New avenues for phase matching in nonlinear hyperbolic metamaterials

Abstract

Nonlinear optical processes, which are of paramount importance in science and technology, involve the generation of new frequencies. This requires phase matching to avoid that light generated at different positions interferes destructively. Of the two original approaches to achieve this, one relies on birefringence in optical crystals, and is therefore limited by the dispersion of naturally occurring materials, whereas the other, quasi-phase-matching, requires direct modulation of material properties, which is not universally possible. To overcome these limitations, we propose to exploit the unique dispersion afforded by hyperbolic metamaterials, where the refractive index can be arbitrarily large. We systematically analyse the ensuing opportunities and demonstrate that hyperbolic phase matching can be achieved with a wide range of material parameters, offering access to the use of nonlinear media for which phase matching cannot be achieved by other means. With the rapid development in the fabrication of hyperbolic metamaterials, our approach is destined to bring significant advantages over conventional techniques for the phase matching of a variety of nonlinear processes.

Phase matching in hyperbolic wire media for nonlinear frequency conversion

“…These behave like a metal in the direction parallel to the wires and like a dielectric orthogonal to them. While wire media and layered hyperbolic media are both hyperbolic, their effective properties differ significantly: which permittivity components are positive or negative, and their temporal and spatial dispersion differ such that the conditions to realize phase matching for wire media and for layered media [15] are very different, as we show here. While wire media are often periodic in two dimensions, and can thus be seen as a special case of photonic crystals, they differ from the latter in that the period of wire media is much smaller than the wavelength.…”

“…This property allows the propagation of arbitrarily large wavenumbers, which, in principle, offers the possibility to compensate dispersion of any magnitude. Indeed, some of us previously showed that multi-layered hyperbolic metamaterials provide a number of means to achieve phase matching thanks to their unusual dispersion [15]. In this paper, we explore the possibility of achieving phase matching in hyperbolic wire metamaterials, subwavelength structures consisting of a dilute array of metal wires in a dielectric background.…”

“…Using the nomenclature of Duncan et al [15], a normal surface is north-south hyperbolic (NS) if (ii) At high frequencies, i.e., , the TM mode is elliptical with a similar dispersion relation to the TE mode, and a mode bound to the surfaces of the wires results from the coupling of surface plasmon polaritons (SPP) of the wires [16]. Figure 2(a) is a phase diagram showing the solutions as a function of frequency and filling fraction for gold wires in GaAs.…”

New degrees of freedom in nonlinear metamaterials

“…Unique dispersion of hyperbolic metamaterials proved useful for nonlinear processes . In particular, the advantages of hyperbolic dispersion, and of combining that with the normal dispersion at other frequencies, brought a new degree of freedom to realize phase matching in layered structures , potentially enabling the use of non‐conventional nonlinear dielectrics. It should be noted that in layered hyperbolic materials, optimal phase matching conditions imply oblique incidence setups, which may be challenging in practice.…”

Gain-enhanced high-k transmission through metal-semiconductor hyperbolic metamaterials

“…The coupling of multiple MD interfaces enables even smaller effective wavelengths, or conversely higher effective indices, or so-called high-k propagation, of the optical waves [2][3][4] . The phenomenon of large effective indices and propagating high-k modes lies at the heart of sub-diffractionlimited imaging devices [5][6][7] , sensors based on plasmonic resonances 8,9 , as well as applications of hyperbolic metamaterials (HMMs), including asymmetric transmission devices 10 , nonlinear optics 11 , and lifetime reduction of dye molecules 12,13 and quantum dots 14 . Inherent to the increase in the effective index in MD systems, is a concomitant increase in dissipation losses 15,16 .…”