Transmission eigenvalues and thermoacoustic tomography

The spectrum of the interior transmission problem is related to the unique determination of the acoustic properties of a body in thermoacoustic imaging. Under a non-trapping hypothesis, we show that sparsity of the interior transmission spectrum implies a range separation condition for the thermoacoustic operator. In odd dimension greater than or equal to three, we prove that the transmission spectrum for a pair of radially symmetric non-trapping sound speeds is countable, and conclude that the ranges of the associated thermoacoustic maps have only trivial intersection

Photonic crystal polarizers and polarizing beam splitters

We have experimentally demonstrated polarizers and polarizing beam splitters based on microwave-scale two-dimensional photonic crystals. Using polarized microwaves within certain frequency bands, we have observed a squared-sinusoid (Malus) transmission law when using the photonic crystal as a polarizer. The photonic crystal also functions as a polarizing beamsplitter; in this configuration it can be engineered to split incident polarizations in either order, making it more versatile than conventional, Brewster-angle beamsplitters.Comment: 7 pages, 3 figures, published Journal Applied Physics 93, 9429 (2003

Faster-than-light effects and negative group delays in optics and electronics, and their applications

Recent manifestations of apparently faster-than-light effects confirmed our predictions that the group velocity in transparent optical media can exceed c. Special relativity is not violated by these phenomena. Moreover, in the electronic domain, the causality principle does not forbid negative group delays of analytic signals in electronic circuits, in which the peak of an output pulse leaves the exit port of a circuit before the peak of the input pulse enters the input port. Furthermore, pulse distortion for these superluminal analytic signals can be negligible in both the optical and electronic domains. Here we suggest an extension of these ideas to the microelectronic domain. The underlying principle is that negative feedback can be used to produce negative group delays. Such negative group delays can be used to cancel out the positive group delays due to transistor latency (e.g., the finite RC rise time of MOSFETS caused by their intrinsic gate capacitance), as well as the propagation delays due to the interconnects between transistors. Using this principle, it is possible to speed up computer systems.Comment: 13 pages, 5 figures, 2001 Photonic West Plenary Tal

Weak-wave advancement in nearly collinear four-wave mixing

We identify a new four-wave mixing process in which two nearly collinear pump beams produce phase-dependent gain into a weak bisector signal beam in a self-defocusing Kerr medium. Phase matching is achieved by weak-wave advancement caused by cross-phase modulation between the pump and signal beams. We relate this process to the inverse of spatial modulational instability and suggest a time-domain analog.Comment: 7 pages, 3 figure

Locating Cities and Their Governments in Multi-Level Sustainability Governance

Cities and their governments are increasingly recognized as important actors in global sustainability governance. With the adoption of the 2030 Agenda for Sustainable Development, their role in the global endeavor to foster sustainability has once again been put in the spotlight. Several scholars have highlighted pioneering local strategies and policies to implement the Sustainable Development Goals and render urban areas more sustainable. However, the question of how such urban sustainability actions are embedded in complex interactions between public and private actors operating at different levels has not been studied in enough detail. Building upon a multi-level governance approach, this article explores the entanglement and interconnectedness of cities and local governments with actors and institutions at various levels and scales to better capture the potential and limitations of urban policymaking contributing to global sustainability. The article finds that on the one hand cities and their governments are well positioned to engage other actors into a policy dialogue. On the other hand, local authorities face considerable budgetary and institutional capacity constraints, and they heavily rely on support from actors at other governmental levels and societal scales to carry out effective sustainability actions in urban areas