Visibility Extension via Reflection

This paper studies a variant of the Art Gallery problem in which the "walls" can be replaced by \emph{reflecting-edges}, which allows the guard to see further and thereby see a larger portion of the gallery. We study visibility with specular and diffuse reflections. The number of times a ray can be reflected can be taken as a parameter. The Art Gallery problem has two primary versions: point guarding and vertex guarding. Both versions are proven to be NP-hard by Lee and Aggarwal. We show that several cases of the generalized problem are NP-hard, too. We managed to do this by reducing the 3-SAT and the Subset-Sum problems to the various cases of the generalized problem. We also illustrate that if $\cal P$ is a funnel or a weak visibility polygon, the problem becomes more straightforward and can be solved in polynomial time. We generalize the $\mathcal{O}(\log n)$-approximation ratio algorithm of the vertex guarding problem to work in the presence of reflection. For a bounded $r$, the generalization gives a polynomial-time algorithm with $\mathcal{O}(\log n)$-approximation ratio for several special cases of the generalized problem. Furthermore, Chao Xu proved that although reflection helps the visibility of guards to be expanded, similar to the normal guarding problem, even considering $r$ specular reflections we may need $\lfloor \frac{n}{3} \rfloor$ guards to cover a simple polygon $\cal P$. In this article, we prove that considering $r$ diffuse reflections the minimum number of vertex or boundary guards required to cover $\cal P$ decreases to $\lceil \frac{\alpha}{1+ \lfloor \frac{r}{4} \rfloor} \rceil$, where $\alpha$ indicates the minimum number of guards required to cover $\cal P$ without reflection. funnel or a weak visibility polygon, then the problem becomes more straightforward and can be solved in polynomial time.Comment: 32 pages, 10 figure

Jurisprudence under the perspective of the new media and its effect on the communication of law

Despite the law knowledge presumption, Jurisprudence has not always considered the effects introduced by the communication of law in the transition from the print to the electric revolution, using here concepts and ideas of McLuhan´s theory. The use of Internet by Brazilian Courts (on line transmission of trials, the digital process, transformation of courts in source of news on what concerns their decisions) is an interesting example of how the new medium interferes in the substance of the message of law, since the movement of the messages must be considered to understand the epistemological domain of law. New elements are introduced by the new media and interact with the old meanings, concepts and processes of law and of the old media and can themselves bring new conflicts that are relevant to the comprehension of the complete and real dynamics of Law

Polarization effects in the nonlinear interference of down-converted photons

We study polarization effects in the nonlinear interference of photons generated via frequency non-degenerate spontaneous parametric down conversion. Signal and idler photons generated in the visible and infrared (IR) range, are split in different arms of a nonlinear Michelson interferometer. The interference pattern for signal photons is detected, and it is shown to be dependent on the polarization rotation of idler photons, introduced by a birefringent sample. Based on this concept, we realize two new methods for measurement of sample retardation in the IR range by using well-developed and inexpensive components for visible light. The accuracy of the methods meets current industry standards. The developed IR polarimetry technique is relevant to material research, optical inspection, and quality control.Comment: Submitted for publicatio

Instabilities of a Bose-Einstein condensate in a periodic potential: an experimental investigation

By accelerating a Bose-Einstein condensate in a controlled way across the edge of the Brillouin zone of a 1D optical lattice, we investigate the stability of the condensate in the vicinity of the zone edge. Through an analysis of the visibility of the interference pattern after a time-of-flight and the widths of the interference peaks, we characterize the onset of instability as the acceleration of the lattice is decreased. We briefly discuss the significance of our results with respect to recent theoretical work.Comment: 7 pages, 3 figures; submitted to Optics Express (Focus Issue on Cold Atomic Gases in Optical Lattices

Sub-wavelength resolution of optical fields probed by single trapped ions: Interference, phase modulation, and which-way information

Taking recent experiments as examples, we discuss the conditions for sub-wavelength probing of optical field structures by single trapped atoms. We calculate the achievable resolution, highlighting its connection to the fringe visibility in an interference experiment. We show that seemingly different physical pictures, such as spatial averaging, phase modulation, and which-way information, describe the situation equally and lead to identical results. The connection to Bohr's moving slit experiment is pointed out.Comment: 6 pages, 1 figure; to appear in EPJ D, special issue on "Quantum fluctuations and coherence in optical and atomic structures

Single spontaneous photon as a coherent beamsplitter for an atomic matterwave

In spontaneous emission an atom in an excited state undergoes a transition to the ground state and emits a single photon. Associated with the emission is a change of the atomic momentum due to photon recoil. Photon emission can be modified close to surfaces and in cavities. For an ion, localized in front of a mirror, coherence of the emitted resonance fluorescence has been reported. In free space experiments demonstrated that spontaneous emission destroys motional coherence. Here we report on motional coherence created by a single spontaneous emission event close to a mirror surface. The coherence in the free atomic motion is verified by atom interferometry. The photon can be regarded as a beamsplitter for an atomic matterwave and consequently our experiment extends the original recoiling slit Gedanken experiment by Einstein to the case where the slit is in a robust coherent superposition of the two recoils associated with the two paths of the quanta.Comment: main text: 5 pages, 4 figure; supplementary information: 8 pages, 1 figur

Ultra-wide detuning planar Bragg grating fabrication technique based on direct UV grating writing with electro-optic phase modulation

A direct UV grating writing technique based on phase-controlled interferometry is proposed and demonstrated in a silica-on-silicon platform, with a wider wavelength detuning range than any previously reported UV writing technology. Electro-optic phase modulation of one beam in the interferometer is used to manipulate the fringe pattern and thus control the parameters of the Bragg gratings and waveguides. Various grating structures with refractive index apodization, phase shifts and index contrasts of up to 0.8×10-3 have been demonstrated. The method offers significant time/energy efficiency as well as simplified optical layout and fabrication process. We have shown Bragg gratings can be made from 1200 nm to 1900 nm exclusively under software control and the maximum peak grating reflectivity only decreases by 3dB over a 250 nm (~32THz) bandwidth