There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

BACKGROUND Singularities are critical points for which the behavior of a mathematical model governing a physical system is of a fundamentally different nature compared to the neighboring points. Exceptional points are spectral singularities in the parameter space of a system in which two or more eigenvalues, and their corresponding eigenvectors, simultaneously coalesce. Such degeneracies are peculiar features of nonconservative systems that exchange energy with their surrounding environment. In the past two decades, there has been a growing interest in investigating such nonconservative systems, particularly in connection with the quantum mechanics notions of parity-time symmetry, after the realization that some non-Hermitian Hamiltonians exhibit entirely real spectra. Lately, non-Hermitian systems have raised considerable attention in photonics, given that optical gain and loss can be integrated as nonconservative ingredients to create artificial materials and structures with altogether new optical properties. ADVANCES As we introduce gain and loss in a nanophotonic system, the emergence of exceptional point singularities dramatically alters the overall response, leading to a range of exotic functionalities associated with abrupt phase transitions in the eigenvalue spectrum. Even though such a peculiar effect has been known theoretically for several years, its controllable realization has not been made possible until recently and with advances in exploiting gain and loss in guided-wave photonic systems. As shown in a range of recent theoretical and experimental works, this property creates opportunities for ultrasensitive measurements and for manipulating the modal content of multimode lasers. In addition, adiabatic parametric evolution around exceptional points provides interesting schemes for topological energy transfer and designing mode and polarization converters in photonics. Lately, non-Hermitian degeneracies have also been exploited for the design of laser systems, new nonlinear optics phenomena, and exotic scattering features in open systems. OUTLOOK Thus far, non-Hermitian systems have been largely disregarded owing to the dominance of the Hermitian theories in most areas of physics. Recent advances in the theory of non-Hermitian systems in connection with exceptional point singularities has revolutionized our understanding of such complex systems. In the context of optics and photonics, in particular, this topic is highly important because of the ubiquity of nonconservative elements of gain and loss. In this regard, the theoretical developments in the field of non-Hermitian physics have allowed us to revisit some of the well-established platforms with a new angle of utilizing gain and loss as new degrees of freedom, in stark contrast with the traditional approach of avoiding these elements. On the experimental front, progress in fabrication technologies has allowed for harnessing gain and loss in chip-scale photonic systems. These theoretical and experimental developments have put forward new schemes for controlling the functionality of micro- and nanophotonic devices. This is mainly based on the anomalous parameter dependence in the response of non-Hermitian systems when operating around exceptional point singularities. Such effects can have important ramifications in controlling light in new nanophotonic device designs, which are fundamentally based on engineering the interplay of coupling and dissipation and amplification mechanisms in multimode systems. Potential applications of such designs reside in coupled-cavity laser sources with better coherence properties, coupled nonlinear resonators with engineered dispersion, compact polarization and spatial mode converters, and highly efficient reconfigurable diffraction surfaces. In addition, the notion of the exceptional point provides opportunities to take advantage of the inevitable dissipation in environments such as plasmonic and semiconductor materials, which play a key role in optoelectronics. Finally, emerging platforms such as optomechanical cavities provide opportunities to investigate exceptional points and their associated phenomena in multiphysics systems.

Exceptional points in optics and photonics.

Recent advances in shape–memory polymers: Structure, mechanism, functionality, modeling and applications

Mathematical Handbook for Scientists and Engineers

A review of stimuli-responsive shape memory polymer composites

S-MAC is a robust medium access control protocol for wireless sensor networks which is designed to be energy efficient. S-MAC nodes reduce energy expenditure by periodically turning off their receivers (sleeping) in a coordinated manner. Nodes form virtual clusters based on common sleep schedules. However, some nodes in S-MAC may have to wake up more often than the other nodes. This paper demonstrates in some wireless sensor networks using S-MAC, a significant proportion of the nodes may have to stay awake much longer than envisaged. The paper then proposes a modification of the protocol to eliminate the need for some nodes to stay awake longer than the other nodes. The modified version improves the energy efficiency and increases the life span of a wireless sensor network.

