Second Harmonic Beam Shaping and Sensing in Dielectric Bow-Tie Antenna via Convex Optimization Array Synthesis Approach

Abstract

We propose a convex optimization approach for an array synthesis pattern to enhance the electromagnetic field in the gap region of a dielectric bow-tie antenna. This method allows the induction of the desired antenna modes by exploiting the concurrent excitation of the structure with plane waves with different propagation directions and complex amplitudes. By engineering the excitation coefficients of the array, different modes are excited in the bow-tie antenna and the radiation pattern of the generated second harmonic (SH) field is modified accordingly. Using our approach, we demonstrate both the feasibility of performing synthesis of the SH radiation pattern in dielectric antennas and the possibility of developing innovative sensing applications in photonics.Electronics 2019, 8, 901 2 of 11 causes a change in the scattered field, and this can be modelled at first order as a modulation of the 217 phase and amplitude of the incident plane waves. To make the discussion as simple as possible, yet 218 capturing the main idea we want to exploit here, we model the perturbing object as an extra phase 219 term in only one of the incident plane waves (see caption of Figure 1). This model is exact only when 220 the perturbing object is a slab that ensures high transmission with a fixed phase delay. To provide a 221 more realistic scenario, in the Appendix, we also describe the case where the perturbation is due to 222 the presence of a small dielectric particle. Let us define a figure of merit (FOM) as the ratio between 223 the far field at θ = π/2 in the absence of the simple perturbation (i.e., when ϕ = 0) with respect to the 224 far field in the presence of the perturbation (i.e., ϕ ≠ 0). Figure 5 summarizes the obtained results. 225FOM values of the bow-tie nanoantenna-based platform in the nonlinear regime are significantly higher 226 than those featured in the linear regime in the range 0 < ϕ < 3/2π. As can be seen in Figure 5b,c, the far 227 field of the SH signal is dramatically modified when ϕ = π while no significant variations are detected 228 for the FW radiation pattern. Although this is a preliminary analysis of this phenomenon, the 229 advantage of using the SH radiation pattern for sensing applications is clear. However, by further 230 engineering the nanoantenna geometries to attain higher nonlinearities, SH bow-tie sensing 231 platforms have the potential to overcome standard linear platform performances.

Vertical Second Harmonic Generation in Asymmetric Dielectric Nanoantennas

“…This peculiarity is related to the symmetry of the AlGaAs second-order nonlinear susceptibility. As a matter of fact, engineering the SH radiation pattern is strongly necessary in a lot of low-power and low-cost applications such as biological or chemical sensing [27]- [30]. It is known that the symmetry of the system needs to be weakened to shape the SH radiation into more suitable patterns with high emission in the normal direction and following this concept different studies have been already carried out [31,32].…”