The Application of Negative Refractive Index Metamaterials to mm and Sub-mm Wavelength Instrumentation

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Abstract

The manipulation of electromagnetic radiation via the use of periodic arrays of sub-wavelength metallic structures (unit cells), nowadays named "metamaterials", has been known of in the microwave engineering community for over fifty years. In the last decade interest in such sub-wavelength structures grew, mainly due to their ability to interact with radiation in ways natural materials could not e.g. by producing a negative refractive index (NRI). This project sought to see whether NRI metamaterials could provide benefits to the mm and sub-mm wavelength astronomical instrumentation currently in use. To aid rapid design and optimisation of devices made from a cascaded set of metamaterial unit cells, a hybridised Transmission Line (TL) model was developed where the matrix components used in the TL model were "seeded" with data taken from a Finite Element Method (FEM) model of a simpler structure. A comparison between the two found that the TL model was capable of providing results that differed from the FEM model by no more than ~10E−4 for the transmitted intensity, |S21|^2, and <1° for transmitted phase, arg(S21). A slab of material with a refractive index, n = −1, can exhibit an effect known as "superlensing". A three unit cell thick NRI slab was designed, manufactured and experimentally tested. It was found to be capable of producing an NRI across a fractional band of at least 21%, producing a refractive index value of n = −1 at around 90 GHz. The experimental and simulated transmission and reflection data show good match with each other. A highly birefringent air gap Half Wave Plate (HWP) was designed, manufactured and experimentally tested. Defining its useful bandwidth as the region where the phase difference, is equal to (−180 ± 3)° a single HWP had a fractional bandwidth of 0.3%. The bandwidth was extended by using the Pancharatnam method, developed in the 1950's to produce highly achromatic optical wave plates. The method however is applicable to other frequencies and polarisation control technologies. Optimising a three HWP TL-based Pancharatnam model, the HWP's modelled fractional bandwidth increased to 6.6%. Experimental data agrees with the model showing a plateauing of the phase difference at −180°. A highly birefringent polypropylene embedded Quarter Wave Plate (QWP) was also designed, manufactured and tested. Defining its useful bandwidth as the region where the differential phase is (90 ± 2)° a single QWP produced a fractional bandwidth of 0.6%. By optimising a four QWP TL-based Pancharatnam model, the QWP's performance was improved to 7.8%. Experimental data, whilst not in complete agreement with the model does show a reduction in the gradient of phase difference where it crossed 90°. It was found that current designs for NRI metamaterials fall short of the standards required to be used in quasi-optical astronomical instrumentation due to high dispersion and absorption. The high dispersion limits NRI metamaterials to uses in instruments built for narrowband applications. Whilst the Pancharatnam method can increase bandwidths where a flat differential phase response is required, this comes at the cost of increased absorption. To reach their full potential, NRI metamaterials' lossiness must be reduced e.g. possibly by cryogenic means or the use of "active" metamaterials.

Keyword(s)

Pancharatnam; artificial dielectric; astronomical instrumentation ; finite element method; frequency selective surfaces; metamaterial; negative refractive index; transmission line model; wave plate

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