Diffractionless Flow of Light in All-Optical Microchips

We introduce the concept of a hybrid 2D–3D photonic band gap (PBG) heterostructure which enables both complete control of spontaneous emission of light from atoms and planar light-wave propagation in engineered wavelength-scale microcircuits. Using three-dimensional (3D) light localization, this heterostructure enables flow of light without diffraction through micron-scale air waveguide networks. Achieved by intercalating two-dimensional photonic crystal layers containing engineered defects into a 3D PBG material, this provides a general and versatile solution to the problem of “leaky modes” and diffractive losses in integrated optics.

Figure 1

(a) Template for the square spiral heterostructure consisting of a capping layer grown on top of a square spiral photonic crystal. The “inverse” structure consisting of air spirals in a Si background is depicted in (b). The upper 3D PBG cladding is separated to help visualize the 2D PC layer. A linear waveguide (missing row of rods) is depicted in the 2D microchip. (c) The analogous woodpile based heterostructure. The 2D PC consists of a square lattice of square rods. A single mode air waveguide is created by removing one row of square rods.

Figure 2

Photonic band structure for the inverted optical heterostructure, in the absence of on-chip air waveguides or point defects. The dark shaded region corresponds to frequency bands of propagating electromagnetic modes while the frequency range $(0.339–0.423)/\lambda$ (shown in white) is the full PBG for the bulk 3D (silicon based) inverse square spiral PC. The hatched region $[(0.339–0.369)a/\lambda ]$ shows the on-chip 3D PBG obtained after insertion of the 2D PC layer. In the frequency range $(0.369–0.423)a/\lambda$, all propagating modes are confined to the 2D PC layer. The inset shows the band structure and electromagnetic dispersion relation for an air waveguide channel within the 2D PC obtained by removing one row of dielectric rods [see Fig. 1b] in the 2D PC layer. The lightly shaded region indicates the frequencies of propagating modes in the 2D PC layer.

Figure 3

An on-chip air waveguide inside the heterostructure of Fig. 1b allows transmission of electromagnetic signals around a sharp $90°$ bend. The 3D PBG material on top and bottom is not shown. The electric field is sampled on a horizontal plane which bisects the 2D PC layer. The plane is color coded according to the electric field intensity, where dark and bright correspond to low and high intensity, respectively. The arrows indicate the direction of the electric field vectors along various field lines. The mode exhibits a transverse magnetic character in regions where the intensity is highest. The equal intensity contours (white) in the vertical cross section of the waveguide are also illustrated. The transmission and reflection properties of the bend, shown in the inset, reveal nearly perfect transmission over a bandwidth of more than 130 nm for wavelengths near $1.5\mu \mathrm{m}$.

Figure 4

Air waveguide mode resonantly coupled to a point defect (microcavity) on the optical microchip is depicted. The inverse square spiral PBG material above and below is not shown. The defect is created by changing the dielectric constant of one rod in the vicinity of the waveguide from 11.9 to 1.5 ($2a$ from the waveguide). The dielectric constant of the adjacent rod (also adjacent to the waveguide) is adjusted to 5.9 for computational convenience. The electric field intensity and electric field vectors (color coded as in Fig. 3) provide a steady state snapshot ($a/\lambda =0.352$) of the field configuration from a point source placed at the center of the $ϵ=1.5$ rod. The inset shows results from a separate calculation of transmission and reflection spectra of light sent along the waveguide from a source placed a large distance away from the defect.