Helicity Density Maximization in a Planar Array of Achiral High-Density Dielectric Nanoparticles

We investigate how a periodic array composed of achiral isotropic high-refractive index dielectric nanospheres generates nearfield over the array surface reaching helicity density very close to its upper bound. The required condition for an array of nanospheres to generate optimally chiral nearfield, which represents the upper bound of helicity density, is derived in terms of array effective electric and magnetic polarizabilities that almost satisfy the effective Kerker condition for arrays. The discussed concepts find applications in improving chirality detection based on circular dichroism (CD) at surface level instead of in the bulk. Importantly the array would not contribute to the generated CD signal when used as a substrate for detecting chirality of a thin layer of chiral molecules. This eliminates the need to separate the CD signal generated by the array from that of the chiral sample

Theory of coupled resonator optical waveguides exhibiting high-order exceptional points of degeneracy

We present an approach and a theoretical framework for generating high-order exceptional points of degeneracy (EPDs) in photonic structures based on periodic coupled resonator optical waveguides (CROWs). Such EPDs involve the coalescence of Floquet-Bloch eigenwaves in CROWs, without the presence of gain and loss, which contrasts with the parity-time symmetry required to develop exceptional points based on gain and loss balance. The EPDs arise here by introducing symmetry breaking in a conventional chain of coupled resonators through periodic coupling to an adjacent uniform optical waveguide, which leads to unique modal characteristics that cannot be realized in conventional CROWs. Such remarkable characteristics include high quality factors (Q factors) and strong field enhancement, even without any mirrors at the two ends of a cavity. We show for the first time the capability of CROWs to exhibit EPDs of various orders, including the degenerate band edge (DBE) and the stationary inflection point. The proposed CROW of finite length shows an enhanced quality factor when operating near the DBE, and the Q factor exhibits an unconventional scaling with the CROW's length. We develop the theory of EPDs in such unconventional CROW using coupled-wave equations, and we derive an analytical expression for the dispersion relation. The proposed unconventional CROW concepts have various potential applications including Q switching, nonlinear devices, lasers, and extremely sensitive sensors

Helicity Maximization of Structured Light to Empower Nanoscale Chiral Matter Interaction

Structured light enables the characterization of chirality of optically small nanoparticles by taking advantage of the helicity maximization concept recently introduced in[1]. By referring to fields with nonzero helicity density as chiral fields, we first investigate the properties of two chiral optical beams in obtaining helicity density localization and maximization requirements. The investigated beams include circularly polarized Gaussian beams and also an optical beam properly composed by a combination of a radially and an azi-muthally polarized beam. To acquire further enhancement and localization of helicity density beyond the diffraction limit, we also study chiral fields at the vicinity of a spherical dielectric nanoantenna and demon-strate that the helicity density around such a nanoantenna is a superposition of helicity density of the illu-minating field, scattered field, and an interference helicity term. Moreover, we illustrate when the nanoan-tenna is illuminated by a proper combination of azimuthal and radially polarized beams, the scattered nearfields satisfy the helicity maximization conditions beyond the diffraction limit. The application of the concept of helicity maximization to nanoantennas and generating optimally chiral nearfield result in helici-ty enhancement which is of great advantage in areas like detection of nanoscale chiral samples, microsco-py, and optical manipulation of chiral nanoparticles

Focused Azimuthally Polarized Vector Beam and Spatial Magnetic Resolution below the Diffraction Limit

An azimuthally electric-polarized vector beam (APB), with a polarization vortex, has a salient feature that it contains a magnetic-dominant region within which electric field ideally has a null while longitudinal magnetic field is maximum. Fresnel diffraction theory and plane-wave spectral (PWS) calculations are applied to quantify field features of such a beam upon focusing through a lens. The diffraction-limited full width at half maximum (FWHM) of the beam's longitudinal magnetic field intensity profile and complementary FWHM (CFWHM) of the beam's annular-shaped total electric field intensity profile are examined at the lens's focal plane as a function of the lens's paraxial focal distance. Then, we place a subwavelength dense dielectric Mie scatterer in the minimum-waist plane of a self-standing converging APB and demonstrate for the first time that a very high resolution magnetic field at optical frequency is achieved with total magnetic field FWHM of 0.23{\lambda} (i.e., magnetic field spot area of 0.04{\lambda}^2) within a magnetic-dominant region. The theory shown here is valuable for development of optical microscopy and spectroscopy systems based on magnetic dipolar transitions which are in general much weaker than their electric counterparts

Novel concept for pulse compression via structured spatial energy distribution

We present a novel concept for pulse compression scheme applicable at RF, microwave and possibly to optical frequencies based on structured energy distribution in cavities supporting degenerate band-edge (DBE) modes. For such modes a significant fraction of energy resides in a small fraction of the cavity length. Such energy concentration provides a basis for superior performance for applications in microwave pulse compression devices (MPC) when compared to conventional cavities. The novel design features: larger loaded quality factor of the cavity and stored energy compared to conventional designs, robustness to variations of cavity loading, energy feeding and extraction at the cavity center, substantial reduction of the cavity size by use of equivalent lumped circuits for low energy sections of the cavity, controlled pulse shaping via engineered extraction techniques. The presented concepts are general, in terms of equivalent transmission lines, and can be applied to a variety of realistic guiding structures.Comment: 18 pages, 10 figure

Exceptional Point of Degeneracy in Backward-Wave Oscillator with Distributed Power Extraction

We show how an exceptional point of degeneracy (EPD) is formed in a system composed of an electron beam interacting with an electromagnetic mode guided in a slow wave structure (SWS) with distributed power extraction from the interaction zone. Based on this kind of EPD, a new regime of operation is devised for backward wave oscillators (BWOs) as a synchronous and degenerate regime between a backward electromagnetic mode and the charge wave modulating the electron beam. Degenerate synchronization under this EPD condition means that two complex modes of the interactive system do not share just the wavenumber, but they rather coalesce in both their wavenumbers and eigenvectors (polarization states). In principle this new condition guarantees full synchronization between the electromagnetic wave and the beam's charge wave for any amount of output power extracted from the beam, setting the threshold of this EPD-BWO to any arbitrary, desired, value. Indeed, we show that the presence of distributed radiation in the SWS results in having high-threshold electron-beam current to start oscillations which implies higher power generation. These findings have the potential to lead to highly efficient BWOs with very high output power and excellent spectral purity