OPTICAL PROPERTIES OF INHOMOGENEOUS TWO-COMPONENT MATERIALS

ABSTRACT Effective medium and multiple scattering theories for the optical properties of two-component materials are reviewed. Such materials have numerous applications in the field of coatings for energy efficiency. The transmittance and reflectance of a coating or slab of a composite can be obtained from the effective dielectric and magnetic permeabilities of the material. For materials with inhomogeneities much smaller than the wavelength of the impinging radiation, the effective dielectric permeability can be evaluated in the quasistatic limit. We review the rigorous Bergman-Milton bounds for the effective dielectric permeability as well as various effective medium theories that have been put forward for describing the optical properties of specific microstructures. Specifically we treat the effects of pair and three-point correlations on the bounds and obtain novel effective medium theories taking these effects into account. Materials with large inhomogeneities on the order of, or larger than, the wavelength must be described by different theories. The effective magnetic permeability must be taken into account. The specular reflectance, the direct transmittance and the diffuse scattering are treated by use of a four flux theory.

[1]  Gunnar A. Niklasson,et al.  Noble‐metal‐based transparent infrared reflectors: Experiments and theoretical analyses for very thin gold films , 1986 .

[2]  G Gouesbet,et al.  Four-flux models to solve the scattering transfer equation: special cases. , 1986, Applied optics.

[3]  R. Pettit,et al.  Optical modeling and aging characteristics of thermally stable black chrome solar selective coatings , 1984 .

[4]  M. Okuyama,et al.  Ni cermet selective absorbers for solar photothermal conversion , 1979 .

[5]  Thompson,et al.  Fractal sandstone pores: Implications for conductivity and pore formation. , 1985, Physical review letters.

[6]  D. Stroud,et al.  Self-consistent approach to electromagnetic wave propagation in composite media: Application to model granular metals , 1978 .

[7]  Salvatore Torquato,et al.  Microstructure of two-phase random media.III: The n-point matrix probability functions for fully penetrable spheres , 1983 .

[8]  Fonseca,et al.  Multiple-scattering theories including correlation effects to obtain the effective dielectric constant of nonhomogeneous thin films. , 1985, Physical review. B, Condensed matter.

[9]  M. D. Coutts,et al.  Optical Properties of Granular Silver and Gold Films , 1973 .

[10]  Torquato,et al.  Effective properties of two-phase disordered composite media: II. Evaluation of bounds on the conductivity and bulk modulus of dispersions of impenetrable spheres. , 1986, Physical review. B, Condensed matter.

[11]  O. Hunderi,et al.  Effective medium models for the optical properties of inhomogeneous materials. , 1981, Applied optics.

[12]  J. Garnett,et al.  Colours in Metal Glasses and in Metallic Films , 1904 .

[13]  Optical properties of dense regular cermets with relevance to selective solar absorbers , 1979 .

[14]  David R. McKenzie,et al.  The conductivity of lattices of spheres - II. The body centred and face centred cubic lattices , 1978, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[15]  Salvatore Torquato,et al.  Microstructure of two‐phase random media. I. The n‐point probability functions , 1982 .

[16]  P. Sheng.  Theory for the Dielectric Function of Granular Composite Media , 1980 .

[17]  R. Buhrman,et al.  Ultrafine metal particles , 1976 .

[18]  G. Niklasson,et al.  Projection effects in electron micrographs of three-dimensional fractal aggregates: theory and application to gas-evaporated specimens , 1989 .

[19]  G. Niklasson.  Optical properties of gas‐evaporated metal particles: Effects of a fractal structure , 1987 .

[20]  G. Milton.  Concerning bounds on the transport and mechanical properties of multicomponent composite materials , 1981 .

[21]  J. E. Martin.  Topological and geometrical properties of random fractals , 1985 .

[22]  W. Doyle.  The Clausius‐Mossotti problem for cubic arrays of spheres , 1978 .

[23]  B. Persson,et al.  Optical properties of small metallic particles in a continuous dielectric medium , 1983 .

[24]  M. V. Berry,et al.  Optics of Fractal Clusters Such as Smoke , 1986 .

[25]  T. Witten,et al.  Long-range correlations in smoke-particle aggregates , 1979 .

[26]  Graeme W. Milton,et al.  Bounds on the complex permittivity of a two‐component composite material , 1981 .

