Effective Propagation Constant Research Articles

Transmission of Vortex Solitons in Three-Dimensional χ(2) Helical-Periodically Poled Ferroelectric Crystals

It is well known that bright vortex solitons are unstable in the χ2 nonlinear media due to the strong azimuthal modulation instability. To solve this problem, a quadratic (χ2) LiNbO3 ferroelectric crystal with a special kind of helical-periodically poled structure is proposed. The proposed structure is designed by embedding topological charges into the crystal with a quasi-phase matching technique. Simulation results indicate that vortex solitons containing fundamental-frequency and second-harmonic waves can robustly propagate over a distance. Two types of vortex states are obtained: double vortices state and vortex–antivortex state. The dependence of effective area, propagation constants, and maximum light intensity on the control parameters are presented. These results provide a new solution for robust transmission of bright vortex solitons in a χ2 nonlinear media.

Unsafe food additive sensing through octagonal-core photonic crystal fibre sensor

To detect food additives, a simple photonic crystal fibre design based on an octagonal hole and hollow circular cladding holes in two layers has been introduced. The numerical study of the design is conducted by simulation in the COMSOL Multiphysics software with the infiltrated test analytes: saccharin, sorbitol, and butyl acetate, operating in the wavelength variation from 1.6 to 4.0 μm. The performance of the proposed sensor is determined by analysing the principal optical parameters: effective refractive index, power fraction, relative sensitivity, confinement loss, chromatic dispersion, propagation constant, V-parameter, spot size, and beam divergence. At the optimal wavelength of 2.0 μm, the sensor design depicts high relative sensitivities of 98.06% for saccharin, 97.05% for sorbitol, 95.81% for butyl acetate, and 3.82 × 10−23 dBm−1 for saccharin, 3.44 × 10−22 dBm−1 for sorbitol, and 1.81 × 10−21 dBm−1 for butyl acetate for confinement loss, which is extremely low. Hence, the proposed food additive sensor is suitable for actual sensing applications based on these obtained results.

Photonic Crystal Fiber Sensor for Detecting Sulfuric Acid in Different Concentrations

A high-performance photonic crystal fiber sensor for sulfuric acid detection is designed and investigated, undertaken through a full vector Finite Element Method on COMSOL Multiphysics software to establish the optical properties of effective refractive index, power fraction, relative sensitivity, confinement loss, chromatic dispersion, and propagation constant. Different aqueous sulfuric acid concentrations of 0%, 10%, 20%, 30%, and 40% were selected as the test analytes. The dimensions of two cladding rings of the hexagon- and circular-shaped air holes and a circular core hole denoted outstanding outcomes of relative sensitivity and confinement loss. At 1.1 µm optimum wavelength, 0%, 10%, 20%, 30%, and 40% sulfuric acid concentrations depict relative sensitivities of 97.08%, 97.67%, 98.06%, 98.39%, and 98.67%, respectively, and confinement losses of 1.32 × 10−12 dB/m, 4.11 × 10−12 dB/m, 1.46 × 10−12 dB/m, 6.34 × 10−12 dB/m, and 2.12 × 10−12 dB/m, respectively.

Oblique Incidence Optimal Design of Microwave Dielectric-Magnetic Absorbing Composites

The impedance matching equation of a single-layer dielectric-magnetic absorber excited by an oblique incidence plane wave is resolved with an expression providing the optimal thickness and highlighting the composite crucial parameters. The effective propagation constant of the nonuniform refracted plane wave into the absorber is represented by a new formulation as a function of the true refraction angle which is a real number unlike the complex quantity resulting from the Snell’s law, usually applied in the literature. The proposed design process is applied to compute microwave absorption performances of different dielectric-magnetic materials, considering both normal and oblique incidence. Furthermore, the incidence angle effect is investigated.

Unambiguous derivation of the effective refractive index of biological suspensions and an extension to dense tissue such as blood.

