Homoclinic points of algebraic -actions

Let be an action of by continuous automorphisms of a compact abelian group . A point in is called homoclinic for if as . We study the set of homoclinic points for , which is a subgroup of . If is expansive, then is at most countable. Our main results are that if is expansive, then (1) is nontrivial if and only if has positive entropy and (2) is nontrivial and dense in if and only if has completely positive entropy. In many important cases is generated by a fundamental homoclinic point which can be computed explicitly using Fourier analysis. Homoclinic points for expansive actions must decay to zero exponentially fast, and we use this to establish strong specification properties for such actions. This provides an extensive class of examples of -actions to which Ruelle's thermodynamic formalism applies. The paper concludes with a series of examples which highlight the crucial role of expansiveness in our main results.

     

Enhanced transduction of photonic crystal dye lasers for gas sensing via swelling polymer film

We present the enhanced transduction of a photonic crystal dye laser for gas sensing via deposition of an additional swelling polymer film. Device operation involves swelling of the polymer film during exposure to specific gases, leading to a change in total effective refractive index. Experimental results show an enhancement of 16.09 dB in sensing ethanol vapor after deposition of a polystyrene film. We verify different responses of the polystyrene film when exposed to either ethanol vapor or increased humidity, indicating selectivity. The concept is generic and, in principle, straightforward in its application to other intracavity-based detection schemes to enable gas sensing.