arXiv subjects

S. Bittner

Publications and source records attributed to S. Bittner.

At least 19 recordsLinked to original sources

arXiv2026

Graphs on chip: a silicon photonics platform

We present a versatile photonic waveguide network platform implementing quantum (wave) graphs, proposed by Kottos \& Smilansky [Phys. Rev. Lett. \textbf{79}, 4794 (1997)] to investigate ray-wave correspondence and quantum chaos. Realized on a silicon-on-insulator chip at telecom wavelengths, it enables a unique capability: the direct, non-invasive imaging of individual optical wave functions with unprecedented resolution via third-harmonic generation in silicon, which we use to study the localization of intensity distributions. Furthermore, by investigating two graphs with contrasting classical dynamics -- one strongly chaotic, the other one ergodic, but non-mixing -- we reveal strikingly different spectral statistics, in quantitative agreement with random matrix theory and a minimal unitary quantum-map model. This establishes silicon photonics networks as a versatile and scalable platform for investigating quantum chaos and non-linear graphs, and paves the way for optical quantum computing in complex networks.

quant-ph↗

arXiv2024

Exploring non-Euclidean photonics: Pseudosphere microlaser

Classical and wave properties of microlasers with the shape of a truncated pseudosphere are investigated through experiments and numerical simulations. These pseudosphere microlasers are surface-like organic microlasers with constant negative curvature, which were fabricated with high optical quality by direct laser writing. It is shown that they behave, in many ways, similar to two-dimensional flat disks, regardless of their different Gaussian curvature. We derive the monodromy matrices for geodesics on the pseudosphere and demonstrate that the periodic geodesics are marginally stable. Actually, due to the rotational symmetry, the pseudosphere is an integrable system.

physics.optics↗

arXiv2024

Spontaneous phase locking in a broad-area semiconductor laser

Broad-area semiconductor lasers are employed in many high-power applications, however, their spatio-temporal dynamics is complex and intrinsically unstable due to the interaction of several transverse lasing modes. A dynamical and spatio-spectral analysis with ultra-high resolution of commercial broad-area lasers reveals multiplets of phase-locked first- and second-order transverse modes that are spontaneously created by the nonlinear dynamics for a wide range of operation parameters. Phase locking between modes of different transverse order is demonstrated by comparing the linewidths of the lasing modes to that of their beat note and by a direct measurement of their phase fluctuation correlations. The spontaneous phase locking is unexpected since the overall dynamics is unstable and the system lacks any intentional feature to induce locking. This partially synchronized dynamical state with groups of synchronized and unsynchronized laser modes coexisting is similar to what is called a chimera state in networks of coupled oscillators, hence indicating that such states may exist in a wider range of systems than previously assumed. Moreover, some of the phase-locked modes do not exist on the passive-cavity level, but are created by the nonlinear dynamics, an effect not previously observed in the context of partially synchronized laser modes.

physics.optics↗

arXiv2019

Three-dimensional micro-billiard lasers: the square pyramid

Microlasers are of ample interest for advancing quantum chaos studies at the intersection of wave dynamics and geometric optics in resonators. However, the mode structures of three-dimensional microlasers without rotational symmetry remain largely unexplored due to fabrication limitations. Previous studies of such cavities revealed lasing modes localized on periodic orbits exclusively confined to a single plane. In this work, we report on the characterization of pyramidal, polymer-based microlasers and demonstrate that the lasing modes are localized on a genuine three-dimensional periodic orbit. The consequences on the laser features are further discussed, in particular stability and polarization issues.

physics.optics↗

arXiv2018

Dynamical control of square microlaser emission via symmetry classes

A major objective in photonics is to tailor the emission properties of microcavities which is usually achieved with specific cavity shapes. Yet, the dynamical change of the emission properties during operation would often be advantageous. The implementation of such a method is still a challenging issue. We present an effective procedure for the dynamical control of the emission lobes which relies on the selection of a specific coherent superposition of degenerate modes belonging to different symmetry classes. It is generally applicable to systems exhibiting pairs of degenerate modes. We explored it experimentally and analytically with organic square microlasers, which emit narrow lobes parallel to their sidewalls. By means of the pump polarization, emission lobes are switched on and off selectively with an extinction ratio better 1/50.

physics.optics↗

arXiv2016

Waves and rays in plano-concave laser cavities, Part~II: a semiclassical approach

