Photoemission electron microscopy to characterize slow light in a photonic crystal line defect

Using femtosecond nonlinear photoemission electron microscopy (PEEM) we provide a detailed characterization of slow light in a small-size asymmetric photonic crystal structure. We show that PEEM is capable of providing a unique description of the light propagation in such structures by direct imaging of the guided mode. This noninvasive characterization technique allows modal properties such as effective index, phase velocities, and group velocities to be determined. Combining experimental results with finite element method simulation calculations, we study slow light phenomena in a photonic crystal defect mode, and we produce a comprehensive picture of the mechanisms behind it. Our results illustrate the usefulness of electron microscopy in exploring nano-optical applications.

Figure 1

(a) Schematic showing a view of the sample configuration. (b) Side view illustrating the coupling of incident light into the ITO layer. Incident light diffracts off the trench edge into the thin ITO layer where the waveguide selects for allowed modes. The guided modes interfere with the incident light to create a stationary interference pattern at the ITO surface that is recorded in PEEM.

Figure 2

(a) PEEM image of photonic crystal structure taken with continuous wave illumination at 244 nm. (b) Scanning electron microscopy image of a cross section of a typical hole array milled and exposed by focused-ion beam milling.

Figure 3

Band diagrams generated with MEEP for (a) TE modes in a 2D hexagonal air-hole lattice in ITO, (b) TE-like modes in a thin-film ITO lattice with symmetric air cladding. The thick black line represents the light line. (c) All modes in a thin-film ITO lattice on a glass substrate. Note the disappearance of the band gap with the introduction of the asymmetric cladding. The experimental region for this work is indicated by a circle located near the $K$ point.

Figure 4

(a)–(c) Colorized PEEM image and accompanying periodograms at laser wavelengths $\lambda =390$, 395, and 400 nm, respectively. (d)–(f) Fast Fourier transforms of the pixel intensity along the defect channel. The black dashed line represents a Gaussian fit to the experimental data.

Figure 5

(a) Time-averaged $E$-field distribution at the ITO surface obtained from the numerical simulation for illumination at $\lambda =400\mathrm{nm}$. (b) A comparison between the Fourier transforms from simulation (blue dashed line) and PEEM image (orange line). The peak at 180 nm in the simulation data results from the PC hole periodicity and is more prominent in the simulated data.

Figure 6

(a) Experimental and calculated results for the effective index vs wavelength for the defect mode of the photonic waveguide. The difference in parameters between the two sets of calculated data are given in Table 1. (b) Experimental and calculated group index vs wavelength obtained from Eq. (7) and a polynomial least-squares fit for the effective index data in part (a) of the figure. The parameters used for the two simulation models are listed in Table 1.

Figure 7

Band diagram in the $\mathrm{\Gamma }\to K$ direction calculated with MEEP for a PC with parameters corresponding to simulation-2. Only TE-like bands are shown. Yellow dots represent the experimentally determined ${k_{\mathrm{reduced}}}_{}$ of the guided mode in the $\mathrm{\Gamma }\to K$ direction projected on the first Brillouin zone. The dashed black line shows ${k_{\mathrm{reduced}}}_{}$ obtained in simulation-2. A vertical line marks $a/\lambda =0.5$, which corresponds to the projected Brillouin zone edge for the defect waveguide in the reduced zone scheme.