arXiv subjects

Martina Hentschel

Publications and source records attributed to Martina Hentschel.

At least 37 records · Page 2Linked to original sources

arXiv2018

The optical Möbius strip cavity: Tailoring geometric phases and far fields

The Möbius strip, a long sheet of paper whose ends are glued together after a $180^{\circ}$ twist, has remarkable geometric and topological properties. Here, we consider dielectric Möbius strips of finite width and investigate the interplay between geometric properties and resonant light propagation. We show how the polarization dynamics of the electromagnetic wave depends on the topological properties, and demonstrate how the geometric phase can be manipulated between $0$ and $π$ through the system geometry. The loss of the Möbius character in thick cavities and for small twist segment lengths allows one to manipulate the polarization dynamics and the far-field emission, and opens the venue for applications.

physics.optics↗

arXiv2017

Consequences of a wave-correction extended ray dynamics for integrable and chaotic optical microcavities

Ray optics has proven to be an effcient and versatile tool to describe dielectric optical microcavities and their far-field emission based on the principle of ray-wave correspondence. Whereas often the well-known ray-optics at planar interfaces yields reasonable results, semiclassically and boundary-curvature induced corrections will become more important as the cavity size is further reduced. In this paper we summarize the various ray optics descriptions of optical microresonators, paying in addition special attention to the differences that arise between chaotic vs. non-chaotic (integrable or nearly integrable) resonator geometries, respectively. Whereas the far-field pattern in the chaotic case is known to be determined by the overlap of the unstable manifold with the leaky region, it results from the emission of trajectories with the smallest nonzero decay rates in the non-chaotic situation. We present an enhanced ray optical description, extended by wave-inspired (semiclassical) corrections, and discuss their consequences for the ray dynamics. In particular we find clear indications for the presence of attractors resulting from the non-Hamiltonian character of the extended ray dynamics in phase space. We illustrate their impact on the far-field emission and show that it can considerably differ from the conventional ray description result.

physics.optics↗

arXiv2016

The 3D Limaçon: Properties and Applications

We perform electromagnetic wave simulations of fully three-dimensional optical Limaçon-microcavities, one basis for their future applications in microlasers and photonic devices. The analysis of the three-dimensional modes and far-fields reveals an increase of the quality factors as compared to the two-dimensional case. The structure of the far-field in the third dimension shows pronounced maxima in the emission directionality inclined to the resonator plane which may be exploited for coupling the resonator modes to the environment. This triggers ideas for technical applications, like the suggested sensor that can detect small changes in the environment based on changes in the emission profile.

physics.optics↗

arXiv2016

Ray picture and ray-wave correspondence in triangular microlasers

We apply ray-optical methods to dielectric optical microcavities in the shape of triangles made of low refractive index material. We find ray trajectories that maximize the intensity inside the cavity to determine the far-field emission characteristics and to complement the concept of the unstable manifold applicable to chaotic microlasers. As these maximum intensity trajectories need not to be periodic, we suggest that they provide a more general explanation for emission patterns of microlasers than short periodic orbits. Further, the geometrical optics description is extended by the inclusion of intensity amplification along the optical path to achieve a better description of active, lasing cavities. Far-field emission patterns of equilateral triangle cavities obtained in this way agree well with our full electromagnetic wave simulations and with previously reported experimental results.

physics.optics↗

arXiv2015

Nonlinear dynamical tunneling of optical whispering gallery modes in the presence of a Kerr nonlinearity

The effect of a Kerr nonlinearity on dynamical tunneling is studied, using coupled whispering gallery modes in an optical microcavity. The model system that we have chosen is the 'add-drop filter', which comprises an optical microcavity and two waveguide coupled to the cavity. Due to the evanescent field's scattering on the waveguide, the whispering gallery modes in the microcavity form doublets, which manifest themselves as splittings in the spectrum. As these doublets can be regarded as a spectral feature of dynamical tunneling between two different dynamical states with a spatial overlap, the effect of a Kerr nonlinearity on the doublets is numerically investigated in the more general context of the relationship between cubic nonlinearity and dynamical tunneling. Within the numerical realization of the model system, it is observed that the doublets shows a bistable transition in its transmission curve as the Kerr-nonlinearity in the cavity is increased. At the same time, one rotational mode gets dominant over the other one in the transmission, since the two states in the doublet have uneven linewidths. By using coupled mode theory, the underlying mode dynamics of the phenomena is theoretically modelled and clarified.

