Discrete breathers in an electric lattice with an impurity: Birth, interaction, and death.

We have simulated aspects of intrinsic localized modes or discrete breathers in a modulated lumped transmission line with nonlinear varactors and a defect unit cell. As the inductance or capacitance of this cell is increased, a transition from instability to stability takes place. Namely, there exist threshold values of the inductance or capacitance of a lattice impurity for a breather to be able to attach to. A resistive defect can also anchor a breather. Moreover, by either gradually lowering all the source resistances, or else increasing the modulation frequency, multiple secondary ILMs can be spontaneously generated at host sites (with only a single inductive or capacitive defect). Further, if two impurities are subcritically spaced (the separation increasing with the amplitude of the modulation voltage), a breather can pop up midway, with no breathers at the impurity sites themselves. Finally, an ILM can pull closer its neighbors on both sides, only to perish once these ILMs have gotten sufficiently close. To our knowledge, these effects have not been reported for any discrete nonlinear system.

Primary pleomorphic liposarcoma of the thoracic epidural space: case report.

BACKGROUND CONTEXT: Pleomorphic liposarcoma (PLS) is a rare malignant soft tissue tumor comprising 5%-15% of liposarcomas and characterized by high malignant potential. To our knowledge only three cases of this entity have been reported in the spine. PURPOSE: We describe the only reported case of a purely epidural PLS with no macroscopic bone involvement at diagnosis. STUDY DESIGN/SETTING: A case presenting clinical evidence that PLS may arise from the epidural fat is reported. METHODS: The clinical presentation, management, and outcome in a case of primary PLS of the thoracic spine, and a review of the literature, are presented. RESULTS: A 70-year-male presented with sudden onset lower extremity weakness, constipation, and back pain. Magnetic resonance imaging revealed an epidural lesion at T5 with noted mass effect compressing the spinal cord and extension to the T5-T6 foramen. Urgent decompressive laminectomy with gross total resection was performed. Histopathology revealed high-grade PLS. Adjunct radiotherapy was prescribed. The tumor recurred 3 months later. In spite of repeat surgery, additional radiation, and chemotherapy, the patient developed widespread metastases and succumbed to his disease 1 year after treatment began. CONCLUSIONS: Spinal PLS is a rare entity, but nonetheless may arise from epidural fat and should be considered in the differential diagnosis of primary spinal cord lesions.

Pulse propagation through a slab with time-periodic dielectric function ε(t).

We describe pulse propagation through a slab with periodic dielectric function ε(t), thus extending our previous investigation for monochromatic incidence [Phys. Rev. A 79, 053821 (2009)]. Based on the concepts of phase and group delays, we prove that, for an incident quasi-monochromatic pulse, the transmitted pulse can be expressed as a superposition of partial pulses that are exact replicas of the incident pulse and that exit the slab with a time delay. These partial pulses have harmonic carrier frequencies ω c - nΩ (n is an integer, ω c is the carrier frequency of the incident pulse, and Ω = 2π/T is the slab modulation frequency). We find numerically that these partial pulses can be fast (peak velocity vn > c or vn < 0) or slow (vn << c). Further, we investigate the peak velocity v p of the outcoming pulse for several cases. We find that this peak velocity v p and the partial peak velocities vn do not diverge--as occurs to the group velocity v g of the bulk dynamic-periodic medium when ω c = Ω/2. We expect that these results could be verified in the microwave regime [see Halevi et al., Proc. SPIE 8095, 80950I (2011)].

The value of postoperative MR in tethered cord: a review of 140 cases.

PURPOSE: This study aimed to determine the justification for routine postoperative MRI (POMR) following surgical release of tethered cord (TC) given that an MR, in this situation, mostly serves as a baseline and rarely has immediate clinical implications. Furthermore, later in the course of the disease, the presence of retethering is mostly assessed by clinical parameters, rather than imaging. METHODS: A single-center retrospective review of patients who underwent tethered cord release surgery between the years 1997 and 2009 at the Department of Pediatric Neurosurgery, Tel Aviv Medical Center, Israel was performed. Collected data including basis for diagnosis, pathology, associated clinical and radiologic findings, surgical procedure and outcome, postoperative follow-up and morbidities, and postoperative MRI findings were recorded and analyzed. RESULTS: One hundred forty patients operated upon between 1997 and 2009 for tethered cord syndrome were reviewed. Routine postoperative MR was performed in all cases 6-18 months after surgery. All cases were fully untethered. MR revealed relevant information in eight cases, two with residual dermoid, and six with significant terminal syrinx. None of these findings led to repeat surgery or special treatment. Retethering operations were performed in two cases in which retethering was diagnosed based on clinical evaluation. CONCLUSIONS: Based on analysis of our series of 140 consecutive patients who all underwent POMR 6-18 months after TC release, we suggest that POMR as routine clinical practice is not justified for uncomplicated cases of TC release. In cases of high risk for retethering, or significant preoperative syrinx or dermoid, POMR is recommended to establish a baseline for future clinical follow-up.

Electrically tuned phase transition and band structure in a liquid-crystal-infilled photonic crystal.

