Optical bright and dark states in side-coupled resonator structures

We analyze side-coupled standing-wave cavity structures consisting of Fabry-Perot and photonic crystal resonators coupled to two waveguides. We show that optical bright and dark states, analogous to those observed in coherent light-matter interactions, can exist in these systems. These structures may be useful for variable, switchable delay lines

Least-Squares Approximation by Elements from Matrix Orbits Achieved by Gradient Flows on Compact Lie Groups

Let $S(A)$ denote the orbit of a complex or real matrix $A$ under a certain equivalence relation such as unitary similarity, unitary equivalence, unitary congruences etc. Efficient gradient-flow algorithms are constructed to determine the best approximation of a given matrix $A_0$ by the sum of matrices in $S(A_1), ..., S(A_N)$ in the sense of finding the Euclidean least-squares distance $$\min \{\|X_1+ ... + X_N - A_0\|: X_j \in S(A_j), j = 1, >..., N\}.$$ Connections of the results to different pure and applied areas are discussed

Chemotactic predator-prey dynamics

A discrete chemotactic predator-prey model is proposed in which the prey secrets a diffusing chemical which is sensed by the predator and vice versa. Two dynamical states corresponding to catching and escaping are identified and it is shown that steady hunting is unstable. For the escape process, the predator-prey distance is diffusive for short times but exhibits a transient subdiffusive behavior which scales as a power law $t^{1/3}$ with time $t$ and ultimately crosses over to diffusion again. This allows to classify the motility and dynamics of various predatory bacteria and phagocytes. In particular, there is a distinct region in the parameter space where they prove to be infallible predators.Comment: 4 pages, 4 figure

Bulk and wetting phenomena in a colloidal mixture of hard spheres and platelets

Density functional theory is used to study binary colloidal fluids consisting of hard spheres and thin platelets in their bulk and near a planar hard wall. This system exhibits liquid-liquid coexistence of a phase that is rich in spheres (poor in platelets) and a phase that is poor in spheres (rich in platelets). For the mixture near a planar hard wall, we find that the phase rich in spheres wets the wall completely upon approaching the liquid demixing binodal from the sphere-poor phase, provided the concentration of the platelets is smaller than a threshold value which marks a first-order wetting transition at coexistence. No layering transitions are found in contrast to recent studies on binary mixtures of spheres and non-adsorbing polymers or thin hard rods.Comment: 6 pages, 4 figure

Designing coupled-resonator optical waveguide delay lines

We address the trade-offs among delay, loss, and bandwidth in the design of coupled-resonator optical waveguide (CROW) delay lines. We begin by showing the convergence of the transfer matrix, tight-binding, and time domain formalisms in the theoretical analysis of CROWs. From the analytical formalisms we obtain simple, analytical expressions for the achievable delay, loss, bandwidth, and a figure of merit to be used to compare delay line performance. We compare CROW delay lines composed of ring resonators, toroid resonators, Fabry-Perot resonators, and photonic crystal defect cavities based on recent experimental results reported in the literature

Coupled Resonator Optical Waveguides: Toward the Slowing and Storage of Light

The development of a simple, solid-state-based technology to slow the propagation of light could prove an important step in the realization of the high-bit-rate communication systems of the future. The use of coupled resonator optical waveguides (CROWs) as practical elements to slow and store light pulses is one possibility

Transmission and group delay of microring coupled-resonator optical waveguides

We measured the transmission and group delay of microring coupled-resonator optical waveguides (CROWs). The CROWs consisted of 12 weakly coupled, microring resonators fabricated in optical polymers (PMMA on Cytop). The intrinsic quality factor of the resonators was 18,000 and the interresonator coupling was 1%, resulting in a delay of 110-140 ps and a slowing factor of 23-29 over a 17 GHz bandwidth

Polymer Microring Coupled-Resonator Optical Waveguides

We present measurements of the transmission and dispersion properties of coupled-resonator optical waveguides (CROWs) consisting of weakly coupled polymer microring resonators. The fabrication and the measurement methods of the CROWs are discussed as well. The experimental results agree well with the theoretical loss, waveguide dispersion, group delay, group velocity, and group-velocity dispersion (GVD). The intrinsic quality factors of the microrings were about 1.5 times 10^4 to 1.8 times 10^4, and group delays greater than 100 ps were measured with a GVD between -70 and 100 ps/(nm x resonator). With clear and simple spectral responses and without a need for the tuning of the resonators, the polymer microring CROWs demonstrate the practicability of using a large number of microresonators to control the propagation of optical waves