Evaluating the beam shape coefficients of Bessel-Gauss beams with radial quadrature: a comparison with angular spectrum decomposition and finite series methods.

The Bessel-Gauss beam (BGB) stands as a physically realizable beam extensively employed in applications such as micromanipulation and optical trapping. In these contexts, the assessment of beam shape coefficients (BSCs) becomes imperative. Previous research reveals that the BSCs of the BGBs obtained with different methods deviate from each other under certain circumstances. In this paper, the formulation of BSCs employs the radial quadrature method, and a comparative analysis is conducted with counterparts formulated using the angular spectrum decomposition and the finite series technique. Contributions stemming from evanescent waves and the situation of the BSC blowing-ups are discussed, offering a deep insight of pertinent BSC evaluation methods. The paper provides an alternative approach for calculating the BSCs of the BGBs.

Equivalence between radial quadrature and finite series for spherical wave expansion of Bessel beams.

The radial quadrature method was recently proposed for formulating the beam shape coefficients (BSCs) for shaped beams. A new deduction of BSCs using the R-quadrature method is presented in this paper, using the integral of the spherical Bessel functions in the interval ranging from zero to infinity. Based on the scalar description of the Bessel beam, the equivalence between the R-quadrature and the finite series (FS) method is confirmed. The spherical wave expansion of the scalar function allows us to simplify the formulation of the BSCs in the R-quadrature and the FS and to speed up the numerical BSC calculation. As a by-product, FS expansions of the associated Legendre functions are established, which we do not find in the literature.

Observation of photonic Peierls transition for manipulating microwave in metallic diaphragm-array periodic structures.

Peierls transition that modifies electronic band structure has attracted intensive attention in solid state physics. In the present work, we report that a photonic analog of Peierls transition has been observed in a 1-D triangular metal diaphragm array, where the photonic bandgap structures have been designed at will by adjusting periodically metal diaphragm positions. It is shown by the numerical analysis that the transmission and radiation effect of the present periodic metal structure designed through the Peierls transition rule exhibits the behavior significantly different from an original periodic structure with each unit cell containing a metal diaphragm. The near- and far-field measurement results are in good agreement with our theoretical simulation. The present effect of photonic Peierls transition can serve as a working mechanism for designing new types of guided wave devices. It can be seen that the photonic Peierls transition would be one of the simplest ways for modifying the transport characteristics of electromagnetic waves in periodic structures.

A kind of planar waveguides for cheating the high-speed digital signals into misidentifying the characteristic impedance.

Since a planar periodic transmission line can suppress drastically the electromagnetic coupling, it would be advantageous to use such a kind of transmission lines in solving the problem of miniaturization of circuit area. By adjusting the lattice constants and geometric parameters of periodic microstrip lines, a time domain characteristic impedance that is the same as that of conventional microstrip lines (CMLs) can be achieved. Such periodic microstrip lines can therefore be used to trick high-speed digital signals, causing a digital signal to misjudge the time domain characteristic impedance of the transmission lines. The theoretical analysis has been verified by our experimental measurement results. Besides, a specific expression for the characteristic impedance of lossless periodic artificial materials is deduced by a circuit model and a standard of misidentification for the characteristic impedance of periodic microstrip lines is given for the digital signals.

Möbius shifts associated with the third-order and the fourth-order rainbows of a spheroidal droplet computation.

Vector-ray tracing (VRT) is employed to calculate Möbius shifts of the third-order and the fourth-order rainbows for a spheroidal droplet. When the aspect ratio of a spheroidal droplet is small, approximation expressions for calculating the Möbius shift (i.e., deviation of the geometrical rainbow angle for a spheroidal droplet and that for a spherical droplet) were given by Lock and Können [Appl. Opt.56, G88 (2017)APOPAI0003-693510.1364/AO.56.000G88]. The assessment of applicability ranges of the Lock approximation is obtained by comparing with a VRT simulation for a water droplet with the refractive index m=1.333. For this, a parameter ΔD is defined that measures the disagreement between the two methods. A threshold value of 5% for ΔD is chosen below which the agreement is considered to be good. For the third-order rainbow, it is shown that this is the case for the Lock approximation for water droplets (m=1.333) with aspect ratios in the range of 0.97≤a/c≤1.03. For the fourth-order rainbow, the application range of the Lock approximation is 0.99≤a/c≤1.01 for water droplets. For the first-order and second-order rainbows, the application ranges are briefly revisited with the current method. The influence of the droplet refractive index on the Möbius shift is also investigated.

Internal morphology-dependent resonances of a coated spherical particle.

Morphology-dependent resonances (MDRs) for a coated spherical particle are important because of their extensive applications. However, MDRs for coated spherical particles are more complicated than those for homogeneous particles. In this paper, a general expression is proposed for calculating the scattering efficiency of a specific layer of coated particle. Reformulations of internal scattering efficiency are made, which provides a new, to the best of our knowledge, method to investigate the resonance in the core and in the shell independently. MDRs in the core can be shown in four cases on the outmost scattering efficiency curve. To investigate the reason of the resonance, the relationships between MDRs in the core, outmost scattering efficiency, and partial wave are analyzed. It is numerically shown that the expressions are reliable and efficient, which provides a theoretical fundamental for studying of resonances of multilayered particles and for measurement.

