Limits...
New avenues for phase matching in nonlinear hyperbolic metamaterials.

Duncan C, Perret L, Palomba S, Lapine M, Kuhlmey BT, de Sterke CM - Sci Rep (2015)

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Centre for Ultrahigh bandwidth Devices for Optical Systems (CUDOS), School of Physics, University of Sydney, NSW 2006, Australia.

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.

No MeSH data available.


Dispersion of the permittivities of (a) GaAs (εd; Ref. 34) and Au (εm; Drude model with plasma frequency 2.1 × 1015 Hz), compared with εxx and εzz of a layered medium containing (b) 40%, (c) 50% and (d) 60% dielectric.
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f2: Dispersion of the permittivities of (a) GaAs (εd; Ref. 34) and Au (εm; Drude model with plasma frequency 2.1 × 1015 Hz), compared with εxx and εzz of a layered medium containing (b) 40%, (c) 50% and (d) 60% dielectric.

Mentions: The same combination of dielectric and metal may exhibit normal surfaces of all three types, depending on frequency, as Figs. 2(b)–(d) illustrate. The figures show how the dispersion relations of homogenized layered media with different fill fractions vary with frequency. The dispersion of the constituents, taken here to be GaAs and gold, is shown in Fig. 2(a). Anomalous dispersion is ignored in calculating εd,m in order to make Fig. 2 represent clearly the qualitative features that are common to all normally dispersive materials. We thus assume, for simplicity, that (i) εm and εd are normally dispersive; and, in addition, that (ii) εd > 0 > εm at all frequencies. It follows from Eqs. (1) and (2) that in general a layered medium is EW at low frequencies, NS at high frequencies and elliptical or metallic in the intermediate range between these two. To formalise the meaning of “low”, “intermediate” and “high” in this context, the figure marks three defining frequencies: the critical frequencyωc where εd = −εm, the singular frequencyωs at which εzz diverges, and ω0, where εxx = 0. The medium is NS when ω > ωs, ω0, EW when ω < ωs, ω0, and elliptical when ω0 < ω < ωs. Whether the medium behaves elliptically or like a metal in the intermediate regime depends on the fill fraction of dielectric (p), a dependence shown in the progression of Fig. 2, (b)–(d). If p < 50% then ωs < ωc < ω0 and thus the intermediate regime is metallic, while p = 50% implies ωc = ωs = ω0 and hence that there is no intermediate regime, and p > 50% implies that ω0 < ωc < ωs and the intermediate regime is elliptical.


New avenues for phase matching in nonlinear hyperbolic metamaterials.

Duncan C, Perret L, Palomba S, Lapine M, Kuhlmey BT, de Sterke CM - Sci Rep (2015)

Dispersion of the permittivities of (a) GaAs (εd; Ref. 34) and Au (εm; Drude model with plasma frequency 2.1 × 1015 Hz), compared with εxx and εzz of a layered medium containing (b) 40%, (c) 50% and (d) 60% dielectric.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4355635&req=5

f2: Dispersion of the permittivities of (a) GaAs (εd; Ref. 34) and Au (εm; Drude model with plasma frequency 2.1 × 1015 Hz), compared with εxx and εzz of a layered medium containing (b) 40%, (c) 50% and (d) 60% dielectric.
Mentions: The same combination of dielectric and metal may exhibit normal surfaces of all three types, depending on frequency, as Figs. 2(b)–(d) illustrate. The figures show how the dispersion relations of homogenized layered media with different fill fractions vary with frequency. The dispersion of the constituents, taken here to be GaAs and gold, is shown in Fig. 2(a). Anomalous dispersion is ignored in calculating εd,m in order to make Fig. 2 represent clearly the qualitative features that are common to all normally dispersive materials. We thus assume, for simplicity, that (i) εm and εd are normally dispersive; and, in addition, that (ii) εd > 0 > εm at all frequencies. It follows from Eqs. (1) and (2) that in general a layered medium is EW at low frequencies, NS at high frequencies and elliptical or metallic in the intermediate range between these two. To formalise the meaning of “low”, “intermediate” and “high” in this context, the figure marks three defining frequencies: the critical frequencyωc where εd = −εm, the singular frequencyωs at which εzz diverges, and ω0, where εxx = 0. The medium is NS when ω > ωs, ω0, EW when ω < ωs, ω0, and elliptical when ω0 < ω < ωs. Whether the medium behaves elliptically or like a metal in the intermediate regime depends on the fill fraction of dielectric (p), a dependence shown in the progression of Fig. 2, (b)–(d). If p < 50% then ωs < ωc < ω0 and thus the intermediate regime is metallic, while p = 50% implies ωc = ωs = ω0 and hence that there is no intermediate regime, and p > 50% implies that ω0 < ωc < ωs and the intermediate regime is elliptical.

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Centre for Ultrahigh bandwidth Devices for Optical Systems (CUDOS), School of Physics, University of Sydney, NSW 2006, Australia.

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.

No MeSH data available.