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 physics of exceptional point (EP) singularities, has been a key to a wide range of unique physical applications in open systems. In this context, the mutual interactions among four coupled states around a fourth-order EP (EP4) in a physical system is yet to be explored. Here, we investigate the unique features of an EP4 in a fabrication feasible planar optical waveguide with a multilayer gain-loss profile based on only two tunable parameters. A unique `fourth-order $\beta$-switching' phenomenon due to quasi-static gain-loss variation around EP4 has been explored. An exclusive chiral light dynamics following the dynamical variation of the gain-loss profile has been reported for the first time, which enables a special type of asymmetric higher-order mode conversion scheme. Here, all the coupled modes associated with an EP4 are fully converted into different specific higher-order modes based on the choice of encirclement directions. The proposed scheme would present EP4 as a new light manipulation tool for integrated photonic devices.

Exotic light dynamics around a fourth order exceptional point

We have studied mask based process for the microfabrication of polymeric (IXn) branching waveguides both theoretically and experimentaly. The simulation is based on the two-dimensional finite-difference beam propagation method (FDBPM) for the design of the waveguiding devices. The transmission efficiency of truncated structural Y-branch (TSYB) for wide angle (IX2) splitter with a full branching angle 2A greater than 20 is improved compared to that of normal Y-branch (NYB) structure. The maximum transmission at the output is obtained in phase matching between the inner and the outer paths at the point of bending of the truncated structure. An analysis for the optimum phase matching taking symmetric cladding refractive index at the branching zone, is made to improve the transmission efficiency η. For more output ports in (IXn) multiple branching waveguides it is observed that equal output power is not obtained for normal (IXn) branching waveguides. We have designed here a new truncated structural (IX3) branch [TS(IX3)B] structure for obtaining equal transmissions in higher branching angle structure using same phase matching consideration. Phase matching consideration is also followed in designing TS(IXn) B structures. We have fabricated the polymeric devices over Si-SiO2 substrate. The cladding and the waveguiding layers are the Epoxy and PMMA/DRI, respectively. The thickness and refractive index of the waveguiding layers are controlled either by spinning speed or viscosity of the solution and its mixing ratio, respectively. The standard photolithography technique is used here with positive resist coating and followed by dry plasma etching in presence of oxygen. Experiments for the transmission efficiency of the devices are made and compared with the theoretical values.

Branching Waveguides with Truncated Structure and Phase Matching

Improved crystallization characteristics of ZnO thin film grown onto a-C:H film used as a buffer layer

Effect of substitutions of chemical nitrogen fertilizer with organics on growth and yield of Sarpagandha grown under coconut plantation.

The experiment was carried out for two consecutive years during 2010 and 2012 at the experimental grape orchard at Horticultural Research and Development Farm, Govt. of W.B, Taldangra, Bankura. The experiment was conducted in randomized block design with four replications. The vines were trained on ‘Y’-trellies system and spacing of 2×3 m2. The vine was pruned on 30th January. As per fruit maturity, the cultivars Pusa Navrang were considered to be the earliest harvesting. Among the twelve cultivars, maximum fruit yield was recorded in Arka Neelamani (7.81 kg vine-1). The number of bunches/vine were varied significantly among the cultivars with number of bunches/ vine highest in cultivar Arka Trishna. But bunch weight was highest in cultivar Arkavati (264.2 g). Size of the bunch was maximum in Arka Kanchan. However, different cultivars of grape exhibited significant variation with respect to average ten berries weight. The ten berries weight was highest in Arka Magestic. The cultivars Arka Trishna gave the highest juice %, total soluble solids, lowest acidity, highest TSS/acid ratio and sugar content. Ascorbic acid content highest was recorded from cultivar Pusa Navrang as compared to other cultivars. Incidence of major insects and diseases determine the economic feasibility of a cultivar in the area. It appears from the good performed cultivars less incidence of major insects and diseases during flowering to fruiting period. On the basis of marketable yield, fruit quality and tolerance to pest, cultivars Arka Neelamani for table purpose can be recommended for commercial cultivation under Bankura conditions of West Bengal.

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Somnath Ghosh

Papers

Exotic light dynamics around a fourth order exceptional point

Branching Waveguides with Truncated Structure and Phase Matching

Improved crystallization characteristics of ZnO thin film grown onto a-C:H film used as a buffer layer

Effect of substitutions of chemical nitrogen fertilizer with organics on growth and yield of Sarpagandha grown under coconut plantation.

Performance of Some Grape Cultivars for Commercial Cultivation in West Bengal