Mie Modes Research Articles

Effect of dielectric permittivity variation in the transmission spectra of non-compact 2D-arrays of dielectric spheres

Transmission spectra of two dimensional photonic crystals made of arrays of dielectric spheres are affected by the sphere dielectric permittivity. In this paper we present a systematic study of this influence for different compactness of the lattices. The transmission spectra were simulated by finite-different time-domain method. The system studied is a plane of spheres of dielectric permittivity e (ranging from 2 to 9) arranged in triangular symmetry with varying compactness. Compactness is characterized as the ratio (R) of the sphere diameter (Φ) over the lattice period (Λ) and is considered from R = 1, close packed samples, to R = 0, 2. The transmission spectra of these samples are calculated for normal incident radiation of wavelengths in the interval extending from 0.8 to 5 times the sphere diameter. The sphere arrays present a number of resonant modes that appear as dips in the transmission spectra. The frequency position of the resonances is discussed in relation to those of the Mie modes of the is...

Collective Excitations of Finite‐Temperature Nano Plasmas

AbstractElectron density fluctuations as well as current density correlations are considered for excited nano plasmas. Calculations are performed by classical MD simulations at high temperatures for expanding nearly spherical clusters of laser irradiated sodium atoms. The resonance structures observed in the frequency spectrum of the bi‐local correlation functions are analyzed. Mie modes and volume plasmon type excitations are observed as well as breathing modes. We investigate the relation between the bi‐local correlation functions of the electron density fluctuations and current density via the equation of continuity.The collective excitations are of significance for the dielectric function and further properties such as the photo absorption coefficients. Results are presented for an exemplarily taken set of parameter values of the nano plasma (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

ELECTRIC-FIELD DISTRIBUTIONS OF DIELECTRIC SINGLE LAYERS OF SPHERES WITH DIFFERENT COMPACTNESS

The internal electric-fleld distribution from single layers of dielectric spheres with high refractive index (n = 2:65) has been analyzed for a number of difierent compactness cases by FDTD (Finite- Difierence Time-Domain) method. The fleld distributions from the transmission spectra were compared with the internal electric-fleld distribution of the Mie modes of an isolated sphere. In general, the agreement is very good in almost all cases studied. The results show that TE and TM Mie modes are the origin of the resonances in the transmission spectra of the single layers. The resonances of the monolayer attributed to TE11 and TM11 Mie modes are only excited for compactness values lower than 0.38, suggesting a dependence of periodical arrangement efiects for these modes. Moreover, the fleld distribution corresponding to some of the dips in the spectrum cannot be directly attributed to Mie modes (TE21). The result indicates these are formed by degenerated or weakly coupled Mie modes induced by the periodic structure.

Disorder effect in the transmission spectra of a noncompact single layer of dielectric spheres derived from microwave spectroscopy

Single layers of dielectric spheres are an interesting system to study from the fundamental and applied points of view. In this paper we present a systematic study of the influence of structural disorder on the transmission spectra of arrangements of spheres of different compactness. Glass sphere (ε=7) planes were built and their transmission spectra in the microwave range measured. Transmission behavior of this system is highly tolerant to disorder. Even in completely disordered arrangements, there is a highly rejected band with the dips of the spectrum observable. These results suggest that the collective modes of the sphere planes are formed by weakly coupled Mie modes of the individual spheres, and this coupling is governed by the average distance among the spheres. Disorder tolerance allows simpler fabrication procedures where the position of the spheres does not need to be precisely controlled.

Porous silicon microspheres: synthesis, characterization and application to photonic microcavities

Porous silicon microspheres have been synthesized by chemical vapour deposition of disilane gas. Their spectral signatures are similar to those of electrochemically grown porous silicon, in particular they yield photoluminescence and they show an oxidation behaviour upon their exposure to the open air. The particles are highly spherical and poly-disperse in size with diameters of approximately 0.5 to 5 micrometres, and they have a very smooth surface. Because of these reasons they work as optical microcavities with well defined resonating Mie modes. These modes have been identified in the near-infrared range. They blue-shift considerably whenever the microspheres are in contact with air because of the aforementioned oxidation process.

