H. Susanto

Ultrafast optical switching using parity-time symmetric Bragg gratings

This paper reports on time-domain modeling of an optical switch based on the parity–time (PT) symmetric Bragg grating. The switching response is triggered by suddenly switching on the gain in the Bragg grating to create a PT-symmetric Bragg grating. Transient and dynamic behaviors of the PT Bragg gratings are analyzed using the time-domain numerical transmission line modeling method including a simple gain saturation model. The on/off ratio and the switching time of the PT Bragg grating optical switch are analyzed in terms of the level of gain introduced in the system and the operating frequency. The paper also discusses the effect the gain saturation has on the operation of the PT-symmetric Bragg gratings.

Integrability of PT-symmetric dimers

The coupled discrete linear and Kerr nonlinear Schrodinger equations with gain and loss describing transport on dimers with parity-time (PT)-symmetric potentials are considered. The model is relevant among others to experiments in optical couplers and proposals on Bose-Einstein condensates in PT-symmetric double-well potentials. It is known that the models are integrable. Here, the integrability is exploited further to construct the phase portraits of the system. A pendulum equation with a linear potential and a constant force for the phase difference between the fields is obtained, which explains the presence of unbounded solutions above a critical threshold parameter. The behavior of all solutions of the system, including changes in the topological structure of the phase plane, is then discussed.

Newton's method's basins of attraction revisited

In this paper, we revisit the chaotic number of iterations needed by Newtons method to converge to a root. Here, we consider a simple modified Newton method depending on a parameter. It is demonstrated using polynomiography that even in the simple algorithm the presence and the position of the convergent regions, i.e. regions where the method converges nicely to a root, can be complicatedly a function of the parameter.

Localized standing waves in inhomogeneous Schrödinger equations

A nonlinear Schrodinger equation arising from light propagation down an inhomogeneous medium is considered. The inhomogeneity is reflected through a non-uniform coefficient of the nonlinear term in the equation. In particular, a combination of self-focusing and self-defocusing nonlinearity, with the self-defocusing region localized in a finite interval, is investigated. Using numerical computations, the extension of linear eigenmodes of the corresponding linearized system into nonlinear states is established, particularly nonlinear continuations of the fundamental state and the first excited state. The (in)stability of the states is also numerically calculated, from which it is obtained that symmetric nonlinear solutions become unstable beyond a critical threshold norm. Instability of the symmetric states is then investigated analytically through the application of a topological argument. Determination of instability of positive symmetric states is reduced to simple geometric properties of the composite phase plane orbit of the standing wave. Further the topological argument is applied to higher excited states and instability is again reduced to straightforward geometric calculations. For a relatively high norm, it is observed that asymmetric states bifurcate from the symmetric ones. The stability and instability of asymmetric states is also considered.

Impact of dispersive and saturable gain/loss on bistability of nonlinear parity–time Bragg gratings

We report on the impact of realistic gain and loss models on the bistable operation of nonlinear parity-time (PT) Bragg gratings. In our model we include both dispersive and saturable gain and show that levels of gain/loss saturation can have a significant impact on the bistable operation of a nonlinear PT Bragg grating based on GaAs material. The hysteresis of the nonlinear PT Bragg grating is analyzed for different levels of gain and loss and different saturation levels. We show that high saturation levels can improve the nonlinear operation by reducing the intensity at which the bistability occurs. However, when the saturation intensity is low, saturation inhibits the PT characteristics of the grating.

Boundary Driven Waveguide Arrays: Supratransmission and Saddle-Node Bifurcation

In this paper, we consider a semi-infinite discrete nonlinear Schrodinger equation driven at one edge by a driving force. The equation models the dynamics of coupled waveguide arrays. When the frequency of the forcing is in the allowed band of the system, there will be a linear transmission of energy through the lattice. Yet, if the frequency is in the upper forbidden band, then there is a critical driving amplitude for a nonlinear tunneling, which is called supratransmission, of energy to occur. Here, we discuss mathematically the mechanism and the source of the supratransmission. By analyzing the existence and the stability of the rapidly decaying static discrete solitons of the system, we show rigorously that two of the static solitons emerge and disappear in a saddle-node bifurcation at a critical driving amplitude. One of the emerging solitons is always stable in its existence region and the other is always unstable. We argue that the critical amplitude for supratransmission is then the same as the c...

Controllable plasma energy bands in a one-dimensional crystal of fractional Josephson vortices

We consider a one-dimensional chain of fractional vortices in a long Josephson junction with alternating ±kappa phase discontinuities. Since each vortex has its own eigenfrequency, the intervortex coupling results in eigenmode splitting and in the formation of an oscillatory energy band for plasma waves. The band structure can be controlled at the design time by choosing the distance between vortices or during experiment by varying the topological charge of vortices or the bias current. Thus one can construct an artificial vortex crystal with controllable energy bands for plasmons.

CALCULATED THRESHOLD OF SUPRATRANSMISSION PHENOMENA IN WAVEGUIDE ARRAYS WITH SATURABLE NONLINEARITY

In this work, we consider a semi-infinite discrete nonlinear Schrodinger equation with saturable nonlinearity driven at one edge by a driving force. The equation models the dynamics of coupled photorefractive waveguide arrays. It has been reported that when the frequency of the driving force is in the forbidden band, energy can be trasmitted along the lattices provided that the driving amplitude is above a critical value. This nonlinear tunneling is called supratransmission. Here, we explain the source of supratransmission using geometric illustrations. Approximations to the critical amplitude for supratransmission are presented as well.

Discrete solitons in electromechanical resonators

We consider a particular type of parametrically driven discrete Klein-Gordon system describing microdevices and nanodevices, with integrated electrical and mechanical functionality. Using a multiscale expansion method we reduce the system to a discrete nonlinear Schrödinger equation. Analytical and numerical calculations are performed to determine the existence and stability of fundamental bright and dark discrete solitons admitted by the Klein-Gordon system through the discrete Schrödinger equation. We show that a parametric driving can not only destabilize onsite bright solitons, but also stabilize intersite bright discrete solitons and onsite and intersite dark solitons. Most importantly, we show that there is a range of values of the driving coefficient for which dark solitons are stable, for any value of the coupling constant, i.e., oscillatory instabilities are totally suppressed. Stability windows of all the fundamental solitons are presented and approximations to the onset of instability are derived using perturbation theory, with accompanying numerical results. Numerical integrations of the Klein-Gordon equation are performed, confirming the relevance of our analysis.

Variational approximations for traveling solitons in a discrete nonlinear Schrödinger equation

Traveling solitary waves in the one-dimensional discrete nonlinear Schrodinger equation with saturable onsite nonlinearity are studied. A variational approximation (VA) for the solitary waves is derived in analytical form. The stability is also studied by means of the VA, demonstrating that the solitons are stable, which is consistent with previously published results. Then, the VA is applied to predict parameters of traveling solitons with non-oscillatory tails (embedded solitons, ESs). Two-soliton bound states are considered too. The separation distance between the solitons forming the bound state is derived by means of the VA. A numerical scheme based on the discretization of the equation in the moving coordinate frame is derived and implemented using the Newton–Raphson method. In general, good agreement between the analytical and numerical results is obtained. In particular, we demonstrate the relevance of the analytical prediction of characteristics of the embedded solitons.