Simulation of the optical caustics associated with the primary rainbow for oblate spheroidal drops illuminated by a Gaussian beam.

A vector ray-tracing model (VRT) has been developed to compute the optical caustics associated with the primary rainbow for an oblate spheroidal water drop illuminated by a Gaussian beam. By comparing the optical caustic structures (in terms of limiting rainbow and hyperbolic umbilic fringes) for a water drop with a Gaussian beam (GB) illumination with that for the same drop, but with parallel beam (PB) illumination, the influence of the Gaussian beam on the optical caustics is investigated. For a water drop with GB illumination and different drop/beam ratios (i.e., the ratio between the drop equatorial radius and the Gaussian beam waist), the location of cusp points and the curvature of the limiting rainbow fringe are also studied. We anticipate that these results not only confirm the approach to compute optical caustics for oblate spheroidal drops illuminated by a shaped beam, but may also lead to a new method for measuring the aspect ratio of spheroidal drops.

Phase critical angle scattering for measurement of transient nanoscale growth rate of a micron-sized bubble.

We developed phase critical angle scattering (PCAS) to simultaneously measure the spherical and transparent bubble size at the micron scale and transient bubble growth at the nanoscale. The theoretical derivation of PCAS reveals that the phase of the fine structure of critical angle scattering caused by reflection and first-order refraction is highly sensitive to and linearly shifts with bubble diameter growth. Experiments on a single growing bubble are implemented with a Fourier imaging system. The results show that the PCAS technique can measure the tiny bubble growth down to tens of nanometers, providing a promising tool for accurate characterization of bubble dynamics.

Model for computing optical caustic partitions for the primary rainbow from tilted spheriodal drops.

A model is proposed to compute the salient optical caustic partitions occurring in the primary rainbow for oblate spheroidal drops. By computing the boundary limits of outgoing rays, the optical caustic structures (termed rainbow and hyperbolic umbilic fringes) for tilted drops are calculated and compared with those for aligned (untilted) drops. The curvature of the rainbow fringe and the shifts of cusp caustics are discussed as well. The observed properties of the caustics can potentially be used for drop measurements. The model could also be applied to compute the optical caustics for drops with arbitrary shape, arbitrary orientation, and shaped beam illumination.

Calculation of light scattering of an elliptical Gaussian beam by a spherical particle.

The use of an elliptical Gaussian beam (EGB) for applications relying on light scattering depends much on the ability to evaluate the beam shape coefficients (BSC) effectively and accurately. Based on the angular spectrum decomposition (ASD) of the radial components of the beam field, we present the formulations of the BSCs for the EGB. Numerical calculations of the BSCs, the beam reconstruction, and light scattering are performed. The fidelity of the reconstructed field to the given one is discussed so as to examine the BSC calculation. A comparison of the ASD method with the quadrature and localized approximation methods leads to the conclusion that the ASD method is much faster than the quadrature method, and it is very powerful for acquiring reliable and accurate results of BSCs, even for far off-axis locations and high ellipticities of the EGB.

Selective far-field addressing of coupled quantum dots in a plasmonic nanocavity.

Plasmon-emitter hybrid nanocavity systems exhibit strong plasmon-exciton interactions at the single-emitter level, showing great potential as testbeds and building blocks for quantum optics and informatics. However, reported experiments involve only one addressable emitting site, which limits their relevance for many fundamental questions and devices involving interactions among emitters. Here we open up this critical degree of freedom by demonstrating selective far-field excitation and detection of two coupled quantum dot emitters in a U-shaped gold nanostructure. The gold nanostructure functions as a nanocavity to enhance emitter interactions and a nanoantenna to make the emitters selectively excitable and detectable. When we selectively excite or detect either emitter, we observe photon emission predominantly from the target emitter with up to 132-fold Purcell-enhanced emission rate, indicating individual addressability and strong plasmon-exciton interactions. Our work represents a step towards a broad class of plasmonic devices that will enable faster, more compact optics, communication and computation.

Beam shape coefficient calculation for a Gaussian beam: localized approximation, quadrature and angular spectrum decomposition methods.

Three methods for calculating the beam shape coefficients (the quadrature, the angular spectrum decomposition (ASD), and the localized approximation methods) are studied. The normalized associated Legendre function is employed in the calculation so as to prevent overflow. The two-dimensional integrations in the quadrature and the ASD methods are developed to the one-dimensional integration to speed up the calculation. The Gaussian beams reconstructed with different methods are compared, showing the difference in the remodeling effects of these methods. The reason for the presence of pseudodistribution in the localized model is given.

Compact formulation of the beam shape coefficients for elliptical Gaussian beam based on localized approximation.

It has been proved that localized approximation (LA) is the most efficient way to evaluate the beam shape coefficients (BSCs) in generalized Lorenz-Mie theory. The BSCs are usually expressed in the form of multiple summations of an infinite series of terms, which is cumbersome to calculate, and the infinite series is frequently slowly convergent. In this paper, we present a compact expression of the BSCs for an elliptical Gaussian beam based on the LA that is more convenient and efficient for numerical computations. A comparison with the integral LA is made, showing the reliability, stability, and efficiency of the presented formulation.

