Point Dipole Source Research Articles

Renormalization of photon dyadic Green function by finite element method and its applications in the study of spontaneous emission rate and energy level shift

The spontaneous emission rate and the energy level shift of a quantum dot in any micro-nanostructures can be expressed by the classical dyadic Green's function. However, the real part of the dyadic Green's function is divergent, when the source point and the field point are at the same position. This leads to an unphysical divergent level shift. Theoretically, the dyadic Green's function can be decomposed into a homogeneous part and a scattering part. Traditionally, the homogeneous field contribution is introduced into the definition of the transition frequency and the only need is to consider the effect of the scattering part which is non-divergent. Another renormalization method is to average the Green tensor over the volume of the quantum dot. In this work, a finite element method is proposed to address this problem. The renormalized dyadic Green function is expressed by the averaged radiation field of a point dipole source over the quantum dot volume. For the vacuum case, numerical results of the renormalized Green tensor agree well with the analytical ones. For the nanosphere model, the renormalized scattering Green tensor, which is the difference between the renormalized Green tensor and the analytical renormalized one in homogeneous space, agrees well with the analytical scattering Green tensor in the center of the quantum dot. Both of the above models clearly demonstrate the validity and accuracy of our method. Compared with the previous scattering Green function method where two different finite element runs are needed for one frequency point, our renormalization method just needs one single run. This greatly reduces the computation burden. Applying the theory to a gap plasmonic nano-cavity, we find extremely large modifications for the spontaneous emission rate and the energy level shift which are independent of the size of the quantum dot. For frequency around the higher order mode of the nano-cavity, spontaneous emission enhancement is about Г/Г0 2.02106 and the energy level shift is about △ 1000 meV for a dipole moment 24D. These findings are instructive in the fields of quantum light-matter interactions.

Plasmon-activated intermolecular nonradiative energy transfer in spherical nanoreactors

The effect of silver nanoparticles upon intermolecular radiationless energy transfer between the dye molecules confined in the nanopores of silica was studied both experimentally and by theoretical modeling. Silver nanoparticles were synthesized directly inside the nanopores of silica from AgNO3 using aqueous solution of NaBH4 as a reducing agent. Silica samples with or without nanoparticles were soaked with ethanol solutions of dyes, Acridine Orange (AO) as a donor of electronic excitation energy, and Nile Blue as the acceptor. Studies of fluorescence spectra of samples at different acceptor concentration have shown that addition of nanoparticles decreases the relative quantum yield of fluorescence of donor accompanied by the increase of that of acceptor. This was interpreted as a plasmonic contribution to the rate of nonradiative energy transfer. A theoretical model was proposed, which describes the quenching kinetics of the excited donor molecules in the presence of accepting molecules and metal nanoparticles in a polarized spherical nanopore, as well as the changes in spectral bands of the system. Besides, simulation of the interaction of a point dipole source field with plasmonic silver nanoparticles in a silica cavity was carried out using finite-difference time-domain (FDTD) method. The results of field calculation with the two models are in a good qualitative agreement between each other and predict the regions of local electric field enhancement in the gap between silver nanoparticles and walls of pores that is supposed to account for the experimentally observed increased efficiency of the nonradiative intermolecular singlet–singlet energy transfer in porous silica matrix with silver nanoparticles. The results obtained can be of interest for FRET SNOM.

Scattering of an Electromagnetic Surface Wave from a Hertzian Dipole by the Edge of an Impedance Wedge

In this paper, extensions of the results obtained in our previous paper devoted to the diffraction of waves from a Hertzian dipole (point source) located over an impedance wedge are presented. The surface waves components and the edge wave, produced by a surface wave from a point source coming to the edge, are discussed. The geometric optics laws for the surface waves reflected by and transmitted across the edge are also addressed.

Nanoscale 2.5-dimensional surface patterning with plasmonic lithography

We report an extension of plasmonic lithography to nanoscale 2.5-dimensional (2.5D) surface patterning. To obtain the impulse response of a plasmonic lithography system, we described the field distribution of a point dipole source generated by a metallic ridge aperture with a theoretical model using the concepts of quasi-spherical waves and surface plasmon–polaritons. We performed deconvolution to construct an exposure map of a target shape for patterning. For practical applications, we fabricated several nanoscale and microscale structures, such as a cone, microlens array, nanoneedle, and a multiscale structure using the plasmonic lithography system. We verified the possibility of applying plasmonic lithography to multiscale structuring from a few tens of nanometres to a few micrometres in the lateral dimension. We obtained a root-mean-square error of 4.7 nm between the target shape and the patterned shape, and a surface roughness of 11.5 nm.

Modeling super-resolution SERS using a T-matrix method to elucidate molecule-nanoparticle coupling and the origins of localization errors.

