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

The initial/secondary absorption and compressive strength of alkali-activated slag (AAS) paste has been investigated. Emphasis has been given to secondary absorption of AAS paste based on the method described in ASTM C1585-04 [Standard Test Method for Measurement of Rate of Absorption of Water by Hydraulic Cement Concretes, Annual Book of ASTM Standards, ASTM International, West Conshohocken, PA, 2004, pp. 1–4]. The paste was produced by activating blast furnace slag with sodium hydroxide/potassium hydroxide and sodium silicate solution. The major parameters studied were alkali content, silicate content, and the type of activator. Experimental investigation revealed that initial rate of absorption (Si) and secondary rate of absorption (Ss) decreases with increase in alkali and silicate content up to a certain limit with an increase in compressive strength. The maximum compressive strength was found to be 50.40 MPa for the specimens having lowest sorptivity. It was also found that the sorptivity ratio (Si/Ss) plays a significant role on compressive strength in turn on the durability of AAS composites. This paper is an attempt to introduce the simple method of measuring initial and secondary sorptivity described in ASTM C1585-04 to study the strength and durability of AAS. The microstructure study was carried out using SEM/EDAX.

Sorptivity Ratio and Compressive Strength of Alkali-Activated Blast Furnace Slag Paste

Bond-Slip Effects on the Behaviour of RC Beam under Monotonic Loading - An Integrated 3D Computational Model using EAS Approach

The collaboration of at least a threshold number of secret shareholders in a threshold secret sharing scheme is a strict requirement to ensure its intended functionality. Due to its promising characteristics, such a scheme has been proposed to solve a range of security problems in mobile ad hoc networks. However, discovering a sufficient number of secret shareholders in such dynamic and unpredictable networks is not easy. In this paper, we propose a more efficient shareholder discovery mechanism compared to our previous work. The discovery process is performed in a multihop fashion to adapt to the mobile ad hoc network environment. We introduce batch extension that gradually extends the shareholders' collaboration boundary by more than one hop at a time around the service requestor, to find at least the threshold number of the unknown shareholders. Through the batch extension, reply aggregation is applicable, hence reducing the redundancy use of reply routes, decreasing the required packet transmission, and lessening the service delay, compared to the previously proposed mechanism. Our simulation results show that, with the appropriate batch size, the latest mechanism is more efficient with an insignificant increase of control overhead.

Improvement on the Multihop Shareholder Discovery for Threshold Secret Sharing in MANETs

The fabrication of polymeric single-mode step and Gaussian refractive index profile Y-branch is described. We used poly (methyl methacrylate) and a mixture of two inter miscible monomers for the cladding and the core, respectively, of the device. The cores of the device with step-index profile were fabricated by mask-based photolithography technique whereas for Gaussian-index profiles, maskless laser direct-writing technique was used. We fabricated normal and truncated Y-branch structures. Truncated structures with phase-front accelerator shows less radiation loss and hence more efficiency for the wide-angle Y-junction compared to that of normal structures. For truncated structure the efficiency of graded-index profile is more, than that of step-index profile though normal step-index profile structure is better than that of normal graded-index.

Somnath Ghosh

Papers

Sorptivity Ratio and Compressive Strength of Alkali-Activated Blast Furnace Slag Paste

Bond-Slip Effects on the Behaviour of RC Beam under Monotonic Loading - An Integrated 3D Computational Model using EAS Approach

Improvement on the Multihop Shareholder Discovery for Threshold Secret Sharing in MANETs

Low-Loss Wide-Angle Polymeric Single-Mode Y-Junctions

Kendu: an underutilized and lesser known fruit of West Bengal.