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

Theoretical total cross sections for the double charge transfer in proton-helium collisions are analysed using the four-body boundary corrected continuum intermediate state approximation in the energy range of 30 to 500 keV. We have also obtained differential double capture cross sections as a functions of projectile scattering angle. The intermediate continuum state of each of the active electron has been taken into account in this formalism. Our calculated results are compared with the previous experimental and theoretical values. The agreement is very encouraging.

Double charge transfer cross sections in collision of protons with helium atom

A new procedure for benzoylation of aromatic and aliphatic amines has been developed in neat phase without use of any solvent or alkali.

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Benzoylation of Amines sans Alkali: A Green Protocol in Neat Phase

The main focus of this work is to improve the strength, stiffness, wear resistance and fatigue strength of polyoxymethylene (POM). For this purpose, POM is incorporated with a lubricating additive polytetrafluoroethylene (PTFE) and reinforced with silanized multiwalled carbon nanotubes (CNTs). PTFE filled POM composites with varying weight fraction of PTFE and hybrid composites with 1 wt% silanized CNTs and varying weight fractions of PTFE were fabricated by melt compounding using a twin screw extruder followed by injection molding. Tensile, flexural, wear and fatigue behavior of the developed composites were evaluated. Incorporation of PTFE resulted in a significant decline of tensile properties, flexural properties and fatigue strength, whereas specific wear rate and coefficient of friction increased significantly. Reinforcing PTFE filled POM composites with 1 wt% functionalized CNTs has led to improvement of strength, stiffness, wear resistance and fatigue strength. Hybrid composites with 10 wt% PTFE and 1 wt% functionalized CNTs resulted in improvement of strength and stiffness by 31% and 50% respectively and decrease in wear rate and friction coefficient by 67% and 44% respectively as compared to pristine POM.

https://iopscience.iop.org/article/10.1088/2053-1591/ab0f4a/pdf

Mechanical, wear and fatigue behavior of functionalized CNTs reinforced POM/PTFE composites

Single-stranded DNA (ssDNA) is a prerequisite for electrochemical sensor-based detection of parasite DNA and other diagnostic applications. To achieve this detection, an asymmetric polymerase chain reaction method was optimised. This method facilitates amplification of ssDNA from the human lymphatic filarial parasite Wuchereria bancrofti. This procedure produced ssDNA fragments of 188 bp in a single step when primer pairs (forward and reverse) were used at a 100:1 molar ratio in the presence of double-stranded template DNA. The ssDNA thus produced was suitable for immobilisation as probe onto the surface of an Indium tin oxide electrode and hybridisation in a system for sequence-specific electrochemical detection of W. bancrofti. The hybridisation of the ssDNA probe and target ssDNA led to considerable decreases in both the anodic and the cathodic currents of the system's redox couple compared with the unhybridised DNA and could be detected via cyclic voltammetry. This method is reproducible and avoids many of the difficulties encountered by conventional methods of filarial parasite DNA detection; thus, it has potential in xenomonitoring.

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Optimisation of an asymmetric polymerase chain reaction assay for the amplification of single-stranded DNA from Wuchereria bancrofti for electrochemical detection

We propose a framework to study the topological properties of an optical bound state in the continuum (BIC). Here, the formation of a BIC has been shown using the interaction between proximity resonances undergoing avoided resonance crossing in a simple fabrication, feasible gain-loss assisted microcavity. Similar to a Friedrich-Wingten (FW)-type BIC, the formation of an ultrahigh-quality ($Q$) mode due to the precise destructive interference between resonances has been reported. The enhancement in the $Q$ factor was found to be more than four orders of magnitude greater than the other participating resonances. Furthermore, multiple such FW-type high-$Q$ operating points from the same set of proximity resonances have been identified. Upon further inspection, we report the formation of a special-BIC line in the system parameter space connecting the locations of these operating points. Further, we closely investigate the light dynamics of systems near single and multiple quasi-BICs. Aiming to develop a scheme to enhance the performance of optical sensing in a microcavity, we study the sensitivity of transmission coefficients and quality factor to sense even ultrasmall perturbations in the system configuration. Our proposed scheme would open up a vast potential for an enhanced desired optical response in enhanced nonlinear applications, low-threshold nano- and microlasers, and device-level sensors.

Somnath Ghosh

Papers

Double charge transfer cross sections in collision of protons with helium atom

Benzoylation of Amines sans Alkali: A Green Protocol in Neat Phase

Mechanical, wear and fatigue behavior of functionalized CNTs reinforced POM/PTFE composites

Optimisation of an asymmetric polymerase chain reaction assay for the amplification of single-stranded DNA from Wuchereria bancrofti for electrochemical detection

Ultrasensitive light confinement: Driven by multiple bound states in the continuum