Towards Complete Photonic Band Gap Structures Below Infrared Wavelengths

Abstract

Photonic crystals are structures with a periodically modulated dielectric constant. In analogy to the case of an electron moving in a periodic potential, certain photon frequencies can become forbidden, independent of photon polarization and the direction of propagation — a complete photonic bandgap (CPBG) [1, 2]. As early as 1975, photonic crystals with such a gap have been shown to offer the possibility of controlling the spontaneous emission of embedded atoms and molecules in volumes much greater than the emission wavelength [3] and, later on, to be an important ingredient in a variety of technological applications [4]. However, as yet no two- (2D) and three-dimensional (3D) photonic crystals are available with complete bandgaps below infrared (IR) wavelengths and fabrication of photonic crystals with such a gap poses a significant technological challenge already in the near-IR [5, 6]. One faces the extreme difficulty in satisfying combined requirements on the dielectric contrast and the modulation (the total number and the length of periodicity steps). In order to achieve a CPBG below the IR wavelengths, the modulation is supposed to be on the scale of optical wavelengths or even shorter and, as for any CPBG structure, must be achieved with roughly ten periodicity steps in each direction. This task is currently beyond the reach of reactive ion and chemical etching techniques even for 2D structures, because the hole filling fraction must be rather high and the etching must be deep enough [7]. (See, however, [8] for a recent progress using holographic techniques.) Fortunately, in 3D, such a modulation occurs naturally in colloidal crystals formed by monodisperse colloidal suspensions of microspheres. The latter are known to self-assemble into 3D crystals with excellent long-range periodicity on the optical scale [9], removing the need for complex and costly microfabrication. Colloidal systems of microspheres crystalize either in a face-centered-cubic (fec) or (for small sphere filling fraction) in a body-centered-cubic (bcc) lattice [9]. Since larger sphere filling fractions favour opening of larger gaps, simple fec structures of spheres have been one of the main subjects of our investigation.