A fractal-based fibre for ultra-high throughput optical probes

A core component of all scanning near-field optical microscopy (SNOM) systems is the optical probe, which has evolved greatly but still represents the limiting component for the system. Here, we introduce a new type of optical probe, based on a Fractal Fibre which is a special class of photonic crystal fibre (PCF), to directly address the issue of increasing the optical throughput in SNOM probes. Optical measurements through the Fractal Fibre probes have shown superior power levels to that of conventional SNOM probes. The results presented in this paper suggest that a novel fibre design is critical in order to maximize the potential of the SNOM

A Potential of Interaction between Two- and Three-Dimensional Solitons

A general method to find an effective potential of interaction between far separated 2D and 3D solitons is elaborated, including the case of 2D vortex solitons. The method is based on explicit calculation of the overlapping term in the full Hamiltonian of the system (_without_ assuming that the ``tail'' of each soliton is not affected by its interaction with the other soliton, and, in fact,_without_ knowing the exact form of the solution for an isolated soliton - the latter problem is circumvented by reducing a bulk integral to a surface one). The result is obtained in an explicit form that does not contain an artificially introduced radius of the overlapping region. The potential applies to spatial and spatiotemporal solitons in nonlinear optics, where it may help to solve various dynamical problems: collisions, formation of bound states (BS's), etc. In particular, an orbiting BS of two solitons is always unstable. In the presence of weak dissipation and gain, the effective potential can also be derived, giving rise to bound states similar to those recently studied in 1D models.Comment: 29 double-spaced pages in the latex format and 1 figure in the ps format. The paper will appear in Phys. Rev.

Rotating optical soliton clusters

We introduce the concept of soliton clusters -- multi-soliton bound states in a homogeneous bulk optical medium, and reveal a key physical mechanism for their stabilization associated with a staircase-like phase distribution that induces a net angular momentum and leads to cluster rotation. The ringlike soliton clusters provide a nontrivial generalization of the concepts of two-soliton spiraling, optical vortex solitons, and necklace-type optical beams.Comment: 4 pages, 5 figure

Instabilities of Higher-Order Parametric Solitons. Filamentation versus Coalescence

We investigate stability and dynamics of higher-order solitary waves in quadratic media, which have a central peak and one or more surrounding rings. We show existence of two qualitatively different behaviours. For positive phase mismatch the rings break up into filaments which move radially to initial ring. For sufficient negative mismatches rings are found to coalesce with central peak, forming a single oscillating filament.Comment: 5 pages, 7 figure

Induced Coherence and Stable Soliton Spiraling

We develop a theory of soliton spiraling in a bulk nonlinear medium and reveal a new physical mechanism: periodic power exchange via induced coherence, which can lead to stable spiraling and the formation of dynamical two-soliton states. Our theory not only explains earlier observations, but provides a number of predictions which are also verified experimentally. Finally, we show theoretically and experimentally that soliton spiraling can be controled by the degree of mutual initial coherence.Comment: 4 pages, 5 figure

Approximate solutions and scaling transformations for quadratic solitons

We study quadratic solitons supported by two- and three-wave parametric interactions in chi-2 nonlinear media. Both planar and two-dimensional cases are considered. We obtain very accurate, 'almost exact', explicit analytical solutions, matching the actual bright soliton profiles, with the help of a specially-developed approach, based on analysis of the scaling properties. Additionally, we use these approximations to describe the linear tails of solitary waves which are related to the properties of the soliton bound states.Comment: 11 pages, 9 figures; submitted for publicatio

Higher-order nonlinear modes and bifurcation phenomena due to degenerate parametric four-wave mixing

We demonstrate that weak parametric interaction of a fundamental beam with its third harmonic field in Kerr media gives rise to a rich variety of families of non-fundamental (multi-humped) solitary waves. Making a comprehensive comparison between bifurcation phenomena for these families in bulk media and planar waveguides, we discover two novel types of soliton bifurcations and other interesting findings. The later includes (i) multi-humped solitary waves without even or odd symmetry and (ii) multi-humped solitary waves with large separation between their humps which, however, may not be viewed as bound states of several distinct one-humped solitons.Comment: 9 pages, 17 figures, submitted to Phys. Rev.

Polychromatic solitons in a quadratic medium

We introduce the simplest model to describe parametric interactions in a quadratically nonlinear optical medium with the fundamental harmonic containing two components with (slightly) different carrier frequencies [which is a direct analog of wavelength-division multiplexed (WDM) models, well known in media with cubic nonlinearity]. The model takes a closed form with three different second-harmonic components, and it is formulated in the spatial domain. We demonstrate that the model supports both polychromatic solitons (PCSs), with all the components present in them, and two types of mutually orthogonal simple solitons, both types being stable in a broad parametric region. An essential peculiarity of PCS is that its power is much smaller than that of a simple (usual) soliton (taken at the same values of control parameters), which may be an advantage for experimental generation of PCSs. Collisions between the orthogonal simple solitons are simulated in detail, leading to the conclusion that the collisions are strongly inelastic, converting the simple solitons into polychromatic ones, and generating one or two additional PCSs. A collision velocity at which the inelastic effects are strongest is identified, and it is demonstrated that the collision may be used as a basis to design a simple all-optical XOR logic gate.Comment: 9 pages, 8 figures, accepted to Phys. Rev.

Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity

We consider solutions to the second-harmonic generation equations in two-and three-dimensional dispersive media in the form of solitons localized in space and time. As is known, collapse does not take place in these models, which is why the solitons may be stable. The general solution is obtained in an approximate analytical form by means of a variational approach, which also allows the stability of the solutions to be predicted. Then, we directly simulate the two-dimensional case, taking the initial configuration as suggested by the variational approximation. We thus demonstrate that spatiotemporal solitons indeed exist and are stable. Furthermore, they are not, in the general case, equivalent to the previously known cylindrical spatial solitons. Direct simulations generate solitons with some internal oscillations. However, these oscillations neither grow nor do they exhibit any significant radiative damping. Numerical solutions of the stationary version of the equations produce the same solitons in their unperturbed form, i.e., without internal oscillations. Strictly stable solitons exist only if the system has anomalous dispersion at both the fundamental harmonic and second harmonic (SH), including the case of zero dispersion at SH. Quasistationary solitons, decaying extremely slowly into radiation, are found in the presence of weak normal dispersion at the second-harmonic frequency