The term photonic crystals appears because of the analogy between electron waves in crystals and the light waves in artificial periodic dielectric structures. During the recent years the investigation of one-, two-and three-dimensional periodic structures has attracted a widespread attention of the world optics community because of great potentiality of such structures in advanced applied optical fields. The interest in periodic structures has been stimulated by the fast development of semiconductor technology that now allows the fabrication of artificial structures, whose period is comparable with the wavelength of light in the visible and infrared ranges.

http://ieeexplore.ieee.org/iel5/6354/16969/00781867.pdf

Photonic crystals

Recent theoretical work on the microscopic structure and surface tension of the liquid-vapour interface of simple (argon-like) fluids is critically reviewed. In particular, the form of pairwise intermolecular correlations in the liquid surface and the capillary wave treatment of the interface are examined in some detail. It is argued that conventional capillary wave theory, which leads to divergences in the width of the density profile, is unsatisfactory for describing all the equilibrium aspects of the interface. The density functional formalism which has been developed to study the liquid-vapour interface can also be profitably applied to other problems in the statistical mechanics of non-uniform fluids; here a new generalization of the ‘linear’ theory of spinodal decomposition is formulated and by considering a ‘nearly uniform’ fluid, some useful results for the long-wavelength behaviour of the liquid structure factor of various monatomic liquids are obtained. Some other topics of current inte...

The nature of the liquid-vapour interface and other topics in the statistical mechanics of non-uniform, classical fluids

(b) Write out the equations for the time dependence of ρ11, ρ22, ρ12 and ρ21 assuming that a light field interaction V = -μ12Ee iωt + c.c. couples only levels |1> and |2>, and that the excited levels exhibit spontaneous decay. (8 marks) (c) Under steady-state conditions, find the ratio of populations in states |2> and |3>. (3 marks) (d) Find the slowly varying amplitude ̃ ρ 12 of the polarization ρ12 = ̃ ρ 12e iωt . (6 marks) (e) In the limiting case that no decay is possible from intermediate level |3>, what is the ground state population ρ11(∞)? (2 marks) 2. (15 marks total) In a 2-level atom system subjected to a strong field, dressed states are created in the form |D1(n)> = sin θ |1,n> + cos θ |2,n-1> |D2(n)> = cos θ |1,n> sin θ |2,n-1>

The Quantum Theory of Light

We propose a modification in the three-dimensional Ewald summation technique for calculations of long-range Coulombic forces for systems with a slab geometry that are periodic in two dimensions and have a finite length in the third dimension. The proposed method adds a correction term to the standard Ewald summation formula. To test the current method, molecular dynamics simulations on water between Pt(111) walls have been carried out. For a more direct test, the calculation of the pair forces between two point charges has been also performed. An excellent agreement with the results from simulations using the rigorous two dimensional Ewald summation technique were obtained. We observed that a significant reduction in computing time can be achieved when the proposed modification is used.

Ewald summation for systems with slab geometry

Wave propagation and group velocity

Ion-ion repulsion in a liquid metal is regarded as the principal factor determining the ionic arrangement. This interaction is idealized in a hard-sphere model; the known solution of the Percus-Yevick equation for this model gives a simple closed form for $a(K)$ (the liquid structure factor) which depends only on the effective packing density of the fluid. This fact enables us to make an estimate for the resistivities of most liquid metals for which model potentials are available. Agreement with experiment is generally good, particularly when the potential is known to be accurate. The sensitivity of the resistivity to the depth of the model potential well is indicated.

Structure and Resistivity of Liquid Metals

This book deals with the reflection of electromagnetic and particle waves by interfaces. The interfaces can be sharp or diffuse. The topics of the book contain absorption, inverse problems, anisotropy, pulses and finite beams, rough surfaces, matrix methods, numerical methods, reflection of particle waves and neutron reflection. Exact general results are presented, followed by long wave reflection, variational theory, reflection amplitude equations of the Riccati type, and reflection of short waves. The Second Edition of the Theory of Reflection is an updated and much enlarged revision of the 1987 monograph. There are new chapters on periodically stratified media, ellipsometry, chiral media, neutron reflection and reflection of acoustic waves. The chapter on anisotropy is much extended, with a complete treatment of the reflection and transmission properties of arbitrarily oriented uniaxial crystals. The book gives a systematic and unified treatment reflection and transmission of electromagnetic and particle waves at interfaces. It is intended for physicists, chemists, applied mathematicians and engineers, and is written in a simple direct style, with all necessary mathematics explained in the text

Theory of reflection

The scattering of electrons moving through nonpolar liquids is discussed. The Hartree field of an atom is assumed not to change on passing from gas to liquid. The screening of the long-range polarization potential is given by a self-consistent local field, which is found in terms of the pair correlation function. A microscopic dielectric function follows as a byproduct. The overlap of atomic force fields in the liquid is handled by the use of an effective potential suggested by Cohen. Detailed calculations are made for electrons in liquid argon. The principal result is that the Ramsauer minimum no longer exists in the liquid. The drift velocity in a steady electric field is found from the solution of the Boltzmann equation given by Cohen and Lekner. Agreement between experiment and theory is good.

Motion of Electrons in Liquid Argon

Formulae are derived for the sums over Coulomb forces exerted on a charged particle by other charged particles, the central cell system being repeated to infinity by periodic boundary conditions. Such sums are needed in molecular dynamics simulations involving either ions or neutral molecules represented as bound conglomerates of charges, and in astrophysical simulations of gravitating masses. The derived sums are rapidly convergent, being expressed in terms of Bessel functions Kr(z), which decrease exponentially with z. The force expressions are integrated analytically to give the potential function, which may be used in Monte Carlo simulations. The geometries considered are: (i) systems confined between two parallel walls, and (ii) unconfined three-dimensional systems.

John Lekner

Papers

Structure and Resistivity of Liquid Metals

Theory of reflection

Motion of Electrons in Liquid Argon

Summation of Coulomb fields in computer-simulated disordered systems

Theory of hot electrons in gases, liquids, and solids