We studied a nematic liquid crystal (LC) cylinder under the action of an axial electric field E(0). Elaborate modeling of the free energy leads to the conclusion that the configuration of the molecules is "escaped radial" for low E(0); a phase transition, however, occurs for a critical value E(c), the configuration becoming axial for E(0) >E(c). From these results, the position-dependent dielectric tensor is determined and the photonic band (PB) structure is calculated for a photonic crystal of LC cylinders. It is shown that by varying E(0) a PB gap can be fully tuned from open to closed. Also, switching to a supercritical field can give rise to interesting polarization and directional effects in the propagation of light.

Spontaneous emission in one-dimensional photonic crystals.

We study the spontaneous emission of an atom embedded in a one-dimensional photonic crystal or superlattice using a classical electrodynamic theory of radiation. The rate of emission is a function of the frequency of the emitted photon, the dipole's position and orientation, as well as the geometric and material parameters of the superlattice. The emission spectrum shows an oscillatory behavior which follows the photonic band structure. For TE modes, there are frequency regions where radiative emission is completely prohibited due to the absence of modes with k//>omega/c; the radiation is then TM polarized. In addition to the radiative modes, there are always evanescent modes with k//>omega/c which are waveguided by the dielectric layers. The evanescent contribution to the spontaneous emission is dominant if a dielectric layer is in the near field region of the dipole. For TM modes, emission rates greatly vary for parallel and perpendicular dipole moments. In a photonic crystal with a high filling fraction of the dielectric and perpendicular dipoles located in the low-index layer, the decay rate can be as much as 76 times the free space value for a single atom and 50 times for a gas of atoms. We also find that the rate of emission presents a strong dependence on the atom's position.

Dipole radiation in a one-dimensional photonic crystal. II. TM polarization.

As in a recent paper [I. Alvarado-Rodríguez, P. Halevi, and Adán S. Sánchez, Phys. Rev. E 63, 056613 (2001); 65, 039901(E) (2002)], we study the power emitted by an oscillating dipole in a superlattice (SL) modeled by means of a periodic distribution of Dirac-delta functions (Dirac-comb SL). However, while in the aforementioned paper the radiation was restricted to the transverse electric (TE) polarization mode, here we focus our attention on the transverse magnetic (TM) mode. Employing the same methodology, again we find that the power spectra are dominated by slope discontinuities. These occur - if at all - at the band edges for on-axis propagation, depending on the dipole's position and orientation. The largest enhancement or inhibition is present for normalized frequencies such that (omegad/c) less, similar 2pi; here, omega is the dipole frequency, c is the speed of light in vacuum, and d is the distance between the barriers. For substantial values of the grating strength considerable enhancement or suppression of the radiated power (in comparison to the free-space value) is obtained. We also find that the power emitted by a gas of randomly oriented dipoles exhibits slope discontinuities at all band edges for on-axis propagation. In comparison with the TE polarization case, the TM polarization exhibits several different qualitative features.

Dipole radiation in a one-dimensional photonic crystal: TE polarization.

We study the power emitted by an oscillating dipole in a superlattice (SL) modeled by means of a periodic distribution of Dirac delta functions (Dirac comb SL). The radiation is permitted to propagate in all directions in space; however, it is restricted to the transverse electric (TE) polarization mode. The calculation is based on a classical theory of radiation in nonuniform dielectric media by Dowling and Bowden [Phys. Rev. A 46, 612 (1992)]. The emitted power is derived in terms of a single integral, with no approximations. A SL has no omnidirectional photonic band gaps, and therefore the power is always finite. The power spectrum exhibits slope discontinuities, which occur at the band edges for on-axis propagation. It also depends strongly on the dipole's position in the SL and on the grating strength that characterizes the Dirac comb model. The power peaks for low frequencies, and there can be large enhancement of emission as compared to free space. The closer the dipole is to a barrier (Dirac delta) and the greater the grating strength, the stronger the enhancement is. These conclusions are expected to be relevant for a real SL.

Density of states for a dielectric superlattice. II. TM polarization

We present an analysis of the band structure, the equifrequency surfaces, and the density of states (DOS) for the transverse magnetic (TM) polarization mode of the dielectric superlattice, modeled by means of Dirac-delta functions. This complements a recent article [Phys. Rev E 59, 3624 (1999)] that analyzes the case of transverse electric (TE) polarization. Unfortunately, for this simple model, there is no manifestation of the Brewster effect in the band structure for the TM modes. For large values of the frequency or the grating strength, the equifrequency surfaces essentially degenerate into a set of concentric, hollow, and narrow cylinders centered on the superlattice axis. The DOS is enhanced relative to free space for any frequency and it exhibits discontinuities in the slope at the band edges. These results are relevant to the spontaneous emission by an atom or to dipole radiation in one-dimensional periodic structures. The differences between TE and TM modes are discussed. We take the opportunity to correct an error in the DOS calculation for TE polarization in the article referred above.

Tunable photonic crystals with semiconducting constituents

We propose that the photonic band structure (PBS) of semiconductor-based photonic crystals (PCs) can be made tunable if the free-carrier density is sufficiently high. In this case, the dielectric constant of the semiconductor, modeled as varepsilon(omega) = varepsilon(0)(1-omega(2)(p)/omega(2)), depends on the temperature T and on the impurity concentration N through the plasma frequency omega(p). Then the PBS is strongly T and N dependent; it is even possible to obliterate a photonic band gap. This is shown by calculating the 2D PBS for PCs that incorporate either intrinsic InSb or extrinsic Ge.