Highly Directional Emission from Photonic Crystal Waveguides of Subwavelength Width

Recently it has been shown that it is possible to achieve directional emission out of a subwavelength aperture in a periodically corrugated metallic thin film. We report on theoretical and experimental studies of a related phenomenon concerning light emitted from photonic crystal waveguides that are less than a wavelength wide. We find that the termination of the photonic crystal end facets and an appropriate choice of the wavelength are instrumental in achieving very low numerical apertures. Our results hold promise for the combination of photonic crystal waveguides with conventional optical systems such as fibers, waveguides, and freely propagating light beams.

Figure 1

(a) A scanning electron microscope image of the photonic crystal structure studied in our experiment. (b) The schematics of the setup. The laser beam is focused on the entrance of the first waveguide, and a fiber tip is used to detect the light locally at the output side. The $x$, $y$, and $z$ axes define the coordinate system used throughout this work.

Figure 2

(a) Lateral intensity distribution as seen by the tip only a few nanometers from the crystal exit. (b)–(i) The same as in (a) but for tip-sample separations of 3.5, 6.5, 9.4, 12.4, 15.3, 18.3, 21.2, and 24.2 micrometers, respectively. The scale of the color code is adapted for each image individually to show the full contrast. (j) Vertical cross sections of (a), (b), and (i) plotted by the blue, black, and red curves, respectively. The heights of the curves are scaled to facilitate the comparison. (k) Horizontal cross sections of (a), (b), and (i) plotted by the blue, black, and red curves, respectively.

Figure 3

(a)–(i) Snapshots of the wave front and intensity distribution of light at $\omega a/2\pi c=0.39$, exiting a photonic crystal waveguide for nine different structure terminations. The inset superposed on the upper left side of each graph displays the PC output termination. The symbols in (e) display the measured widths of the central spot at the corresponding locations. (j) The intensity distribution for the structure in (b) but at $\omega a/2\pi c=0.33$.

Figure 4

Power transmitted within 10° of the waveguide axis as a function of $\omega a/2\pi c$ for three different output terminations corresponding to those in Figs. 3b, 3d, 3e. The region around $\omega a/2\pi c=0.4$ corresponds to a mini stop band in the structure and is not suitable for guiding [16].

Figure 5

Power coupled into the waveguide as a function of the lateral displacement of a dipole source from the center of waveguide ($x=0$). Letters $e$, $h$, and $j$ indicate that the terminations correspond to those used in Figs. 3e, 3h, 3j. The inset shows the power coupled in the waveguide as the dipole is placed at $x=2a$ but at different positions along the $y$ direction inside and outside the PC structure (marked by the dashed line). The rapid $y$ dependence of the signal is a clear signature of surface bound evanescent modes. Note that all oscillations in this figure are due to the modulations of the dielectric constant in the PC.