physics.optics↗

arXiv2014

Abnormal high-$Q$ modes of coupled stadium-shaped microcavities

It is well known that the strongly deformed microcavity with fully chaotic ray dynamics cannot support high-Q modes due to its fast chaotic diffusion to the critical line of refractive emission. Here, we investigate how the Q factor is modified when two chaotic cavities are coupled, and show that some modes, whose Q factor is about 10 times higher than that of the corresponding single cavity, can exist. These abnormal high-Q modes are the result of an optimal combination of coupling and cavity geometry. As an example, in the coupled stadium-shaped microcavities, the mode pattern extends over both cavities such that it follows a whispering-gallery-type mode at both ends, whereas a big coupling spot forms at the closest contact of the two microcavities. The pattern of such a 'rounded bow tie' mode allows the mode to have a high-Q factor. This mode pattern minimizes the leakage of light at both ends of the microcavities as the pattern at both ends is similar to whispering gallery mode.

physics.optics↗

arXiv2014

Understanding deviations from ray optics at curved interfaces

Ray optics is a useful tool even in the regime where, actually, full wave-calculations would be appropriate. However, wave-inspired adjustments are needed to ensure the accuracy of ray-based predictions. These corrections are known as the Goos-Hänchen shift, a lateral shift along the interface, and the Fresnel filtering effect, an angular shift, that violates Snell's law and the principle of ray-path reversibility. Whereas they are well established at planar interfaces, an accurate description of microlasers and other microoptics devices requires their precise knowledge at the curved boundaries characteristic for these devices. Here, we present analytical and numerical results that highlight the role of boundary curvature and show the clear deviations from the planar case. We introduce an intuitive picture that allows for a straightforward understanding why Fresnel filtering grows considerably with curvature whereas the Goos-Hänchen shift becomes less important.

physics.optics↗

arXiv2012

Diffusion on edges of insulating graphene with intravalley and intervalley scattering

Band gap engineering in graphene may open the routes towards transistor devices in which electric current can be switched off and on at will. One may, however, ask if a semiconducting band gap alone is sufficient to quench the current in graphene. In this paper we demonstrate that despite a bulk band gap graphene can still have metallic conductance along the sample edges (provided that they are shorter than the localization length). We find this for single-layer graphene with a zigzag-type boundary which hosts gapless propagating edge states even in the presence of a bulk band gap. By generating inter-valley scattering, sample disorder reduces the edge conductance. However, for weak scattering a metallic regime emerges with the diffusive conductance G = (e^2/h)(l_KK' / L) per spin, where l_KK' is the transport mean-free path due to the inter-valley scattering and L >> l_KK' is the edge length. We also take intra-valley scattering by smooth disorder (e.g. by remote ionized impurities in the substrate) into account. Albeit contributing to the elastic quasiparticle life-time, the intra-valley scattering has no effect on G.

cond-mat.mes-hall↗

arXiv2012

Are Fresnel filtering and the angular Goos-Hänchen shift the same?

The law of reflection and Snell's law are among the tenets of geometrical optics. Corrections to these laws in wave optics are respectively known as the angular Goos-Hänchen shift and Fresnel filtering. In this paper we give a positive answer to the question of whether the two effects are common in nature and we study both effects in the more general context of optical beam shifts. We find that both effects are caused by the same principle, but have been defined differently. We identify and discuss the similarities and differences that arise from the different definitions.

physics.optics↗

arXiv2012

Quasiattractors in coupled maps and coupled dielectric cavities

We study the origin of attracting phenomena in the ray dynamics of coupled optical microcavities. To this end we investigate a combined map that is composed of standard and linear map, and a selection rule that defines when which map has to be used. We find that this system shows attracting dynamics, leading exactly to a quasiattractor, due to collapse of phase space. For coupled dielectric disks, we derive the corresponding mapping based on a ray model with deterministic selection rule and study the quasiattractor obtained from it. We also discuss a generalized Poincaré surface of section at dielectric interfaces.

nlin.CD↗

arXiv2011

Nonorthogonal pairs of copropagating optical modes in deformed microdisk cavities

Recently, it has been shown that spiral-shaped microdisk cavities support highly nonorthogonal pairs of copropagating modes with a preferred sense of rotation (spatial chirality) [Wiersig et al., Phys. Rev. A 78, 053809 (2008)]. Here, we provide numerical evidence which indicates that such pairs are a common feature of deformed microdisk cavities which lack mirror symmetries. In particular, we demonstrate that discontinuities of the cavity boundary such as the notch in the spiral cavity are not needed. We find a quantitative relation between the nonorthogonality and the chirality of the modes which agrees well with the predictions from an effective non-Hermitian Hamiltonian. A comparison to ray-tracing simulations is given.

