Maxwell optical properties

Hornyak, G. L., Patrissi, C. J., and Martin, C. R., Fabrication, characterization, and optical properties of gold nanoparticle/porous alumina composites the nonscattering Maxwell-Garnett. J. Phys Chem. 101,1548 (1997). 

Inhomogeneous particles. For particles composed of a matrix and inclusions one approach for calculating optical properties is to assume an average dielectric coefficient (e) for the composed particle. A number of so-called mixing rules have been proposed a frequently used one is the Maxwell-Gamett mixing rule (cf. Bohren Huffman 1983). For a matrix with dielectric coefficient em, and a number of different kinds of inclusions with dielectric coefficients ej and volume fractions f) one uses... 

In photonic materials, the band gap is determined by geometric arrangement of a dielectric material. The underlying principle of how photonic materials work is best explained using Maxwell s equations (Joannopoulos et al., 1995). Once again, the central importance of Maxwell s equations is confronted when optical properties of materials are discussed. In photonic materials, a periodic stmcture is produced in one, two, or three dimensions. The periodic property is a dielectric constant. A trivial macroscopic onedimensional example would be a collection of individual microscope shdes separated by layers of Saran Wrap . This would produce a one-dimensional modulation in the... 

A basic waveguide structure, which is sketched in Fig. 1, is composed of a guiding layer surrounded by two semi-infinite media of lower refractive indices. The optical properties of the stmcture are described by the waveguiding layer refractive index Hsf, and thickness t, and by the refractive indices of the two surrounding semi-infinite media, here called (for cover) and (for substrate). Application of Maxwell s equations and boundary conditions leads to the well-known waveguide dispersion equation [6] ... 

G6rardy, J. M., and Ausloos, M. (1982). Absorption spectrum of clusters of spheres from the general solution of Maxwell s equations. II. Optical properties of aggregated metal spheres. Phys. Rev. B 25 4204- 229. 

Maxwell DJ, Emory SR, Me S (2001) Nanostructured thin-film materials with surface-enhanced optical properties. Chem Mater 13 1082-1088... 

Metals form a class of solids with characteristic macroscopic properties. They are ductile, have a silver-white luster, and they conduct electricity and heat remarkably well. An early, but still relevant microscopic model aimed at explaining the electrical conductivity, heat conductivity, and optical properties was proposed by Drude [10]. His model incorporates two important successes of modem science the discovery of the electron in 1887 by J. J. Thomson, and the molecular kinetic gas theory put forward by Boltzmann and Maxwell in the second half of the 19th century. 

The fascinating optical properties of metal nanoparticles have caught the attention of many researchers from the pioneering and almost parallel works of G. Mie and J.C. Maxwell-Garnett at the beginning of the twentieth century. These original properties, like many other phenomena specifically appearing in matter divided to the nanoscale, are linked with confinement effects, since quasi-free conduction 461... 

One important macroscopic quantity related to the optical properties of non-metallic solids is their refractive index, which is closely related to their dielectric constant. Maxwell s equations for electromagnetic waves propagating in absorbing materials (see for instance [43]) lead to wave equations for the electric and magnetic fields in the material, and a solution for the amplitude of one component of these fields is ... 

A key issue in nanostructured materials is the dipole coupling between nanocrystals which will cause the optical properties of a nanocrystal ensemble to become like those of the bulk material. There has been extensive investigation of the interactions between particles embedded within media for a range of boundary conditions. We have found that the effective dielectric function given by Eq. (10), based on the Maxwell-Garnett model [1] is very accurate for quite dense nanocrystal arrays. In practice, one measures the transmittance of a thin film of the dense nanoparticle based film. Conventional solutions are simply... 

For the calculations of the optical properties of polymer films with embedded particles in the exact route, the extinction cross sections Cext(v) of single particles were calculated based on the solution of the Maxwell equations for spherical particles which is the Mie theory [9, 10]. To reduce the effort for the calculations, often the quasi-static approximation (Rayleigh theory), which con-... 

The magnetic, electric, and optical properties of a material are all related mathematically through the Maxwell equations. 

The optical properties of an infinite medium without any electric charge other than that due to polarization are described by Maxwell s equations [in International System (SI) of units] ... 

Polymer solutions are isotropic at equilibrium. If there is a velocity gradient, the statistical distribution of the polymer is deformed from the isotropic state, and the optical property of the solution becomes anisotropic. This phenomena is called flow birefringence (or the Maxwell effect). Other external fields such as electric or magnetic fields also cause birefringence, which is called electric bire ingence (or Kerr effect) and magnetic birefiingence (Cotton-Mouton effect), respectively. 

For particles with other shapes, the optical properties are numerically calculated by solving the Maxwell equations. For this purpose, the finite-difference... 

The first exact expression of this type was derived by Maxwell [1881] for the dc conductivity of a dispersion of spheres in a continnons medinm. Maxwell Garnett [1904] derived a similar expression for dielectric and optical properties. Wagner [1914] extended Maxwell s model to the complex domain and this model has thereafter been known as the Maxwell-Wagner model. It gives the following expression for complex conductivity ... 

Porous silicon materials are described as a mixture of air, silicon, and, in some cases, silicon dioxide. The optical properties of a porous silicon layer are determined by the thickness, porosity, refractive index, and the shape and size of pores and are obtained from both experimental- and model-based approaches. Porous silicon is a very attractive material for refractive index fabrication because of the ease in changing its refractive index. Many studies have been made on one- and two-dimensional refractive index lattice structures. The refractive index is a complex function of wavelength, i.e., n(X) = n(X) — ik(k), where k is the extinction coefficient and determines how light waves propagate inside a material (Jackson 1975). The square of the refractive index is the dielectric function e(co) = n(co), which contributes to Maxwell s equations. 

Porous silicon can be specified as an effective medium, whose optical properties depend on the relative volumes of silicon and pore-filling medium. Full theoretical solutions can be provided by different effective medium approximation methods such as Maxwell-Gamett s, Looyenga s, or Bruggeman s (Arrand 1997). Effective medium theory describes the effective refractive index, fieff, of porous silicon as a function of the complex refractive index of silicon, fisi, and that of the porefilling material, flair = 1, for air. The porosity P and the topology of the porous structure will also affect fleff (Theiss et al. 1995). 

Following classical EM theory, prior to nineteenth century, individually Gustav Mie and J. C. Maxwell Garnett first showed the theoretical background behind the novel optical property of nanoparticles, that is, SPR, which also depends on the dielectric constant, refractive index, and their individual shape and size. The theories that help modem science to predict the optical property of noble metals are elaborated in the following sections. 

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