Scattering Theory and PT\mathcal{P}\mathcal{T}-Symmetry

We outline a global approach to scattering theory in one dimension that allows for the description of a large class of scattering systems and their $\mathcal{P}$-, $\mathcal{T}$-, and $\mathcal{P}\mathcal{T}$-symmetries. In particular, we review various relevant concepts such as Jost solutions, transfer and scattering matrices, reciprocity principle, unidirectional reflection and invisibility, and spectral singularities. We discuss in some detail the mathematical conditions that imply or forbid reciprocal transmission, reciprocal reflection, and the presence of spectral singularities and their time-reversal. We also derive generalized unitarity relations for time-reversal-invariant and $\mathcal{P}\mathcal{T}$-symmetric scattering systems, and explore the consequences of breaking them. The results reported here apply to the scattering systems defined by a real or complex local potential as well as those determined by energy-dependent potentials, nonlocal potentials, and general point interactions.Comment: Slightly expanded revised version, 38 page

A CMOS image sensor integrated with plasmonic colour filters

Multi-pixel, 4.5 × 9 μm, plasmonic colour filters, consisting of periodic subwavelength holes in an aluminium film, were directly integrated on the top surface of a complementary metal oxide semiconductor (CMOS) image sensor (CIS) using electron beam lithography and dry etch. The 100 × 100-pixel plasmonic CIS showed full colour sensitivities across the visible range determined by a photocurrent measurement. The filters were fabricated in a simple process utilising a single lithography step. This is to be compared with the traditional multi-step processing when using dye-doped polymers. The intrinsic compatibility of these plasmonic components with a standard CMOS process allows them to be manufactured in a metal layer close to the photodiodes. The incorporation of such plasmonic components may in the future enable the development of advanced CIS with low cost, low cross-talk and increased functionality

Extraordinary Transmission Characteristics of Subwavelength Nanoholes with Rectangular Lattice

We investigate the extraordinary optical transmission (EOT) properties of nanohole arrays with a rectangular lattice for label-free refractive index sensing applications. We show that the deviation within the periodicities along the two axes at the nanohole plane leads to more advantageous spectral quality of EOT signal compared to the conventional square lattice geometries. We introduce a way to further improve the sensitivity of the aperture system by carefully choosing the periodicities. We introduce nanohole arrays with a rectangular lattice supporting EOT signals with larger figure-of-merit values as well as enabling much stronger light transmission. We also model a nanohole system covered with a thin dielectric layer, mimicking biomolecules captured on the gold surface, in order to show its biosensing capability. We also show that certain deviation amounts between periodicities create spectral splitting within the EOT signal leading to larger spectral shifts in the presence of a thin dielectric film. Keywords: Plasmonics, Nanoholes, Extraordinary optical transmission, Rectangular lattice, Label-free biosensin