Arbitrary Profile Research Articles

General method based on WKB approximation and digital holography to characterize planar waveguides

Future optical technologies are basically depending on and employing different types of optical waveguides. The fabrication of waveguides with different properties represents an expanding direction in both the industrial and scientific fields. In the current paper, we focus on studying the polymeric planar waveguides fabricated by the method of UV–excimer–laser lithography. We propose a general technique based on the WKB approximation and digital holographic interferometry to characterize slab waveguides with arbitrary refractive index profile. The necessary theoretical model is derived and the characterization method given in detail. Two samples are fabricated from polymethylmethacrylate (PMMA) polymeric material using different parameters for the used UV-laser. Then a phase-shifting digital holographic technique with the help of a Mach–Zehnder-like interferometer, is used to characterize the samples and measure their modified refractive index profiles. The resulting profiles are then fed to the proposed theoretical model and a full TE mode analysis is obtained. These results prove the ability of the proposed technique to analyze planar waveguides having any complicated refractive index profile.

An Efficient Multi-Scale Modeling Method that Reveals Coupled Effects Between Surface Roughness and Roll-Stack Deformation in Cold Sheet Rolling

Abstract In thin-gauge cold rolling of metal sheet, the surface roughness of work rolls (WRs) is known to affect the rolled sheet surface morphology, the required rolling load, and the roll wear. While modeling of rough surfaces using statistical asperity theory has been widely applied to problems involving semi-infinite solids, the application of asperity distributions and their elastic-plastic behavior has not been considered in roll-stack models for cold sheet rolling. In this work, a simplified-mixed finite element method (SM-FEM) is combined with statistical elastic-plastic asperity theory to study contact interference and coupling effects between a rough work roll (WR) surface and the roll-stack mechanics in cold sheet rolling. By mixing equivalent rough surface contact foundations, Hertz foundations, and Timoshenko beam stiffness, an approach is created to efficiently model interactions between the micro-scale asperities and the macro-scale roll-stack deformation. Nonlinearities from elastic-plastic material behavior of the asperities and the sheet, as well as changing contact conditions along the roll length, are also accommodated. Performance of the multi-scale SM-FEM approach is made by comparison with a continuum finite element virtual material model. 3D studies for a 4-high mill reveal new multi-scale coupling behaviors, including nonuniform roughness transfer, and perturbations to the sheet thickness “crown” and contact force profiles. The described multi-scale SM-FEM approach is general and applies to rough surface contact problems involving plates and shear-deformable beams having multiple contact interfaces and arbitrary surface profiles.

Optical control of the density and spin spatial profiles of a planar Bose gas

We demonstrate the arbitrary control of the density profile of a two-dimensional Bose gas by shaping the optical potential applied to the atoms. We use a digital micromirror device (DMD) directly imaged onto the atomic cloud through a high resolution imaging system. Our approach relies on averaging the response of many pixels of the DMD over the diffraction spot of the imaging system, which allows us to create an optical potential with an arbitrary intensity profile and with micron-scale resolution. The obtained density distribution is optimized with a feedback loop based on the measured absorption images of the cloud. Using the same device, we also engineer arbitrary spin distributions thanks to a two-photon Raman transfer between internal ground states.

Algorithm for flow of highly-concentrated emulsions through a narrow constriction

A multipole-accelerated 3D boundary-integral algorithm is developed to model pressure-driven flow of a highly-concentrated emulsion of many deformable drops through a periodic channel with tight constrictions. The drops are monodisperse, free from surfactant, and the Reynolds number is small for Stokes equations to apply. The channel surface consists of four solid panels: front and back parallel to each other, and band-like top and bottom panels with an arbitrary profile. The algorithm is for arbitrary channel aspect ratios, but the results are obtained for extreme cases, when the channel depth (front-back distance) is the same as the minimum channel height and both can be much smaller than the non-deformed drop diameter, making the drops flow as a monolayer. Strong hydrodynamic interactions (especially, drop-wall) necessitate very high surface resolutions combined with novel desingularization tools for the boundary integrals. Multipole acceleration gives, at least, two orders of magnitude gain over direct summations and facilitates long-time simulations, with many drop rearrangements. Examples for homoviscous emulsions with 40-92 drops in two types of channels at 80-90% drop volume fractions and different capillary numbers demonstrate single-file drop motion intermittent with pairs or triplets of drops in the constriction. Such squeezing interactions can result in extreme drop elongations, but are still not sufficient to promote breakup for the channel geometries, capillary numbers and drop confinements considered. Integral properties (the entire drop-phase and constriction flow velocities) are also analyzed.

