Visualizing the Photonic Band Structure

Masaya Notomi and Toshiaki Tamamura
Materials Science Laboratory

Since it had been predicted that photonic insulators can be developed by photonic crystals possessing full bandgap, many researchers have been trying to realize them with expectations that they would enable us to realize ultra-small optical circuits and to artificially control spontaneous emission. However, a well-known fact that light likes to go straight leads to essential difficulty in realizing 3D photonic insulators. One of problems in the photonic crystal research is that we cannot experimentally measure the photonic band structure. We noted on the fact that beam propagation in photonic crystals is governed by their band structure, and clarified that it is possible to construct the band structure from the beam propagation measurement. Furthermore, we succeeded in direct measurement on the band structure of a 3D Si/SiO2 photonic crystal which was fabricated by autocloning mode of bias-sputtering on a lithographically patterned substrate (in collaboration with Tohoku University).
Beam propagation direction of Bloch waves in photonic crystals is a normal direction of equi-frequency surface of the photonic band, which corresponds to Fermi surface in metals. Therefore, we can deduce the shape of equi-frequency surface from the information on wavevectors of incident waves, beam propagation angles, and symmetry of crystal, and we can determine the band structure by sweeping the wavelength. We launched a nearly-collimated beam to the cleaved edge of the 3D photonic crystal sample, and determined the propagation direction by CCD camera monitoring (Fig. 1). Figure 2 shows the photonic band structure around the K point determined by the measured data of propagation angles. This figure shows that a gap is open on the K point around a wavelength of 0.93 m, and two bands having three-hold rotational symmetry are formed around this photonic gap.
The method described here is considerably simple and accurate, and it enables us to determine the detailed shape of equi-frequency surface which is essentially important to design the photonic crystal circuit. In addition, such detailed band information is quite important on currently-going research works toward 3D full photonic bandgap materials.

Fig. 1: Schematic of a 3D Si/SiO2 photonic crystal and set up for the band structure determination experiment.

Fig. 2: Experimentally determined 3D photonic band structure (w-kx-ky) around the K of the Si/SiO2 photonic crystal.