A new five-layer structure of the dielectric interference filter for the infra-red region of spectrum is investigated. The main spectral parameters of such a narrow-band filter are determined. The dependence of the transmission band half-width on the thickness of a dividing layer in this system is investigated. It is shown that, in the case of the application of PbTe, GeTe, and SnTe layers with a given thickness; their number can be limited to five at providing the necessary selectivity of the filter: practically the 100-% transmission at the resonance frequency and 0,005 % outside the transmission band.

In this paper, we propose and demonstrate a novel guided-mode resonant filter based on a metallic grating sandwiched between two dielectric layers for TE polarization. A theoretical model based on rigorous coupled wave analysis has been developed. The transmission spectra of the grating-based structure show a high transmission band with the corresponding amplitude up to 70 % inside the infra-red region. Moreover, the observed optical properties can be exactly tuned by the structural parameters. These properties allow using such structures as compact optical filters, and their spectral characteristics can be easily tuned and scaled.

Enhanced optical transmission through metallic 1-D grating-based structures has been studied using the rigorous coupled wave analysis. The results have shown that optical transmission is determined by waveguide properties of the grating slit, and there is a minimum width of slit for ТЕ polarization, when high transmission occurs due to waveguide effect. In contrast, this limitation doesn't exist for TM polarization, and extraordinary transmission is obtained at the sub-wavelength slit. As a result, high transmission is reached due to resonance of electromagnetic field inside the grating slit.

Possibilities of new numerical method for solving the wave equation of multilayer planar waveguide were investigated. The method is based on the use of Fourier transform to the wave equation and its solution in the frequency domain by using the numerical method. The final task of finding propagation constants and the Fourier images of the fields in discrete form is reduced to the problem on the eigenvalues and eigenvectors. The new method provides highly accurate calculation of propagation constants and their fields and is characterized by high numerical stability.

In this work, optical properties of nanocomposite materials based on plasmon metallic spherical nanoparticles have been studied. The authors have compared four different effective theories that take into account the size dispersion, interaction between nanoparticles and extrinsic size effect for calculation of the effective refractive index of Au, Ag and Cu nanoparticles in polymer. It has been demonstrated that size distribution induces an inhomogeneous broadening and change in the amplitude of plasmon band. The lowest shift of resonance characteristics has been observed for copper based nanocomposite for all the effective theories. It has been shown that the same nanocomposite material but with other parameters (size and concentration of inclusions) can be described by the different effective theories.

Purpose. A theoretical overview of the conceptions related to financial support of the city government, as well as scientific and applied substantiation of the conditions necessary for the formation of the territorial infrastructure, which will enhance potential prospects of its enterprise development. Methodology. By way of scientific generalization, we have determined the peculiarities of using enterprise approach to creating the objects of territorial community infrastructure and developed an analytical approach to assessing the schedule of the received payment disbursement in terms of credit price, provided a quantitative assessment to different options of liabilities discharge. Findings. Analysis has been used to justify the dependence of the raised funds costs on the schedule of their disbursement. Economic prerequisites, which significantly influence the final results of the enterprise project, have been specified. Emphasis has been made on the possibility to optimize financial and credit relationships between business subjects and banks. The optimal interest rate, which ensures satisfactory demand for credit financing, has been identified. Feasibility of the accelerated schedule of credit resources disbursement has been proved for the conditions of putting the object into the starting operational capacity. Organizational and economic prerequisites of financial solutions to social problems associated with the territorial community demands were determined in terms of enterprise approach principles. Originality. It has been established that there is an analytical dependence between the total costs of the credit reimbursement and the term of the business object commissioning into operation. It was found that the crediting schedule (accelerated, regular, slow) influences the value of the involved costs. The advantages of using enterprise approach to implementation of projects related to the development of infrastructure on the community residential territory have been determined. Practical value. It was proposed to apply an alternative approach to ensuring development of the territorial community in conditions of limited target financing.

Results of analysis focused on dielectric/metal/dielectric and metal/dielectric/ metal symmetric nanowaveguides have been presented. The waveguides based on gold, silver and aluminum have been studied. It has been shown that silver as metal is the most suitable to be used in metal/dielectric/metal waveguide from the viewpoint waveguide thickness minimization and the minimal absorption under optical wave propagation.

Представлено результати числового аналізу дифракції оптичних хвиль поперечної магнітної (ТМ) поляризації на гратках за наявності резонансу електромагнітного поля. Використано RCWA, в якому модифіковано систему рівнянь. Модифікація полягає в тому, що у системі диференціальних рівнянь змінено матриці Теплиця, які формуються на основі комплексних рядів Фур'є періодичної функції діелектричної проникності гратки та оберненої їй функції. Прямокутна функція зміни діелектричної проникності на періоді замінена на функцію трапеції, проте рельєф гратки лишається прямокутним. Така заміна функції діелектричної проникності точніше відповідає реальним граткам. Виявлено зменшення осциляцій коефіцієнтів відбивання та пропускання залежно від кількості використаних зв'язаних хвиль та кращу збіжність результатів розрахунку для видозміненої системи рівнянь, особливо для металевих граток на діелектричних підкладках, в яких може спостерігатися резонанс локалізованих плазмонів, або резонанс електромагнітного поля в щілині гратки. Показано, що для діелектричних граток, розташованих на металевій підкладці, немає ні покращання, ні погіршення збіжності у разі використання модифікованої системи рівнянь у порівнянні з традиційним розкладом діелектричної проникності в ряд Фур'є. Для структури металева гратка на металевій підкладці досліджувався резонанс поверхневих плазмон-поляритонів, у разі виникнення якого коефіцієнт відбивання від гратки рівний нулю. Тут виникає особливо складна залежність коефіцієнта відбивання від кількості використаних зв'язаних хвиль під час аналізу для обох модифікацій систем рівнянь. Спостерігаються сильні осциляції коефіцієнта відбивання від гратки за певних значень зв'язаних хвиль, які з їх ростом зменшуються.