The van de Hulst formula provides an expression for the effective refractive index or effective propagation constant of a suspension of particles of arbitrary shape, size, and refractive index in an optically homogeneous medium. However, its validity for biological matter, which often consists of very dense suspensions of cells, is unclear because existing derivations of the formula or similar results rely on far-field scattering and/or on the suspension in question being dilute. We present a derivation of the van de Hulst formula valid for suspensions of large, tenuous scatterers-the type biological suspensions are typically made of-that does not rely on these conditions, showing that they are not strictly necessary for the formula to be valid. We apply these results specifically to blood and epithelial tissue. Furthermore, we determine the true condition for the formula to be valid for these types of tissues. We finally provide a simple way to estimate-and, more importantly, correct-the error incurred by the van de Hulst formula when this condition is not met.

Full-Wave Calculation of Complex Propagation Constant for a Medium of Conducting Wires

This article presents a full-wave numerical method that, in conjunction with Monte Carlo simulation, is used to calculate the effective propagation constant of a random volume of conducting wires of arbitrary length and curvature. Bistatic scattering from many realizations of nonoverlapping metallic wires confined within a fictitious spherical enclosure is calculated to determine the mean electric field scattered by the random medium. This mean scattered field is then used to determine the effective permittivity of the random medium using an inverse scattering scheme. These values are then compared with the values given by the Foldy approximation for many particle sizes, geometries, and number densities within a given medium. An investigation into the results is undertaken to determine an expanded macromodel for 3-D electromagnetic propagation through such a random medium, and the applicability of Foldy's approximation is determined using this model.

Reconfigurable multiport switch in coupled mode devices

We consider a coupled mode system where the effective propagation constants of localized modes are amenable to modulation. Starting from an unmodulated system where power transfer is heavily suppressed, we demonstrate that small, periodic modulation of the propagation constants enhance power transfer using a slowly varying envelope approximation for the field mode amplitudes. We calculate an approximate modulation frequency enabling complete transfer between otherwise negligibly coupled elements. The ability to control these modulations by electrical or thermal effects allows for reconfigurable multiport switching. We use an array of coupled silica waveguides and the thermo-optic effect to test our predictions in the telecom C-band. However, this requires a refractive index modulation with period of the order 10−3 m and yields total power transfer with a propagation distance of the order of 10−1 m, which might make it unattractive for integrated photonic applications. Nevertheless, our results are valid for devices described by an equivalent coupled mode matrix for space or time propagation; for example, arrays of microring or terahertz resonators, microwave cavities, radio frequency antennas, or RLC circuits.

Design and analysis of visible photonics resonators coated with CuO thin film

The optical and structural properties of CuO film deposited on n-Si via spin-coating method have been ascertained for diverse annealing times. The characterizations were made using x-ray diffraction (XRD), field emission scanning electron microscopy (FESEM), UV–vis spectroscopy, ellipsometry spectroscopy and photoluminescence. A detailed analysis revealed the favorable behavior of CuO film for visible photonics resonators such as Fabry–Perot (FP) and ring resonators. The best suitable property was obtained for a film annealed for 15 min. Accordingly, the CuO-film-coated resonators were simulated and analyzed theoretically using the MODE Solutions tool by Lumerical and MATLAB. In the FP resonator, the transmission intensity, contrast factor and finesse were computed for different annealing times and angles of light incidence. Further, for the CuO ring resonator, an eigenmode solver was incorporated (in the wavelength range 300–900 nm) to compute the effective refractive index, propagation constant, group velocity, losses, dispersion and transmission intensity. Additionally, utilizing the basic expressions, the free spectral range, full-width at half-maximum and quality factor were derived.

Temporal derivation operator applied on the historic and school case of slab waveguides families eigenvalue equations: another method for computation of variational expressions

Starting from the well-known and historic eigenvalue equations describing the behavior of 3-layer and 4-layer slab waveguides, this paper presents another specific analytical framework providing time-laws of evolution of the effective propagation constant associated to such structures, in case of temporal variation of its various geometrical features. So as to develop such kind of time-propagator formulation and related principles, a temporal derivation operator is applied on the studied school case equations, considering then time varying values of all the geometrical characteristics together with the effective propagation constant. Relevant calculations are performed on three different cases. For example, we first investigate the variation of the height of the guiding layer for the family of 3-layer slab waveguides: then, considering the 4-layer slab waveguide's family, we successively address the variation of its guiding layer and of its first upper cladding. As regards the family of 4-layer waveguides, calculations are performed for two different families of guided modes and light cones. Such another approach yields rigorous new generic analytical relations, easily implementable and highly valuable to obtain and trace all the family of dispersion curves by one single time-integration and one way.

