Second-harmonic double-resonance cones in dispersive hyperbolic metamaterials

Domenico de Ceglia, Maria Antonietta Vincenti, Salvatore Campione, Filippo Capolino, Joseph W. Haus, and Michael Scalora

Phys. Rev. B 89, 075123 – Published 19 February 2014

Abstract

We study the formation of second-harmonic double-resonance cones in hyperbolic metamaterials. An electric dipole on the surface of the structure induces second-harmonic light to propagate into two distinct volume plasmon-polariton channels: a signal that propagates within its own peculiar resonance cone and a phase-locked signal that is trapped under the pump's resonance cone. Metamaterial dispersion and birefringence induce a large angular divergence between the two volume plasmon polaritons, making these structures suitable for subwavelength second- and higher-harmonic imaging microscopy.

Received 23 May 2013

DOI:https://doi.org/10.1103/PhysRevB.89.075123

Authors & Affiliations

Domenico de Ceglia^1,*, Maria Antonietta Vincenti¹, Salvatore Campione², Filippo Capolino², Joseph W. Haus^1,3, and Michael Scalora⁴

¹National Research Council–AMRDEC, Charles M. Bowden Research Laboratory, Redstone Arsenal, Alabama 35898, USA
²Department of Electrical Engineering and Computer Science, University of California Irvine, California 92697, USA
³Electro-Optics Program, University of Dayton, 300 College Park, Dayton, Ohio 45469, USA
⁴Charles M. Bowden Research Laboratory, AMRDEC, U.S. Army RDECOM, Redstone Arsenal, Alabama 35898, USA

^*domenico.deceglia@us.army.mil

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Vol. 89, Iss. 7 — 15 February 2014

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Images

Figure 1
(a) Schematic of an electric line dipole p on the surface of a hyperbolic metamaterial made of a semi-infinitely extended metal-dielectric multilayer. Red/green arrows represent FF/SH photons radiated into the structure. (b) Real parts of the extraordinary [red (dashed-dotted line)] and ordinary [blue (solid line)] permittivities of the uniaxial anisotropic effective-medium model of a metal-dielectric stack with a metal fill factor $f$ = 0.5. The black (dashed) line is the RC angle $θ_{RC}$ .
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Figure 2
FF and SH magnetic-field intensity distributions generated by a dipole located 5 nm above the hyperbolic metamaterial. In (a)–(d), the field is calculated using the effective-medium approximation (EMA), whereas, in (e)–(h), the field is calculated for the lamellar discrete metal dielectric (DMD) geometry. In (a), the dipole emission wavelength is $λ_{FF}$ = 810 nm. (b) The same as in (a) for the generated SH signal ( $λ_{SH}$ = 405 nm). (c) The same as in (a) assuming $λ_{FF}$ = 1010 nm. (d) The same as in (b) at $λ_{SH}$ = 505 nm. (e)–(h) The same as in (a)–(d), respectively, calculated for the discrete geometry. The solid and dashed red arrows point in the same direction since they are associated with the FF and phase-locked SH RCs, respectively. The green arrows indicate the homogeneous SH RC. The color scale is linear and is compressed in order to show the field pattern inside the stack. The maximum is located in the volume of metamaterial just below the dipole.
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Figure 3
Isofrequency diagrams at 810 nm (red) and 405 nm (green) on the (a) $k_{x}$ - $β_{z}$ and (b) $k_{x}$ - $α_{z}$ planes for the metal-dielectric multilayer described in Fig. 1. The solid lines refer to Bloch theory, and the dashed lines refer to the anisotropic effective-medium approximation (labeled EMA). The arrows indicate the direction of the group velocity; (c) RC angle with respect to the $z$ axis evaluated via Bloch theory, i.e., $〈 θ_{BT} 〉$ and with the anisotropic effective-medium model, i.e., $θ_{EMA}$ .
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Figure 4
Sketch of the super-resolved near-field imaging at the SH wavelength. Two small particles with nonzero $χ^{(2)}$ and interparticle distance of 50 nm are illuminated with a TM-polarized plane wave ( $λ_{FF} = 810 nm$ ). Second-harmonic light (represented by the two green arrows) creates a super-resolved image of the two particles.
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Figure 5
Magnetic-field intensity pattern at the (a) FF and (b) SH frequency for the setup in Fig. 1. (c) Cross section of (a) and (b) at $z$ = 150 nm.
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