Energy efficient medium access control with single sleep schedule for wireless sensor networks

An attempt is made to study the dependence of the diffusivity-mobility ratio on a quantizing magnetic field in degenerate n-Cd3As2 in the extreme quantum limit according to the Bodnar model which has recently been shown in the literature to be the most valid model for Cd3As2. The results obtained are then compared to those derived on the basis of the Kane model since many authors have continued to use the Kane model for Cd3As2.



Es wird der Versuch unternommen, die Abhangigkeit des Diffusions—Beweglichkeitsverhaltnisses im quantisierenden Magnetfeld in entartetem n-Cd3As2 im extremen Quantengrenzfall entsprechend dem Modell von Bodnar zu bestimmen, von dem kurzlich in der Literatur gezeigt wurde, das es das verlaslichste Modell fur Cd3As2 darstellt. Die erhaltenen Ergebnisse werden dann mit denen verglichen, die auf der Grundlage des Modells von Kane abgeleitet wurden, da viele Autoren nach wie vor das Kanesche Modell fur Cd3As2 benutzen.

Effect of Magnetic Quantization on the Diffusivity—Mobility Ratio in n-Cd3As2

Highly popular Web sites can suffer classical congestion collapse because of the ability of outgoing 'bursty' data to congest the server side link. Using the well known and recognized network simulator ns we look at the effect that this congestion collapse has on user perceived performance (UPP) of a simulated Web site. We developed a protocol overlay for HTTP/1.1 and a complementary distribution infrastructure to alleviate the effects of this congestion. Our protocol HTTP(P2P) shows promise for increasing the maximum load of Web sites during times of high and very high Web site load and link contention. In our simulated environment, HTTP(P2P) significantly decreases the time required for users to download the Web page they request. The protocol also distributes the redirected traffic over the network to reduce secondary transient network congestion.

HTTP(P2P): a transaction based (HTTP) peer-to-peer protocol for the dissemination of Web-objects in congested networks

Conversion Electron Mossbauer Spectroscopy (CEMS) was employed in order to study the mixing induced by swift Au and Ag ions at the Fe/Si interface in the Fe/Fe57/Si system. An increase in the amount of mixing with ion fluence and electronic energy loss (Se) has been observed. Atomic Force Microscopy (AFM) results provided indirect evidence to support the above observations.

Conversion Electron Mössbauer Study of Mixing Induced by Swift Heavy Ions at the Fe/Si Interface

An attempt is made to investigate the electric field-aided photoemission from quantum wells in ultrathin films of degenerate wide-gap semiconductors, taking n-type GaAs as an example. It is found that the photoemission varies in a step-like manner with photon energies close to the electron affinity and exhibits oscillatory character in its dependence on the film thickness, both in presence and absence of an electric field. For photon energies significantly lower than the electron affinity, a quantized nature of the emission is observed in certain ranges of film thicknesses. Besides, the rate of increase of the photoemission with electric field is seen to increase with increasing film thickness over the range of thicknesses of interest in ultrathin films.



Am Beispiel von n-GaAs wird die feldgestutzte Photoemission von Quantenwells in ultradunnen Schichten degenerierter Breitbandhalbleiter untersucht. Die Photoemission andert sich stufenformig, wenn die Photonenenergie nahe der Elektronenaffinitat ist und zeigt Oszillationen in der Abhangigkeit von der Schichtdicke sowohl mit als auch ohne angelegtes elektrisches Feld. Fur Photonenenergien merklich unterhalb der Elektronenaffinitat ist die Emission in gewissen Dickenbereichen quantisiert. Die Wachstumsrate der Photoemission im elektrischen Feld nimmt mit der Schichtdicke im gesamten interessierenden Bereich ultradunner Schichten zu.

Somnath Ghosh

Papers

Energy efficient medium access control with single sleep schedule for wireless sensor networks

Effect of Magnetic Quantization on the Diffusivity—Mobility Ratio in n-Cd3As2

HTTP(P2P): a transaction based (HTTP) peer-to-peer protocol for the dissemination of Web-objects in congested networks

Conversion Electron Mössbauer Study of Mixing Induced by Swift Heavy Ions at the Fe/Si Interface

Effect of an electric field on size-quantized photoemission from nanometer films of semiconductors