Jens U. Nöckel

Hexagonal microlasers based on organic dyes in nanoporous crystals

Abstract.Molecular sieves, such as nanoporous AlPO4-5, can host a wide variety of laser active dyes. We embeded pyridine-2 molecules as a representative of a commercially available dye which fits into the channel pores of the host matrix. Many efficient dye molecules, such as rhodamines, do not fit into the pores. But modifying the structure of the dyes to appear like the used templates allows us to increase the amount of encapsulated dyes. The properties of resulting microlasers depend on size and shape of the microresonators, and we discuss a model for microscopic hexagonal ring resonators. In terms of pump needed to reach lasing threshold molecular sieve microlasers are comparable to VCSELs. For dyes that fit into the pores we observed a partial regeneration of photo-induced damage.

DIRECTIONAL EMISSION FROM ASYMMETRIC RESONANT CAVITIES

Asymmetric resonant cavities with highly noncircular but convex cross sections are predicted theoretically to have high-Q whispering gallery modes with highly anisotropic emission. We develop a ray dynamics model for the emission pattern and present numerical and experimental confirmation of the theory.

Resonance line shapes in quasi-one-dimensional scattering.

An S matrix approach is developed to describe elastic scattering resonances of systems where the scattered particle is asymptotically confined and the scattering potential lacks continuous symmetry. Examples are conductance resonances in microstructures or transmission resonances in waveguide junctions. The generic resonance is shown to have the asymmetric Fano lineshape. The asymmetry parameter q is independent of coupling to the quasi-bound level implying a scaling property of the resonances which can be tested in transport experiments.that cause this phenomenon are identified in this paper using first a coupled-channel theory that starts from the full scattering Hamiltonian, and secondly a more general S-matrix approach. The latter is model-independent and thus yields predictions for the possible lineshapes in a wide variety of systems. Modelindependent results are desirable because knowledge of the microstructure potentials is often incomplete. We show for the most general multiprobe, multisubband structure that the total transmssion never varies by more than unity on resonance, generalizing a result previously known only for resonant tunneling structures. The role of symmetry is investigated to clarify which features (e.g. reflection zeros) are a consequence of special invariance properties and which are robust in the unsymmetric case. The eect of a resonance is found to decrease with increasing number of leads in a rotationally symmetric structure. Only in a two-probe geometry can zeros in transmission and reflection occur together for a single resonance. The known result that resonances in symmetric resonant tunneling devices always display exactly unit variation of the transmission is shown to be violated in structures where the nonresonant transmission exceeds one. Time reversal invariance is not required in the present treatment. Two model systems displaying asymmetric resonances are discussed. Their advantage is that the resonance lifetime can be tuned externally, making it possible to test a scaling property of the Fano lineshape that we derive below.

Directional tunneling escape from nearly spherical optical resonators.

We report the surprising observation of directional tunneling escape from nearly spherical fused-silica optical resonators, in which most of the phase space is filled with nonchaotic regular trajectories. Experimental and theoretical studies of the dependence of the far-field emission pattern on both the degree of deformation and the excitation condition show that nonperturbative phase-space structures in the internal ray dynamics profoundly affect tunneling leakage of the whispering-gallery modes.

Curvature-induced radiation of surface plasmon polaritons propagating around bends

We present a theoretical study of the curvature-induced radiation of surface plasmon polaritons propagating around bends at metal-dielectric interfaces. We explain qualitatively how the curvature leads to distortion of the phase front, causing the fields to radiate energy away from the metal-dielectric interface. We then quantify, both analytically and numerically, radiation losses and energy transmission efficiencies of surface plasmon polaritons propagating around bends with varying radii as well as sign of curvature.

Surface plasmon polariton propagation around bends at a metal–dielectric interface

A short-wavelength analysis for the transmission coefficients of surface plasmon polaritons around a finite-radius metallic bend shows lower losses than on flat surfaces may occur. The maximum transmittance depends non-monotonically on the bend radius

Mode structure and ray dynamics of a parabolic dome microcavity.