Photonic band effects in three dimensional lattices of macroscopic-sized dielectric spheres derived from microwave transmission spectroscopy

Several structures of dielectric spheres (glass) have been arranged and the electromagnetic absorption properties of the resulting materials have been measured in the microwave domain. In all cases strong rejected bands are present while keeping nearly transparent for other frequencies. The physical origin of the observed bands is studied by recording the spectra of the materials as they are grown layer by layer. These data show the appearance of a peak attributed to Bragg scattering generated by the spheres layers. Besides, higher order bands are developed over the resonances that are found even in the single layer of spheres. These are caused by a complex interaction of isolated sphere Mie modes and Bragg scattering in planes perpendicular (or nearly) to the incident radiation.

Evolution of the electromagnetic modes of a single layer of dielectric spheres with compactness

Although lattices of microspheres are considered very interesting forms of photonic crystals both from the fundamental and applied points of view, some fundamental aspects of their behavior are not well understood. Here, we present an experimental study of the frequency variations in the resonant modes of a single layer of spheres with its compactness. Transmission spectra of single layers of dielectric spheres (with a dielectric permittivity of 7.0) were measured for different compactness values, and also simulated by finite-integration time-domain method. The results were gathered in a map of resonant modes of the layer ranging from the compact case to very diluted ones and compared with the resonance values of well known phenomena as the Bragg scattering value and the isolated sphere Mie modes. This comparison allowed establishing different regions dominated by individual effects, being the clearer the tendency to the Bragg scattering limit for low compact layers.

Resonant light transport through Mie modes in photonic glasses

We present an optical characterization of photonic glasses, composed of randomly arranged, monodisperse dielectric spheres packed at high filling fractions. We provide a detailed optical study of the resonant behavior of diffuse light transport through such systems. By means of independent static and dynamic measurements, we show resonances in the transport mean free path, diffusion constant, and also energy velocity of light. We also show that the main transport parameters can be controlled by varying the sphere diameter.

Quantum electromagnetic fields in the presence of adielectric microsphere

A general quantization scheme of the electromagnetic (EM) fields,including the near-field, of a dielectric material is presented.By expanding the classical EM fields in terms of orthonormalmodes, the Lagrangian is expressed as a sum of the Lagrangiansof the independent harmonic oscillators. For a dielectricsphere, as an example, two possible modes satisfying the boundaryconditions, as well as the orthonormality conditions, areexplicitly obtained: spherical modes and Mie modes. Using thesemodes, the EM fields are quantized and the transformationbetween two one-photon states having different modes is alsodiscussed. We apply our results to calculate the expectationvalue of the quantum momentum-density operator for a one-photonstate and show that it is equivalent to the classical Poyntingvector. Our rigorous results may be useful in the study of thequantum optical properties of the EM near-fields of adielectric microsphere of sub-wavelength size.

Sum rules for surface plasmon frequencies

Surfaces exhibit spatially localized collective electronic excitations. The Mie modes of a particulate is one well-known example. We derive sum rules which (1) relate the surface mode frequencies of complementary systems like a sphere and a void and (2) relate the surface mode frequencies of a system with several interfaces to the ones for the individual surfaces. Our approach is of general nature since the results are based on properties of the Poisson equation and should be of interest for spectroscopies of matter in different fields of physics, in particular for scanning transmission electron microscopy.

Splitting of high-Q Mie modes induced by light backscattering in silica microspheres

We have observed that very high-Q Mie resonances in silica microspheres are split into doublets. This splitting is attributed to internal backscattering that couples the two degenerate whispering-gallery modes propagating in opposite directions along the sphere equator. We have studied this doublet structure by high-resolution spectroscopy. Time-decay measurements have also been performed and show a beat note corresponding to the coupling rate between the clockwise and counterclockwise modes. A simple model of coupled oscillators describes our data well, and the backscattering efficiency that we measure is consistent with what is observed in optical fibers.