The Fourier convolution theorem (FCT) is used to filter images in k-space. The literature provides theoretical proof but not experimental evidence of the extension of FCT to Z-space. Using two-dimensional images, this research presents empirical evidence of: 1. the extension of the FCT to Z-space, and 2. the difference between k-space filtering and Z-space filtering. The following procedure is carried out using FCT and extension of FCT to Z-space. The convolving function is sampled in image space and on the Argand plane. Multiplication between convolving function and sinc function determines the so-called 'sinc-shaped convolving function' and precedes direct Fourier and direct Z transformations so to obtain a rectangular region in the frequency domain of the sinc-shaped convolving function. The spatial size of the rectangular region is determined by the numerical values of bandwidth and sampling rate. Pointwise multiplication between the frequency domain of sinc-shaped convolving function and frequency domain of departing image is inverse Fourier and inverse Z transformed so as to obtain k-space and Z-space filtered images. Frequency domain analysis of filtered images shows the difference between k-space filtering and Z-space filtering. Using the FCT as theoretical framework, the novelty of this research is to empirically extend FCT to Z-space and to report experimental evidence of the difference between k-space filtering and Z-space filtering. [ABSTRACT FROM AUTHOR]

Spherical Bessel functions (sBFs) appear commonly in many areas of physics wherein there is both translation and rotation invariance, and often integrals over products of several arise. Thus, analytic evaluation of such integrals with different weighting functions (which appear as toy models of a given physical observable, such as the galaxy power spectrum) is useful. Here, we present a generalization of a recursion-based method for evaluating such integrals. It gives relatively simple closed-form results in terms of Legendre functions (for the exponentially damped case) and Gamma, incomplete Gamma, and hypergeometric functions (for the Gaussian-damped case). We also present a new, non-recursive method to evaluate integrals of products of sBFs with Gaussian damping in terms of incomplete Gamma functions and hypergeometric functions. [ABSTRACT FROM AUTHOR]

A new class of localized solutions of paraxial parabolic equation is introduced. Each solution is a product of some Gaussian-type localized axisymmetric function (different from the fundamental mode) and an amplitude factor. The latter can be expressed via an arbitrary solution of the Helmholtz equation on an auxiliary two-sheet complex surface. The class under consideration contains both well known and novel solutions, including those describing optical vortices of various orders. [ABSTRACT FROM AUTHOR]

This research presents a sampling technique for Fourier convolution theorem (FCT) based k‐space filtering. One polynomial function and three transfer functions were selected: (1) Gaussian, (2) Bessel, (3) Butterworth, and (4) Chebyshev. The functions were sampled on the image grid, and they are called filtering functions. Each filtering function was multiplied by the Sinc function to obtain the "Sinc‐shaped convolving function." The k‐space of the Sinc‐shaped convolving function is calculated by direct Fourier transform (FT) and it is featured by a central region. This central region of the k‐space is rectangular in its shape because it is consequential to the direct FT of the product between the filtering function and the Sinc function. Low‐pass and high‐pass filtering is obtained by inverse FT of the pointwise multiplication between the k‐space of the departing image and the k‐space of the Sinc‐shaped convolving function. A variety of cut‐off frequencies, bandwidth, sampling rates, and numbers of poles of the filters were verified as effective to filter the images. Filtering strength can be modified by fine‐tuning the size of the central rectangular k‐space region of the Sinc‐shaped convolving functions. K‐space analysis of departing images and filtered images provide additional evidence of effective filtering. Moreover, k‐space filtering was compared to Z‐space filtering using the extension of the FCT to Z‐space. The novelty of this research is the sampling technique used to determine the Sinc‐shaped convolving function. The sampling technique uses fine‐tuning of bandwidth and sampling rate to determine the strength of the k‐space filter. [ABSTRACT FROM AUTHOR]