physics.optics↗

arXiv2011

Chaos-assisted emission from asymmetric resonant cavity microlasers

We study emission from quasi-one-dimensional modes of an asymmetric resonant cavity that are associated with a stable periodic ray orbit confined inside the cavity by total internal reflection. It is numerically demonstrated that such modes exhibit directional emission, which is explained by chaos-assisted emission induced by dynamical tunneling. Fabricating semiconductor microlasers with the asymmetric resonant cavity, we experimentally demonstrate the selective excitation of the quasi-one-dimensional modes by employing the device structure to preferentially inject currents to these modes and observe directional emission in good accordance with the theoretical prediction based on chaos-assisted emission.

nlin.CD↗

arXiv2011

Photoabsorption spectra and the X-ray edge problem in graphene

We study the photoabsorption cross section and Fermi-edge singularities (FES) in graphene. For fillings below one half, we find, besides the expected FES in form of a peaked edge at the threshold (Fermi) energy, a second singularity to arise at excitation energies that correspond to the Dirac point in the density of states. We can explain this behaviour by comparing our results with the photoabsorption cross section of a metal with a small central band gap where we find a very similar signature. The existence of the second singularity might prove useful for an experimental determination of the Dirac point. We also demonstrate that the photoabsorption signal is enhanced by the zigzag edge states due to their metallic-like character. Since the presence of the edge states indicates a topological defect at the boundary, our study gives an example for a Fermi-edge singularity in a system with a topologically nontrivial electronic spectrum.

cond-mat.mes-hall↗

arXiv2011

Designing coupled microcavity lasers for high-Q modes with unidirectional light emission

We design coupled optical microcavities and report directional light emission from high-$Q$ modes for a broad range of refractive indices. The system consists of a circular cavity that provides a high-$Q$ mode in form of a whispering gallery mode, whereas an adjacent deformed microcavity plays the role of a waveguide or collimator of the light transmitted from the circular cavity. As a result of this very simple, yet robust, concept we obtain high-$Q$ modes with promising directional emission characteristics. No information about phase space is required, and the proposed scheme can be easily realized in experiments.

physics.optics↗

arXiv2010

Measurement of the Goos-Hänchen shift in a microwave cavity

We present measurements of the Goos-Hänchen shift in a two-dimensional dielectric microwave cavity. Microwave beams are generated by a suitable superposition of the spherical waves generated by an array of antennas; the resulting beams are then reflected at a planar interface. By measuring the electric field including its phase, Poynting vectors of the incoming and reflected beams can be extracted, which in turn are used to find the incoming angle and the positions where the beam hits the interface and where it is reflected. These positions directly yield the Goos-Hänchen shift. The results are compared to the classical Artmann result and a numerical calculation using Gaussian beams.

physics.optics↗

arXiv2010

Ray model and ray-wave correspondence in coupled optical microdisks

We introduce a ray model for coupled optical microdisks, in which we select coupling-efficient rays among the splitting rays. We investigate the resulting phase-space structure and report island structures arising from the ray-coupling between the two microdisks. We find the microdisks's refractive index to influence the phase-space structure and calculate the stability and decay rates of the islands. Turning to ray-wave correspondence, we find many resonances to be directly related to the presence of these islands. We study the relation between the (ray-picture originating) island structures and the (wave-picture originating) spectral properties of resonances, especially the leakiness of the resonances which is represented as the imaginary part of the complex wave vector.

physics.optics↗

arXiv2010

Chaos-assisted directional light emission from microcavity lasers

We study the effect of dynamical tunneling on emission from ray-chaotic microcavities by introducing a suitably designed deformed disk cavity. We focus on its high quality factor modes strongly localized along a stable periodic ray orbit confined by total internal reflection. It is shown that dominant emission originates from the tunneling from the periodic ray orbit to chaotic ones; the latter eventually escape from the cavity refractively, resulting in directional emission that is unexpected from the geometry of the periodic orbit, but fully explained by unstable manifolds of chaotic ray dynamics. Experimentally performing selective excitation of those modes, we succeeded in observing the directional emission in good agreement with theoretical prediction. This provides decisive experimental evidence of dynamical tunneling in a ray-chaotic microcavity.

nlin.CD↗

arXiv2010

The Mesoscopic Kondo Box: A Mean-Field Approach

We study the mesoscopic Kondo box, consisting of a quantum spin 1/2 interacting with a chaotic electronic bath as can be realized by a magnetic impurity coupled to electrons on a quantum dot, using a mean-field approach for the Kondo interaction. Its umerical efficiency allows us to analyze the Kondo temperature, the local magnetic susceptibility, and the conductance statistics for a large number of samples with energy levels obtained by random matrix theory. We see pronounced parity effects in the average values and in the probability distributions, depending on an even and odd electronic occupation of the quantum dot, respectively. These parity effects are directly accessible in experiments.

cond-mat.str-el↗