Highly confined ultraviolet surface plasmon polaritons on nanostructured metal interfaces: interface-topology design, low-loss material screening, and experimental realization

Chubchev et al. (Optics Express 26, 9050, 2018) predicted numerically that a periodically nanostructured aluminum-dielectric interface with corrugation period $a \approx 10$ nm supports a surface plasmon polariton (SPP) Bloch mode whose wavenumber lies in the second Brillouin zone, in the far-ultraviolet window where $\mathrm{Re}\,\varepsilon_m(\omega) > -\varepsilon_d$ and flat-surface SPPs cannot exist. The mode wavelength is set by the structure period ($\lambda_{SPP} \approx a$, about an order of magnitude below the free-space UV wavelength), with computed propagation lengths up to about 53 SPP wavelengths after profile optimization. The open problem is to turn this prediction into a realized, design-optimized waveguiding platform through three linked tasks: (i) design 'topologically more complicated interfaces' that combine the long propagation of thin-film long-range SPP geometries with the deep subwavelength confinement of the nanostructured mode; (ii) identify materials and UV spectral windows beyond aluminum that provide the required low-loss permittivity behavior ($\mathrm{Re}\,\varepsilon_m > -\varepsilon_d$ with small $\mathrm{Im}\,\varepsilon_m$); and (iii) experimentally realize and validate the mode on fabricated nanostructures, including its robustness to fabrication imperfections, roughness, native oxide, and disorder. The mode has not been experimentally observed, and no designs of the requested combined topologies are known, so the problem remains open.

Background

A surface plasmon polariton (SPP) is an electromagnetic surface wave propagating along a metal-dielectric interface, coupled to collective oscillations of the metal's conduction electrons. On a flat interface the SPP exists only at frequencies where the real part of the metal permittivity satisfies $\mathrm{Re}\,\varepsilon_m(\omega) < -\varepsilon_d$ ($\varepsilon_d$ being the dielectric permittivity), and its wavevector $k_x = k_0\sqrt{\varepsilon_m\varepsilon_d/(\varepsilon_m+\varepsilon_d)}$ grows as $\mathrm{Re}\,\varepsilon_m \to -\varepsilon_d$. Plasmonic waveguiding is governed by a fundamental tradeoff between the transverse confinement length $\delta$ (the evanescent decay length of the field into the dielectric) and the propagation length $l_{pr}$ (the distance over which the intensity falls by a factor of $e$), conventionally compared as $\delta(\omega)$-$l_{pr}(\omega)$ tradeoff curves. The standard geometries each fail on one side: a thin metal film in a symmetric dielectric environment supports a long-range SPP (Sarid, 1981) that travels far but is weakly confined, while chains of plasmonic nanoparticles confine the field to the chain period but, near the particle plasmon resonance where the field sits inside the lossy metal, propagate only a few SPP wavelengths (Gramotnev and Bozhevolnyi, 2010). Periodically structured surfaces can also mimic SPP dispersion on perfect conductors ('spoof' SPPs, Pendry et al., 2004), but those modes live in the regime $\varepsilon_m \gg \varepsilon_d$, near the light cone, and their wavelength is not deeply subwavelength. In the ultraviolet, gold and silver are unusable because interband transitions make them strongly lossy, whereas aluminum has its interband transitions in the visible and comparatively low loss in the UV, with $\mathrm{Re}\,\varepsilon_m$ passing through $-\varepsilon_d$ at $\omega \approx 0.73\,\omega_{pl}$ (free-space wavelengths of order 100 nm); other UV-plasmonic metals mentioned in this literature include sodium, rubidium, and, recently, molybdenum.