Symmetric supermodes in cyclic multicore fibers

Nearest-neighbor coupled-mode theory is a powerful framework to describe electromagnetic-wave propagation in multicore fibers but it lacks precision as the separation between cores decreases. We use abstract symmetries to study a ring of evenly distributed identical cores around a central core, a common configuration used in telecommunications and sensing. We find its normal modes and their effective propagation constants while including the effect of all high-order inter-core couplings. Finite-element simulations support our results to good agreement. Only two of these effective modes involve fields in all the cores. These two modes display opposite-sign phase configurations between the fields in the external cores and the central core. These two modes still appear in the limit where the external cores become a continuous ring. Our results might help improve predictions for crosstalk in telecommunications or precision in sensing applications.

Numerical Analysis of Optical Properties Using Octagonal Shaped Photonic Crystal Fiber

Abstract In this paper, we propose a design of octagonal photonic crystal fiber with relevant parameters such as effective mode index, propagation constant, second-order dispersion and field distribution of fundamental mode (LP01). The measured parameters can be applied for generating supercontinuum, and also this model is used especially for generating vortex modes and OAM modes in space division multiplexing (SDM) applications. Highly negative dispersion is achieved at −800 ps/nm.km at wavelength of 1.1 μm, and second-order dispersion profile leads to study about the nonlinearity as well as broadband spectrum of the proposed model.

Embedding the Photon with Its Relativistic Mass As a Particle into the Electromagnetic Wave Explains the Gouy Phase Shift as an Energetic Effect

In the paper “Embedding the photon with its relativistic mass as a particle into the electromagnetic wave” a new aspect concerning the relationship between photon and electromagnetic wave has been developed by considering the question why the energy and the mass density of an electromagnetic wave are propagating in the same direction [1]. For instance, in optical resonators the energy density usually propagates along curved lines. However, according to Newton’s first law the mass density should propagate along a straight line, if no force is exerted it. To solve this problem, the assumption has been made that a transverse force is exerted on the mass density and in consequence on the mass of the photons which forces them to follow the propagating energy density. This leads to the result that the photon is moving within a transverse potential which allows describing the transverse quantum mechanical motion of the photon by a Schrödinger equation. These results are used to show that in case of a Gaussian wave the effective axial propagation constant kz, nm (z) can be expressed as kz, nm (z) = [Eph ‒ Enm (z)] /ћc where Eph is the total energy of the photon, and the Enm (z) are the energy eigenvalues of the transverse quantum mechanical motion of the photon. Since according to this result ћckz, nm (z)] represents a real energy, it has been concluded that also the effective axial propagation constant represents a real propagation constant. This leads to the conclusion that λnm (z) =2π/ kz, nm (z)=hc/�(Eph ‒ Enm (z)� represents the real local wave length of the electromagnetic wave at the position z. According to this conclusion, λnm (z) increases inversely proportional to the energy difference Eph-Enm (z), which decreases with decreasing z, and therefore describes the Gouy phase shift in agreement with wave optics. This shows that the deeper physical reason for Gouy phase shift consists in the fact that the energy of the photon is increasingly converted into its transverse quantum mechanical motion when the photon approaches the focus. This explains the Gouy phase shift as an energetic effect.

Low-Voltage Permittivity Control of Coplanar Lines Based on Hafnium Oxide Ferroelectrics Grown on Silicon

This paper is dedicated to the study of the tunable electromagnetic properties of HfO2 doped with Zr (further referred to as HfZrO) grown on high-resistivity silicon using atomic layer deposition (ALD) techniques. Two metallic coplanar lines patterned on HfZrO having different lengths have been used to determine the effective permittivity and wave propagation constant in HfZrO in the frequency range 1–14 GHz, hence covering the L, S, C, X and (part of the) Ku bands. We have observed a significant modulation of the effective permittivity when a bias voltage is applied within the range 0–5 V, with an almost constant increase of 27% in a frequency range of 8 GHz. We have also extracted the attenuation constant, phase constant and loss tangent: the losses due to the thin HfZrO ferroelectric layer increase of maximum 21% at 5 V, which represents the saturation upper limit for ferroelectric’s polarization. These results could have a significant impact on effective design of ferroelectric-based microwave circuits with tunable characteristics.

