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

Today tail pipe emission control has become one of the most important challenges in internal combustion engines. Oxides of nitrogen (NOx) are one of the major hazardous pollutants that come out from diesel engines tail pipe emission. Oxides of nitrogen (NOx) in the atmosphere cause serious environmental problems, such as photochemical oxidant, acid rain, and global warming. There are various techniques existing for NOx control but each technique has its own advantages and disadvantages. At present, there is no single optimal technique that can control NOx without causing other side effects. Technologies available for NOx reductions either increase other polluting gas emissions or increase fuel consumption. Injection of aqueous solutions of urea in the tail pipe of a diesel engine for the reduction of oxides of nitrogen (NOx) was carried out in a four stroke, single cylinder, water cooled, constant speed diesel engine. Four observations were made for the exhaust emission NOx analysis of concentration of urea solution 0%, 10%, 20%, and 30% by weight with different flow rates of urea solution as reductant by fitting Marine Ferromanganese nodule as SCR catalyst. It was observed that 64% of NOx reduction achieved..

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Reduction Of Nox Emission By Urea Injection And Marine Ferromanganese Nodule As SCR of Diesel Engine

We explore exceptional points (EP) in a dual-mode symmetric planar optical waveguide with transverse variation of inhomogeneous loss profile; where modal evolution alongside an EP is reported in the context of selective optical mode conversion.

All-Lossy Quasi-Guided Dual-Mode Optical Waveguide Exhibiting Exceptional Singularities

Topological photonics provides a new platform to control and manipulate the flow of light in photonic devices that exhibit topological phase transitions. One way to introduce such transition of geometric phases in photonic waveguides is to modulate the structure of the photonic crystals, array waveguides, or the metamaterials in such a way that it eventually changes the bulk topology. Such topological waveguides localize the light at the boundary of the two distinct bulk systems with different topological invariant. Based on this fundamental physics, we demonstrate a robust and controlled propagation of light in a class of specialty optical fiber which exhibits the topological phase transition between a nontrivial one-dimensional (1D) periodic cylinder and its topologically trivial counterpart. The key idea is to explore the possibility of topological phase transition of 1D photonic bands over the momentum space by tuning the unit-cell dimension and its individual thicknesses. We have systematically computed the trivial and the nontrivial topological invariants, the Zak phase, of designed cylindrical 1D lattices with inversion symmetry over the first Brillouin zone. To establish the presence and the robustness of the localized edge mode, we have studied the reflectance of the geometry in the presence of disorder. Also, the simulated field profile and the back-reflectionless propagation of the edge mode through the fiber have been shown. Besides conventional fibers, such topological optical fibers are definitely a waveguide geometry for robust delivery of light and thus would be very significant to open up a new paradigm in guided wave photonics.

Specialty topological fiber using periodic lattice geometries

Exploiting scattering-matrix in a gain-loss assisted optical-microcavity, interplay between asymmetric-state-conversion and cavity-control parameters around exceptional points is analyzed; where occupying a least area by coupled states during switching, maximum conversion-efficiency with minimal asymmetry is achieved.

Exceptional Points in an Specialty Microcavity: Interplay between State-Conversion and Cavity Control Parameters

We report a planar 1D photonic bandgap waveguide exhibiting four second-order exceptional points (EP2s). The interactions between the selective pairs of supported quasi-guided TE modes are modulated by spatial distribution of transverse in-homogeneous gain-loss profile.

Somnath Ghosh

Papers

Reduction Of Nox Emission By Urea Injection And Marine Ferromanganese Nodule As SCR of Diesel Engine

All-Lossy Quasi-Guided Dual-Mode Optical Waveguide Exhibiting Exceptional Singularities

Specialty topological fiber using periodic lattice geometries

Exceptional Points in an Specialty Microcavity: Interplay between State-Conversion and Cavity Control Parameters

Hosting exceptional points in 1D photonic bandgap waveguide for mode engineering