We consider the wave and ray dynamics of an electromagnetic field in a parabolic dome microcavity. The structure of the fundamental s wave involves a main lobe in which the electromagnetic field is confined around the focal point in an effective volume of the order of a cubic wavelength, while modes with finite angular momentum have a structure that avoids the focal area and have correspondingly larger effective volumes. The ray dynamics indicate that the fundamental s wave is robust with respect to small geometrical deformations of the cavity, while the higher order modes are unstable, giving rise to optical chaos. We discuss the incidence of these results on the modification of the spontaneous emission dynamics of an emitter placed in such a parabolic dome microcavity.

Bragg-induced orbital angular-momentum mixing in paraxial high-finesse cavities

Numerical calculation of vector electromagnetic modes of plano-concave microcavities reveals that the polarization-dependent reflectivity of a flat Bragg mirror can lead to unexpected cavity field distribution for nominally paraxial modes. Even in a rotationally symmetric resonator, certain pairs of orbital angular momenta are necessarily mixed in an excitation-independent way to form doublets. A characteristic mixing angle is identified, which even in the paraxial limit can be designed to have large values. This correction to Gaussian theory is of zeroth order in deviations from paraxiality. We discuss the resultant nonuniform polarization fields. Observation will require small cavities with sufficiently high Q. Possible applications are proposed.

Asymmetric Resonant Optical Cavities

A new and useful type of optical resonator has been proposed based on the principles of chaos [1]. The asymmetric resonant cavity (ARC) is an extension of the concept of spherical or cylindrical dielectric resonators which have high-Q ”whispering gallery” (WG) modes trapped by total internal reflection [2]. In the ARC such a cylinder or sphere is deformed substantially but in a smooth and convex manner, leading to an oval cross-section, as shown in the figure. The deformation allows control of the Q value of the WG modes and also induces highly directional emission from these modes, making this an attractive design for microlasers. This overcomes a major drawback of symmetric resonators which have intrinsically isotropic emission patterns and require additional optical elements to guide the emission of the light. Recent experiments measuring the lasing emission from deformed micro-droplets [1,3] and deformed cylindrical dye jets [4] have confirmed the basic predictions of the theory with respect to directional emission. The essential novelty of the ARC concept from the theoretical point of view lies in its connection to the theory of quantum or wave chaos [1]. Since the dielectric is strongly deformed, the wave equation is not separable, so the modes cannot be described in terms of standard special functions; nor can they be described by perturbation theory. Instead, its properties are inferred from the geometric optics limit, using semiclassical methods and taking into account the fact that an increasing deformation makes the ray dynamics more and more chaotic. The ray-optics model for ARCs makes the striking prediction that their WG resonances fall into subsets, all of which have the same lifetime for large deformation [1]. This is because the resonance lifetime is controlled by chaotic motion which is independent of wavelength and lasts until the total internal reflection condition is violated and the light escapes by refraction. The same model predicts the directions of high emission for the ARC resonances (see figure), which for a glass resonator surprisingly are not perpendicular to the points of highest surface curvature. The ray predictions (histogram, bottom right) are in excellent agreement with actual wave solutions (left, and top right). The ARC design is of significant interest for passive and active optical device applications such as add-drop filters and microlasers. Initial exper-

Optical Feedback and the Coupling Problem in Semiconductor Microdisk Lasers

The smaller the size of a light-emitting microcavity, the more important it becomes to understand the effects of the cavity boundary on the optical mode profile. Conventional methods of laser physics, such as the paraxial approximation, become inapplicable in many of the more exotic cavity designs to be discussed here. Cavities in the shape of microdisks, pillars and rings can yield low lasing thresholds in a wide variety of gain media: quantum wells, wires and even dots, as well as quantum cascade superlattices and GaN. An overview of the experimental and theoretical status is provided, with special emphasis on the light extraction problem.