[27]  G. Niklasson,et al.  Optical properties and solar selectivity of coevaporated Co‐Al2O3 composite films , 1984 .

[28]  David E. Aspnes,et al.  Finite-wavelength effects in composite media , 1982 .

[29]  David J. Bergman,et al.  Rigorous bounds for the complex dielectric constant of a two-component composite , 1982 .

[30]  Stroud,et al.  Complex dielectric response of metal-particle clusters. , 1986, Physical review. B, Condensed matter.

[31]  G Gouesbet,et al.  Four-flux models to solve the scattering transfer equation in terms of Lorenz-Mie parameters. , 1984, Applied optics.

[32]  A. Liebsch,et al.  Optical properties of randomly distributed particles , 1984 .

[33]  Kenneth M. Golden,et al.  Bounds on the complex permittivity of a multicomponent material , 1986 .

[34]  M. Beran.  Use of the vibrational approach to determine bounds for the effective permittivity in random media , 1965 .

[35]  G. Niklasson,et al.  Temperature-dependent transmittance of luminous and solar radiation for quartz fibers immersed in carbon tetrachloride. , 1987, Applied optics.

[36]  B. U. Felderhof,et al.  Spectral broadening in suspensions of metallic spheres , 1985 .

[37]  W. Doyle.  Absorption of Light by Colloids in Alkali Halide Crystals , 1958 .

[38]  D. Aspnes.  Optical properties of thin films , 1982 .

[39]  D. R. McKenzie,et al.  The conductivity of lattices of spheres I. The simple cubic lattice , 1978, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[40]  G. Niklasson,et al.  Infrared optical properties of evaporated alumina films. , 1981, Applied optics.

[41]  P. Zavracky,et al.  Selective black absorbers using MgO/Au cermet films , 1976 .

[42]  Schwartz,et al.  Electromagnetic propagation in close-packed disordered suspensions. , 1985, Physical review. B, Condensed matter.

[43]  Walter Bogaerts,et al.  Materials for photothermal solar energy conversion , 1983 .

[44]  L. Fonseca,et al.  Multiple scattering renormalized T matrix theory for the dielectric constant of non-homogeneous thin films☆ , 1985 .

[45]  Kay,et al.  Optical properties and microstructure of gold-fluorocarbon-polymer composite films. , 1985, Physical review. B, Condensed matter.

[46]  Ross C. McPhedran,et al.  Bounds and exact theories for the transport properties of inhomogeneous media , 1981 .

[47]  S. Torquato,et al.  Bounds on the conductivity of a suspension of random impenetrable spheres , 1986 .

[48]  R. Buhrman,et al.  Far-infrared absorption in ultrafine Al particles , 1976 .

[49]  G. Niklasson,et al.  Surfaces for selective absorption of solar energy: an annotated bibliography 1955–1981 , 1983 .

[50]  S. Torquato.  Bulk properties of two‐phase disordered media. III. New bounds on the effective conductivity of dispersions of penetrable spheres , 1986 .

[51]  S. Torquato.  Microstructure characterization and bulk properties of disordered two-phase media , 1986 .

[52]  P. Chylek,et al.  Dielectric constant of a composite inhomogeneous medium , 1983 .

[53]  C. Boned,et al.  Some comments on the complex permittivity of ellipsoids dispersed in continuum media , 1983 .

[54]  J. Cox,et al.  Improved dielectric films for multilayer coatings and mirror protection , 1964 .

[55]  P. Leath,et al.  The theory and properties of randomly disordered crystals and related physical systems , 1974 .

[56]  D. A. G. Bruggeman.  Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen , 1935 .

[57]  S. Hackwood,et al.  New display based on electrically induced index‐matching in an inhomogeneous medium , 1982 .

[58]  G. Niklasson.  CoAl2O3 selective solar absorbing films: structure and effective medium theory for the optical properties , 1988 .

[59]  David J. Bergman,et al.  The dielectric constant of a composite material—A problem in classical physics , 1978 .

[60]  B. U. Felderhof.  Bounds for the complex dielectric constant of a two-phase composite , 1984 .

[61]  C. Granqvist.  Photothermal conversion of solar energy by gold cermet coatings: applicability of the Bruggeman effective medium theory , 1979 .

[62]  P. McCormick,et al.  Black chrome selective surfaces I. Deposit growth and properties , 1982 .

[63]  Craig F. Bohren,et al.  Extinction by a spherical particle in an absorbing medium , 1979 .