A Versatile Flow-Profile Engineering Method in the Stokes Flow Regime for Complex-Shaped Flows

Flow profiles are frequently engineered in microfluidic channels for enhanced mixing, reaction control, and material synthesis. Conventionally, flow profiles are engineered by inducing inertial secondary flow to redistribute the streams, which can hardly be reproduced in microfluidic environments with negligible inertial flow. The employed symmetric channel structures also limit the variety of achievable flow profiles. Moreover, each of the flow profiles specifically corresponds to a strictly defined flow condition and cannot be generalized to other flow environments. To address these issues, we present a systematic method to engineer the flow profile using inertialess secondary flow. The flow is manipulated in the Stokes regime by deploying a cascaded series of microsteps with various morphologies inside a microchannel to shape the flow profile. By tuning the shapes of the microsteps, arbitrary outflow profiles can be customized. A numerical profile-transformation program is developed for rapid prediction of the output profiles of arbitrary sequences of predefined microsteps. The proposed method allows the engineering of stable flow profiles, including asymmetric ones, over a wide range of flow conditions for complex microfluidic environmental prediction and design.

Multifunctional ultrathin reflective metasurface via polarization-decoupled phase for arbitrary circularly or elliptically polarized waves.

Metasurface offers a promising platform in the design of multifunctional devices owing to its unique ability for EMWs manipulation. However, wave-manipulation capabilities for metasurfaces face challenges in manipulating orthogonal EMWs with arbitrary circularly or elliptically polarized EMWs in the microwave region. Herein, single-layer reflective metasurfaces are proposed for independent manipulation of an arbitrary set of orthogonal circularly or elliptically polarized EMWs via polarization-decoupled phase. Taking advantage of single-layer anisotropic meta-atoms, the proposed metasurface can act as a tandem phase modulator, which introduces polarization-decoupled phase profiles for arbitrary circularly and elliptically polarized EMWs based on the Jones matrix. In this way, the proposed metasurface can distinguish a set of orthogonal EMWs with circular or elliptical polarization states and impose arbitrary phase profiles on them independently and simultaneously. For proof-of-concept, bifunctional metasurfaces operating in the microwave region are presented for independent manipulation of three different sets of orthogonal circularly or elliptically polarized EMWs. They create dual independent channels associated with a pair of orthogonal polarization states, performing functions including polarization beam splitting and orbital angular momentum (OAM) multiplexing. Measured and simulated results show a good agreement, confirming that the proposed single-layer reflective metasurfaces are efficient devices that enable meta-devices to independently control arbitrary circular and elliptical polarized EMWs, achieving arbitrary functionalities.

Multi-frequency coherent emission from superstructure thermal emitters

Long-range spatial coherence can be induced in incoherent thermal emitters by embedding a periodic grating within a material supporting propagating polaritons or dielectric modes. However, only a single spatially coherent mode is supported by purely periodic thermal emitters. While various designs have been proposed for the purpose of allowing arbitrary emission profiles, the limitations associated with the partial spatial coherence of thermal emitters are not known. Here, we explore superstructure gratings (SSGs) to control the spatial and spectral properties of thermal emitters. SSGs have long-range periodicity but employ a unit cell that provides multiple Bragg vectors to interact with light. These Bragg vectors allow simultaneous launching of polaritons with different frequencies/wavevectors in a single grating, manifesting as additional spatial and spectral modes in the thermal emission profile. However, SSGs still have a well-defined period, which allows us to assess the role that finite spatial coherence plays in thermal emitters. We find that the spatial coherence length defines the maximum possible SSG period that can be used. This provides a fundamental limit on the degree of spatial coherence that can be induced in a thermal emitter and has broader implications for the use of techniques such as inverse design for structure optimization.

ХАРАКТЕРИСТИКИ ПРЯМОГО РЕБРА С ЭНЕРГОВЫДЕЛЕНИЕМ

The heat conduction equation for a straight fin with an arbitrary profile in the presence of energy release in the fin is obtained in the article. The resulting equation differs from the approximate equation given in the literature by the presence of energy release and a more accurate determination of the length of the arc element. The equation is solved for the fin of a rectangular profile with continuously operating heat sources. The efficiency of the fin and the heat flow through the base of the fin are determined. It is shown that energy release in the fin increases its efficiency in comparison with the efficiency of the fin in the absence of energy release. There is also a decrease in the heat flow in the presence of energy release in the fin. The restriction on the values of energy release in the fin is found as condition for the applicability of the finning. The fin efficiency must be less than one. If the efficiency exceeds one, the fin plays the opposite role: the flow is directed in the reverse side. To increase the build-up coefficient of the surface, tend to reduce the distance between the fins. There is a limit to such reduction. Theoretically, the distance between the fins should be at least double the maximum thickness of the boundary layer. As experience shows, this distance can be reduced to about one thickness. An approach to achieve the largest build-up coefficient at finning is described in the article.