This second paper on the Fabry-Perot cavity presents a semi-classical approach, which means that we consider the transition from wave optics to geometrical optics. The basic concepts are the periodic orbits and their stability. For the plano-concave Fabry-Perot cavity in the paraxial approximation, the derivation of the trace formula demonstrates that the spectrum is based only on the axial periodic orbit and its repetitions. Experiments with micro-lasers illustrate the relation to periodic orbits. The methods presented in this paper are not limited to laser cavities and can be applied to a large range of wave systems.

physics.optics↗

arXiv2016

Origin of emission from square-shaped organic microlasers

The emission from open cavities with non-integrable features remains a challenging problem of practical as well as fundamental relevance. Square-shaped dielectric microcavities provide a favorable case study with generic implications for other polygonal resonators. We report on a joint experimental and theoretical study of square-shaped organic microlasers exhibiting a far-field emission that is strongly concentrated in the directions parallel to the side walls of the cavity. A semiclassical model for the far-field distributions is developed that is in agreement with even fine features of the experimental findings. Comparison of the model calculations with the experimental data allows the precise identification of the lasing modes and their emission mechanisms, providing strong support for a physically intuitive ray-dynamical interpretation. Special attention is paid to the role of diffraction and the finite side length.

physics.optics↗

arXiv2015

Unidirectional light emission from low-index polymer microlasers

We report on experiments with deformed polymer microlasers that have a low refractive index and exhibit unidirectional light emission. We demonstrate that the highly directional emission is due to transport of light rays along the unstable manifold of the chaotic saddle in phase space. Experiments, ray-tracing simulations, and mode calculations show very good agreement.

physics.optics↗

arXiv2014

Localized lasing modes of triangular organic microlasers

We investigated experimentally the ray-wave correspondence in organic microlasers of various triangular shapes. Triangular billiards are of interest since they are the simplest cases of polygonal billiards and the existence and properties of periodic orbits in triangles are not yet fully understood. The microlasers with symmetric shapes that were investigated exhibited states localized on simple periodic orbits, and their lasing characteristics like spectra and far-field distributions could be well explained by the properties of the periodic orbits. Furthermore, asymmetric triangles that do not feature simple periodic orbits were studied. Their lasing properties were found to be more complicated and could not be explained by periodic orbits.

physics.optics↗

arXiv2014

Dielectric Square Resonator Investigated with Microwave Experiments

We present a detailed experimental study of the symmetry properties and the momentum space representation of the field distributions of a dielectric square resonator as well as the comparison with a semiclassical model. The experiments have been performed with a flat ceramic microwave resonator. Both the resonance spectra and the field distributions were measured. The momentum space representations of the latter evidenced that the resonant states are each related to a specific classical torus, leading to the regular structure of the spectrum. Furthermore, they allow for a precise determination of the refractive index. Measurements with different arrangements of the emitting and the receiving antennas were performed and their influence on the symmetry properties of the field distributions was investigated in detail, showing that resonances with specific symmetries can be selected purposefully. In addition, the length spectrum deduced from the measured resonance spectra and the trace formula for the dielectric square resonator are discussed in the framework of the semiclassical model.

physics.optics↗

arXiv2014

Scattering Experiments with Microwave Billiards at an Exceptional Point under Broken Time Reversal Invariance

Scattering experiments with microwave cavities were performed and the effects of broken time-reversal invariance (TRI), induced by means of a magnetized ferrite placed inside the cavity, on an isolated doublet of nearly degenerate resonances were investigated. All elements of the effective Hamiltonian of this two-level system were extracted. As a function of two experimental parameters, the doublet and also the associated eigenvectors could be tuned to coalesce at a so-called exceptional point (EP). The behavior of the eigenvalues and eigenvectors when encircling the EP in parameter space was studied, including the geometric amplitude that builds up in the case of broken TRI. A one-dimensional subspace of parameters was found where the differences of the eigenvalues are either real or purely imaginary. There, the Hamiltonians were found PT-invariant under the combined operation of parity (P) and time reversal (T) in a generalized sense. The EP is the point of transition between both regions. There a spontaneous breaking of PT occurs.

nlin.CD↗

arXiv2013

Experimental Observation of Localized Modes in a Dielectric Square Resonator

We investigated the frequency spectra and field distributions of a dielectric square resonator in a microwave experiment. Since such systems cannot be treated analytically, the experimental studies of their properties are indispensable. The momentum representation of the measured field distributions shows that all resonant modes are localized on specific classical tori of the square billiard. Based on these observations a semiclassical model was developed. It shows excellent agreement with all but a single class of measured field distributions that will be treated separately.