Modified iterative vector similarity measure for particle size analysis based on forward light scattering.

The vector similarity measure (VSM), originally applied to information retrieval, has been recently introduced to analyze particle size distribution (PSD) based on forward light scattering. The VSM technique can predict the PSD with low sensitivity to the experimental errors. However, the simulations and experiments of multi-modal distributed particle systems were not satisfying. In this paper, a modified inverse algorithm is presented to improve the VSM technique. Simulated results and experimental evidence show that with this modification the VSM technique can reconstruct the PSD more efficiently.

Simulation of optical caustics associated with the tertiary rainbow of oblate droplets.

In this paper, a vector ray tracing (VRT) model is used to simulate optical caustic structures, including rainbow and hyperbolic umbilic (HU) fringes, in the tertiary rainbow region of light scattering from oblate spheroidal droplets. In order to apply the optical caustic structures to particle diagnostics, the evolution of rainbow and HU fringes with an increase in the aspect ratio of oblate spheroidal droplets is investigated in detail, and the curvature of rainbow fringes are calculated. Next, on the basis of the VRT model, the location of cusp caustics is calculated and compared with theoretical prediction.

Analysis of light-emission enhancement of low-efficiency quantum dots by plasmonic nano-particle.

In this paper, a nano-pillar array integrated near quantum dots (QDs), which serves as a Purcell cavity as well as a column antenna, is studied in order to enhance the spontaneous emission (SE) rate of low emission efficiency QDs. A systematic analysis for treating the isolated nano-pillar and loose ordered pillar is demonstrated by solving the electromagnetic field equations. As an illustrative example of potential applications, we proposed a new structure that Germanium (Ge) QDs are located in close proximity to the isolated Indium Tin Oxide (ITO) nano-pillar to raise its efficiency. From the results of numerical calculation, it is predicted that ITO pillars with slim (e.g., the radius is 25 nm and the height is 500 nm) and flat morphology (e.g., the radius is 40 nm and the height is 60 nm) exhibit superior enhancement over 20 folds. Finite difference time domain (FDTD) simulation is utilized for demonstrating the distinctive enhancement when QDs radiate at surface plasmonic resonance frequency of ITO nano-pillar. It can be found that the QDs emission enhancement profile accords with our results obtained from numerical analysis.

Application of vector ray tracing to the computation of Möbius shifts for the primary and secondary rainbows.

The Möbius approximation for the primary rainbow and the Können approximation for the secondary rainbow have been modified to yield consistent predictions of the Möbius shift of the top and bottom rainbows, respectively. The applicability ranges of the Möbius and Können approximations are investigated by comparison to vector ray tracing (VRT) simulations. For the primary rainbow, these results indicate that the Möbius approximation is valid for spheroidal water droplets (m=1.333) in the range of aspect ratios 0.98≤a/c≤1.02. For the secondary rainbow, the Können approximation predicts the Möbius shift well for spheroidal water droplets within the range 0.99≤a/c≤1.01. For a spheroidal droplet with side-on incidence, the difference between the approximations and VRT simulations are discussed. Furthermore, the dependence of Möbius shifts on the relative refractive index of droplet is discussed.

Diffraction of a plane wave by an infinitely long circular cylinder or a sphere: solution from Mie theory.

Diffraction of an infinitely long circular cylinder normally illuminated by a plane wave is discussed from the classical Mie theory. A rigorous expression of the diffracted light is obtained, which is simply characterized by a factor (θ/2)/sin(θ/2) and the sinc function sin(αθ)/(αθ). Numerical calculation shows an apparent difference between our results and those from scalar wave diffraction theory, especially in large diffraction angles. The factor (θ/2)/sin(θ/2) is introduced into the diffracted light by a sphere, which leads to an alternative approximation of the diffracted light.

Propagation and modulation of Airy beams through a four-level electromagnetic induced transparency atomic vapor.

We study the propagation properties of an Airy beam through a four-level electromagnetic induced transparency (EIT) atomic vapor. The analytical expression for the Airy beam passing through the ABCD optical system of the EIT vapor is deduced and employed to analyze the propagation characteristics of the beam. It is shown that both the deflection position and the intensity of the Airy beam can be modulated by the Rabi frequency of the control light. Such a tunable optical behavior may have some potential applications in medicine science.

Smoothness-constrained projection method for particle analysis based on forward light scattering.

The iterative projection method, originally proposed by Kaczmarz and Cimmino, was recently applied to particle size analysis with forward light scattering. Modification was made to improve the convergent procedure. However, there are still limitations. It is found that the solutions are oscillatory when the method is applied to a set of underdetermined linear equations without any additional constraints. A new version of the projection method, combined with the constraints of nonnegativity and smoothness, is proposed and is studied in the presence of experimental noise. Compared with the early versions of the projection method, this one shows fast convergence, is more stable against random noise, and is insensitive to particle size distributions.