We present novel designs for aspheric lenses used in terahertz (THz) imaging. As different surfaces result in different beam shaping properties and in different losses from reflection and absorption, the resultant imaging resolution (i.e. the focal spot size) depends critically on the design approach. We evaluate the different lens designs using Kirchhoff's scalar diffraction theory, and test the predictions experimentally. We also show that our lenses can achieve sub-wavelength resolution. While our lens designs are tested with THz radiation, the design considerations are applicable also to other regions of the electro-magnetic spectrum.

Nanoantennas have demonstrated unprecedented capabilities for manipulating the intensity and direction of light emission over a broad frequency range. The directional beam steering offered by nanoantennas has important applications in areas including microscopy, spectroscopy, quantum computing, and on-chip optical communication. Although both the physical principles and experimental realizations of directional linear nanoantennas has become increasingly mature, angular control of nonlinear radiation using nanoantennas has not been explored yet. Here we propose a novel concept of nonlinear Yagi-Uda nanoantenna to direct second harmonic radiation from a metallic nanosphere. By carefully tuning the spacing and dimensions of two lossless dielectric elements, which function respectively as a compact director and reflector, the second harmonic radiation is deflected 90 degrees with reference to the incident light (pump) direction. This abnormal light-bending phenomenon is due to the constructive and destructive interference between the second harmonic radiation governed by a special selection rule and the induced electric dipolar and magnetic quadrupolar radiation from the two dielectric antenna elements. Simultaneous spectral and spatial isolation of scattered second harmonic waves from incident fundamental waves pave a new way towards nonlinear signal detection and sensing.

A generalized modal expansion theory for investigating arbitrary 3-D bounded and unbounded electromagnetic fields is presented. When an inhomogeneity is enclosed with impenetrable boundaries, the field excited by arbitrary sources is expanded with a complete set of eigenmodes, which are classified into trapped modes and radiation modes. As the boundaries tend to infinity, trapped modes remain unchanged, while radiation modes form a continuum. To illustrate the theory, several real-life structures are investigated with a conformal finite-difference technique in the frequency domain. Perfectly matched layers (PMLs) are imposed at finite extent to emulate the unbounded problems. Numerical examples show that, only a few system modes are prominent in expanding an excited field, leading to a reduced modal picture which provides a quick guidance as well as useful physical insight for engineering design and optimization of electromagnetic devices and components.

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Second-harmonic (SH) generation is tremendously important for nonlinear sensing, microscopy and communication system. One of the great challenges of current designs is to enhance the SH signal and simultaneously tune its radiation direction with a high directivity. In contrast to the linear plasmonic scattering dominated by a bulk dipolar mode, a complex surface-induced multipolar source at the doubled frequency sets a fundamental limit to control the SH radiation from metallic nanostructures. In this work, we harness plasmonic hybridization mechanism together with a special selection rule governing the SH radiation to achieve the high-intensity and tunable-direction emission by a metallic particle-in-cavity nanoantenna (PIC-NA). The nanoantenna is modelled with a first-principle, self-consistent boundary element method, which considers the depletion of pump waves. The giant SH enhancement arises from a hybridized gap plasmon resonance between the small particle and the large cavity that functions as a concentrator and reflector. Centrosymmetry breaking of the PIC-NA not only modifies the gap plasmon mode boosting the SH signal, but also redirects the SH wave with a unidirectional emission. The PIC-NA has a significantly larger SH conversion efficiency compared to existing literature. The main beam of the radiation pattern can be steered over a wide angle by tuning the particle's position. * ljiang@eee.hku.hk † wsha@eee.hku.hk