We study the effect of localized modes in lattices of size N with parity-time (PT) symmetry. Such modes are arranged in pairs of quasidegenerate levels with splitting delta approximately exp(-N/xi) where xi is their localization length. The level "evolution" with respect to the PT breaking parameter gamma shows a cascade of bifurcations during which a pair of real levels becomes complex. The spontaneous PT symmetry breaking occurs at gammaPT approximately min{delta}, thus resulting in an exponentially narrow exact PT phase. As N/xi decreases, it becomes more robust with gammaPT approximately 1/N2 and the distribution P(gammaPT) changes from log-normal to semi-Gaussian. Our theory can be tested in the frame of optical lattices.
We propose a new class of optical synthetic materials that are described by non-Hermitian Hamiltonians. The building blocks of such systems are coupled PT-symmetric elements (dimers), with coupling t. Despite the lack of global PT-symmetry, these systems have a robust parameter region of real spectra (exact phase) even in cases where the complex refractive index n = β + iγ of each PT dimer is random. The validity of our proposition is confirmed for representative cases where we calculate the borders of the exact phase in terms of β, γ and t.
We consider waveguides formed by single or multiple two-dimensional chaotic cavities connected to leads. The cavities are chaotic in the sense that the ray (or equivalently, classical particle) dynamics within them is chaotic. Geometrical parameters are chosen to produce a mixed phase space (chaotic regions surrounding islands of stability where motion is regular). Incoming rays (or particles) cannot penetrate into these islands but incoming plane waves dynamically tunnel into them at a certain discrete set of frequencies (energies). The support of the corresponding quasi-bound states is along the trajectories of periodic orbits trapped within the cavity. We take advantage of this difference in the ray/wave behavior to demonstrate how chaotic waveguides can be used to design beam splitters and microlasers. We also present some preliminary experimental results in a microwave realization of such chaotic waveguide.
We propose the construction of electromagnetic (or electronic) switches and beam splitters by use of chaotic two-dimensional multiport waveguides. A prototype two-port waveguide is locally deformed to produce a ternary incomplete horseshoe characteristic of mixed phase space (chaotic regions surrounding islands of stability where motion is regular). Owing to tunneling to the phase-space stability islands, quasi-bound states (QBS) appear. Then we attach transversal ports to the waveguide in the deformation region in positions where the phase-space structure is only slightly perturbed. We show how QBS can be guided out of the waveguide through the attached transversal ports,giving rise to frequency-selective switches and beam splitters.
In this work, scientific methods and findings known from mesoscopic physics, primarily used for semiconductor nanostructures, will be transferred to photonic systems, enabled by the analogy of mesoscopic ballistic transport and transport processes in photonics. Therefore a numerical method is developed that is based on Greens functions in combination with the Landauer-Büttiker formalism, and that allows describing coherent transport processes in low-dimensional semiconductor structures. This so-called scattering formalism is tested and elucidated in the framework of the ballistic rectifier. It is furthermore shown to be fruitful in gaining substantial results of comprehensively examined optical systems developed within this work -the chaotic beam splitter with its broad range of applications for photonic devices and the Müller cell, which acts as a biological wave guide in the retina of vertebrates, ensuring light transport through the retina while increasing the optical performance in most parts of the entire eye. The quantum scattering formalism allows investigating novel aspects of transport in optical systems. Based on dynamical tunneling a high effective single-mode laser and a variety of other applications within the context of deformed waveguides are presented and the reduction of scattering light in the surrounding area of the fovea in the human eye is predicted via theoretical analysis of the properties of human Müller cells.In addition to the intense study of these last two passive optical systems, this work gives special attention to PT -symmetric active optical systems. Fundamental analytical results for the impact and implication of localization and disorder in such active PT -symmetric systems are investigated here.Based on this, the possibility of designing optical metamaterials with particular spatial ordered regions of gain and loss are inspected. The study concludes by transferring the scattering formalism to these active optical systems for characterization and classification of transport properties. KurzfassungIn der vorliegenden Arbeit wird die Analogie zwischen mesoskopischem ballistischem Transport und Transportvorgängen in der Photonik genutzt, um Methoden und Erkenntnisse aus der Theorie der mesoskopischen Physik, die bisher vornehmlich auf Halbleiter-Nanostrukturen angewandt wurden, auf photonische Systeme zu übertragen. Dazu wird eine numerische Methode entwickelt, die ihren Ursprung in der Theorie der Greenschen Funktionen in Verbindung mit dem Landauer-Büttiker-Formalismus zur Beschreibung von kohärenten Transportvorgängen in niedrigdimensionalen Halbleiterstrukturen hat. Am Beispiel des ballistischen Gleichrichters wird diese im Weiteren genutzte numerische Methode des Streuformalismus erläutert und getestet. Sie erweist sich als äußerst effizient, um zu substanziellen Erkenntnissen über hier entwickelte und eingehend untersuchte optische Systeme zu gelangen -den chaotischen Strahlenteiler mit seinen hier abgeleiteten vielfältigen Anwendungen für die Photonik und die Müllerschen Zell...
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