Ivan M. Uzunov

Time shift in the presence of linear and nonlinear gain, spectral filtering, third-order of dispersion and self-steepening effect

We study the soliton time shift in the presence of linear and nonlinear gain, saturation of the nonlinear refractive index, spectral filtering, third-order of dispersion and self-steepening effect. The applied model generalizes the complex cubicquintic Ginzburg-Landau equation (CCQGLE) with the basic higher-order effects in fibers: the intrapulse Raman scattering (IRS), third-order of dispersion (TOD) and self-steepening effect. Soliton perturbation theory (SPT) is derived with which the influence of the saturation of the nonlinear refraction index, self-steepening and TOD on the appearance of the Poincare-Andronov-Hopf bifurcation is analyzed. It has been shown that TOD and self-steepening effect can lead to reduction in the time shift of the pulse. This prediction has been verified by numerical solution of generalized CCQGLE.

Localized Pulsating Solutions of the Generalized Complex Cubic-Quintic Ginzburg-Landau Equation

We study the dynamics of the localized pulsating solutions of generalized complex cubic-quintic Ginzburg-Landau equation (CCQGLE) in the presence of intrapulse Raman scattering (IRS). We present an approach for identification of periodic attractors of the generalized CCQGLE. Using ansatz of the travelling wave and fixing some relations between the material parameters, we derive the strongly nonlinear Lienard-Van der Pol equation for the amplitude of the nonlinear wave. Next, we apply the Melnikov method to this equation to analyze the possibility of existence of limit cycles. For a set of fixed parameters we show the existence of limit cycle that arises around a closed phase trajectory of the unperturbed system and prove its stability. We apply the Melnikov method also to the equation of Duffing-Van der Pol oscillator used for the investigation of the influence of the IRS on the bandwidth limited amplification. We prove the existence and stability of a limit cycle that arises in a neighborhood of a homoclinic trajectory of the corresponding unperturbed system. The condition of existence of the limit cycle derived here coincides with the relation between the critical value of velocity and the amplitude of the solitary wave solution (Uzunov, 2011).

Symmetry properties of nonlinear pulse propagation in birefringent optical fibers with stimulated Raman scattering

A set of couled nonlinear equations describing propagation of two polarization light modes inside optical fibers with stimulated Raman scattering are considered. Using a Lie group technique, the most general Lie algebra is derived for the two cases: with and without orthogonal Raman gain. The optimal set of reduced systems of ordinary differential equations for the case without orthogonal Raman gain is obtained.

Influence of intrapulse Raman scattering on the stationary pulses in the presence of linear and nonlinear gain as well as spectral filtering

In this paper we present numerical investigation of the influence of intrapulse Raman scattering (IRS) on the stable stationary pulses. Our basic equation, namely cubic-quintic Ginzburg-Landau equation describes the propagation of ultra-short optical pulses under the effect of IRS in the presence of linear and nonlinear gain as well as spectral filtering. Our aim is to examine numerically the influence of IRS, on the stable stationary pulses in the presence of constant linear and nonlinear gain as well as spectral filtering. Numerical solution of our basic equation is performed by means of the “fourth-order Runge-Kutta method in the interaction picture method” method. We found that the small change of the value of the parameter which describes IRS leads to qualitatively different behavior of the evolution of pulse amplitudes. In order to study the observed strong dependence on the IRS, the perturbation method of conserved quantities of the nonlinear Schrodinger equation is applied. The numerical analysis of the derived nonlinear system of ordinary differential equations has shown that our numerical findings are related to the existence of the Poincare-Andronov-Hopf bifurcation.

Influence of the intrapulse Raman scattering on the localized pulsating solutions of generalized complex-quintic Ginzburg-Landau equation

We study the dynamics of the localized pulsating solutions of generalized complex cubic– quintic Ginzburg-Landau equation (CCQGLE) in the presence of intrapulse Raman scattering (IRS). We present an approach for identification of periodic attractors of the generalized CCQGLE. At first using ansatz of the travelling wave, and fixing some relations between the material parameters, we derive the strongly nonlinear Lienard - Van der Pol equation for the amplitude of the nonlinear wave. Next, we apply the Melnikov method to this equation to analyze the possibility of existence of limit cycles. For a set of fixed material parameters we show the existence of limit cycle that arises around a closed phase trajectory of the unperturbed system and prove its stability.

Parametric study of thin-film zero-group velocity resonators (ZGVR)

Here we demonstrate experimentally a novel, small form factor, resonant architecture employing the intrinsic zero-group-velocity dispersion of the first order symmetric Lamb wave S1 propagating in piezoelectric AlN film membranes. Designs with different topologies were fabricated and compared. FEM analysis is used to verify the observed differences while providing a deeper insight to the resonator performance. Technique for improvement of the device performance are further proposed.

Lie group symmetry classification of solutions to coupled nonlinear Schrödinger equations

By applying the Lie group reduction method a full symmetry classification of one parameter group invariant solutions of two coupled nonlinear Schrodinger equations is presented. The physical situations under consideration include propagation of two polarization modes in weak and strong birefringent fibers, propagation of two waves at different carrier wavelengths, and nonlinear directional couplers.

Lattice FBAR Filters: Basic Properties and Opportunities for Improving the Frequency Response

The paper contains a relatively detailed consideration of lattice filters with bulk acoustic-wave resonators (FBAR): basic theory, investigation and improving of their design. First FBARs and their parameters are introduced briefly. Then the basic structure of lattice filters and its modification with twice lower number of resonators are introduced. A theory of lattice FBAR filters is presented, which allows unified explanation of many of their properties: condition for small or large gain of the filter; existence of maxima of the filter frequency response; emergence of transmission zeros; etc. The effect of using two different resonators instead of a single resonator in the arms of the lattice filter is investigated next. It is demonstrated that this approach suggests extension of the passband bandwidth and increasing the stopband attenuation. The properties of the considered filters are illustrated by comparing their frequency responses. Similar comparison between some good representatives of lattice and ladder filters is also given at the end, accompanied by comments about the benefits of both filter architectures. KeywordsFilm Bulk Acoustic-Wave Resonators (FBAR); RF Filters; FBAR Filters; Circuit Theory

Improvement of the frequency response of FBAR filters by using parallel or series connected resonators instead of single resonators

The paper investigates an opportunity for improving the frequency response of FBAR lattice filters by replacing some of the single FBARs with two resonators connected in parallel or in series. The method is applied for the basic lattice filter architecture and its modification with twice lower number of FBARs. The theoretical results presented in the paper allow to estimate the change of the resonance frequencies of resonators, connected in series or in parallel; and to derive the conditions for improving the frequency response of the new circuits. Two different options for circuits with improved frequency responses are considered. The theoretical results are confirmed with computer simulations.

Problems and Properties of a Current Amplifier When Realized in Ultra Deep Sub-micron Technology

The paper considers the problems related to short-channel effects in a current amplifier, when realized in ultra-deep sub-micron technology. A short description of the circuit and a limitation concerning its basic parameters is given at the beginning. Several steps, allowing an approximate design of the circuit, are outlined. They are applied for design of three versions of the amplifier, each of them is realized with FETs having different channel length: 90 nm, 45 nm and 30 nm. Their basic properties are simulated and discussed, demonstrating the major benefit of the shortening of the channel length—extension of the frequency bandwidth. The problems arising with the shorter channels length are also considered briefly.