Chubchev, Nechepurenko, Dorofeenko, Vinogradov, and Lisyansky (2018) studied an aluminum-vacuum interface modulated as $s(x) = h\cos(2\pi x/a)$ with period $a = 10$ nm, solving the lossy eigenproblem exactly by a coordinate transformation that flattens the interface together with a Bloch-harmonic expansion (a Bloch mode is a wave in a periodic medium whose field is multiplied by a phase factor over each period; the Brillouin zone is the elementary wavenumber interval of the periodicity, and in the extended-zone scheme the second zone spans $\pi/a < k_x < 2\pi/a$). Bragg reflection between neighboring corrugations opens a band gap at the first zone edge, and for sufficient corrugation amplitude a part of the dispersion curve moves, in the second Brillouin zone, into the frequency window $\mathrm{Re}\,\varepsilon_m(\omega) > -\varepsilon_d$ where flat-surface SPPs do not exist; a pass band survives there because a periodic system can transport energy through evanescent fields. The resulting mode has $\mathrm{Re}\,k_x \approx 2\pi/a$, hence $\lambda_{SPP} \approx a \approx 10$ nm, is a backward wave, and is confined transversely on the scale of the period. Its propagation length is about 17 SPP wavelengths for the sinusoidal profile with $h = 5$ nm, rising to about 53 SPP wavelengths ($\approx 628$ nm) after Nelder-Mead optimization of the surface profile ($h = 18.5$ nm, $a = 10$ nm). Physically the mode is analogous to a wave on a chain of highly polarizable surface spikes, and a dipole-chain model reproduces its dispersion. The paper is purely numerical: it analyzes only aluminum, does not treat fabrication or disorder, and states that it 'would also be highly desirable to obtain topologically more complicated interfaces that combine advantages of the aforementioned systems without their shortcomings.' The unfulfilled desideratum, together with material screening and experimental validation, constitutes the present problem.

Problem Statement

Establish the second-Brillouin-zone Bloch SPP predicted by Chubchev et al. (2018) as a realizable, optimizable ultraviolet waveguiding platform. The three following tasks serve this single objective of bringing the mode from numerical prediction to demonstrated, material-optimized, fabrication-robust waveguiding, and progress on each is meaningful only insofar as it advances that goal:

1. Interface topology design. Construct interface geometries beyond the single corrugated surface of the source paper - the 'topologically more complicated interfaces' the authors called for, that is, geometries other than the source's isolated single corrugated surface that combine a long-range-SPP-supporting structure (such as a thin film or a multilayer) with the periodically nanostructured interface - that combine the long propagation length of thin-film and other long-range SPP geometries with the subwavelength confinement of the second-Brillouin-zone mode ($\lambda_{SPP} \approx a$, transverse confinement on the scale of the period), improving on the baseline of about 53 SPP wavelengths of propagation at period-scale confinement, and map the resulting confinement-propagation tradeoff curves for the ultraviolet regime. A design resolves Task 1 only if all three requirements are met: the geometry lies outside the class of a single corrugated surface, its propagation length exceeds the baseline of about 53 SPP wavelengths at period-scale confinement, and its confinement-propagation tradeoff curves for the ultraviolet regime are mapped.

2. Material and spectral-window screening. Identify materials beyond aluminum, and their ultraviolet windows, whose permittivity simultaneously satisfies $\mathrm{Re}\,\varepsilon_m(\omega) > -\varepsilon_d$ at the operating frequency (so that the second-Brillouin-zone branch sits outside the flat-surface SPP regime) with sufficiently small $\mathrm{Im}\,\varepsilon_m$ for low-loss propagation, and quantify the achievable mode properties in those windows.

3. Experimental realization and validation. Fabricate the nanostructured interface, achieve excitation of the mode (its wavenumber $\mathrm{Re}\,k_x \approx 2\pi/a$ lies far outside the light cone, so coupling must be engineered), and validate the predicted dispersion ($\lambda_{SPP} \approx a$ in the $\mathrm{Re}\,\varepsilon_m > -\varepsilon_d$ window), confinement, and propagation length, including the effect of realistic fabrication tolerances, surface roughness, native oxide, and structural disorder on the mode.

Task 1 is the core deliverable: it is the design question left open by the source paper, 'topologically more complicated interfaces' that combine the advantages of the long-range SPP geometries and of the second-Brillouin-zone mode without their shortcomings. A complete solution must address Task 1. Tasks 2 and 3 are complementary, optional directions toward the same platform goal; they can strengthen a solution but are not required for one.

References

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