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ABSTRACT: 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-H\"anchen 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.
08/2012;
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ABSTRACT: 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 Poincar\'e surface of section at
dielectric interfaces.
03/2012;
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ABSTRACT: 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.
05/2011;
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ABSTRACT: 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.
04/2011;
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ABSTRACT: 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 the 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.
Optics Letters 04/2011; 36(7):1116-8. · 3.40 Impact Factor
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ABSTRACT: We present measurements of the Goos-H\"anchen 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-H\"anchen shift. The results are compared to the classical Artmann result and a numerical calculation using Gaussian beams. Comment: 10 pages, 5 figures
10/2010;
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ABSTRACT: We study the emission properties of electrically pumped triangular-shaped microlasers with rounded corners. We find no signs of directional emission for the relatively large cavities (dimension approximately 100 microm) used in our experiments, in full agreement with ray simulation results. The broad emission characteristics that we observe can be fine-tuned by adjusting the resonator geometry as is verified through simulations which might prove useful for applications in optical devices.
Optics Express 08/2010; 18(16):16437-42. · 3.59 Impact Factor
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ABSTRACT: 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.
Physical Review Letters 04/2010; 104(16):163902. · 7.37 Impact Factor
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ABSTRACT: We discuss electromagnetic modes in cavities formed by metamaterials with negative refraction and demonstrate that the straightforward approach to substitute negative values of the electric permittivity and the magnetic permeability leads to quasi-bound states with a negative quality factor. To ensure positive quality factors and a consistent physical interpretation of the quasi-bound states it is essential to include the frequency dispersion of the permittivity and the permeability, as required by positive field energy and causality. The basic mode equation and the boundary conditions including linear frequency dispersion are derived. As an example we consider a disk-like cavity with deformed cross sectional shape. The transition from the unphysical nondispersive case with negative quality factors to the dispersive case with positive quality factors is demonstrated numerically and in an analytical perturbative treatment. Comment: 7 pages, 4 figures
01/2010;
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ABSTRACT: The limaçon-shaped semiconductor microcavity is a ray-chaotic cavity sustaining low-loss modes with mostly unidirectional emission patterns. Investigating these modes systematically, we show that the modes correspond to ray description collectively rather than individually. In addition, we present experimental data on multimode lasing emission patterns that show high unidirectionality and closely agree with the ray description. The origin of this agreement is well explained by the collective correspondence mechanism.
Phys. Rev. A. 08/2009; 80(3).
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ABSTRACT: We perform ray and wave simulations of passive and active spiral-shaped optical microcavities, comparing our results to experimental data obtained with mid-infrared quantum cascade spiral microlasers. Focusing on the angular emission characteristics, we find that both ray and wave simulations are consistent with the experimental data, showing richly-featured, multidirectional far-field emission patterns in the case of uniform pumping and TM-polarized light. Active cavity simulations using the Schr odinger-Bloch model indicate that selective pumping of the quantum cascade spiral microlasers near the resonator boundary will yield unidirectional laser emission.
Optics Express 07/2009; 17(12):10335-43. · 3.59 Impact Factor
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Changling Yan,
Qi Jie Wang,
Laurent Diehl, Martina Hentschel,
Jan Wiersig,
Nanfang Yu,
Christian Pflügl,
Federico Capasso,
Mikhail A. Belkin,
Tadataka Edamura,
Masamichi Yamanishi,
Hirofumi Kan
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ABSTRACT: We report experimental demonstration of directional light emission from limaçon-shaped microcavity semiconductor lasers. Quantum cascade lasers (QCLs) emitting at λ ≈ 10 μm are used as a model system. Both ray optics and wave simulations show that for deformations in the range 0.37<ε<0.43, these microcavities support high quality-factor whispering gallerylike modes while having a directional far-field profile with a beam divergence θ∥ ≈ 30° in the plane of the cavity. The measured far-field profiles are in good agreement with simulations. While the measured spectra show a transition from whispering gallerylike modes to a more complex mode structure at higher pumping currents, the far field is insensitive to the pumping current demonstrating the predicted “universal far-field behavior” of this class of chaotic resonators. Due to their relatively high quality factor, our microcavity lasers display reduced threshold current densities compared to conventional ridge lasers with millimeter-long cavities. The performance of the limaçon-shaped QCLs is robust with respect to variations of the deformation near its optimum value of ε = 0.40.
Applied Physics Letters 06/2009; 94(25):251101-251101-3. · 3.84 Impact Factor
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ABSTRACT: The key characteristic of an optical mode in a microcavity is its quality factor describing the optical losses. The numerical computation of this quantity can be very demanding for present-day devices. Here we show for a certain class of whispering-gallery cavities that the quality factor is related to dynamical tunneling, a phenomenon studied in the field of quantum chaos. We extend a recently developed approach for determining dynamical tunneling rates to open cavities. This allows us to derive an analytical formula for the quality factor which is in very good agreement with full solutions of Maxwell’s equations.
Physical Review A 05/2009; 79(6). · 2.88 Impact Factor
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ABSTRACT: The availability of microlasers with highly directional far-field characteristics is crucial for future applications. To this end we study the far-field emission of active microcavities with a spiral shape using the Schrödinger-Bloch model. We find that they can provide directional emission under the conditions of (i) pumping along the resonator boundary and (ii) for specific resonator geometries. We systematically study the far-field characteristics under variation of the pumped area and the cavity geometry and identify a directionality optimized regime. Our results consistently explain previously obtained experimental results.
