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.
Highlights
Nonlinear optical processes, which are of paramount importance in science and technology, involve the generation of new frequencies
The solution set in k/k0 of Eq (4) represents the surface formed by revolving a conic section about the z-axis, which suggests the threefold typology illustrated in Fig. 1(b): borrowing the geometers’ nomenclature, a normal surface is (i) north-south hyperbolic (NS) if exx . 0 . ezz; (ii) east-west hyperbolic (EW) if ezz . 0 . exx; and (iii) elliptical if all diagonal components are positive
Matching extraordinary fundamental frequency (FF) with extraordinary SH is possible because normal surfaces of different types do intersect, which we demonstrate presently
Summary
Of the two original approaches to achieve this, one relies on birefringence in optical crystals, and is 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. The advent of metamaterials — artificially engineered materials with exotic properties — has opened wide opportunities for nonlinear optics[6], offering novel approaches for phase matching[7] These include the use of metamaterials with dual resonances, matched for SHG8,9; generation in reflection, exploiting negative refractive indices[10,11,12,13,14]; dispersion engineering in arrays and transmission lines[15,16,17]; as well as boosting conventional QPM techniques[18,19]. We provide a realistic example with practically available materials, and show that phase matching is feasible in spite of a noticeable dissipation, and even when the dispersion would not be sufficient for a classical birefringent scheme
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