Floquet description of optically pumped magnetometers

We present theoretical description of Voigt and Faraday effect based optically pumped magnetometers using the Floquet expansion. Our analysis describes the spin-operator dynamics of the first, $\hat{F}(t)$, and second, $\hat{F}^2(t)$, order moments and takes into account of different pumping profiles and decoherence effects. We find that the theoretical results are in good agreement with the experimental demonstrations over a wide range of fields and pumping conditions. Finally, the theoretical analysis presented here is generalized and can be extended to different magnetometry schemes with arbitrary pumping profiles and multiple radio-frequency fields.

Cost-Performance Trade-off in thermoelectric air conditioning system with graded and constant material properties

Thermoelectric (TE) air cooling is a solid-state technology that has the potential to replace conventional vapor compression-based air conditioning. In this paper, we present a detailed system-level modeling for thermoelectric air conditioning system with position-dependent (graded) and constant material properties. Strategies for design optimization of the system are provided in terms of cost-performance trade-off. Realistic convection heat transfer at both sides of the system are taken into account in our modeling. Effects of convection heat transfer coefficients, air flowrate, and thermoelectric material properties are investigated with varying key parameters such as TE leg thickness, module fill factor, and input current. Both constant material properties and graded properties are considered for the TE materials, and they are compared in terms of the degree of cooling, coefficient of performance (COP), and power consumption. For graded materials, we employ one-dimensional finite element methods to solve the coupled electrical and thermal current equations with arbitrary profile of material properties varying with position along the TE legs. We find that graded materials can enhance the degree of cooling, but only at the expense of COP, compared to the case of constant property materials. With constant material properties of ZT = 1 and relatively low electric current, the power consumption of TE coolers can be lower than those of conventional air conditioners at an equivalent cooling capacity. Considering additional advantages such as demand-flexible operation, low noise, and high scalability, thermoelectric cooling could be a competitive technology for future air conditioning applications..

Study of numerical error of a Eulerian–Lagrangian scheme in the presence of particle source

Eulerian–Lagrangian (EL–LG) scheme is a numerical scheme that tracks pseudo particles in Eulerian cells. It is widely used in the computational fluid dynamics, however, numerical errors associated with a particle source term has not yet been investigated much. Hence this study focuses on numerical errors of EL–LG caused by particle sources. The purposes are: (i) to clarify causes and situations that bring larger numerical errors by source terms and (ii) to suggest an idea to reduce them. For those purposes, we focus on the particle continuity equation and carry out systematic analysis of the numerical error by setting the following three simple cases: Case (A) No source, Case (B) Constant source, and Case (C) source with arbitrary spatial profile. For each case, we have obtained a theoretical expression of the numerical error. It has been clarified that the errors become relatively large when (i) the spatial profile of the particle source has a large gradient and (ii) the source is localized in the region with high flow-velocity. These were caused by the treatment of the particle source: If pseudo particles due to the source are added in a simple way at the start or the end of the time step, this can lead to larger numerical errors. To reduce those errors, a time-averaging scheme has been suggested. Although the analyzed cases are simple, the results obtained in this study would give important knowledge and insight into numerical errors associated with particle sources in EL–LG schemes.

Shape optimization of acoustic horns for improved directivity control and radiation efficiency based on the multimodal method.

The multimodal method is used to develop an approach for optimizing the shape of axisymmetric acoustic horns for both well-controlled directivity and high radiation efficiency over a wide frequency range. A horn with an arbitrary profile can be efficiently modeled with the multimodal method by projecting the wave field over transverse modes in connected short cylinders; the radii of the cylinders are used directly as design variables. Many design variables are employed in the optimization process to ensure design flexibility and computational accuracy. The relative weights for the design objectives of constant directivity, high radiation efficiency, and acceptable shape smoothness are adjusted by two coefficients in the objective function. The optimization problem is solved with a gradient-based algorithm, which takes advantage of algebraic gradient expressions. Numerical experiments demonstrate that the optimization procedure generates smooth horn contours that exhibit considerably improved performance over the target frequency band. Interestingly, a high-quality horn produced with moderate weight coefficients is similar in shape to constant-directivity horns invented earlier while having good low-frequency loading properties. The proposed method provides an attractive alternative to conventional horn design approaches.

