Reverse chromatic aberration and its numerical optimization in a metamaterial lens

Abstract

In planar metamaterial lenses, the focal point moves with the frequency. Here it is shown numerically that this movement can be controlled by properly engineering the dimensions of the metamaterial-based phase shifters that constitute the lens. In particular, such lenses can be designed to exhibit unusual chromatic aberration with the focal length increasing, rather than decreasing, with the frequency. It is proposed that such an artificial "reverse" chromatic aberration may optimize the transverse resolution of millimeter wave diagnostics of plasmas and be useful in compensating for the natural "ordinary" chromatic aberration of other components in an optical system. More generally, optimized chromatic aberration will allow for simultaneous focusing of several objects located at different distances and emitting or reflecting at different frequencies.

Metamaterial Lens of Specifiable Frequency-Dependent Focus and Adjustable Aperture for Electron Cyclotron Emission in the DIII-D Tokamak

“…The unit cells of such materials typically have sub-wavelength dimensions, allowing for the fabrication of surfaces whose filtering properties vary smoothly on length scales appropriate for lens applications. One application, which we have investigated previously, is to engineer an MEFSS-based lens exhibiting RCA with a specific ( f ) dependence [12]. This paper describes in detail our methods to tailor the focusing characteristics of an MEFSSbased lens to meet the requirements for ECE detection at DIII-D.…”

“…Previous lenses of this kind have been designed by partitioning an MEFSS into a set of discrete annular zones concentric with a perpendicular axis ( Fig. 1a), with each zone associated with a certain phase-advance [14,12]. Outer zones (i.e.…”

“…those with larger annular radii) impart greater phase-advances than those near the axis, such that an incident collimated beam of light that passes through a zoned MEFSS will undergo a transformation in its radial phase profile and taper to a focal point a certain distance beyond the lens. Owing to the high number of degrees of freedom in the design of each unit cell, it is possible to identify a geometrical configuration having specified focal lengths for certain frequencies-including a configuration with RCA, as we have previously shown numerically in the 8-12 GHz band [12]. The appropriate unit cell parameters for each zone were chosen based on the results of simulations of radiation passing through single unit cells.…”

“…In the present paper, we have expanded upon the methods of Ref. [12] to design an RCA lens optimized for ECE in the DIII-D tokamak. The lens has an aperture diameter of 0.30 m, equal to the diameter of the viewing port onto which it might be installed.…”

“…This is the same procedure followed in a previous work of ours. [12] In Fig. 5b, by contrast, the target functions were determined as per Appendix A.…”