Excitation Thresholds for Nonlinear Localized Modes on Lattices

Breathers are spatially localized and time periodic solutions of extended Hamiltonian dynamical systems. In this paper we study excitation thresholds for (nonlinearly dynamically stable) ground state breather or standing wave solutions for networks of coupled nonlinear oscillators and wave equations of nonlinear Schr\"odinger (NLS) type. Excitation thresholds are rigorously characterized by variational methods. The excitation threshold is related to the optimal (best) constant in a class of discr ete interpolation inequalities related to the Hamiltonian energy. We establish a precise connection among $d$, the dimensionality of the lattice, $2\sigma+1$, the degree of the nonlinearity and the existence of an excitation threshold for discrete nonlinear Schr\"odinger systems (DNLS). We prove that if $\sigma\ge 2/d$, then ground state standing waves exist if and only if the total power is larger than some strictly positive threshold, $\nu_{thresh}(\sigma, d)$. This proves a conjecture of Flach, Kaldko& MacKay in the context of DNLS. We also discuss upper and lower bounds for excitation thresholds for ground states of coupled systems of NLS equations, which arise in the modeling of pulse propagation in coupled arrays of optical fibers.Comment: To appear in Nonlinearit

Fiber laser systems shine brightly

Describes the advancements in active fiber laser systems. Outline of cladding pumping technique for enhanced power scaling; Improved energies and peak powers; Extended wavelength range; Frequency doubling with fiber sources

Sine-Gordon breathers generation in driven long Josephson junctions

We consider a long Josephson junction excited by a suitable external ac-signal, in order to generate control and detect breathers. Studying the nonlinear supratransmission phenomenon in a nonlinear sine-Gordon chain sinusoidally driven, Geniet and Leon explored the bifurcation of the energy transmitted into the chain and calculated a threshold $A (\omega)$ for the external driving signal amplitude, at which the energy flows into the system by breathers modes. I numerically study the continuous sine-Gordon model, describing the dynamics of the phase difference in a long Josephson junction, in order to deeply investigate the "continuous limit" modifications to this threshold. Wherever the energy flows into the system due to the nonlinear supratransmission, a peculiar breather localization areas appear in a $(A, \omega)$ parameters space. The emergence of these areas depends on the damping parameter value, the bias current, and the waveform of driving external signal. The robustness of generated breathers is checked by introducing into the model a thermal noise source to mimic the environmental fluctuations. Presented results allows one to consider a cryogenic experiment for creation and detection of Josephson breathers.Comment: 8 pages, 3 figure

Opto-electronic high order feedback neural network

A novel neural network design, in which nonlinearities are created by feedback, is described. It is called the HOFNET. The design is suitable for optical implementation because it is tolerant of the limited dynamic ranges present in optical systems. An optical system with electronic feedback was constructed and its operation is described

Zero supermode-based multipartite entanglement in χ(2)\chi^{(2)} nonlinear waveguides arrays

We show that arrays of $\chi^{(2)}$ nonlinear waveguides in the second harmonic generation regime are a promising source of continuous-variable entanglement. We indeed demonstrate analytically that optical arrays with odd number of waveguides injected with the zero-eigenvalue fundamental supermode entangle this fundamental supermode with a collective harmonic field. Moreover the fundamental individual modes are multipartite entangled and their entanglement grows with propagation length. The device is scalable, robust to losses, does not rely on specific values of nonlinearity and coupling and is easily realized with current technology. It thus stands as an unprecedented candidate for generation of multipartite continuous-variable entanglement for optical quantum information processing.Comment: Main text: 7 pages, 6 figures. Supplemental material: 5 pages, 2 figure. v2 closer to published versio

