Michał H. Tyc

Polarized light transmission through generalized Fibonacci multilayers: I. Dynamical maps approach and II. Numerical results

Summary I. Dynamical maps approach: The theory of polarized light propagation in dielectric generalized Fibonacci multilayers is developed. The matrix formulation and dynamical maps technique is used. New objects: diagonal antitraces, symmetric and antisymmetric nondiagonal antitraces of characteristic matrices are introduced. Dynamical maps for these objects are derived. Transmittance for s- and p-type polarized light of the studied aperiodic multilayers placed between two homogenous media is expressed in terms of traces and antitraces of characteristic matrices. Three interesting physical situations are considered, allowing to study the influence of surrounding media on light transmission properties of Fibonacci-type multilayers. II. Numerical results: The theory of polarized light propagation in generalized Fibonacci multilayers, recently developed in the framework of matrix formulation and dynamical maps technique, is applied. Transmittance of studied systems is numerically calculated and presented in gray scale figures. The main tendencies in dependences of transmittance on model parameters are presented and discussed. We find a strong dependence of transmittance on refractive indices of surrounding media. We show that the proposed approach can be useful in optical engineering.

Negative differential resistance in aperiodic semiconductor superlattices

Influence of external DC electric field on the electron tunnelling through aperiodic semiconductor superlattices is studied numerically in the framework of generalized Kronig–Penney model and Landauer formalism. Spatial dependence of electron effective mass and dielectric constant as well as band non-parabolicity effects and non-abrupt interfaces are taken into account. Influence of model parameters on the Landauer resistance is investigated. Areas of negative differential resistance are found and presented as two-dimensional grayscale maps.

Electromagnetic wave propagation through aperiodic superlattices composed of left- and right-handed materials

Using the transfer matrix formalism and dynamical maps technique, we calculate numerically transmittance of polarized electromagnetic wave through aperiodic superlattices (generalized Fibonacci, generalized Thue-Morse, double-periodic and Rudin-Shapiro), built of left- and right-handed materials. In our calculations, strong dispersion of left-handed materials is taken into account, leading to tunnelling effects in a wide range of wavelengths and incidence angles. The results are presented in gray scale transmittance maps.

Photonic band structure of one-dimensional aperiodic superlattices composed of negative refraction metamaterials

The dispersion relation for polarized light transmitting through a one-dimensional superlattice composed of aperiodically arranged layers made of ordinary dielectric and negative refraction metamaterials is calculated with finite element method. Generalized Fibonacci, generalized Thue-Morse, double-periodic and Rudin-Shapiro superlattices are investigated, using their periodic approximants. Strong dispersion of metamaterials is taken into account. Group velocities and effective refraction indices in the structures are calculated. The self-similar structure of the transmission spectra is observed.

Two-dimensional Wannier-Mott exciton in a uniform electric field

A new treatment of the problem of a two-dimensional Wannier-Mott exciton in a uniform electric field, based on the parabolic coordinates, is presented. The quasi-stationary Hamiltonian is regularized, and the efficient numerical methods are applied. The dependence of the exciton binding energy on the electric field is computed. The results are very close to those obtained by the perturbation theory calculations.

One-dimensional photonic quasicrystals: application to Bragg reflectors

The new designing of Bragg reflectors as generalized Fibonaccian AlAs-GaAs semiconductor optical superlattices is presented. We found aperiodic superlattices which, with 1μm thickness, have reflectances exceeding 99% in the 1.31 μm wavelength range. These aperiodic Bragg reflectors can be used in fabrication of vertical-cavity surface-emitting lasers (VCSELs).

“Social temperature”—relation between binary choice model and Ising model

Although social or economic systems do not fulfill standard demands of thermodynamic equilibrium, a term “temperature” has been invoked in many approaches to such systems [1]. We examine a class of decision making problems—utility function models [2], and discuss the status of “temperature” [3]. We investigate the circumstances when this concept is well justified and analogy to a temperature, as the one known from statistical physics, is not only formal.

Photonic band structure of the quasi-one-dimensional photonic quasicrystals

We calculate, using finite difference method, the dispersion relation of photons transmitting through a one-dimensional photonic quasicrystal arranged in a generalized Fibonacci, generalized Thue-Morse and double periodic sequence. The structure of dispersion curves clearly shows their self-similar structure. With this method of calculation, we can obtain distribution of the electric field and energy density, group velocity and effective refraction index for the structure. We discuss taking into consideration the dispersion in layer materials and negative index materials.

Equivalence of different binary choice models

There are various classes of models, in which individuals are assumed to make their binary choices dependent upon gains and losses, including social ones, which they evaluate for themselves. At each discrete time step t every individual has to make a binary decision: σit = +1 or σit = −1: σit+1 = f(σit,{σjt}). In different approaches, deterministic part is distinguished from a random (non‐rational) part.Within impact function approach [1], the decision σit+1 at time t+1 is either σit or −σit, with probabilities F(−2Ii(σit,{σjt})) and 1−F(−2Ii(σit,{σjt})), repectively. Here Ii–impact function, F–some cumulative probability distribution function. Without randomness, the above process reduces to purely deterministic one: σit+1 = −sgn[σitIi(σit,{σjt})].Within utility function approach [2], σit+1 = argmax{−1,+1}Uidet(σit+1,σit,{σjt})+ei(σit+1, where Uidet–deterministic part of utility function, ei–random term.In threshold model [3] (mean‐field approach): P(σit+1 = +1) = P(mith