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

Studies on Enamides. Part 6. An Improvised Methodology for Orton Rearrangement under Neutral Condition.

A highly efficient methodology in solid state has been developed for the synthesis of α-diazocarbonyl/sulfonyl compounds from active methylene precursors using tosyl azide or 4-carboxybenzenesulfonyl azide and potassium carbonate, devoid of any aqueous work-up, save a column filtration over silica gel.

Diazo Transfer Reaction in Solid State.

We report emergence of multiple exceptional points (EPs) in a gain-loss assisted 1D planar four coupled optical waveguide system supporting four hybrid-modes. Performing different encirclement schemes, we establish the non-chiral optical-mode conversion of the hybrid-modes.

Exceptional points and non-chiral mode conversion of hybrid-modes in a manifold coupled planar waveguide

The synthesis of 2-arylcoumaranones and 2-phenyllbenzofuran has been achieved in good yields under acid catalysed conditions from readily accessible and suitably substituted aryl α-diazo-arylmethyl ketones.

Studies on Oxygen Heterocycles. Part 2. Synthesis of 2-Arylcoumaranones and 2-Phenylbenzofuran.

Direct transition of trivial optical lattice to its non-trivial counterpart verified by customization of bandgap is reported. Numerical simulations show that no localization transition is observed in non-trivial lattices due to deliberate refractive-index disorder. ©2019 The Author(s).

Somnath Ghosh

Papers

Studies on Enamides. Part 6. An Improvised Methodology for Orton Rearrangement under Neutral Condition.

Diazo Transfer Reaction in Solid State.

Exceptional points and non-chiral mode conversion of hybrid-modes in a manifold coupled planar waveguide

Studies on Oxygen Heterocycles. Part 2. Synthesis of 2-Arylcoumaranones and 2-Phenylbenzofuran.

Transverse Localization of light: Towards a paradigm shift from trivial to non-trivial lattice