Giant phase-conjugate reflection with a normal mirror in front of an optical phase-conjugator

We theoretically study reflection of light by a phase-conjugating mirror preceded by a partially reflecting normal mirror. The presence of a suitably chosen normal mirror in front of the phase conjugator is found to greatly enhance the total phase-conjugate reflected power, even up to an order of magnitude. Required conditions are that the phase-conjugating mirror itself amplifies upon reflection and that constructive interference of light in the region between the mirrors takes place. We show that the phase-conjugate reflected power then exhibits a maximum as a function of the transmittance of the normal mirror.Comment: 8 pages, 3 figures, RevTe

Bound Modes in Dielectric Microcavities

We demonstrate how exactly bound cavity modes can be realized in dielectric structures other than 3d photonic crystals. For a microcavity consisting of crossed anisotropic layers, we derive the cavity resonance frequencies, and spontaneous emission rates. For a dielectric structure with dissipative loss and central layer with gain, the beta factor of direct spontaneous emission into a cavity mode and the laser threshold is calculated.Comment: 5 pages, 3 figure

Minimizing the cost of fault location when testing from a finite state machine

If a test does not produce the expected output, the incorrect output may have been caused by an earlier state transfer failure. Ghedamsi and coworkers generate a set of candidates and then produce further tests to locate the failures within this set. We consider a special case where there is a state identification process that is known to be correct. A number of preset and adaptive approaches to fault location are described and the problem of minimizing the cost is explored. Some of the approaches lead to NP-hard optimization problems for which possible heuristics are suggested

Superluminal Optical Phase Conjugation: Pulse Reshaping and Instability

We theoretically investigate the response of optical phase conjugators to incident probe pulses. In the stable (sub-threshold) operating regime of an optical phase conjugator it is possible to transmit probe pulses with a superluminally advanced peak, whereas conjugate reflection is always subluminal. In the unstable (above-threshold) regime, superluminal response occurs both in reflection and in transmission, at times preceding the onset of exponential growth due to the instability.Comment: 9 pages, 6 figures, RevTex, to appear in Phys. Rev.

Carrier inversion noise has important influence on the dynamics of a semiconductor laser

We find that, although inversion noise has only a marginal effect on the linewidth of a semiconductor laser in continuous wave operation, in the presence of dynamics, it may play an important role in determining the final dynamical state. It is, therefore, essential to include realistic carrier noise when analysing semiconductor laser dynamics

Approximate Deadline-Scheduling with Precedence Constraints

We consider the classic problem of scheduling a set of n jobs non-preemptively on a single machine. Each job j has non-negative processing time, weight, and deadline, and a feasible schedule needs to be consistent with chain-like precedence constraints. The goal is to compute a feasible schedule that minimizes the sum of penalties of late jobs. Lenstra and Rinnoy Kan [Annals of Disc. Math., 1977] in their seminal work introduced this problem and showed that it is strongly NP-hard, even when all processing times and weights are 1. We study the approximability of the problem and our main result is an O(log k)-approximation algorithm for instances with k distinct job deadlines

Arithmetical Congruence Preservation: from Finite to Infinite

Various problems on integers lead to the class of congruence preserving functions on rings, i.e. functions verifying $a-b$ divides $f(a)-f(b)$ for all $a,b$. We characterized these classes of functions in terms of sums of rational polynomials (taking only integral values) and the function giving the least common multiple of $1,2,\ldots,k$. The tool used to obtain these characterizations is "lifting": if $\pi\colon X\to Y$ is a surjective morphism, and $f$ a function on $Y$ a lifting of $f$ is a function $F$ on $X$ such that $\pi\circ F=f\circ\pi$. In this paper we relate the finite and infinite notions by proving that the finite case can be lifted to the infinite one. For $p$-adic and profinite integers we get similar characterizations via lifting. We also prove that lattices of recognizable subsets of $Z$ are stable under inverse image by congruence preserving functions

Gradual sub-lattice reduction and a new complexity for factoring polynomials

We present a lattice algorithm specifically designed for some classical applications of lattice reduction. The applications are for lattice bases with a generalized knapsack-type structure, where the target vectors are boundably short. For such applications, the complexity of the algorithm improves traditional lattice reduction by replacing some dependence on the bit-length of the input vectors by some dependence on the bound for the output vectors. If the bit-length of the target vectors is unrelated to the bit-length of the input, then our algorithm is only linear in the bit-length of the input entries, which is an improvement over the quadratic complexity floating-point LLL algorithms. To illustrate the usefulness of this algorithm we show that a direct application to factoring univariate polynomials over the integers leads to the first complexity bound improvement since 1984. A second application is algebraic number reconstruction, where a new complexity bound is obtained as well