Quasiperiodic Envelope Solitons

We analyse nonlinear wave propagation and cascaded self-focusing due to second-harmonic generation in Fibbonacci optical superlattices and introduce a novel concept of nonlinear physics, the quasiperiodic soliton, which describes spatially localized self-trapping of a quasiperiodic wave. We point out a link between the quasiperiodic soliton and partially incoherent spatial solitary waves recently generated experimentally.Comment: Submitted to PRL. 4 pages with 5 figure

Isotropic photonic band gap and anisotropic structures in transmission spectra of two-dimensional 5-fold and 8-fold symmetric quasiperiodic photonic crystals

We measured and calculated transmission spectra of two-dimensional quasiperiodic photonic crystals (PCs) based on a 5-fold (Penrose) or 8-fold (octagonal) symmetric quasiperiodic pattern. The photonic crystal consisted of dielectric cylindrical rods in air placed normal to the basal plane on vertices of tiles composing the quasiperiodic pattern. An isotropic photonic band gap (PBG) appeared in the TM mode, where electric fields were parallel to the rods, even when the real part of a dielectric constant of the rod was as small as 2.4. An isotropic PBG-like dip was seen in tiny Penrose and octagonal PCs with only 6 and 9 rods, respectively. These results indicate that local multiple light scattering within the tiny PC plays an important role in the PBG formation. Besides the isotropic PBG, we found dips depending on the incident angle of the light. This is the first report of anisotropic structures clearly observed in transmission spectra of quasiperiodic PCs. Based on rod-number and rod-arrangement dependence, it is thought that the shapes and positions of the anisotropic dips are determined by global multiple light scattering covering the whole system. In contrast to the isotropic PBG due to local light scattering, we could not find any PBGs due to global light scattering even though we studied transmission spectra of a huge Penrose PC with 466 rods.Comment: One tex file for manuscript and 12 PNG files for figures consisting of Fig.1a-d, 2,3, ...

Physical nature of critical wave functions in Fibonacci systems

We report on a new class of critical states in the energy spectrum of general Fibonacci systems. By introducing a transfer matrix renormalization technique, we prove that the charge distribution of these states spreads over the whole system, showing transport properties characteristic of electronic extended states. Our analytical method is a first step to find out the link between the spatial structure of these critical wave functions and the quasiperiodic order of the underlying lattice.Comment: REVTEX 3.0, 11 pages, 2 figures available upon request. To appear in Phys. Rev. Let

Multi-component optical solitary waves

We discuss several novel types of multi-component (temporal and spatial) envelope solitary waves that appear in fiber and waveguide nonlinear optics. In particular, we describe multi-channel solitary waves in bit-parallel-wavelength fiber transmission systems for high performance computer networks, multi-colour parametric spatial solitary waves due to cascaded nonlinearities of quadratic materials, and quasiperiodic envelope solitons due to quasi-phase-matching in Fibonacci optical superlattices.Comment: 12 pages, 11 figures; To be published in: Proceedings of the Dynamics Days Asia-Pacific: First International Conference on Nonlinear Science (Hong-Kong, 13-16 July, 1999), Editor: Bambi Hu (Elsevier Publishers, 2000

Trace and antitrace maps for aperiodic sequences, their extensions and applications

We study aperiodic systems based on substitution rules by means of a transfer-matrix approach. In addition to the well-known trace map, we investigate the so-called `antitrace' map, which is the corresponding map for the difference of the off-diagonal elements of the 2x2 transfer matrix. The antitrace maps are obtained for various binary, ternary and quaternary aperiodic sequences, such as the Fibonacci, Thue-Morse, period-doubling, Rudin-Shapiro sequences, and certain generalizations. For arbitrary substitution rules, we show that not only trace maps, but also antitrace maps exist. The dimension of the our antitrace map is r(r+1)/2, where r denotes the number of basic letters in the aperiodic sequence. Analogous maps for specific matrix elements of the transfer matrix can also be constructed, but the maps for the off-diagonal elements and for the difference of the diagonal elements coincide with the antitrace map. Thus, from the trace and antitrace map, we can determine any physical quantity related to the global transfer matrix of the system. As examples, we employ these dynamical maps to compute the transmission coefficients for optical multilayers, harmonic chains, and electronic systems.Comment: 13 pages, REVTeX, now also includes applications to electronic systems, some references adde

Size constancy in bat biosonar?

Perception and encoding of object size is an important feature of sensory systems. In the visual system object size is encoded by the visual angle (visual aperture) on the retina, but the aperture depends on the distance of the object. As object distance is not unambiguously encoded in the visual system, higher computational mechanisms are needed. This phenomenon is termed "size constancy". It is assumed to reflect an automatic re-scaling of visual aperture with perceived object distance. Recently, it was found that in echolocating bats, the 'sonar aperture', i.e., the range of angles from which sound is reflected from an object back to the bat, is unambiguously perceived and neurally encoded. Moreover, it is well known that object distance is accurately perceived and explicitly encoded in bat sonar. Here, we addressed size constancy in bat biosonar, recruiting virtual-object techniques. Bats of the species Phyllostomus discolor learned to discriminate two simple virtual objects that only differed in sonar aperture. Upon successful discrimination, test trials were randomly interspersed using virtual objects that differed in both aperture and distance. It was tested whether the bats spontaneously assigned absolute width information to these objects by combining distance and aperture. The results showed that while the isolated perceptual cues encoding object width, aperture, and distance were all perceptually well resolved by the bats, the animals did not assign absolute width information to the test objects. This lack of sonar size constancy may result from the bats relying on different modalities to extract size information at different distances. Alternatively, it is conceivable that familiarity with a behaviorally relevant, conspicuous object is required for sonar size constancy, as it has been argued for visual size constancy. Based on the current data, it appears that size constancy is not necessarily an essential feature of sonar perception in bats

Luminescence Properties of a Fibonacci Photonic Quasicrystal

We report the realization of an active one-dimensional Fibonacci photonic quasi-crystal via spin coating. Manipulation of the luminescence properties of an organic dye embedded in the quasi-crystal is presented and compared to theoretical simulations. The luminescence occurs via the pseudo-bandedge mode and follows the dispersion properties of the Fibonacci crystal. Time resolved luminescence measurement of the active structure shows faster spontaneous emission rate, indicating the effect of the large photon densities available at the bandedge due to the presence of critically localized states. The experimental results are in excellent agreement with the theoretical calculations.Comment: PDF file, 14 pages 4 figure

Effect of cyclosporin A on proteinuria in the course of glomerulopathy associated with WT1 mutations

Denys–Drash syndrome (DDS) is characterized by progressive glomerulopathy caused by diffuse mesangial sclerosis (DMS), genitourinary defects, and a higher risk of developing Wilms’ tumor. It is commonly assumed that the DMS is unresponsive to any medications. In this report, we present a patient with Denys–Drash syndrome, in whom the cyclosporine A (CsA) was found to induce total remission. This observation and observations of other authors confirm that in genetic forms of nephrotic syndrome, the proteinuric effect of CsA may be due to a non-immunologic mechanism. We confirm the beneficial effect of CsA treatment in DDS; however, the potential nephrotoxicity of this drug will probably not allow long-term use