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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.


(a) FF (1064 nm) and SH normal surfaces in k-space for a medium with d = 100 nm, p = 0.85 and εm taken from tabulated values for silver35. Each dashed curve corresponds to a value of the variable εd(ω) and likewise solid curves εd(2ω), as indicated by the calligraphic numerals. Lines of constant angle to the normal are shown dotted. The matching angle solution for AgGaS2 is circled33. The double solid blue line shows the curve εd(ω) = εd(2ω). (b) the same for FF at 1550 nm; (c) same as (a) with the fill fraction p = 0.7; (d) same as (b) with p = 0.75.
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f4: (a) FF (1064 nm) and SH normal surfaces in k-space for a medium with d = 100 nm, p = 0.85 and εm taken from tabulated values for silver35. Each dashed curve corresponds to a value of the variable εd(ω) and likewise solid curves εd(2ω), as indicated by the calligraphic numerals. Lines of constant angle to the normal are shown dotted. The matching angle solution for AgGaS2 is circled33. The double solid blue line shows the curve εd(ω) = εd(2ω). (b) the same for FF at 1550 nm; (c) same as (a) with the fill fraction p = 0.7; (d) same as (b) with p = 0.75.

Mentions: To plot the dependence of solutions to Eq. (8) on the material parameters εd,m, we fix εm and the geometrical parameters d and p, and let εd be a free variable. For our purposes, we require εd at the FF and SH. The k space is also effectively two dimensional, since the solutions are axially symmetric about kz. Hence, Eq. (8) maps from coordinates in one plane, the space of values of εd, to another, k space, a mapping which we can visualise by plotting εd coordinate curves in cartesian k space, as in Figs. 4(a)–(d). In these figures, the dashed curves labelled with calligraphic numerals indicate constant FF εd and the solid curves constant SH εd. Each curve plotted represents a unit increment. The rectilinear axes show the k solution corresponding to a given permittivity coordinate. Dashed diagonal lines indicate the matching angle with respect to the z-axis. The metal constituent is silver, with permittivities taken from tabulated values. Panels (a) and (c) take the FF to be 1064 nm, while (b) and (d) likewise 1550 nm. Panels (a) and (b) set the fill fraction p = 0.85, whereas in panels (c) and (d), p = 0.75. One may read off solutions for any choice of dielectric; the figures represents Eq. (8) in complete generality in this respect.


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)

(a) FF (1064 nm) and SH normal surfaces in k-space for a medium with d = 100 nm, p = 0.85 and εm taken from tabulated values for silver35. Each dashed curve corresponds to a value of the variable εd(ω) and likewise solid curves εd(2ω), as indicated by the calligraphic numerals. Lines of constant angle to the normal are shown dotted. The matching angle solution for AgGaS2 is circled33. The double solid blue line shows the curve εd(ω) = εd(2ω). (b) the same for FF at 1550 nm; (c) same as (a) with the fill fraction p = 0.7; (d) same as (b) with p = 0.75.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f4: (a) FF (1064 nm) and SH normal surfaces in k-space for a medium with d = 100 nm, p = 0.85 and εm taken from tabulated values for silver35. Each dashed curve corresponds to a value of the variable εd(ω) and likewise solid curves εd(2ω), as indicated by the calligraphic numerals. Lines of constant angle to the normal are shown dotted. The matching angle solution for AgGaS2 is circled33. The double solid blue line shows the curve εd(ω) = εd(2ω). (b) the same for FF at 1550 nm; (c) same as (a) with the fill fraction p = 0.7; (d) same as (b) with p = 0.75.
Mentions: To plot the dependence of solutions to Eq. (8) on the material parameters εd,m, we fix εm and the geometrical parameters d and p, and let εd be a free variable. For our purposes, we require εd at the FF and SH. The k space is also effectively two dimensional, since the solutions are axially symmetric about kz. Hence, Eq. (8) maps from coordinates in one plane, the space of values of εd, to another, k space, a mapping which we can visualise by plotting εd coordinate curves in cartesian k space, as in Figs. 4(a)–(d). In these figures, the dashed curves labelled with calligraphic numerals indicate constant FF εd and the solid curves constant SH εd. Each curve plotted represents a unit increment. The rectilinear axes show the k solution corresponding to a given permittivity coordinate. Dashed diagonal lines indicate the matching angle with respect to the z-axis. The metal constituent is silver, with permittivities taken from tabulated values. Panels (a) and (c) take the FF to be 1064 nm, while (b) and (d) likewise 1550 nm. Panels (a) and (b) set the fill fraction p = 0.85, whereas in panels (c) and (d), p = 0.75. One may read off solutions for any choice of dielectric; the figures represents Eq. (8) in complete generality in this respect.

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.