Hall conditions for edge-weighted bipartite graphs

A weighted variant of Hall's condition for the existence of matchings is shown to be equivalent to the existence of a matching in a lexicographic product. This is used to introduce characterizations of those bipartite graphs whose edges may be replicated so as to yield semiregular multigraphs or, equivalently, semiregular edge-weightings. Such bipartite graphs will be called semiregularizable. Some infinite families of semiregularizable trees are described and all semiregularizable trees on at most 11 vertices are listed. Matrix analogues of some of the results are mentioned and are shown to imply some of the known characterizations of regularizable graphs.

Absorption Measurements in Liquid Core Waveguides Using Cavity

Short liquid core waveguides (LCWs) were included into a fiber-loop cavity ring-down absorption spectrometer to reduce the detection limit over, both, single pass absorption in a LCW and cavityenhanced absorption using a conventional fiber-loop cavity. LCWs of 5 and 10 cm length were interfaced with a pressure-flow system and a multimode fiber-loop cavity using concave fiber lenses with matching numerical apertures and diameters. Two red dyes, Allura Red AC and Congo Red, were detected with a 532 nm pulsed laser at a 5 nM limit of detection in a detection volume of less than 1 μL, corresponding to a minimal detectable absorbance of less than 4 × 10−4 cm−1 and a minimal detectable change in absorption cross section, σmin = Vdet × ε × CLOD, of about 14 μm2 (Allura Red AC) and 37 μm2 (Congo Red).

Loss Determination in Microsphere Resonators by Phase-Shift Cavity Ring-Down Measurements

The optical loss of whispering gallery modes of resonantly excited microresonator spheres is determined by optical lifetime measurements. The phase-shift cavity ring-down technique is used to extract ring-down times and optical loss from the difference in amplitude modulation phase between the light entering the microresonator and light scattered from the microresonator. In addition, the phase lag of the light exiting the waveguide, which was used to couple light into the resonator, was measured. The intensity and phase measurements were fully described by a model that assumed interference of the cavity modes with the light propagating in the waveguide.

Optical Fiber Sensing Based on Reflection Laser Spectroscopy

An overview on high-resolution and fast interrogation of optical-fiber sensors relying on laser reflection spectroscopy is given. Fiber Bragg-gratings (FBGs) and FBG resonators built in fibers of different types are used for strain, temperature and acceleration measurements using heterodyne-detection and optical frequency-locking techniques. Silica fiber-ring cavities are used for chemical sensing based on evanescent-wave spectroscopy. Various arrangements for signal recovery and noise reduction, as an extension of most typical spectroscopic techniques, are illustrated and results on detection performances are presented.