Explaining the Gouy phase shift as an energetic effect

In the paper “Embedding the photon with its relativistic mass as a particle into the electromagnetic wave” [Opt. Express26, 1375 (2018).10.1364/OE.26.00137529402012], it has been shown that the problem why the energy and the mass density of an electromagnetic wave are propagating in the same direction can be solved by the assumption that a transverse force is exerted on the photons. This leads to the result that the photon is moving within a transverse potential, which allows the description of the transverse quantum mechanical motion of the photon by a Schrodinger equation. These results are used to show that, in the case of a Gaussian wave, the effective axial propagation constant k¯z,nm(z) can be expressed as k¯z,nm(z)=[Eph−Enm(z)]/ℏc, where Eph is the total energy of the photon and Enm(z) are the energy eigenvalues of the transverse quantum mechanical motion of the photon. Since, according to this result, ℏck¯z,nm(z) represents a real energy, it has also been concluded that the effective axial propagation constant represents a real propagation constant. This leads to the conclusion that λnm(z)=2π/k¯z,nm(z)=hc/(Eph−Enm(z)) represents the real local wave length of the photon at the position z. According to this conclusion, λnm(z) increases inversely proportionally to the energy difference Eph-Enm(z), which decreases with decreasing z, and therefore describes the Gouy phase shift in agreement with wave optics. This shows that the deeper physical reason for Gouy phase shift consists in the fact that the energy of the photon is increasingly converted into its transverse quantum mechanical motion when the photon approaches the focus. This explains the Gouy phase shift as an energetic effect.

Achieving a strongly negative scattering asymmetry factor in random media composed of dual-dipolar particles

Understanding radiative transfer in random media like micro/nanoporous and particulate materials, allows people to manipulate the scattering and absorption of radiation, as well as opens new possibilities in applications such as imaging through turbid media, photovoltaics and radiative cooling. A strong-backscattering phase function, i.e., a negative scattering asymmetry parameter $g$, is of great interest which can possibly achieve unusual radiative transport phenomena, for instance, Anderson localization of light. Based on the multipole expansion of Foldy-Lax equations and quasicrystalline approximation (QCA), we have rigorously derived analytical expressions for effective propagation constant and scattering phase function for a random system containing dual-dipolar particles, by taking the effect of structural correlations into account. Here we demonstrate that by utilizing structural correlations and the second Kerker condition for a disordered medium composed of randomly distributed silicon nanoparticles, a strongly negative scattering asymmetry factor ($g\sim-0.5$) for multiple light scattering can be realized in the near-infrared. As concentration of scattering particles rises, the backscattering is also enhanced. Moreover, we show that in this circumstance, transport mean free path is largely reduced and even smaller than that predicted by independent scattering approximation. We further explored the dependent scattering effects, including the modification of electric and magnetic dipole excitations and far-field interference effect, both induced by the structural correlations, for volume fraction of particles up to $f_v\sim0.25$. Our results have profound implications in harnessing micro/nanoscale radiative transfer through random media.

Numerical Modeling and De-Embedding of Non-Planar Periodic Guided-Wave Structures via Short-Open Calibration in 3-D FEM Algorithm

In this paper, a numerical short-open calibration (SOC) technique is presented to numerically model and de-embed a variety of non-planar periodic guided-wave structures based on the 3-D full-wave finite element method (FEM). A simple current source or lumped-port model is introduced in formulation of a determinant FEM algorithm. By incorporating the SOC in the FEM solver, the intrinsic port discontinuity caused by this port model is then fully removed or calibrated out of the core non-planar periodic guided-wave structure during the calibration process. Because of the 3-D nature of FEM, the effective per-unit-length parameters of the core periodic guided-wave structure, i.e., effective propagation constant and effective characteristic impedance, are extracted successfully. Two numerical examples, including microstrip line with periodical loading of shorting pins and metal–insulator–metal composite right/left handed structure, are numerically modeled for demonstration and verification. Extracted results have validated the feasibility and accuracy of the presented FEM-SOC, thereby exhibiting its advanced capability in numerical modeling and de-embedding of non-planar structures with complicated configurations.