Filters in photonic configurations are vital for the selective transmission of the pulse. This paper presents the investigation on the deployment of perfect filters to get enhanced reception. We have proposed MZM–MZI (Mach–Zehnder-Modulator–Mach–Zehnder-Interferometer)-based switching network where Bessel filtering proves beneficial for the better quality of reception. The comparison of four different filters shows the Bessel filter can achieve reliable results with the minimum log of Bit Error Rate (BER) of −24.0658 and Extinction Ratio (ER) of 18.11853. The filtering response and switching performance have also been tested on parameters like received spectrum, Quality Factor, and Eye-Opening Factor with various filtering components like rectangular, trapezoidal, and Butterworth. [ABSTRACT FROM AUTHOR]

The main concept of this research is the well-accepted and recognized equation that models the pulse-transfer function (PTF) as the ratio between the Z-transform of the filter output and the Z-transform of the filter input. The proof of concept has been tested to verify the main modelling aspect using theoretical images. The proof of concept is then mathematically extended, so as to use the PTF to filter images in Z-space using Bessel, Butterworth, and type I Chebyshev filters. Z-space filtering is determined using inverse Z-transform of the pointwise multiplication between Z-space of PTF and Z-space of departing image. The filtered image is reconstructed using inverse Z-transform of the Z-space multiplication. Further, the PTF is calculated using scaled data and is called normalized transfer function (NTF). The NTF is then compared to Fourier convolution image. This paper documents methodology and technology used for the calculation of the PTF of discrete digital filters. The proof of concept is verified successfully. The novelty of this research is Z-space filtering in two dimensions using PTF. [ABSTRACT FROM AUTHOR]

In this article, a single operational transresistance amplifier (OTRA) based realization of second order low‐pass (LP), high‐pass (HP), band‐pass (BP), band‐reject (BR), and all‐pass (AP) filter and their individual performance analysis: noise, temperature, and worst‐case analysis have been presented. The proposed circuit can be reconfigured as Butterworth and Bessel filter by changing the values of passive components. The presented filters are suitable for MOS‐C implementation, which facilitates tuning of cut‐off/center frequency and quality factor electronically. The proposed circuits are analyzed theoretically, simulated and experimentally verified in laboratory. All the simulations are performed with CMOS model of OTRA (180 nm) in SPICE and experimentally verified with AD844AN IC. The experimental and simulation results are matching closely. The result obtained from post‐layout simulation of the proposed Butterworth LP filter confirms the feasibility of the design. Finally working of the proposed all‐pass filter is established by the design of a buffer and quadrature oscillator. [ABSTRACT FROM AUTHOR]

Large thermal gradients, complex melt pool instabilities and poor absorptivity are application-limiting detriments in laser powder bed fusion-enabled metal additive manufacturing (AM), ultimately resulting in poor mechanical properties. Current approaches to improving the mechanical robustness of structures printed using metal additive manufacturing (AM) come at the expense of print reliability, consistency cost and integrability. Here, we employ laser beams shaped in amplitude, phase and polarization, to deliver controlled optothermal profiles on the powder bed. Unique optical properties of such beams (such as non-diffractive propagation) result in an improved combination of reduced porosity, increased part density, lower surface roughness and robust tensile properties across a broad scan parameter range, compared to conventional beams. We employ Multiphysics simulations and highspeed imaging for feedback and validation for printing SS 316L. [ABSTRACT FROM AUTHOR]

In this article, a graphene‐based reflective metasurface which can generate Bessel beams at arbitrary directions is proposed at 1.52 THz. It chooses the classical cross structure as the unit cell and extends the coverage of the reflection phase to 360° by adjusting two key parameters while maintaining a relatively high‐reflection amplitude. Combined with the excellent impedance characteristics of graphene in the terahertz regime and the long energy transmission distance of the nondiffraction beam, the reflective metasurface finally realize the pseudo‐Bessel beam with a maximum propagation distance of about 3358.85 um and a deflection of about 15° in yoz‐plane as expected. Two forms of efficiency are proposed for the metasurface, one is the focusing efficiency, the other is the conventional radiation efficiency. The simulation results show that the former shows a trend of increasing first and then decreasing, which conforms to the beam‐forming property of Bessel beam; the latter can be basically maintained at high value of 70% within the nondiffraction propagation distance, which conforms to the energy transmission characteristic of the nondiffraction beam. All the studies show that the graphene‐based metasurface combined with the nondiffraction theory has the advantages of highly controllable beam deflection, long focusing distance, and high‐energy transfer efficiency in the terahertz regime, so it will have a broad application prospect in terahertz telecommunication, wireless energy transmission, near‐field detecting, imaging and many other fields. [ABSTRACT FROM AUTHOR]