A computational method to model diffraction-limited images from super-resolution surface-enhanced Raman scattering microscopy is introduced. Despite significant experimental progress in plasmon-based super-resolution imaging, theoretical predictions of the diffraction limited images remain a challenge. The method is used to calculate localization errors and image intensities for a single spherical gold nanoparticle-molecule system. The light scattering is calculated using a modification of generalized Mie (T-matrix) theory with a point dipole source and diffraction limited images are calculated using vectorial diffraction theory. The calculation produces the multipole expansion for each emitter and the coherent superposition of all fields. Imaging the constituent fields in addition to the total field provides new insight into the strong coupling between the molecule and the nanoparticle. Regardless of whether the molecular dipole moment is oriented parallel or perpendicular to the nanoparticle surface, the anisotropic excitation distorts the center of the nanoparticle as measured by the point spread function by approximately fifty percent of the particle radius toward to the molecule. Inspection of the nanoparticle multipoles reveals that distortion arises from a weak quadrupole resonance interfering with the dipole field in the nanoparticle. When the nanoparticle-molecule fields are in-phase, the distorted nanoparticle field dominates the observed image. When out-of-phase, the nanoparticle and molecule are of comparable intensity and interference between the two emitters dominates the observed image. The method is also applied to different wavelengths and particle radii. At off-resonant wavelengths, the method predicts images closer to the molecule not because of relative intensities but because of greater distortion in the nanoparticle. The method is a promising approach to improving the understanding of plasmon-enhanced super-resolution experiments.

Validation of Frequency-Domain Method to Compute Noise Radiated from Rotating Source and Scattered by Surface

This paper presents a frequency-domain method to compute noise radiated from the rotating source and scattered by the surface, where both the acoustic pressure and acoustic velocity of the noise radiated from the rotating thickness and loading sources are computed with the frequency-domain numerical method and the surface scattering effect is taken into account by employing the frequency-domain equivalent source method. To validate the above method, the analytical solutions for noise radiated from the rotating monopole and dipole point sources and scattered by a rigid sphere are proposed. A good agreement between the numerical results and the analytical solutions has been achieved. Moreover, the Isom noise consistency test is also carried out to validate the frequency-domain numerical method. The analysis of the computational error is investigated as well.

Analytical Acoustic Power Spectrum Formulations for Rotating Monopole and Dipole Point Sources

Analytical acoustic power spectrum formulations for the rotating monopole and dipole point sources are proposed by employing the spherical harmonic series expansion method. Both the analytical acoustic power spectra and the overall acoustic power show a good agreement with the results obtained from other methods. A nondimensional acoustic power ratio (APR) is employed to investigate the effects of the rotational Mach number, the direction of the dipole source, and the number of sources on the acoustic power output.

All-dielectric nanoantennas for unidirectional excitation of electromagnetic guided modes

Engineering of intensity and direction of radiation from a single quantum emitter by means of structuring of their environment at the nanoscale is at the cornerstone of modern nanophotonics. Systems exhibiting spin–orbit coupling of light are of particular interest in this context. In this letter, we have demonstrated that the asymmetrical excitation of a high-index subwavelength (λ/3−λ/2) dielectric nanoparticle by a point dipole source located in a notch at its surface results in formation of a chiral near field, which is similar to that of a circularly polarized dipole or quadrupole. Using numerical simulations, we have shown that this effect is the result of a higher multipole (quadrupole and octupole) modes excitation within the nanoparticle. We have applied this effect for unidirectional excitation of dielectric waveguide and surface plasmon-polariton modes. We have achieved the value of front–to–back ratio up to 5.5 for dielectric waveguide and to 7.5 for the plasmonic one. Our results are important for the integrated nanophotonics and quantum information processing systems.

Analytical solution for sound radiated from the rotating point source in uniform subsonic axial flow

The paper presents an analytical solution for sound radiated from the rotating monopole and dipole point sources in uniform subsonic axial flow by employing the spherical harmonic series expansion method. The analytical results obtained from the present series expansion formulations have a good agreement with the numerical results obtained from the time-domain and frequency-domain numerical methods. The results also indicate that the effect of the freestream Mach number on the directivity pattern is various for different types of the rotating sources.

Image Dipole Method for the Beaming of Plasmons from Point Sources

A point dipole source models the electrical excitation of surface plasmon polaritons (SPPs), and is promising as a compact source for the beaming of plasmons in optical nanocircuits. However, conventional design approaches rely on iterative numerical simulations to achieve beaming from dipole sources, and they consume significant computing resources. Here, we introduce a universal semianalytical approach to solve the reflection of dipole-excited SPPs from the edge of a metal film by developing the image dipole method for SPPs. This approach achieves the directional propagation of SPPs through a multielement dipole array formed by a single dipole source and its reflections. Doing so mitigates the challenges in integrating and achieving coherent excitation among independently driven electrical sources. In addition, we provide design parameters for tuning the amplitude and phase of the image dipoles to engineer the directivity of SPP propagation. The configurations discussed can be readily implemented in the...

