Evaluation of blackbody radiation emitted by arbitrarily shaped bodies using the source model technique.

Planck's famous blackbody radiation law was derived under the assumption that the dimensions of the radiating body are significantly larger than the radiated wavelengths. What is unique about Planck's formula is the fact that it is independent of the exact loss mechanism and the geometry. Therefore, for a long period of time, it was regarded as a fundamental property of all materials. Deviations from its predictions were attributed to imperfections and referred to as the emissivity of the specific body, a quantity which was always assumed to be smaller than unity. Recent studies showed that the emission spectrum is affected by the geometry of the body and in fact, in a limited frequency range, the emitted spectrum may exceed Planck's prediction provided the typical size of the body is of the same order of magnitude as the emitted wavelength. For the investigation of the blackbody radiation from an arbitrarily shaped body, we developed a code which incorporates the fluctuation-dissipation theorem (FDT) and the source model technique (SMT). The former determines the correlation between the quasi-microscopic current densities in the body and the latter is used to solve the electromagnetic problem numerically. In this study we present the essence of combining the two concepts. We verify the validity of our code by comparing its results obtained for the case of a sphere against analytic results and discuss how the accuracy of the solution is assessed in the general case. Finally, we illustrate several configurations in which the emitted spectrum exceeds Planck's prediction as well as cases in which the geometrical resonances of the body are revealed.

Field enhancement and resonance phenomena in complex three-dimensional nanoparticles: efficient computation using the source-model technique.

We present a semi-analytical method for computing the electromagnetic field in and around 3D nanoparticles (NP) of complex shape and demonstrate its power via concrete examples of plasmonic NPs that have nonsymmetrical shapes and surface areas with very small radii of curvature. In particular, we show the three axial resonances of a 3D cashew-nut and the broadband response of peanut-shell NPs. The method employs the source-model technique along with a newly developed intricate source distributing algorithm based on the surface curvature. The method is simple and can outperform finite-difference time domain and finite-element-based software tools in both its efficiency and accuracy.

Absorption enhancement by matching the cross-section of plasmonic nanowires to the field structure of tightly focused beams.

Nanostructured materials, designed for enhanced light absorption, are receiving increased scientific and technological interest. In this paper we propose a physical criterion for designing the cross-sectional shape of plasmonic nanowires for improved absorption of a given tightly focused illumination. The idea is to design a shape which increases the matching between the nanowire plasmon resonance field and the incident field. As examples, we design nanowire shapes for two illumination cases: a tightly focused plane wave and a tightly focused beam containing a line singularity. We show that properly shaped and positioned silver nanowires that occupy a relatively small portion of the beam-waist area can absorb up to 65% of the total power of the incident beam.

Source-model technique analysis of electromagnetic scattering by surface grooves and slits.

A computational tool, based on the source-model technique (SMT), for analysis of electromagnetic wave scattering by surface grooves and slits is presented. The idea is to use a superposition of the solution of the unperturbed problem and local corrections in the groove/slit region (the grooves and slits are treated as perturbations). In this manner, the solution is obtained in a much faster way than solving the original problem. The proposed solution is applied to problems of grooves and slits in otherwise planar or periodic surfaces. Grooves and slits of various shapes, both smooth ones as well as ones with edges, empty or filled with dielectric material, are considered. The obtained results are verified against previously published data.

A Source-Model Technique for analysis of wave guiding along chains of metallic nanowires in layered media.

A method for determining the modes that can be guided along infinite chains of metallic nanowires when they are embedded, as in most realistic set-ups, in layered media is presented. The method is based on a rigorous full-wave frequency-domain Source-Model Technique (SMT). The method allows efficient determination of the complex propagation constants and the surface-plasmon type modal fields. Sample results are presented for silver nanowires with circular and triangle-like cross-sections lying in an air-Si-glass layered structure.

Plasmonic resonance scattering from silver nanowire illuminated by tightly focused singular beam.

We investigate scattering features of tightly focused singular beams by placing a cylindrical nanowire in the vicinity of a line phase singularity. Applying an illumination wavelength corresponding to silver cylinder plasmonic resonance, we compare the scattering response with that of a perfect conductor. The rigorous modeling employs a 2D version of the Richards-Wolf focusing method and the source model technique. It is found that a cylinder with a plasmonic resonance produces a strong scattering response by deflecting the power flow toward the optical singularity region, where otherwise the power approaches zero.

Rigorous modal analysis of metallic nanowire chains.

Nanowire chains (NCs) are analyzed by use of a rigorous, full-wave, Source-Model Technique (SMT). The technique employs a proper periodic Green's function which converges regardless of whether the structure is lossless or lossy. By use of this Green's function, it is possible to determine the complex propagation constants of the NC modes directly and accurately, as solutions of a dispersion equation. To demonstrate the method, dispersion curves and mode profiles for a few NCs are calculated.

Time-domain analysis of bandgap characteristics of two-dimensional periodic structures by use of a source-model technique.

We introduce a time-domain source-model technique for analysis of two-dimensional, transverse-magnetic, plane-wave scattering by a photonic crystal slab composed of a finite number of identical layers, each comprising a linear periodic array of dielectric cylinders. The proposed technique takes advantage of the periodicity of the slab by solving the problem within a unit cell of the periodic structure. A spectral analysis of the temporal behavior of the fields scattered by the slab shows a clear agreement between frequency bands where the spectral density of the transmitted energy is low and the bandgaps of the corresponding two-dimensionally infinite periodic structure. The effect of the bandwidth of the incident pulse and its center frequency on the manner it is transmitted through and reflected by the slab is studied via numerical examples.

