Enhanced Coupling of Light From Subwavelength Sources Into a Hyperbolic Metamaterial Fiber

Abstract

A hyperbolic metamaterial has one or two negative components of the dielectric permittivity tensor while the others are positive. In an optical hber inhomogenously hlled with hyperbolic inhomogeneous metamaterials, modes with large angular momentum are localized near the centre of the hber. Such a hyperbolic metamaterial hber with radial anisotropy has no cutoff frequency for the transverse electric or the transverse magnetic modes simultaneously. This makes it possible to couple the near-held evanescent modes, associated with large transverse wavevectors of small subwavelength sized sources to these high angular momentum hber modes well below the conventional cutoff frequencies in the buttcoupling geometry. Such hyperbolic and inhomogeneous hbers can out-couple power from a subwavelength sized source very efhciently and the coupling can be more than seven orders of magnitude larger compared to a conventional step index waveguides over lengthscales of few wavelengths. Specihcally, we show that radial hyperbolicity (ε <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> <; 0, ε <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</sub> > 0, ε <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">φ</sub> > 0) is more advantageous than axial hyperbolicity (ε <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</sub> <; 0, ε <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> > 0, ε <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">φ</sub> > 0) for such near-held coupling effects. These inhomogeneous hyperbolic hbers can be synthesized from nanoporous alumina microtubes and have immense potential to be used as near-held couplers for nanophotonic devices and near-held imaging probes.