Exact Buffer Overflow Calculations for Queues via Martingales

Let _n be the first time a queueing process like the queue length or workload exceeds a level n. For the M/M/1 queue length process, the mean _n and the Laplace transform e^-sn is derived in closed form using a martingale introduced in Kella and Whitt (1992). For workload processes and more general systems like MAP/PH/1, we use a Markov additive extension given in Asmussen and Kella (2000) to derive sets of linear equations determining the same quantities. Numerical illustrations are presented in the framework of M/M/1 and MMPP/M/1 with an application to performance evaluation of telecommunication systems with long-range dependent properties in the packet arrival process. Different approximations that are obtained from asymptotic theory are compared with exact numerical results.     

Fresnel filtering in lasing emission from scarred modes of wave-chaotic optical resonators

We study lasing emission from asymmetric resonant cavity GaN microlasers. By comparing far-field intensity patterns with images of the microlaser we find that the lasing modes are concentrated on three-bounce unstable periodic ray orbits; i.e., the modes are scarred. The high-intensity emission directions of these scarred modes are completely different from those predicted by applying Snell's law to the ray orbit. This effect is due to the process of "Fresnel filtering" which occurs when a beam of finite angular spread is incident at the critical angle for total internal reflection.     

Taking detection to the limit with optical microcavities: Recent advances presented at the 560. WE Heraeus Seminar

We provide a review on the applications of whispering gallery mode resonators in sensing, and biosensing in particular. We highlight the most recent developments in this area, which were presented at the 560. WE Heraeus Seminar “Taking Detection to the Limit – Biosensing with Optical Microcavities”.     

Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities

We study level crossing in the optical whispering-gallery (WG) modes by using toroidal microcavities. Experimentally, we image the stationary envelope patterns of the composite optical modes that arise when WG modes of different wavelengths coincide in frequency. Numerically, we calculate crossings of levels that correspond with the observed degenerate modes, where our method takes into account the not perfectly transverse nature of their field polarizations. In addition, we analyze anticrossing with a large avoidance gap between modes of the same azimuthal number.     

Crystalline MgF2 whispering gallery mode resonators for enhanced bulk index sensitivity

We report on experiments on refractrometric sensing with crystalline Whispering Gallery Mode (WGM) resonators made of magnesium fluoride, which has a refractive index that is only slightly larger than that of water (Δn ≈ 0.05). The resulting evanescent field of a WGM resonator placed in an aqueous environment penetrates therefore deep into the surrounding medium, which makes it a promising candidate for sensing applications. We measured a bulk index sensitivity of 1.09 nm/RIU (refractive index unit) in a resonator with a radius of R = 2.91 mm and intrinsic Q-factors of more than 10⁸ in aqueous environments. Furthermore, we describe the fabrication process of crystalline WGM resonators.     

Direct experimental observation of the single reflection optical Goos-Hänchen shift

We report a precise direct measurement of the Goos-H?nchen shift after one reflection off a dielectric interface coated with periodic metal stripes. The spatial displacement of the shift is determined by image analysis. A maximal absolute shift of 5.18 and 23.39 mum for TE and TM polarized light, respectively, is determined. This technique is simple to implement and can be used for a large range of incident angles.