Efficient and spurious-free integral-equation-based optical waveguide mode solver.

Modal analysis of waveguides and resonators by integra-lequation formulations can be hindered by the existence of spurious solutions. In this paper, spurious solutions are shown to be eliminated by introduction of a Rayleigh-quotient based matrix singularity measure. Once the spurious solutions are eliminated, the true modes may be determined efficiently and reliably, even in the presence of degeneracy, by an adaptive search algorithm. Analysis examples that demonstrate the efficacy of the method include an elliptical dielectric waveguide, two unequal touching dielectric cylinders, a plasmonic waveguide, and a realistic micro-structured optical fiber. A freely downloadable version of an optical waveguide mode solver based on this article is available.

Comparison of different methods for rigorous modeling of photonic crystal fibers.

We present a summary of the simulation exercise carried out within the EC Cost Action P11 on the rigorous modeling of photonic crystal fiber (PCF) with an elliptically deformed core and noncircular air holes with a high fill factor. The aim of the exercise is to calculate using different numerical methods and to compare several fiber characteristics, such as the spectral dependence of the phase and the group effective indices, the birefringence, the group velocity dispersion and the confinement losses. The simulations are performed using four rigorous approaches: the finite element method (FEM), the source model technique (SMT), the plane wave method (PWM), and the localized function method (LFM). Furthermore, we consider a simplified equivalent fiber method (EFM), in which the real structure of the holey fiber is replaced by an equivalent step index waveguide composed of an elliptical glass core surrounded by air cladding. All these methods are shown to converge well and to provide highly consistent estimations of the PCF characteristics. Qualitative arguments based on the general properties of the wave equation are applied to explain the physical mechanisms one can utilize to tailor the propagation characteristics of nonlinear PCFs.

Modal dynamics in hollow-core photonic-crystal fibers with elliptical veins.

Modal characteristics of hollow-core photonic-crystal fibers with elliptical veins are studied by use of a recently proposed numerical method. The dynamic behavior of bandgap guided modes, as the wavelength and aspect ratio are varied, is shown to include zero-crossings of the birefringence, polarization dependent radiation losses, and deformation of the fundamental mode.

Analysis of arbitrary defects in photonic crystals by use of the source-model technique.

A novel method derived from the source-model technique is presented to solve the problem of scattering of an electromagnetic plane wave by a two-dimensional photonic crystal slab that contains an arbitrary defect (perturbation). In this method, the electromagnetic fields in the perturbed problem are expressed in terms of the field due to the periodic currents obtained from a solution of the corresponding unperturbed problem plus the field due to yet-to-be-determined correction current sources placed in the vicinity of the perturbation. Appropriate error measures are suggested, and a few representative structures are presented and analyzed to demonstrate the versatility of the proposed method and to provide physical insight into waveguiding and defect coupling mechanisms typical of finite-thickness photonic crystal slabs.

Analysis of strictly bound modes in photonic crystal fibers by use of a source-model technique.

We describe a source-model technique for the analysis of the strictly bound modes propagating in photonic crystal fibers that have a finite photonic bandgap crystal cladding and are surrounded by an air jacket. In this model the field is simulated by a superposition of fields of fictitious electric and magnetic current filaments, suitably placed near the media interfaces of the fiber. A simple point-matching procedure is subsequently used to enforce the continuity conditions across the interfaces, leading to a homogeneous matrix equation. Nontrivial solutions to this equation yield the mode field patterns and propagation constants. As an example, we analyze a hollow-core photonic crystal fiber. Symmetry characteristics of the modes are discussed and exploited to reduce the computational burden.

Wavelet-based analysis of transient electromagnetic wave propagation in photonic crystals.

Photonic crystals and optical bandgap structures, which facilitate high-precision control of electromagnetic-field propagation, are gaining ever-increasing attention in both scientific and commercial applications. One common photonic device is the distributed Bragg reflector (DBR), which exhibits high reflectivity at certain frequencies. Analysis of the transient interaction of an electromagnetic pulse with such a device can be formulated in terms of the time-domain volume integral equation and, in turn, solved numerically with the method of moments. Owing to the frequency-dependent reflectivity of such devices, the extent of field penetration into deep layers of the device will be different depending on the frequency content of the impinging pulse. We show how this phenomenon can be exploited to reduce the number of basis functions needed for the solution. To this end, we use spatiotemporal wavelet basis functions, which possess the multiresolution property in both spatial and temporal domains. To select the dominant functions in the solution, we use an iterative impedance matrix compression (IMC) procedure, which gradually constructs and solves a compressed version of the matrix equation until the desired degree of accuracy has been achieved. Results show that when the electromagnetic pulse is reflected, the transient IMC omits basis functions defined over the last layers of the DBR, as anticipated.

Analysis of bandgap characteristics of two-dimensional periodic structures by using the source-model technique.

We introduce a solution based on the source-model technique for periodic structures for the problem of electromagnetic scattering by a two-dimensional photonic bandgap crystal slab illuminated by a transverse-magnetic plane wave. The proposed technique takes advantage of the periodicity of the slab by solving the problem within the unit cell of the periodic structure. The results imply the existence of a frequency bandgap and provide a valuable insight into the relationship between the dimensions of a finite periodic structure and its frequency bandgap characteristics. A comparison shows a discrepancy between the frequency bandgap obtained for a very thick slab and the bandgap obtained by solving the corresponding two-dimensionally infinite periodic structure. The final part of the paper is devoted to explaining in detail this apparent discrepancy.