[64]  Far-infrared absorption in gas-evaporated Al particles: Effects of a fractal structure , 1986 .

[65]  E. V. Loewenstein,et al.  Optical constants of far infrared materials. 3: plastics. , 1975, Applied optics.

[66]  O. Hunderi,et al.  Nickel pigmented anodic aluminum oxide for selective absorption of solar energy , 1979 .

[67]  D. M. Wood,et al.  Long-wavelength electromagnetic propagation in heterogeneous media , 1980 .

[68]  J. Euler.  Ultraoptische Eigenschaften von Metallen und mittlere freie Weglänge der Leitungselektronen , 1954 .

[69]  G. Goedecke,et al.  Radiative transfer in closely packed media , 1977 .

[70]  D. J. Bergman,et al.  The optical properties of cermets from the theory of electrostatic resonances , 1982 .

[71]  L. Richards,et al.  Multiple scattering calculations for technology. , 1971, Applied optics.

[72]  R. McPhedran,et al.  Surface structure and the optical properties of black chrome , 1985 .

[73]  L. Martinu.  Optical response of composite plasma polymer/metal films in the effective medium approach☆ , 1987 .

[74]  S. Torquato.  Bulk properties of two‐phase disordered media. II. Effective conductivity of a dilute dispersion of penetrable spheres , 1985 .

[75]  Salvatore Torquato,et al.  Effective electrical conductivity of two‐phase disordered composite media , 1985 .

[76]  A. Mathewson,et al.  Absolute Values of the Optical Constants of Some Pure Metals , 1971 .

[77]  Geoffrey Smith,et al.  Dielectric constants for mixed media , 1977 .

[78]  A. Hjortsberg.  Determination of optical constants of absorbing materials using transmission and reflection of thin films on partially metallized substrates: analysis of the new (T,R(m)) technique. , 1981, Applied optics.

[79]  C. Bohren.  Applicability of Effective-Medium Theories to problems of Scattering and Absorption by Nonhomogeneous Atmospheric Particles , 1986 .

[80]  Y. Arie,et al.  Optical properties and selective solar absorption of composite material films , 1977 .

[81]  G. Niklasson.  Comparison between four flux theory and multiple scattering theory. , 1987, Applied optics.

[82]  H. M. Shafey,et al.  Theoretical Study on Radiative Properties of a Painted Layer Containing Spherical Pigment : Case of Normal Incidence , 1979 .

[83]  Wachniewski,et al.  New approach to effective medium for composite materials: Application to electromagnetic properties. , 1986, Physical review. B, Condensed matter.

[84]  T. Hanai.  Theory of the dielectric dispersion due to the interfacial polarization and its application to emulsions , 1960 .

[85]  U. Kreibig,et al.  Dielectric function and infrared absorption of small metal particles , 1980 .

[86]  David J. Bergman,et al.  Exactly Solvable Microscopic Geometries and Rigorous Bounds for the Complex Dielectric Constant of a Two-Component Composite Material , 1980 .

[87]  Melvin N. Miller.  Bounds for Effective Electrical, Thermal, and Magnetic Properties of Heterogeneous Materials , 1969 .

[88]  R. W. Cohen,et al.  Surface plasmons in granular Ag-SiO 2 films , 1975 .

[89]  R. Buhrman,et al.  Optical response of Cermet composite films in the microstructural transition region , 1983 .

[90]  D. E. Aspnes,et al.  Bounds on allowed values of the effective dielectric function of two-component composites at finite frequencies , 1982 .

[91]  Ashcroft,et al.  Theory of far-infrared absorption in small-metal-particle-insulator composites. , 1985, Physical review. B, Condensed matter.

[92]  Barrera,et al.  Renormalized polarizability in the Maxwell Garnett theory. , 1988, Physical review. B, Condensed matter.

[93]  C. Granqvist.  Far infrared absorption in ultrafine metallic particles: Calculations based on classical and quantum mechanical theories , 1978 .

[94]  S. Berthier,et al.  Mean field theory and scaling laws for the optical properties of inhomogeneous media , 1987 .

[95]  S. Shtrikman,et al.  A Variational Approach to the Theory of the Effective Magnetic Permeability of Multiphase Materials , 1962 .

[96]  Graeme W. Milton,et al.  Bounds on the complex dielectric constant of a composite material , 1980 .