Optics Letters 02/2009; 34(2):163-5. · 3.40 Impact Factor
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ABSTRACT: Quasibound states in an open system do not in general form an orthogonal and complete basis. It is, however, expected that the nonorthogonality is weak in the case of well-confined states, except close to a so-called exceptional point in parameter space. We present numerical evidence showing that for passive optical microspiral cavities the parameter regime where the nonorthogonality is significant is rather broad. Here we observe almost-degenerate pairs of well-confined modes which are highly nonorthogonal. Using a non-Hermitian model Hamiltonian we demonstrate that this interesting phenomenon is related to the asymmetric scattering between clockwise and counterclockwise propagating waves in the spiral geometry. Numerical simulations of ray dynamics reveal a clear ray-wave correspondence.
Phys. Rev. A. 11/2008; 78(5).
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ABSTRACT: Extended defects in graphene, such as linear edges, break the translational invariance and can also have an impact on the symmetries specific to massless Dirac-like quasiparticles in this material. The paper examines the consequences of a broken Dirac fermion parity in the framework of the effective boundary conditions varying from the Berry-Mondragon mass confinement to a zigzag edge. The parity breaking reflects the structural sublattice asymmetry of zigzag-type edges and is closely related to the previously predicted time-reversal symmetric edge states. We calculate the local and global densities of the edge states and show that they carry a specific polarization, resembling, to some extent, that of spin-polarized materials. The lack of the parity leads to a nonanalytical particle-hole asymmetry in the edge-state properties. We use our findings to interpret recently observed tunneling spectra in zigzag-terminated graphene. We also propose a graphene-based tunneling device where the particle-hole asymmetric edge states result in a strongly nonlinear conductance-voltage characteristics, which could be used to manipulate the tunneling transport. Comment: 8 pages, 5 figures, to be published in Phys. Rev. B
10/2008;
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ABSTRACT: Recently, an interesting phenomenon of spatial localization of optical modes along periodic ray trajectories near avoided resonance crossings has been observed [Wiersig, Phys. Rev. Lett. 97, 253901 (2006)]. For the case of a microdisk cavity with elliptical cross section, we use the Husimi function to analyze this localization in phase space. Moreover, we present a semiclassical explanation of this phenomenon in terms of the Goos-Hänchen shift, which works very well even deep in the wave regime. This semiclassical correction to the ray dynamics modifies the phase-space structure such that modes can localize either on stable islands or along unstable periodic ray trajectories.
Physical Review E 08/2008; 78(1 Pt 2):016201. · 2.26 Impact Factor
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ABSTRACT: A drawback of optical modes in microdisk cavities is their isotropic light emission. Here we report a novel, robust, and general mechanism that results in highly directional light emission from high-quality modes. This surprising finding is explained by a combination of wave phenomena (wave localization along unstable periodic ray trajectories) and chaotic ray dynamics in open systems (escape along unstable manifolds) and applies even to microlasers operating in the common multimode regime. We demonstrate our novel mechanism for the limaçon cavity and find directional emission with narrow angular divergence for a significant range of geometries and material parameters.
Physical Review Letters 02/2008; 100(3):033901. · 7.37 Impact Factor
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ABSTRACT: We study Fermi edge singularities in photoabsorption spectra of generic mesoscopic systems such as quantum dots or nanoparticles. We predict deviations from macroscopic-metallic behavior and propose experimental setups for the observation of these effects. The theory is based on the model of a localized, or rank one, perturbation caused by the (core) hole left behind after the photoexcitation of an electron into the conduction band. The photoabsorption spectra result from the competition between two many-body responses, Anderson’s orthogonality catastrophe and the Mahan-Nozières-DeDominicis contribution. Both mechanisms depend on the system size through the number of particles and, more importantly, fluctuations produced by the coherence characteristic of mesoscopic samples. The latter lead to a modification of the dipole matrix element and trigger one of our key results: a rounded K-edge typically found in metals will turn into a (slightly) peaked edge on average in the mesoscopic regime. We consider in detail the effect of the “bound state” produced by the core hole.
Phys. Rev. B. 12/2007; 76(24).
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ABSTRACT: Many-body phenomena, a key interest in the investigation of bulk solid state systems, are studied here in the context of the x-ray edge problem for mesoscopic systems. We investigate the many-body effects associated with the sudden perturbation following the x-ray excitation of a core electron into the conduction band. For small systems with dimensions at the nanoscale we find considerable deviations from the well-understood metallic case where Anderson orthogonality catastrophe and the Mahan-Nozieres-DeDominicis response cause characteristic deviations of the photoabsorption cross section from the naive expectation. Whereas the K-edge is typically rounded in metallic systems, we find a slightly peaked K-edge in generic mesoscopic systems with chaotic-coherent electron dynamics. Thus the behavior of the photoabsorption cross section at threshold depends on the system size and is different for the metallic and the mesoscopic case. Comment: 9 pages, 3 figures, Proceedings ``Quantum Mechanics and Chaos'' (Osaka 2006)
05/2007;