Mathematical modelling and design of isolation diaphragms for pressure gauges

The paper discusses some questions of equilibrium, stability and shape optimization of circular membranes with arbitrary profile along the meridian. Such membranes can be used as a flexible barrier to isolate the media on one side of a diaphragm from media on the other side, whilst allowing the transmission of pressure with minimal loss. The main goal of the analysis is to propose techniques for designing such shape of corrugated membranes that satisfy the requirements of so call “slow growing linear or almost linear” behavior of the pressure-volume diagram. The applied Kirchhoff-Love theory for non-shallow shells was used as a base for deriving nonlinear as well as linearized boundary value problems of equilibrium. A genetic algorithm was used to evaluate and optimize the characteristics of corrugated membranes. The presented analysis of the membrane with the maximum linear stroke showed its efficiency and reliability. At the same time, special attention should be paid to the basic parametrization used in modelling, since the mathematically optimal solution is not always suitable from the point of view of membrane production technology.

Power Evolution Modeling and Optimization of Fiber Optic Communication Systems With EDFA Repeaters

In this article, machine learning is used to create a differentiable model for the input-output power spectral profile relations of C-band erbium-doped fiber amplifiers (EDFAs). The EDFA model is demonstrated to generalize to multiple physical devices of the same make while only trained on experimental data from a single unit. The model is combined with a differentiable model for simulating stimulated Raman scattering (SRS) effects during propagation through the the optical fiber to create a differentiable model for a multi-span system with an arbitrary configuration of number of spans, length per span and launch power per span. The cascade system model is used to predict and optimize the power profile output of several such experimental configurations of up to three spans with an arbitrary target power profile. A flat target profile is exemplified experimentally, achieving <; 3 dB of power excursions for EDFAs exhibiting $>$10 dB of excursion per device in the cascade. The experimental data used to create the EDFA model is made public and available online.

Reconfigurable all-dielectric metalens with diffraction-limited performance

Active metasurfaces, whose optical properties can be modulated post-fabrication, have emerged as an intensively explored field in recent years. The efforts to date, however, still face major performance limitations in tuning range, optical quality, and efficiency, especially for non-mechanical actuation mechanisms. In this paper, we introduce an active metasurface platform combining phase tuning in the full 2π range and diffraction-limited performance using an all-dielectric, low-loss architecture based on optical phase change materials (O-PCMs). We present a generic design principle enabling binary switching of metasurfaces between arbitrary phase profiles and propose a new figure-of-merit (FOM) tailored for reconfigurable meta-optics. We implement the approach to realize a high-performance varifocal metalens operating at 5.2 μm wavelength. The reconfigurable metalens features a record large switching contrast ratio of 29.5 dB. We further validate aberration-free and multi-depth imaging using the metalens, which represents a key experimental demonstration of a non-mechanical tunable metalens with diffraction-limited performance.

SNAP structures fabricated by profile design of in-fiber inscribed regions with a femtosecond laser.

Fabricating a surface nanoscale axial photonics (SNAP) microresonator with a specific profile is a challenging and important issue since its advent. We propose a powerful approach for the flexible fabrication of the SNAP structures with arbitrary profiles by a femtosecond laser. Our method is to design the profile of the length distribution of the inscribed lines to match the profile of the required SNAP microresonator, and to combine it with other fabrication parameters to precisely control the radius variation of the SNAP structure. In experiments, we demonstrate the design and fabrication of the SNAP structures with the parabolic, semi-parabolic, and bat profiles. The developed approach is expected to be universal for the fabrication of complex high Q-factor SNAP structures, which lays the groundwork for exploring the versatile performances of the SNAP devices.

