Article pubs.acs.org/journal/apchd5
Plasmonic Interference in Superstructured Metal Photonic Crystals S. C. Lee* and S. R. J. Brueck Department of Electrical and Computer Engineering, Center for High Technology Materials, University of New Mexico, 1313 Goddard SE, Albuquerque, New Mexico 87106, United States S Supporting Information *
ABSTRACT: Surface plasma waves (SPWs) excited by illumination of 2-dimensional superstructured metal photonic crystals (SMPCs) are investigated with extraordinary optical transmission (EOT). An m × m lattice of holes (m = 3 with the period p of 3 μm) fabricated in an Au film atop a GaAs substrate (refractive index nd), referred to as a basis plasmonic antenna (BPA), forms an SMPC that consists of 24 × 24 BPAs with varying spacing between BPAs, d. Two categories of d are examined: κ = d/p = i (i an integer), where SPWs generated at each BPA interfere constructively and κ ≠ i (1) perforated into a metal film with a period, p, referred to as a basis plasmonic antenna (BPA), is chosen. Then, a 2D M × M square array of these sources (M: integer > 1) with a period, P (=mp + d, where d > 0 is the spacing between unit sources), forms a largescale array, referred to as a superstructured metal photonic crystal (SMPC). In this structure, d must be critical to the interaction between BPAs and as a result to EOT. We focus on d’s small enough to induce strong crosstalk effects. The internal periodicity of the unit plasmonic source is not necessarily commensurate with that of the large-scale array and d can be a noninteger multiple of p (i.e., d ≠ ip, i an integer). Only limited results from 1-dimensional Au nanowire arrays have been presented for noninteger-period spacings.9 Multiple resonances corresponding to higher orders of the superlattice period were reported. The results are consistent with the detailed analysis presented below for 2D structures. Regarding a BPA as a plasmonic source, this work discusses the physics of interpolating 2D plasmonic excitations between a single BPA and an SMPC
urface plasma waves (SPWs) bound to a metal/dielectric interface have been widely investigated for extraordinary optical transmission (EOT) and plasmonic applications such as enhanced infrared detection.1−3 Much of this research has been focused on periodic structures such as 1-dimensional gratings, and 2-dimensional (2D) hole and dot arrays. The physics involved in EOT from these structures has been intensively debated and is now well established.4,5 Illuminating a single nanohole provides a point source of SPWs.6 Illuminating a periodic array of nanoholes will provide a stronger excitation of SPWs with a preferential directionality along the principal axes of the array that results in EOT with a resonance wavelength matched to the periodicity. There are several possible avenues for further investigation of interaction between localized plasmonic sources to enhance EOT. Some reports have investigated an increasing number of nanoholes in a periodic structure.7 Another approach is EOT from aperiodic or randomly distributed holes.8 Additionally, the interaction between localized resonances and the propagating SPWs in a superlattice structure has been examined.9−11 Most often, the investigated superlattice period has been an integer multiple of the period of the basic plasmonic source, where the SPWs generated in localized regions add up in phase along the principal directions of the array and the resulting excitation is therefore strongly enhanced. © XXXX American Chemical Society
Received: April 7, 2017
A
DOI: 10.1021/acsphotonics.7b00367 ACS Photonics XXXX, XXX, XXX−XXX
ACS Photonics
Article
with the variation of d. We find important crosstalk effects including a periodic change in the EOT intensity and a dramatic shift of SPW resonance wavelengths away from the internal hole periodicity when d is incommensurate with p. This is very different from the case of d = ip. The crosstalk effects include strong interference between SPWs excited at individual BPAs that requires the understanding of the fundamental issues on the interference between localized excitations. We present clear experimental evidence for this interaction and address its physics with a Fourier transform (FT) structure factor analysis of the SMPCs and a full electromagnetic simulation.
λij =
⎛ εAuεd Re⎜⎜ 2 2 ⎝ εAu + εd i +j p
⎞ ⎟⎟ ⎠
(1)
with integers i and j, εd = the GaAs dielectric constant and εAu the gold dielectric constant.13,14 Assuming a fixed roomtemperature refractive index of GaAs, almost independent of wavelength across the infrared range of this work, nd ∼ 3.3, the peak wavelengths of SPWs for an SMPC of κ = 0 would be λ1 ∼ 10 μm and λ2 ∼ λ1/ 2 ∼ 7 μm for the fundamental and the second order SPW respectively from λ1 = λ10 = λ01 ∼ ndp in eq 1. Figure 2a shows the transmission spectra of the SMPCs for κ = 0, nd2
■
RESULTS AND DISCUSSION Experimentally, this work employed M = 24 SMPCs superstructured from m = 3 BPAs having p = 3 μm. Each BPA plays the role of discrete device with its own internal structure and an SMPC formed by 576 (=24 × 24) BPAs therefore can be regarded as a large-scale integrated plasmonic circuit. The total number of holes in each SMPC is 5184 (=576 × 3 × 3). Figure 1a is a top-down scanning electron microscope (SEM)
Figure 2. (a) Transmission spectra of the SMPCs consisting of the m = 3 BPAs with κ = 0, 1, and 2. (b) Transmission spectra of the SMPCs consisting of the m = 3 BPAs with the variation of κ from 0 to 0.5. As discussed later, the arrowheads over the spectrum for κ = 0.5 (d = p/2) point experimental peak positions corresponding to λ0.5,H (H = 3−5) from eq 3, labeled with the bottom red arrows.
Figure 1. (a) Top-down SEM image of a single BPA integrated on a double-side polished, semi-insulating GaAs substrate. The red dashed square indicates a BPA having an area of 9 × 9 μm2. Inset: a schematic illustration of the experimental configuration employed in this work. (b) Top-down SEM images of the SMPCs for κ = 0, 0.5, 1, and 2. The red dashed square for κ = 2 corresponds to that in (a).
1, and 2. In this figure, the fundamental SPW has a peak EOT intensity, T1, decreasing with increasing κ at a nearly invariant wavelength of 10.11 ± 0.05 μm (T1 = 0.16, 0.08, and 0.05 at λ1 = 10.16, 10.06, and 10.07 μm for κ = 0, 1, and 2, respectively). The asymmetric EOT line shape reflects a Fano resonance between direct and SPW-mediated transmission.15 As is wellknown, the peak EOT wavelength is slightly red-shifted from the SPW wavelength that occurs near the dip for the fundamental resonance, indicated by an arrow in Figure 2a; the experimental results agree well with a ndp prediction.16,17 In contrast, the SMPCs with fractional κ (
