Stable localized modes in asymmetric waveguides with gain and loss

It is shown that asymmetric waveguides with gain and loss can support a stable propagation of optical beams. This means that the propagation constants of modes of the corresponding complex optical potential are real. A class of such waveguides is found from a relation between two spectral problems. A particular example of an asymmetric waveguide, described by the hyperbolic functions, is analyzed. The existence and stability of linear modes and of continuous families of nonlinear modes are demonstrated.Comment: 10 pages, 4 figures. Accepted in Optics Letters, 201

Mamlakat iqtisodiy o’sishini ta’minlashda xorijiy investitsiyalarni jalb qilishning ustuvor yo’llari

Maqolada mamlakat iqtisodiy o‘sishini ta’minlash masalalari, shuningdek, uni amalga oshirish bo‘yicha iqtisodiyotga faol xorijiy investitsiyalarni jalb qilishning ustuvor yo’llari keltirilgan

Analytical mode normalization and resonant state expansion for optical fibers - an efficient tool to model transverse disorder

We adapt the resonant state expansion to optical fibers such as capillary and photonic crystal fibers. As a key requirement of the resonant state expansion and any related perturbative approach, we derive the correct analytical normalization for all modes of these fiber structures, including leaky modes that radiate energy perpendicular to the direction of propagation and have fields that grow with distance from the fiber core. Based on the normalized fiber modes, an eigenvalue equation is derived that allows for calculating the influence of small and large perturbations such as structural disorder on the guiding properties. This is demonstrated for two test systems: a capillary fiber and an endlessly single mode fiber.Comment: 10 pages, 4 figure

Effect of the exchange rate policy on economic growth

The article examines, the exchange rate, changes in the currency policy in Uzbekistan and the impact of exchange rate policy on economic growth in the modern financial and currency system is described in detail