Nanoplasmonic Enhancement of Molecular Fluorescence: Theory and Numerical Modeling

Significant emission enhancement of fluorescent molecules placed in close proximity to metallic nanoparticles has been observed. Recent advances in nanotechnology have enabled the introduction of plasmon-enhanced molecular fluorescence in various applications. Comprehensive theory of the physics behind this enhancement mechanism has also been developed. However, most of the existing analytical tools are applicable mainly for particular nanoparticles in either spherical or ellipsoidal shapes. Since the plasmonic enhancement of molecular fluorescence is dependent on various parameters such as shape, size, and distribution of nearby nanoparticles, it is crucial to have more powerful analysis tools to be able to handle any arbitrary nanoparticles. For this purpose, the 3D finite element method, which is a commonly used technique for arbitrary structures, is implemented and reported in this paper. The emitting molecule is assumed to be an electric dipole point source. The fluorescence enhancement factor is described in term of a local electric field-enhancement factor and the quantum yield of the system. The model is validated by comparison to the approximate quasistatic model and the exact Mie theory. It provides more accurate results than those of the quasistatic model, which makes it become the powerful numerical approach for investigation of arbitrary nanostructure influence on molecular fluorescence. It is then applied for investigating the emission characteristics of the fluorescent molecule when it is placed in the vicinity of more complicated structures including dimers and chains of coupled nanoparticles. It is found that these coupled nanoparticle configurations provide stronger fluorescence enhancement than the single nanoparticle of the same particle size when the inter-particle gap is small. It is attributed to the higher electric-field enhancement in the inter-particle gap region via strong surface plasmon coupling effects of two neighboring nanoparticles.

Computation of instantaneous and time-averaged active acoustic intensity field around rotating source

A vector aeroacoustics method is developed to analyze the acoustic energy flow path from the rotating source. In this method, the instantaneous and time-averaged active acoustic intensity vectors are evaluated from the time-domain and frequency-domain acoustic pressure and acoustic velocity formulations, respectively. With the above method, the acoustic intensity vectors and the acoustic energy streamlines are visualized to investigate the propagation feature of the noise radiated from the monopole and dipole point sources and the rotor in subsonic rotation. The result reveals that a portion of the acoustic energy spirals many circles before moving towards the far field, and another portion of the acoustic energy firstly flows inward along the radial direction and then propagates along the axial direction. Further, an acoustic black hole exists in the plane of source rotation, from which the acoustic energy cannot escape once the acoustic energy flows into it. Moreover, by visualizing the acoustic intensity field around the rotating sources, the acoustic-absorption performance of the acoustic liner built in the casing and centerbody is discussed.

Direct Evaluation of Acoustic-Intensity Vector Field Around an Impedance Scattering Body

The paper presents a direct method for predicting the acoustic-intensity vector field around an impedance scattering body. The results obtained from the present method, combined with the equivalent-source method, graphically display the acoustic-intensity vector field around the scattering body, and reveal the effect of surface impedance on the absorption of the acoustic energy. Three test cases (i.e., the plane wave scattered by a rigid sphere, and the sound of the stationary monopole and dipole point sources scattered by an impedance sphere) are carried out to validate the method. From the analysis of the computational error, it is suggested that the maximum length of the surface element should be less than one-tenth of the wavelength to ensure that the relative error is less than 3%.

Two Types of Frequency-Domain Acoustic-Velocity Formulations for Rotating Thickness and Loading Sources

This paper presents two types of frequency-domain acoustic-velocity formulations for the rotating thickness and loading sources. The acoustic-velocity components of the noise radiated from the rotating monopole and dipole point sources are computed with the two types of frequency-domain formulations and the time-domain acoustic-velocity formulation V1A of Ghorbaniasl et al. (“Acoustic Velocity Formulation for Sources in Arbitrary Motion,” AIAA Journal, Vol. 51, No. 3, 2013, pp. 632–642), respectively. The computational results have a good agreement between each other. Moreover, the Isom noise consistency test for a rotor is also carried out to validate the proposed frequency-domain acoustic-velocity formulations.

