arXiv subjects

F. Maucher

Publications and source records attributed to F. Maucher.

12 recordsLinked to original sources

arXiv2023

Aberration-driven tilted emission in degenerate cavities

The compensation of chromatic dispersion opened new avenues and extended the level of control upon pattern formation in the \textit{temporal domain}. In this manuscript, we propose the use of a nearly-degenerate laser cavity as a general framework allowing for the exploration of higher contributions to diffraction in the \textit{spatial} domain. Our approach leverages the interplay between optical aberrations and the proximity to the self-imaging condition which allows to cancel or reverse paraxial diffraction. As an example, we show how spherical aberrations materialize into a transverse bilaplacian operator and, thereby, explain the stabilization of temporal solitons travelling off-axis in an unstable mode-locked broad-area surface-emitting laser. We disclose an analogy between these regimes and the dynamics of a quantum particle in a double well potential.

physics.optics↗

arXiv2018

An intuitive approach to structuring the three polarization components of light

This paper presents intuitive interpretations of tightly focused beams of light by drawing analogies to two-dimensional electrostatics, magnetostatics and fluid dynamics. We use a Helmholtz decomposition of the transverse polarization components in the transverse plane to introduce generalized radial and azimuthal polarization states. This reveals the interplay between transverse and longitudinal polarization components in a transparent fashion. Our approach yields a comprehensive understanding of tightly focused laser beams, which we illustrate through several insightful examples.

physics.optics↗

arXiv2018

Creating Complex Optical Longitudinal Polarization Structures

In this paper we show that it is possible to structure the longitudinal polarization component of light. We illustrate our approach by demonstrating linked and knotted longitudinal vortex lines acquired upon non-paraxially propagating a tightly focused sub-wavelength beam. Remaining degrees of freedom in the transverse polarization components can be exploited to generate customized topological vector beams.

physics.optics↗

arXiv2016

Excitation of knotted vortex lines in matter waves

We study the creation of knotted ultracold matter waves in Bose-Einstein condensates via coherent two-photon Raman transitions with a $Λ$ level configuration. The Raman transition allows an indirect transfer of atoms from the internal state $\left| a \right\rangle$ to the target state $\left| b \right\rangle$ via an excited state $\left| e \right\rangle$, that would be otherwise dipole-forbidden. This setup enables us to imprint three-dimensional knotted vortex lines embedded in the the probe field to the density in the target state. We elaborate on experimental feasibility as well as on subsequent dynamics of the matter wave.

cond-mat.quant-gas↗

arXiv2016

Self-organization of light in optical media with competing nonlinearities

We study the propagation of light beams through optical media with competing nonlocal nonlinearities. We demonstrate that the nonlocality of competing focusing and defocusing nonlinearities gives rise to self-organization and stationary states with stable hexagonal intensity patterns, akin to transverse crystals of light filaments. Signatures of this long-range ordering are shown to be observable in the propagation of light in optical waveguides and even in free space. We consider a specific form of the nonlinear response that arises in atomic vapor upon proper light coupling. Yet, the general phenomenon of self-organization is a generic consequence of competing nonlocal nonlinearities, and may, hence, also be observed in other settings.

nlin.PS↗

arXiv2013

Quasiperiodic oscillations and homoclinic orbits in the nonlinear nonlocal Schrödinger equation

Quasiperiodic oscillations and shape-transformations of higher-order bright solitons in nonlinear nonlocal media have been frequently observed in recent years, however, the origin of these phenomena was never completely elucidated. In this paper, we perform a linear stability analysis of these higher-order solitons by solving the Bogoliubov-de Gennes equations. This enables us to understand the emergence of a new oscillatory state as a growing unstable mode of a higher-order soliton. Using dynamically important states as a basis, we provide low-dimensional visualizations of the dynamics and identify quasiperiodic and homoclinic orbits, linking the latter to shape-transformations.