Comparison of recent results for the determination of effective propagation constants at attenuating interfaces

A lot of research has been performed, dealing with the propagation characteristics of non-uniform, harmonic, elliptically polarised, plane waves at the interface between a dielectric and an attenuating or two conducting media. This contribution presents an overview of the notations used thereby to describe the propagation of plane waves in attenuating media. The derivation of Fresnel coefficients for the non-uniform wave with coplanar phase and attenuation vectors is described in detail on a basic level and the determination of effective propagation constants is addressed on the basis of recently published results, which are discussed and compared by numeric simulation.

Miniaturized Wideband Metasurface Antennas

The single- and dual-layer metasurfaces are proposed to miniaturize a low-profile wideband antenna. The single- and dual-layer metasurfaces consist of one and two square patch arrays, respectively, both supported by grounded dielectric substrate to form the waveguided metamaterials. After retrieving the effective refractive index along the propagation direction in the waveguided metamaterial, the effective propagation constant is subsequently derived to initially estimate the resonant frequencies of the dual-mode antenna. With the increased effective refractive index, both the proposed antennas realize the gain greater than 6.5 dBi over the bandwidth of ~30% with a reduced radiating aperture of $0.46\lambda _{0} \times 0.46\lambda _{0}$ and a thickness of $0.06\lambda _{0}$ ( $\lambda _{0}$ is the free-space wavelength at 5.5 GHz). Moreover, the dual-layer metasurface provides more freedom to increase the effective refractive index with achievable gap widths compared with the single-layer metasurface.

Higher-order mode suppression in twisted single-ring hollow-core photonic crystal fibers.

A hollow-core single-ring photonic crystal fiber (SR-PCF) consists of a ring of capillaries arranged around a central hollow core. Spinning the preform during drawing introduces a continuous helical twist, offering a novel means of controlling the modal properties of hollow-core SR-PCF. For example, twisting geometrically increases the effective axial propagation constant of the LP01-like modes of the capillaries, providing a means of optimizing the suppression of HOMs, which occurs when the LP11-like core mode phase-matches to the LP01-like modes of the surrounding capillaries. (In a straight fiber, optimum suppression occurs for a capillary-to-core diameter ratio d/D=0.682.) Twisting also introduces circular birefringence (to be studied in a future Letter) and has a remarkable effect on the transverse intensity profiles of the higher-order core modes, forcing the two-lobed LP11-like mode in the untwisted fiber to become three-fold symmetric in the twisted case. These phenomena are explored by means of extensive numerical modeling, an analytical model, and a series of experiments. Prism-assisted side-coupling is used to measure the losses, refractive indices, and near-field patterns of individual fiber modes in both the straight and twisted cases.

Analysis of Optical Properties for Square, Circular and Hexagonal Photonic Crystal Fiber

This paper presents four rings square, circular, and hexagonal photonic crystal fiber (PCF) geometry for analyzing different optical properties in a wavelength ranging from 800 nm to 1600 nm. These three types of geometry have been used for analyzing Effective area, Propagation constant, Confinement loss and Waveguide dispersion. Silica glass is chosen as background material and the cladding region is made of four air hole layers. COMSOL Multiphysics (v.5) software is used to simulate these proposed PCF geometries. From the numerical analysis, it is found that the effective area is small for hexagonal PCF geometry and large for square PCF geometry (11.827 μm2, 10.588 μm2 and 9.405 μm2 for square, circular, and hexagonal PCF geometry respectively). From the analysis, the Confinement loss is approximately zero at wavelength ranges from 800 nm to 1250 nm and approximately zero waveguide dispersion is achieved from 900 nm to 1500 nm for all the three PCF structures. Again, negative dispersion approximately −30.354 ps/(nm⋅km) is achieved for circular PCF structure at the wavelength of 900 nm.