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

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

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

Children's verbalizations of motion events in German

Recent studies in language acquisition have paid much attention to linguistic diversity and have begun to show that language properties may have an impact on how children construct and organize their representations. With respect to motion events, Talmy (2000) has proposed a typological distinction between satellite-framed (S) languages that encode PATH in satellites, leaving the verb root free for the expression of MANNER, and verb-framed (V) languages that encode PATH in the verb, requiring MANNER to be expressed in the periphery of the sentence. This distinction has lead to the hypothesis (Slobin 1996) that MANNER should be more salient for children learning S-languages, who should have no difficulty combining it with PATH, as compared to those learning V-languages. This hypothesis was tested in a corpus elicited from German children and adults who had to verbalize short animated cartoons showing motion events, and the results are compared with previous analyses of French and English corpora elicited in an identical situation (Hickmann et al. 2009). As predicted, and as previously found for English, German children from three years on systematically express both MANNER (in the verb root) and PATH (in particles), in sharp contrast to French children, who rarely package MANNER and PATH together. These results suggest that, when they are engaged in communication, children construct spatial representations in accordance with the particular properties of their mother tongue. Future research is necessary to determine the extent to which cross-linguistic differences in production may reflect deeper differences in the allocation of attention and in conceptual organization

Experimental observation of superluminal group velocities in bulk two-dimensional photonic bandgap crystals

We have experimentally observed superluminal and infinite group velocities in bulk hexagonal two-dimensional photonic bandgap crystals with bandgaps in the microwave region. The group velocities depend on the polarization of the incident radiation and the air-filling fraction of the crystal.Comment: 8 pages, 7 figure

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