nlin.PS↗

arXiv2012

Stability of solitary waves in random nonlocal nonlinear media

We consider the interplay between nonlocal nonlinearity and randomness for two different nonlinear Schrödinger models. We show that stability of bright solitons in presence of random perturbations increases dramatically with the nonlocality-induced finite correlation length of the noise in the transverse plane, by means of both numerical simulations and analytical estimates. In fact, solitons are practically insensitive to noise when the correlation length of the noise becomes comparable to the extent of the wave packet. We characterize soliton stability using two different criteria based on the evolution of the Hamiltonian of the soliton and its power. The first criterion allows us to estimate a time (or distance) over which the soliton preserves its form. The second criterion gives the life-time of the solitary wave packet in terms of its radiative power losses. We derive a simplified mean field approach which allows us to calculate the power loss analytically in the physically relevant case of weakly correlated noise, which in turn serves as a lower estimate of the life-time for correlated noise in general case.

nlin.PS↗

arXiv2011

Rydberg-induced Solitons: Three-dimensional Self-trapping of Matter Waves

We propose a scheme for the creation of stable three dimensional bright solitons in Bose-Einstein condensates, i.e., the matter-wave analog of so-called spatio-temporal "light bullets". Off-resonant dressing to Rydberg $nD$-states is shown to provide nonlocal attractive interactions, leading to self-trapping of mesoscopic atomic clouds by a collective excitation of a Rydberg atom pair. We present detailed potential calculations, and demonstrate the existence of stable solitons under realistic experimental conditions by means of numerical simulations.

physics.atom-ph↗

arXiv2011

Analytical approximation of the exterior gravitational field of rotating neutron stars

It is known that Bäcklund transformations can be used to generate stationary axisymmetric solutions of Einstein's vacuum field equations with any number of constants. We will use this class of exact solutions to describe the exterior vacuum region of numerically calculated neutron stars. Therefore we study how an Ernst potential given on the rotation axis and containing an arbitrary number of constants can be used to determine the metric everywhere. Then we review two methods to determine those constants from a numerically calculated solution. Finally, we compare the metric and physical properties of our analytic solution with the numerical data and find excellent agreement even for a small number of parameters.

gr-qc↗

arXiv2011

Collapse in the nonlocal nonlinear Schrödinger equation

We discuss spatial dynamics and collapse scenarios of localized waves governed by the nonlinear Schrödinger equation with nonlocal nonlinearity. Firstly, we prove that for arbitrary nonsingular attractive nonlocal nonlinear interaction in arbitrary dimension collapse does not occur. Then we study in detail the effect of singular nonlocal kernels in arbitrary dimension using both, Lyapunoff's method and virial identities. We find that for for a one-dimensional case, i.e. for $n=1$, collapse cannot happen for nonlocal nonlinearity. On the other hand, for spatial dimension $n\geq2$ and singular kernel $\sim 1/r^α$, no collapse takes place if $α<2$, whereas collapse is possible if $α\ge2$. Self-similar solutions allow us to find an expression for the critical distance (or time) at which collapse should occur in the particular case of $\sim 1/r^2$ kernels. Moreover, different evolution scenarios for the three dimensional physically relevant case of Bose Einstein condensate are studied numerically for both, the ground state and a higher order toroidal state with and without an additional local repulsive nonlinear interaction. In particular, we show that presence of an additional local repulsive term can prevent collapse in those cases.

nlin.PS↗

arXiv2009

Rotating three-dimensional solitons in Bose Einstein condensates with gravity-like attractive nonlocal interaction

We study formation of rotating three-dimensional high-order solitons (azimuthons) in Bose Einstein condensate with attractive nonlocal nonlinear interaction. In particular, we demonstrate formation of toroidal rotating solitons and investigate their stability. We show that variational methods allow a very good approximation of such solutions and predict accurately the soliton rotation frequency. We also find that these rotating localized structures are very robust and persist even if the initial condensate conditions are rather far from the exact soliton solutions. Furthermore, the presence of repulsive contact interaction does not prevent the existence of those solutions, but allows to control their rotation. We conjecture that self-trapped azimuthons are generic for condensates with attractive nonlocal interaction.

cond-mat.quant-gas↗

arXiv2009

Tracking azimuthons in nonlocal nonlinear media

We study the formation of azimuthons, i.e., rotating spatial solitons, in media with nonlocal focusing nonlinearity. We show that whole families of these solutions can be found by considering internal modes of classical non-rotating stationary solutions, namely vortex solitons. This offers an exhaustive method to identify azimuthons in a given nonlocal medium. We demonstrate formation of azimuthons of different vorticities and explain their properties by considering the strongly nonlocal limit of accessible solitons.

nlin.PS↗