Photonic Crystals: 2D / 3D Approaches
Abstract
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A. Birner, S. Matthias, A. Langner, R. Hillebrand, and F. Müller
Macroporous silicon with its high perfectness represents an ideal 2D photonic crystal (PC) exhibiting novel properties for the propagation of infrared light inside. It has a complete 2D bandgap for infrared light travelling perpendicular to the pore axis. Because of the lithographic pre-structuring technique defects can be intentionally incorporated into the photonic crystal. Omitting a single pore or a whole line of pores creates microresonators or photonic crystal waveguides.
Fig. 1. shows a zoom series of a 2D Si-based photonic crystal (hexagonal lattice) with one missing row of pores. A narrow bar of the PC has been prepared on the Si-wafer to allow optical measurements.
For appropriate pore radii the 2D hexagonal photonic crystal reveals a complete photonic bandgap. i.e., there are NO existing. The photonic band gap has a gap/midgap ratio of about 16% (dotted line).
Fig. 2. The polarizations E (red) and H (blue), i.e. parallel and perpendicular to the pore axis, completely decouple. Frequencies, which correspond to the bandgap range, will not be transferred through the photonic crystal.
Defect structures composed of missing pore rows can fulfil different functions. Fig. 3 shows two examples of defect geometries.
Fig. 3. (a) shows a so-called point defect (micro-resonator). Fig. 3 (b) is a waveguide that acts as a beam splitter. It was created by inhibiting the growth of selected pores.
After appropriate pre-structuring it is possible to get a pitch as small as 700 nm. The preparation of the wafer is done via UV lithography. Fig. 4 shows the corresponding 2D pore system, which was optically characterized by FTIR spectroscopy. The related photonic band gap corresponds to a wavelength of 1.55 µm.
Fig. 4. The experimental procedure requires extremely stable conditions, because we approach the physical limits of the etching technique.
Besides the lateral lithographic structuring also a structuring along the pore axis is possible. A periodic variation of the backside illumination results in a periodic variation of the pore diameter with the pore depth. Together with the 2D lateral periodicity of the pore array these modulated pores form a 3D photonic crystal.