Vesseur, Coenen, Caglayan, Engheta, and Polman (Phys. Rev. Lett. 110, 013902 (2013)) demonstrated plasmonic metal-insulator-metal (MIM) waveguides whose effective refractive index passes through zero at a tunable wavelength in the visible, verified by cathodoluminescence from a 30-keV electron beam acting as a point dipole, and showed that the associated Purcell enhancement is independent of emitter position in the waveguide. Their paper closes with a research program: couple real optical emitters (molecules, quantum dots, gain media) into these n = 0 waveguides and measure absolute spontaneous-emission-rate enhancement and superradiance; mitigate plasmonic losses to extend n = 0 operation deeper into the visible; assemble three-dimensional architectures of coupled n = 0 waveguides into bulk epsilon-near-zero (ENZ) metamaterials; and build functional devices (nanoscale integrated optical circuit elements, nanolasers, active superradiant metamaterials). The objective is to complete, at visible wavelengths, this emitter-level and device-level program: quantitative characterization of emitters (absolute Purcell factors, position-independence, collective superradiant emission), loss mitigation deeper into the visible, and functional devices built from these n = 0 waveguides.

Background

A medium with real permittivity near zero is called epsilon-near-zero (ENZ); when both the effective permittivity and the effective refractive index of a guided mode approach zero, the mode is said to have n = 0. In such a near-zero-index regime the phase of the electromagnetic field barely advances, the effective wavelength is stretched, and the radiative local density of optical states (LDOS, the quantity that sets how fast an embedded emitter can radiate its energy) can be strongly enhanced while remaining spatially uniform. The Purcell factor is the ratio of an emitter's radiative decay rate in a given optical environment to its rate in a reference (usually homogeneous) environment; position-independent Purcell enhancement, where every emitter in the structure decays at the same enhanced rate rather than only at hot spots, is a distinctive promise of n = 0 waveguides. Superradiance is the collectively enhanced emission of a group of emitters that share a common radiative channel.

Rather than resonant material dispersion, Vesseur et al. (2013) exploited structural dispersion: a metal-insulator-metal (MIM) waveguide, consisting of an 85-nm-thick SiO2 core with a rectangular cross-section, fully surrounded by silver, and fabricated by focused-ion-beam milling of a Si/Cr/Ag/SiO2/Ag/Cr multilayer into waveguides whose width (roughly 100-200 nm) sets the cutoff wavelength, supports a gap-plasmon mode (a light wave bound to the insulating slot between the metal films) whose propagation constant goes to zero at a cutoff-like frequency. At cutoff, the mode's effective permittivity and refractive index vanish, and the cutoff wavelength is tunable across the full visible and near-infrared by the waveguide width (a 190-nm-wide guide cuts off near 800 nm, a 120-nm-wide guide near 570 nm). The authors probed this dispersion with cathodoluminescence, light emitted when a focused 30-keV electron beam in a scanning electron microscope acts as a deeply subwavelength point-dipole source inside the structure. They directly observed the vanishing phase advance at n = 0, and verified the predicted enhancement of the radiative LDOS at cutoff, with the striking feature that the Purcell enhancement is essentially independent of the dipole position along the waveguide, in contrast with emission enhancement at interfaces, antennas, or nanoparticle arrays, where the enhancement is local.

Three limitations framed the paper's outlook. First, the electron beam is a versatile probe but not a practical emitter: no molecules, quantum dots, or gain media were placed in the waveguides, so absolute Purcell factors and superradiant collective emission were never measured. Second, the MIM plasmon losses grow at shorter wavelengths and the signal vanishes deeper into the visible, bounding the useful bandwidth. Third, only single waveguides were made; the envisioned three-dimensional arrays, and devices such as nanoscale integrated optical circuit elements, nanolasers, and active (gain-containing) metamaterials exploiting superradiance, remained unrealized. The problem addressed is this emitter-level and device-level completion of the visible n = 0 waveguide platform.

Problem Statement

Complete the emitter-level and device-level program that Vesseur et al. (2013) projected for their experimentally verified visible-wavelength n = 0 MIM plasmonic waveguides. The common scientific objective is to turn the demonstrated position-independent LDOS enhancement at n = 0 cutoff into quantitatively characterized control of real spontaneous emitters and into working devices at visible wavelengths. Specifically: (1) integrate conventional optical emitters, such as molecules, quantum dots, or gain media, inside epsilon-near-zero (n = 0) MIM waveguides operating at visible wavelengths, and measure the absolute Purcell factor, its position-independence over the waveguide, and the spectral bandwidth over which it holds, with quantitative agreement between experiment and electromagnetic modeling of the fabricated geometry; (2) determine and demonstrate whether collectively coupled emitters sharing the n = 0 mode exhibit superradiant emission, as predicted theoretically for ENZ plasmonic channels; (3) mitigate the plasmonic losses that currently extinguish the MIM mode at shorter visible wavelengths, so that near-zero-index behavior is maintained deeper into the visible, down to cutoff wavelengths below the ~570 nm value reported in the source paper; alternative low-loss realizations of the n = 0 cutoff condition are admissible for this sub-goal; and (4) realize and characterize at least one functional device built from these waveguides, such as a nanoscale integrated optical circuit element, a nanolaser, or an active metamaterial exploiting superradiant emission. The three-dimensional bulk-metamaterial assembly originally listed alongside these goals has been achieved by other routes (Maas et al. 2013); the surviving problem is the emitter-integrated, quantitatively characterized, loss-mitigated visible-wavelength n = 0 platform and its devices, across at least the visible band spanned by the source paper's width-tuning demonstration of the cutoff wavelength. The metal-insulator-metal waveguide remains the required platform for the emitter-integrated measurements of sub-goal (1) and for the devices of sub-goal (4); the alternative low-loss realizations permitted in sub-goal (3) serve only to extend n = 0 operation deeper into the visible and do not replace that platform. The problem comprises all four sub-goals above; sub-goal (2) is resolved by a well-supported determination in either direction.

References

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