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

This paper presents results of an experimental study performed to investigate effect of incorporating Lime stone dust on physico-mechanical properties and durability of resulting fly ash geopolymer Paste sample. In this program geopolymer samples having percentage Lime stone dust ranging from 10 to 15% of fly ash were immersed in a 10% magnesium sulfate solution upto a period of 15 weeks and evaluation of its resistance in terms visual appearance, change in weight and compressive strength at regular interval. Addition of Lime stone dust significantly improved durability and physico-mechanical properties.

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Strength And Durability Of Fly Ash Geopolymer Blended With Lime Stone Dust

The appearance of topological singularities, namely exceptional points (EPs) is an intriguing feature of parameter-dependent open quantum or wave systems. EPs are the special type of nonHermitian degeneracies where two (or more) eigenstates of the underlying system coalesce. In this paper, we present a three level non-Hermitian Hamiltonian which hosts three interacting eigenstates. The matrix elements are optimized in such a way that the intermediate eigenstate interacts with both the other states and the underlying system hosts at least two different second order EPs. The impact of quasi-static parameter variation along a cyclic contour around the embedded EPs on the dynamics of interacting eigenvalues is well investigated in the context of cascaded state conversion. Such dynamics of the eigenvalues shows a clear signature of the third order EP with a combined effect of both the second order EPs. Moreover, we examine the accumulation of phases around the identified EPs and study the hallmark of phase exchange during cascaded state conversions accompanied by the parametric encirclement of the third order EP.

Realization of Third Order Exceptional Singularities in a Three level non-Hermitian System: Towards Cascaded State Conversion

Hydrogenated and roughened surfaces of hydrogen plasma treated (HPT) FeCo–SiO2 nanogranular films are found to be efficient field emitters in comparison to their as-grown and furnace annealed counterparts. Partial etching using hydrogen plasma roughens the surface and improves the field emission by enhancing the local electric field at the protrusion tips. A layer of Feδ+–Hδ− dipoles over the roughened HPT film surface and enhanced defects are likely to make the composite surface more emission-active by reducing the overall work function. The reconstruction of the electronic structure is mainly attributed to the Fe2+ to Fe3+ conversion and the appearance of anti-bonding states. Further, hydrogen-induced volume expansion of FeCo particles improves the conductivity. Thus tunnelling of electrons from the valence band becomes easier via these inter-gap anti-bonding states. The agglomeration of nanoparticles, out-diffusion of hydrogen, and further etching of the film at a higher substrate temperature of the plasma treated films reduces the FE current density drastically.

Spectral weight shift in the valence band density of states and concurrent increase in field emission by hydrogenation of FeCo–SiO2 nanocomposites

The role of a prominent photonic bandgap (PBG) in the phenomenon of transverse localization of light in a semi-infinite lossless waveguide lattice consisting of evanescently coupled disordered one-dimensional optical waveguides has been investigated numerically. The interplay between the underlying photonic bandgap due to inherent periodicity of the optical system and various levels of deliberately induced transverse disorder in its refractive index periodicity has been studied. We show that the PBG indeed plays an important role and that its simultaneous presence could catalyze realization of localized light even when the strength of disorder is not sufficiently strong to independently cause localization of light. An important outcome of this study revealed that the PBG could be gainfully exploited to tailor the spectral window for localization of light in potential applications such as lasing in a disordered optical lattice.

Transverse localization of light in 1D disordered waveguide lattices in the presence of a photonic bandgap

Here, we report the synthesis of Au/PbSe and Au/copper indium diselenide (CIS) core/shell nanowires. The nanowires were synthesized by the aqueous electrodeposition of either PbSe or CIS onto gold nanowires prepared by lithographically patterned nanowire electrodeposition. The resulting nanowires are nanocrystalline, exhibit a sharp boundary between the gold core and the semiconducting coating, and are photoconductive, with enhanced light absorption in smaller nanowires.

Somnath Ghosh

Papers

Strength And Durability Of Fly Ash Geopolymer Blended With Lime Stone Dust

Realization of Third Order Exceptional Singularities in a Three level non-Hermitian System: Towards Cascaded State Conversion

Spectral weight shift in the valence band density of states and concurrent increase in field emission by hydrogenation of FeCo–SiO2 nanocomposites

Transverse localization of light in 1D disordered waveguide lattices in the presence of a photonic bandgap

Gold Core–Semiconductor Shell Nanowires Prepared by Lithographically Patterned Nanowire Electrodeposition