In this paper, we deal with a modified fractional Hilfer Sturm-Liouville operator for Bessel potential and we show the self-adjointness of the operator, orthogonality of distinct eigenfunctions and reality of eigenvalues. Also, we obtain an integral representation of solution and we give a numerical method for obtaining numerical results by changing α; β values illustrated by graphics. [ABSTRACT FROM AUTHOR]

This paper considers the problem of microwave heating of polymers, asphalt-paraffin deposits when filling metal, short-circuited cylinder. The problem of formation and optimization of electromagnetic fields. The results of simulation of excitation of a cylinder with the use of maximum and integral criteria.

The real and complex zeros of some special entire functions such as Wright, hyper-Bessel, and a special case of generalized hypergeometric functions are studied by using some classical results of Laguerre, Obreschkhoff, P'olya, and Runckel. The obtained results extend the known theorem of Hurwitz on the exact number of nonreal zeros of Bessel functions of the first kind. Moreover, results on zeros of derivatives of Bessel functions and the crossproduct of Bessel functions are also given, which are related to some recent open problems. [ABSTRACT FROM AUTHOR]

In survival analysis and reliability studies, problems with random sample size arise quite frequently. More specifically, in cancer studies, the number of clonogens is unknown and the time to relapse of the cancer is defined by the minimum of the incubation times of the various clonogenic cells. In this article, we have proposed a new model where the distribution of the incubation time is taken as Weibull and the distribution of the random sample size as Bessel, giving rise to a Weibull–Bessel distribution. The maximum likelihood estimation of the model parameters is studied and a score test is developed to compare it with its special submodel, namely, exponential–Bessel distribution. To illustrate the model, two real datasets are examined, and it is shown that the proposed model, presented here, fits better than several other existing models in the literature. Extensive simulation studies are also carried out to examine the performance of the estimates. [ABSTRACT FROM AUTHOR]

A theoretical prediction of the propagation characteristics of Laguerre--Gaussian beams after passing through a blunt-tip axicon is presented. An ideal axicon generates theoretically perfect diffraction-free and smooth-on-axis intensity Bessel beams, while experiments and calculations show that a zeroth-order Bessel beam deviates from its perfect behavior. Strong intensity modulation occurs due to interference around the center of the beam. The origin of these oscillations should be explored to increase the quality of beam shaping. This research shows that these oscillations can be reduced by stopping the beam center for a small portion or by optimizing input beam parameters. On the other hand, since they have singularity at the beam center, higher-order Bessel beams would be affected less by the bluntness of the axicon. In order to prove this idea, a series of calculations with wavelengths of 1030, 515, and 343 nm were conducted. The tip of the axicon was modeled as a hyperbola with a base angle of 0.5°. Our calculations indicate that zeroth-order Bessel beams are much more sensitive than the higher-order Bessel beams to axicon bluntness. Moreover, not only the axicon geometry and wavelength of the illuminating light, but also the input beam parameters are quite important when enhancing the quality of beam shaping. [ABSTRACT FROM AUTHOR]

An all-pass filter architecture that can be generalized to high orders, and can be realized using active circuits is proposed. Using this, a compact true-time-delay element with a widely tunable delay and a large delay-bandwidth product (DBW) is demonstrated. This is useful for beamforming and equalization in the lower GHz range where the use of LC or transmission line-based solutions to realize large delays is infeasible. Coarse tuning of delay is realized by changing the filter’s order while keeping the bandwidth constant and fine tuning is implemented by changing the filter’s bandwidth utilizing the delay-bandwidth tradeoff. A test chip fabricated in 0.13 \mu \text{m} CMOS process demonstrates a delay tuning range of 250 ps–1.7-ns, over a bandwidth of 2 GHz, while maintaining a magnitude deviation of ±0.7 dB. The filter achieves a DBW of 3.4 and a delay per unit area of 5.8 \mathrm {ns/mm^{2}}$ . The filter has a worst case noise figure of 23 dB, and −40 dB intermodulation (IM3) distortion for 37 mVppd inputs. The chip occupies an active area of 0.6 mm2, and dissipates 112 mW–364 mW of power between its minimum and maximum delay settings. Computed radiation pattern with four antennas spaced \mathrm {\lambda _{fmax}}/2 apart shows ±90° beam steering off broadside. [ABSTRACT FROM PUBLISHER]

