Sergey V. Suchkov

Nonlinear switching and solitons in PT‐symmetric photonic systems

One of the challenges of the modern photonics is to develop all-optical devices enabling increased speed and energy efficiency for transmitting and processing information on an optical chip. It is believed that the recently suggested Parity-Time (PT) symmetric photonic systems with alternating regions of gain and loss can bring novel functionalities. In such systems, losses are as important as gain and, depending on the structural parameters, gain compensates losses. Generally, PT systems demonstrate nontrivial non-conservative wave interactions and phase transitions, which can be employed for signal filtering and switching, opening new prospects for active control of light. In this review, we discuss a broad range of problems involving nonlinear PT-symmetric photonic systems with an intensity-dependent refractive index. Nonlinearity in such PT symmetric systems provides a basis for many effects such as the formation of localized modes, nonlinearly-induced PT-symmetry breaking, and all-optical switching. Nonlinear PT-symmetric systems can serve as powerful building blocks for the development of novel photonic devices targeting an active light control.

Breathers in PT-symmetric optical couplers

We show that parity-time- (PT-) symmetric coupled optical waveguides with gain and loss support localized oscillatory structures similar to the breathers of the classical φ 4 model. The power carried by the PT breather oscillates periodically, switching back and forth between the waveguides, so that the gain and loss are compensated on the average. The breathers are found to coexist with solitons and to be prevalent in the products of the soliton collisions. We demonstrate that the evolution of a small-amplitude breather’s envelope is governed by a system of two coupled nonlinear Schr¨ odinger equations and employ this Hamiltonian system to show that small-amplitude PT breathers are stable.

Solitons in a chain of parity-time-invariant dimers

Dynamics of a chain of interacting parity-time-invariant nonlinear dimers is investigated. A dimer is built as a pair of coupled elements with equal gain and loss. A relation between stationary soliton solutions of the model and solitons of the discrete nonlinear Schrödinger (DNLS) equation is demonstrated. Approximate solutions for solitons whose width is large in comparison to the lattice spacing are derived, using a continuum counterpart of the discrete equations. These solitons are mobile, featuring nearly elastic collisions. Stationary solutions for narrow solitons, which are immobile due to the pinning by the effective Peierls-Nabarro potential, are constructed numerically, starting from the anticontinuum limit. The solitons with the amplitude exceeding a certain critical value suffer an instability leading to blowup, which is a specific feature of the nonlinear parity-time-symmetric chain, making it dynamically different from DNLS lattices. A qualitative explanation of this feature is proposed. The instability threshold drops with the increase of the gain-loss coefficient, but it does not depend on the lattice coupling constant, nor on the solitons velocity.

Wave scattering on a domain wall in a chain of PT-symmetric couplers

We study wave propagation in linear arrays composed of pairs of conjugate waveguides with balanced gain and loss, i.e. arrays of the PT-symmetric couplers, where the linear spectrum is known to feature high-frequency and low-frequency branches. We introduce a domain wall by switching the gain and loss in a half of the array, and analyze the scattering of linear waves on this defect. The analysis reveals two major effects: amplification of both reflected and transmitted waves, and excitation of the reflected and transmitted low-frequency and high-frequency waves by the incident high-frequency and low-frequency waves, respectively.

Scattering of the discrete solitons on the

We study the propagation of linear waves and solitons in an array of optical waveguides with an embedded defect created by a pair of waveguides with gain and loss satisfying the so-called parity-time () symmetry condition. We demonstrate that in the case of small soliton amplitudes, the linear theory describes the scattering of solitons with a good accuracy. We find that the incident high-amplitude solitons can excite the mode localized at the -symmetric defect. We also show that by exciting the localized mode of a large amplitude, it is possible to perform phase-sensitive control of soliton scattering and amplification or damping of the localized mode.

\mathcal {PT}

We study a structure composed of three coupled waveguides with gain and loss, a non-Hermitian trimer. We demonstrate that the mode spectrum can be entirely real if the waveguides are placed in a special order and at certain distances between each other. Such structures generally lack a spatial symmetry, in contrast to parity-time symmetric trimers which are known to feature a real spectrum. We also determine a threshold for wave amplification and analyse the scattering properties of such non-conservative systems embedded into a chain of conservative waveguides.

-symmetric defects

We develop a theory of optical frequency comb generation in ultra-compact surface nanoscale axial photonic (SNAP) bottle microresonators, employing the nonlinear interaction of whispering gallery modes which are confined along an optical fiber with nanoscale radius variation. We predict that a SNAP microresonator with a radius of a few micrometers can generate a frequency comb with an ultra-fine sub-gigahertz spectral spacing, which would require traditional ring resonators of centimeter radius. We identify regimes of stable or quasi-periodic comb dynamics due to soliton excitation, and show that special engineering of the SNAP radius profile can be used to compensate for nonlinearity-induced dispersion.

Non-Hermitian trimers: PT-symmetry versus pseudo-Hermiticity

compiled: June 4, 2015We consider an optical fiber with nanoscale variation of the effective fiber radius supporting whispering gallerymodes slowly propagating along the fiber, and reveal that the radius variation can be designed to supportreflectionless propagation of these modes. We show that reflectionless modulations can realize control oftransmission amplitude and temporal delay, while enabling close packing due to the absence of cross-talk, incontrast to conventional potentials.OCIS codes: 060.2340, 140.3945, 230.3990http://dx.doi.org/10.1364/XX.99.099999We consider an optical fiber with a nanoscale variation of the effective fiber radius that supports whispering gallery modes slowly propagating along the fiber, and reveal that the radius variation can be designed to support the reflectionless propagation of these modes. We show that reflectionless modulations can realize control of the transmission amplitude and temporal delay, while enabling close packing due to the absence of cross talk, in contrast to the conventional potentials.

Frequency comb generation in SNAP bottle resonators

The interaction between breathers has been studied in the model of a nonlinear plane PJ-symmetric coupler. It has been shown that the dynamics of the interaction depends significantly on the relative phase of the breathers. The probability of breaking of the PJ symmetry in the collision of breathers having random initial phases has been estimated for various sets of parameters of the model and breathers. Various scenarios of collision of breathers have been described.

Reflectionless potentials for slow whispering gallery modes in surface nanoscale axial photonic fiber resonators

We study the scattering of linear waves in a long waveguide array with a parity-time (PT) — symmetric defect created by two waveguides with balanced gain and loss. We present exact solutions for the scattering of linear waves on such a defect. We reveal that the refl ected and transmitted linear waves can be amplifi ed substantially aft er interaction with the PT-symmetric defect thus allowing an active control of the wave propagating through the array.