Nonlinear waves in curved potentials, applications in laser physics and supercontinuum generation

Project leaders

Claudio Conti, Ray-kuang Lee

Agreement

TAIWAN - NSTC - National Science and Technology Council

Call

CNR-MoST (ex NSC) 2016-2017

Department

Physical sciences and technologies of matter

Thematic area

Physical sciences and technologies of matter

Status of the project

New

Research proposal

Lord Rayleigh and others studied the effect of geometry on wave propagation since early developments of the theory of sound, for example, in the vibrations of membranes with different shapes. Geometry changes energy velocity, wave transformations upon propagation, and various classical and quantum undulatory phenomena. This effect occurs in constrained micron-scale propagation and at an astrophysical scale. Renowned examples include the Einstein lensing effect, the Hawking radiation, or the Unruh effect. Notwithstanding the old history, the link between geometry and waves is continuously fascinating many researchers, and is currently driving important applications as transformation optics, curved and twisted waveguides, and analogs of gravity in Bose-Einstein condensation or nonlinear optics.
Geometry not only changes linear propagation; studies on solitons in curved manifolds reveal many interesting phenomena on nonlinear waves. Topologically induced localization is perhaps the most striking: constraining the wave in extremely deformed regions, inhibits propagation and traps energy at the points with the largest curvature. In particular, symmetry-breaking in geometry was introduced by the applicants from Taiwan part to analyze crescent waves in an elliptical ring, where strongly localization of wave was predicted due to the confinement induced by the symmetry-breaking in geometry. As a result, thresholdless crescent waves are found numerically and illustrated analytically when the ellipticity of the ring is larger than a critical value. Our previous studies provide an interesting result for the understanding in the interplay between symmetry-breaking phenomenon and nonlinear modes.
In general, we do not know if geometrical localization can compete with nonlinearity, and the kind of dynamics resulting from a nonlinear response sufficiently strong to overcome topological bounds. As a first step, the interaction or competition between geometric manifold and modulation instability (MI) is unaware, even though the latter one has acted as a universal signature of symmetry-breaking phenomena in different areas of nonlinear systems. In this proposal, an alternative way to control of MI in photorefractive crystals is going to study by imposing a variety of curvature in potentials, as well as bending and twisting. Moreover, we may expect that at high nonlinearity shock waves (SW) generate. Indeed, recent studies by the applicants from Italianpart in optics and Bose-Einstein condensation (BEC) reveal that SW originate from singular solutions of the hydrodynamic reduction of the nonlinear Schroedinger equation (NLS) and are regularized by oscillating wave fronts (``dispersive SW'', D-SW). However, we do not know the effect of a curved space on DSW. If we are able to understand the way geometry alters highly nonlinear regimes, we may eventually control them and engineer shock waves and related phenomena, as supercontinuum generation.
This problem has a key difficulty: if geometrical localization occurs in a reduced dimensionality (e.g., a curved surface in a three dimensional space), when nonlinearity is very effective the whole three-dimensional (3D) space becomes involved, and any treatment based on nonlinear wave equations with reduced dimensionality may be questioned. Any theoretical prediction must be numerically tested by using 3D simulations.
In this project we will study the effect of geometrical constraints on modern nonlinear optical processes and laser devices with the goal to understand to what extent controlling geometrical features, deformation in guiding structures as bend and twist, and spatial constraint may alter and control emission in extreme nonlinear regimes as laser emission in vertical vertical-cavity surface-emitting laser (VCSEL) and light propagation in highly nonlinear materials. We will consider both Hamiltonian and Lasers systems for a comprehensive analysis of the effects and possibilities opened by geometry on extreme waves:
For Hamiltonian systems we will consider light propagation in fibers, which can be bended and twisted. In highly nonlinear regimes, shock waves and supercontinuum generation occurs; the effect of geometrical constraints in unknown; but can potentially allow for a novel class of ultra-broad band generation and novel sources for short wavelength (soft-X ray, high UV).
For laser emission, GaAs-based VCSEL with an elliptical ring pattern on the emission aperture defined by p-pad meta was demonstrated. VCSEL may be realized with elliptical shape with varying ellipticity; this parameter controls the local curvature and affects the degree of localization of the laser mode. However, a comprehensive analysis is missing, and the full potentiality is not been developed.
For nonlinear optical propagation we will consider the effect of geometrical transformation, as bending and twisting on guiding structure as optical fibers and waveguides.
The proposing groups are worldwide renowned as leading recent developments in nonlinear optics of complex systems and have reported a number of important achievements, as the direct observation of phase transitions in multi modal lasers and nonlinear optical propagation. The analysis will be curried out by theoretical approaches and experimental investigations. If successful we will contribute to the development of novel broadband coherent sources and novel laser sources with a number of applications ranging from biophysics and spectroscopy, to telecommunications and quantum information.

Research goals

Our goal is to use geometry to control extreme nonlinear regimes. Due to the fact that the nonlinear Schroedinger equations and the Ginzburg-Landau equation allows to analyze lasers and Hamiltonian systems in a unified way, we will tackle these problem in a general perspective and consider the following topics:
1) Shock waves with curvature, generation of temporal and spatial shocks in system with curvatures, as bent optical fibers and waveguides. We want to determine if the shock point and the related generation of supercontinum is affected by geometry, and if geometry can be used to enhance or inhibit the onset of the shock.
2) Shock waves with twisting. A twisted fiber can be described in terms of an effective magnetic potential, the way this alters the shock and the supercontinuum is unknown. We want to understand if the angular momentum induced by the twisting may be used to phase match the harmonic content of the supercontinuum generation.
3) Nonlinear lasing modes and related far-field patterns within elliptical potentials and hyperbolic. We want to determine if an external potential with different curvature changes the laser emission, and the coherent properties of the emitted radiation in terms of multimodal interaction and directionality.
The final goal of the project is determining the conditions for enhancing supercontinumm generation and the efficiency of lasers by controlling the geometrical and topological potential of the considered systems.

Last update: 25/04/2024