In this paper we consider conical square functions in the Bessel, Laguerre and Schrödinger settings where the functions take values in UMD Banach spaces. Following a recent paper of Hytönen, van Neerven and Portal [36] , in order to define our conical square functions, we use γ -radonifying operators. We obtain new equivalent norms in the Lebesgue–Bochner spaces L p ( ( 0 , ∞ ) , B ) and L p ( R n , B ) , 1 < p < ∞ , in terms of our square functions, provided that B is a UMD Banach space. Our results can be seen as Banach valued versions of known scalar results for square functions. [ABSTRACT FROM AUTHOR]

We propose a technique to generate of perfect optical vortex (POV) via Fourier transformation of Bessel-Gauss (BG) beams through encoding of the amplitude of the optical field with binary amplitude digital micro-mirrors device (DMD). Furthermore, we confirm the correct phase patterns of the POV with the method of Mach–Zehnder interferometer. Our approach to generate the POV has the advantages that rapidly switch among the different modes, wide spectral regions and high energy tolerance. Since the POV possess propagation properties that not shape-invariant, we therefore suppose that our proposed approach will find potential applications in optical microscopy, optical fabrication, and optical communication. [ABSTRACT FROM AUTHOR]

The explosion probability before time t of a branching diffusion satisfies a nonlinear parabolic partial differential equation. This equation, along with the natural boundary and initial conditions, has only the trivial solution, i.e. explosion in finite time does not occur, provided the creation rate does not grow faster than the square power at ∞. [ABSTRACT FROM PUBLISHER]

We apply a previously derived and utilized a modified Navier–Stokes equation to the Taylor–Couette flow, that is fluid flow enclosed between two concentric cylinders where the inner cylinder is rotating with some constant speed and the outer cylinder is stationary or vice versa. We report the first analytic solutions describing velocity profiles of such a flow in a turbulent regime. The analytic profiles are compared with results of the reported first direct numerical simulation of Taylor–Couette flow in turbulent regime Pirro and Quadrio (2008). [ABSTRACT FROM AUTHOR]

Abstract: A well-defined boundary-valued problem of wave scattering and diffraction in elastic half-space should have closed-form analytic solutions. This two-dimensional (2-D) scattering around a semi-circular canyon in elastic half-space subjected to seismic plane and cylindrical waves has long been a challenging boundary-value problem. In all cases, the diffracted waves will consist of both longitudinal (P-) and shear (S-) rotational waves. Together at the half-space surface, these in-plane longitudinal P- and shear SV-waves are not orthogonal over the infinite half-space flat-plane boundary. Thus, to simultaneously satisfy both the zero normal and shear stresses at the flat-plane boundary, some approximation of the geometry and/or wave functions often has to be made, or in some cases, relaxed (disregarded). This paper re-examines this two-dimensional (2-D) boundary-value problem from an applied mathematics points of view and redefines the proper form of the orthogonal cylindrical-wave functions for both the longitudinal P- and shear SV-waves so that they can together simultaneously satisfy the zero-stress boundary conditions at the half-space surface. With the zero-stress boundary conditions satisfied at the half-space surface, the most difficult part of the problem will be solved, and the remaining boundary conditions at the finite-canyon surface are then comparatively less complicated to solve. This is now a closed-form analytic solution of the 2-D boundary-valued problem satisfying the half-space zero-stress boundary conditions exactly. [Copyright &y& Elsevier]