Frequency-domain acoustic pressure formulation for rotating source in uniform subsonic inflow with arbitrary direction

Abstract This paper presents a frequency-domain formulation for predicting noise radiated from the rotating thickness and loading sources in uniform subsonic inflow with arbitrary direction. The proposed frequency-domain formulation is an extension of the recently published frequency-domain formulation for the stationary medium. It avoids the singular integral and numerical interpolation problems encountered in the time-domain numerical method. Three test cases, i.e., noise radiation from the rotating monopole and dipole point sources and the Isom thickness noise of a transonic rotor in the subsonic uniform flow, have been carried out to validate the proposed formulation. Both the acoustic pressure spectrum and directivity pattern computed with the present frequency-domain method are in good agreement with those obtained from the time-domain method, thus validating the correctness of the present formulation. Furthermore, the numerical results indicate that the frequency-domain formulation is suitable for tonal noise prediction, while it is inefficient for broadband noise prediction.

Frequency-domain model of tonal blade thickness and loading noise

A tonal thickness noise and loading noise model of rotating blades has been developed as an extension of the exact frequency-domain solutions for rotating monopole and dipole point sources. The present model has two advantages over the previous methods and models for noise prediction. The first is the unified expression for sources in subsonic and supersonic rotation even at rest. The second is that the present model has no limit on the location of the observer and no interpolation error. Two test cases are carried out to validate the present model and emphasize its advantage at the noise prediction for sources in supersonic rotation. Moreover, as a specified application of the present model for the rotating blades whose tip radius is acoustically compact, acoustic energy distribution at different frequencies and in different directions is analyzed. Result shows that the acoustic energy of acoustically compact rotating blades is mainly concentrated at the source frequency while propagating along the axial direction, leaving the rest propagating along the radial direction at the other frequencies.

Kinetic Theory of Radiation from a Point Monochromatic Dipole Source in a Moving Magnetized Plasma

UDC 533.951 We consider the problem of radiation from a point monochromatic dipole source in the warm electron plasma which is moving with constant velocity along a strong magnetic field. The diagonal permittivity tensor calculated for the magnetized plasma with the Maxwell electron velocity distribution is used to describe the electromagnetic properties of the plasma. The dispersion relation is analyzed numerically and expressions for the field amplitudes in the wave zone are derived. The kinetic description is shown to be necessary for finding the amplitudes of waves whose phase velocities are close to the mean velocity of the plasma motion.

Comparison of the time-domain electromagnetic field from an infinitesimal point charge and dipole source

An electromagnetic field is generated through the accelerating movement of two equal but opposite charges of a single dipole. An electromagnetic field can also be generated by a time-varying infinitesimal point charge. In this study, a comparison between the electromagnetic fields of an infinitesimal point charge and a dipole has been presented. First, the time-domain potential function of a point source in a 3D conductive medium is derived. Then the electric and magnetic fields in a 3D homogeneous lossless space are derived via the relation between the potential and field. The field differences between the infinitesimal point charge and the dipole in the step-off time, far-source, and near-source zones are analyzed, and the accuracy of the solutions from these sources is investigated. It is also shown that the field of the infinitesimal point charge in the near-source zone is different from that of the dipole, whereas the far-source zone fields of these two sources are identical. The comparison of real and simulated data shows that the infinitesimal point charge represents the real source better than the dipole source.

On Sound Generation in Cylindrical Flow Ducts with Non-Uniform Wall Impedance

The use of acoustic liners is a common means of noise reduction in jet engine exhausts. The quest for more effective sound absorption mechanisms in cylindrical ducts has led to the consideration of non-uniform liners, with impedance varying circumferentially, axially, or in both directions. The present paper is based on the theory of mode coupling in a non-uniformly lined cylindrical duct and considers the complementary problem of generation of sound or excitation of coupled modes by a source distribution. The sound field due to an arbitrary source distribution is obtained as a superposition of eigenfunctions corresponding to complex eigenvalues for the radial wavenumbers and natural frequencies taking into account that the radial, axial and azimuthal modes are coupled by the non-uniform wall impedance, and including resonant and non-resonant cases. The waveforms are illustrated for point monopole, dipole and quadrupole sources and a continuous monopole distribution. It is shown that a non-uniform liner provides a greater attenuation than a uniform liner with the same average impedance if it is ‘well-matched’ to the sound field, that is, if it has higher impedance at the peaks and lower at the nodes of the standing modes.

Unidirectional Side Scattering of Light by a Single-Element Nanoantenna

Unidirectional side scattering of light by a single-element plasmonic nanoantenna is demonstrated using full-field simulations and back focal plane measurements. We show that the phase and amplitude matching that occurs at the Fano interference between two localized surface plasmon modes in a V-shaped nanoparticle lies at the origin of this effect. A detailed analysis of the V-antenna modeled as a system of two coherent point-dipole sources elucidates the mechanisms that give rise to a tunable experimental directivity as large as 15 dB. The understanding of Fano-based directional scattering opens a way to develop new directional optical antennas for subwavelength color routing and self-referenced directional sensing. In addition, the directionality of these nanoantennas can increase the detection efficiency of fluorescence and surface enhanced Raman scattering.