Angle‐resolved cathodoluminescence of plasmonic crystal waveguide
Authors: Saito Hikaru , Yamamoto Naoki , Sannomiya Takumi 
Published: December 2016

Slow‐light manipulation in a photonic crystal (PhC) waveguide is expected to improve future optical information processing and communication technologies such as optical buffering and light compression [T. Baba,
Nat. Photon
.
2
, 465–473 (2008)]. Waveguiding using bandgap of plasmonic crystal (PlC) has also been demonstrated [S. I. Bozhevolnyi et al.
Phys. Rev. Lett
.
86
, 3008–3011 (2001)]. However, the dispersion characteristics of the guided modes, which are essential to control surface plasmon polariton (SPP) pulses, have not yet been understood. Electron beam spectroscopies at high spatial resolution are powerful characterization tools to observe electromagnetic modes nowadays. Momentum‐resolved spectroscopy in electron microscopy is especially useful to investigate detailed optical properties of locally‐modified structures introduced into a PhC [R. Sapienza et al.
Nat. Mater
.
11
, 781–787 (2012)] and a PlC [H. Saito and N. Yamamoto,
Nano Lett
.
15
, 5764–5769 (2015)]. We have studied the dispersion characteristics of SPPs in a PlC waveguide by angle‐resolved chatodoluminescence performed in a STEM. The guided SPP modes were found to have two unique features : i) energy dependence of the phase shift at the wall, and ii) waveguide bandgap (WBG) due to the periodicity originating from PlC structure, which resulted in small group velocity of the guided SPP modes over a wide energy range.

The investigated PlC waveguide is composed of a silver dot array with a triangular lattice and silver plane surface as shown in Fig. 1a, which was structured by electron beam lithography and physical deposition. A full bandgap is formed from 1.8 eV to 2.3 eV in the present PlC. The SPPs with the energies in the full bandgap are confined in the flat waveguide area and guided parallel to the
Γ
‐
K
direction as illustrated in Fig. 1a. Figure 1b shows the dispersion pattern measured in the PlC waveguide area with the waveguide width
W
of 650 nm, angle‐scanned parallel to the direction of the waveguide. The details of the experimental setup for angle‐resolved chatodoluminescence measurements are explained elsewhere [K. Takeuchi and N. Yamamoto,
Opt. Express
19
, 12365–12374 (2011)]. The guided SPP mode is observed (indicated by green ellipse). We also find the small gap about 0.01 nm
−1
along the curve. The guided SPP mode can be approximately modelled as the guided wave between two interfaces with total internal reflections considering an energy‐dependent phase shift. The details of this model will be explained in the congress. The theoretical curves relatively well fits the experimental curves for various waveguide widths except for the gaps. The measured dispersions indicate that the SPPs in the PlC waveguide become much slower than light in vacuum. The guided SPP in the waveguide with
W
= 520 nm is 7.5 times slower than light in vacuum. The velocity is even more slowed as the energy approaches the gap about 0.01 nm
−1
.

To understand the origin of the gap, photon map imaging was performed for
W
= 1040 nm. Interestingly, the interference fringes appear in the direction of the waveguide with the period of 300 nm, indicating the dot row facing the waveguide causes Bragg reflection, resulting in the WBG. The antinode positions for lower band‐edge energy and upper band‐edge energy are different from each other as illustrated in Figs. 1c and 1d. The antinodes of the lower band‐edge mode are extended between the dots facing the flat waveguide area (Fig. 1c) while the upper band‐edge mode is more tightly confined within the flat waveguide area (Fig. 1d). This difference in the effective waveguide width generates the energy difference between the band‐edge modes, i.e. WBG.

The present results indicated that the PlC waveguide has potential advantages in manipulation of ultrashort pulses since it follows the linear dispersion with small group velocity over a wide energy range. Although the dispersion mainly inside the light cone was measured in this fundamental study, it could be shifted outside the light cone for a practical use. One of the possible solutions is a use of a hybrid waveguide composed of a dielectric strip on a metal surface [T. Liu et al.
Opt. Express
22
, 8219‐8225 (2014)].

This work was supported by Kazato Research Foundation, the Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) Nanotechnology Platform 12025014.