Mid-Infrared nonlinear silicon photonics

Recently there has been a growing interest in mid-infrared (mid-IR) photonic technology with a wavelength of operation approximately from 2-14 mu m. Among several established mid-IR photonic platforms, silicon nanophotonic platform could potentially offer ultra-compact, and monolithically integrated mid-IR photonic devices and device arrays, which could have board impact in the mid-IR technology, such as molecular spectroscopy, and imaging. At room temperature, silicon has a bandgap similar to 1.12 eV resulting in vanishing two-photon absorption (TPA) for mid-IR wavelengths beyond 2.2 mu m, which, coupled with silicon's large nonlinear index of refraction and its strong waveguide optical confinement, enables efficient nonlinear processes in the mid-IR. By taking advantage of these nonlinear processes and judicious dispersion engineering in silicon waveguides, we have recently demonstrated a handful of silicon mid-IR nonlinear components, including optical parametric amplifiers (OPA), broadband sources, and a wavelength translator. Silicon nanophotonic waveguide's anomalous dispersion design, providing four-wave-mixing (FWM) phase-matching, has enabled the first demonstration of silicon mid-IR optical parametric amplifier (OPA) with a net off-chip gain exceeding 13 dB. In addition, reduction of propagation losses and balanced second and fourth order waveguide dispersion design led to an OPA with an extremely broadband gain spectrum from 1.9-2.5 mu m and > 50 dB parametric gain, upon which several novel silicon mid-IR light sources were built, including a mid-IR optical parametric oscillator, and a supercontinuum source. Finally, a mid-IR wavelength translation device, capable of translating signals near 2.4 mu m to the telecom-band near 1.6 mu m with simultaneous 19 dB gain, was demonstrated

Electro-optically tunable microring resonators in lithium niobate

Optical microresonators have recently attracted a growing attention in the photonics community. Their applications range from quantum electro-dynamics to sensors and filtering devices for optical telecommunication systems, where they are likely to become an essential building block. The integration of nonlinear and electro-optical properties in the resonators represents a very stimulating challenge, as it would incorporate new and more advanced functionality. Lithium niobate is an excellent candidate material, being an established choice for electro-optic and nonlinear optical applications. Here we report on the first realization of optical microring resonators in submicrometric thin films of lithium niobate. The high index contrast films are produced by an improved crystal ion slicing and bonding technique using benzocyclobutene. The rings have radius R=100 um and their transmission spectrum has been tuned using the electro-optic effect. These results open new perspectives for the use of lithium niobate in chip-scale integrated optical devices and nonlinear optical microcavities.Comment: 15 pages, 8 figure

Emerging applications of integrated optical microcombs for analogue RF and microwave photonic signal processing

We review new applications of integrated microcombs in RF and microwave photonic systems. We demonstrate a wide range of powerful functions including a photonic intensity high order and fractional differentiators, optical true time delays, advanced filters, RF channelizer and other functions, based on a Kerr optical comb generated by a compact integrated microring resonator, or microcomb. The microcomb is CMOS compatible and contains a large number of comb lines, which can serve as a high performance multiwavelength source for the transversal filter, thus greatly reduce the cost, size, and complexity of the system. The operation principle of these functions is theoretically analyzed, and experimental demonstrations are presented.Comment: 16 pages, 8 figures, 136 References. Photonics West 2018 invited paper, expanded version. arXiv admin note: substantial text overlap with arXiv:1710.00678, arXiv:1710.0861

Solitons in cavity-QED arrays containing interacting qubits

We reveal the existence of polariton soliton solutions in the array of weakly coupled optical cavities, each containing an ensemble of interacting qubits. An effective complex Ginzburg-Landau equation is derived in the continuum limit taking into account the effects of cavity field dissipation and qubit dephasing. We have shown that an enhancement of the induced nonlinearity can be achieved by two order of the magnitude with a negative interaction strength which implies a large negative qubit-field detuning as well. Bright solitons are found to be supported under perturbations only in the upper (optical) branch of polaritons, for which the corresponding group velocity is controlled by tuning the interacting strength. With the help of perturbation theory for solitons, we also demonstrate that the group velocity of these polariton solitons is suppressed by the diffusion process