Analysis of the Double-Bounce Interaction between a Random Volume and an Underlying Ground, Using a Controlled High-Resolution PolTomoSAR Experiment

The radar response of vegetated environments, and forested areas in particular, are usually modeled using a very simple structure made of a random volume, representing a cloud of vegetation particles, lying over a semi-infinite medium with a rough interface, associated with the underlying ground. This Random Volume over Ground model can efficiently handle double-bounce scattering mechanisms, or arbitrary volume reflectivity profiles. This paper proposes to analyze a specific component of the Random Volume over Ground simplified scattering model, which concerns the double-bounce interaction between the ground and the volume. This specific contribution is not considered by classical characterization techniques and is studied in this work using a controlled experiment involving a Synthetic Aperture Radar operated in a Polarimetric and Tomographic configuration in order to image in 3D a controlled miniaturized scene composed of volume lying over a ground. It is shown that ground/volume double-bounce scattering, which remains focused at the ground level even in 3D imaging mode, and has polarimetric patterns that differ largely from those usually expected from double-bounce reflections, with volume-like features, such as a strong cross-polarized reflectivity or decorrelation between co-polarized channels. Moreover, it is shown that the full rank polarimetric patterns of the ground-volume mechanism are tightly linked to the reflectivity of the volume and may mask the ground response. As a consequence, isolating the ground response using 3D imaging does not permit to avoid a generally very strong distortion of the soil response by the double-bounce reflection, and the estimation of different geophysical parameters of the ground, such as its humidity or roughness are significantly altered.

Arbitrary power allocation for multiple beams using amplitude- and phase-coded metasurfaces

Digital-coding metasurfaces provide a convenient method for designing metasurface-based functional devices. By delicately arranging the coding sequences, electromagnetic fields on the metasurfaces can be modulated for applications like wave-front engineering, amplitude controlling and polarization conversion. Theoretically, to fully realize arbitrary profiles for radiation patterns, both amplitude and phase modulations are needed for the responses of meta-atoms. Here, a method is proposed to generate multiple beams with arbitrary power intensity ratios using 2 bit amplitude and 2 bit phase digital-coding metasurfaces. A detailed process for designing the coding sequences is elaborated, and four-layer conformal square-loop meta-atoms are adopted to achieve 16 combinations of amplitude and phase codes. Two prototypes with dual beams of different radiation angles and power allocations are simulated, fabricated and measured. The experimental results match well with the predesigned expectations, which verifies the feasibility of the proposed method. It suggests that the digital-coding metasurface is a good candidate for multi-beam radiation pattern syntheses and is promising for various multi-functional telecommunication and radar applications.

Comparative Evaluation of Statistical and Fractal Approaches for JRC Calculation Based on a Large Dataset of Natural Rock Traces

After the publication of the type-profiles for the estimation of the joint roughness coefficient (JRC) a discussion evolved about how to adequately use these traces. Based on the chart numerous researchers assembled mathematical correlations with various parameters seeking objectivity in the determination of JRC. Within these works differences concerning the database and the mathematical implementations exist. Consequently, each correlation, although predominantly the same parameters are used, leads to different JRC values. In theory, for any arbitrary profile, irrespective of the particular calculation approach, the same JRC should result. This is a requisite because of the referencing of all correlations to the 10 type-profiles. However, it is shown in this study that in most cases equal or even satisfactorily similar results are not obtained. The discrepancies are vast when non-standard profiles are evaluated, in this case, more than 40,000 traces from six different rock surfaces that cover a broad range of roughness categories. The simple intuitive parameter Z2 served as an agent for the statistical methods because of its broad use and consequently good comparability. On the part of the fractal approaches, three definitions were used. However, JRC inferred from fractal correlations are very much dependent on the particular calculation routine. In fact, the theory of fractals is overly complex for the sparse and low-resolution type-profiles. In summary, fractal approaches do not produce safer or more reliable estimates of roughness compared to simple statistical means and using Z2 perfectly suffices to determine the class of JRC.

Solving the Coriolis Vibratory Gyroscope Motion Equations by Means of the Angular Rate B-Spline Approximation

The exact solution of the movement equation of the Coriolis vibratory gyroscope (CVG) with a linear law of variation of the angular rate of rotation of the base is given. The solution is expressed in terms of the Weber functions (the parabolic cylinder functions) and their asymptotic representations. On the basis of the obtained solution, an analytical solution to the equation of the ring dynamics in the case of piecewise linear approximation of an arbitrary angular velocity profile on a time grid is derived. The piecewise linear solution is compared with the more rough piecewise constant solution and the dependence of the error of such approximations on the sampling step in time is estimated numerically. The results obtained make it possible to significantly reduce the number of operations when it is necessary to study long-range dynamics of oscillations of the system, as well as quantitatively and qualitatively control the convergence of finite-difference schemes for solving the movement equations of the Coriolis vibratory gyroscope.