physics.optics↗

arXiv2013

Bound States in Sharply Bent Waveguides: Analytical and Experimental Approach

Quantum wires and electromagnetic waveguides possess common features since their physics is described by the same wave equation. We exploit this analogy to investigate experimentally with microwave waveguides and theoretically with the help of an effective potential approach the occurrence of bound states in sharply bent quantum wires. In particular, we compute the bound states, study the features of the transition from a bound to an unbound state caused by the variation of the bending angle and determine the critical bending angles at which such a transition takes place. The predictions are confirmed by calculations based on a conventional numerical method as well as experimental measurements of the spectra and electric field intensity distributions of electromagnetic waveguides.

cond-mat.mes-hall↗

arXiv2012

Trace formula for chaotic dielectric resonators tested with microwave experiments

We measured the resonance spectra of two stadium-shaped dielectric microwave resonators and tested a semiclassical trace formula for chaotic dielectric resonators proposed by Bogomolny et al. [Phys. Rev. E 78, 056202 (2008)]. We found good qualitative agreement between the experimental data and the predictions of the trace formula. Deviations could be attributed to missing resonances in the measured spectra in accordance with previous experiments [Phys. Rev. E 81, 066215 (2010)]. The investigation of the numerical length spectrum showed good qualitative and reasonable quantitative agreement with the trace formula. It demonstrated, however, the need for higher-order corrections of the trace formula. The application of a curvature correction to the Fresnel reflection coefficients entering the trace formula yielded better agreement, but deviations remained, indicating the necessity of further investigations.

physics.optics↗

arXiv2012

Application of a trace formula to the spectra of flat three-dimensional dielectric resonators

The length spectra of flat three-dimensional dielectric resonators of circular shape were determined from a microwave experiment. They were compared to a semiclassical trace formula obtained within a two-dimensional model based on the effective index of refraction approximation and a good agreement was found. It was necessary to take into account the dispersion of the effective index of refraction for the two-dimensional approximation. Furthermore, small deviations between the experimental length spectrum and the trace formula prediction were attributed to the systematic error of the effective index of refraction approximation. In summary, the methods developed in this article enable the application of the trace formula for two-dimensional dielectric resonators also to realistic, flat three-dimensional dielectric microcavities and -lasers, allowing for the interpretation of their spectra in terms of classical periodic orbits.

physics.optics↗

arXiv2011

Extremal transmission through a microwave photonic crystal and the observation of edge states in a rectangular Dirac billiard

This article presents experimental results on properties of waves propagating in an unbounded and a bounded photonic crystal consisting of metallic cylinders which are arranged in a triangular lattice. First, we present transmission measurements of plane waves traversing a photonic crystal. The experiments are performed in the vicinity of a Dirac point, i.e., an isolated conical singularity of the photonic band structure. There, the transmission shows a pseudodiffusive 1/L dependence, with $L$ being the thickness of the crystal, a phenomenon also observed in graphene. Second, eigenmode intensity distributions measured in a microwave analog of a relativistic Dirac billiard, a rectangular microwave billiard that contains a photonic crystal, are discussed. Close to the Dirac point states have been detected which are localized at the straight edge of the photonic crystal corresponding to a zigzag edge in graphene.

cond-mat.other↗

arXiv2011

PT symmetry and spontaneous symmetry breaking in a microwave billiard

We demonstrate the presence of parity-time (PT) symmetry for the non-Hermitian two-state Hamiltonian of a dissipative microwave billiard in the vicinity of an exceptional point (EP). The shape of the billiard depends on two parameters. The Hamiltonian is determined from the measured resonance spectrum on a fine grid in the parameter plane. After applying a purely imaginary diagonal shift to the Hamiltonian, its eigenvalues are either real or complex conjugate on a curve, which passes through the EP. An appropriate basis choice reveals its PT symmetry. Spontaneous symmetry breaking occurs at the EP.

quant-ph↗

arXiv2011

Double-Slit Experiments with Microwave Billiards

Single and double-slit experiments are performed with two microwave billiards with the shapes of a rectangle, respectively, a quarter stadium. The classical dynamics of the former is regular, that of the latter is chaotic. Microwaves can leave the billiards via slits in the boundary, forming interference patterns on a screen. The aim is to determine the effect of the billiard dynamics on their structure. For this the development of a method for the construction of a directed wave packet by means of an array of multiple antennas was crucial. The interference patterns show a sensitive dependence not only on the billiard dynamics but also on the initial position and direction of the wave packet.

nlin.CD↗