In standard acousto-optic Bragg analysis, the incident light and sound beams are assumed to be uniform plane waves (with constant profiles) leading to the results based on standard weak interaction theory. As a follow-up to earlier work dealing with nonuniform incident optical beams, we revisit the problem of Bragg diffraction under nonuniform profiles, and include Gaussian, third-order Hermite--Gaussian, and zeroth-order Bessel profiles in our investigation, along with a few others. The first-order diffracted beam is examined (using a transfer function formalism based on angular spectra) under several parametric limits [such as the Klein--Cook parameter Q, the effective profile width, and the optical phase-shift parameter (â0) in the sound cell]. Wherever feasible, the numerical results are compared with analytic theory. The scattered first-order profile output versus the optical phase-shift appears to maintain behavior similar to the known first-order characteristics (sin2 in intensity) encountered for the uniform incident beam case. It is observed, however, that such conformity exists seemingly only at relatively small values of Q (typically about 20 to 50). At higher Qs, on the other hand (where one would otherwise expect behavior closer to standard Bragg theory based on large Qs), it is found that the first-order intensity deviates substantially from the expected sin2- (or related) pattern. This deviation actually becomes more severe at even higher Qs. Additionally, the output profiles at higher Qs are also found to be distorted relative to the incident profiles. These results, though anomalous, are nevertheless generally compatible with earlier studies. Based on the transfer function theory, it is also known that for very large optical phase shifts (i.e., when â0 goes to infinity), the scattered first-order output for a Gaussian profile undergoes an axial (spatial) shift past the output plane of the sound cell. This predicted result is corroborated in our numerical simulation for both the Gaussian and third-order Hermite--Gaussian profiles, but not the zeroth-order Bessel or Airy profiles. These results provide both confirmation of some expected behavior for profiled beam scattering (including likely affirmation of the well known and unique diffractionless properties of certain Bessel beams), but also some insight into unexpected and anomalous photon-phonon interaction behavior. [ABSTRACT FROM AUTHOR]

Motivated by the existence problem of Fourier frames on fractal measures, we introduce Bessel and frame measures for a given finite measure on Rd, as extensions of the notions of Bessel and frame spectra that correspond to bases of exponential functions. Not every finite compactly supported Borel measure admits frame measures. We present a general way of constructing Bessel/frame measures for a given measure. The idea is that if a convolution of two measures admits a Bessel measure, then one can use the Fourier transform of one of the measures in the convolution as a weight for the Bessel measure to obtain a Bessel measure for the other measure in the convolution. The same is true for frame measures, but with certain restrictions. We investigate some general properties of frame measures and their Beurling dimensions. In particular, we show that the Beurling dimension is invariant under convolution (with a probability measure) and under a certain type of discretization. Moreover, if a measure admits a frame measure, then it admits an atomic one, and hence a weighted Fourier frame. We also construct some examples of frame measures for self-similar measures. [ABSTRACT FROM AUTHOR]

In this paper we prove that the generalized (in the sense of Caffarelli and Calder'on) maximal operators associated with heat semigroups for Bessel and Laguerre operators are weak type (1, 1). Our results include other known ones, and our proofs are simpler than the ones for the known special cases. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, linear and quadratic finite element models are devised for the three-dimensional Helmholtz problem by using a hybrid variational functional. In each element, continuous and discontinuous Helmholtz fields are defined with their equality enforced over the element boundary in a weak sense. The continuous field is based on the C0 nodal interpolation and the discontinuous field can be condensed before assemblage. Hence, the element can readily be incorporated seamlessly into the standard finite element program framework. Discontinuous fields constructed by the plane-wave, Bessel and singular spherical-wave solutions are attempted. Numerical tests demonstrate that some of the element models are consistently and considerably more accurate than their conventional counterparts. [Copyright &y& Elsevier]

The main object of this paper is to give sufficient conditions for certain families of integral operators which are defined by means of the normalized form of the generalized Bessel functions to be convex of given order in the open unit disk. In particular cases, we find the corresponding simple conditions for integral operators involving the Bessel function, the modified Bessel function and the spherical Bessel function. [ABSTRACT FROM PUBLISHER]

It is shown that M. Krein's method of directing functionals can be used to prove the existence of a scalar spectral measure for certain Sturm-Liouville equations with two singular endpoints. The essential assumption is the existence of a solution of the equation that is square integrable at one singular endpoint and depends analytically on the eigenvalue parameter. [ABSTRACT FROM AUTHOR]