Photonic Bandgap (PBG)

Abstract

Photonic bandgap materials are expected to play an important role in the near future mainly because of their potential capability to provide extremely compact optical circuits. A large variety of applications have been proposed and demonstrated in both the microwave and optical regimes. In this way, the microwave regime has become a useful instrument to experimentally demonstrate applications initially proposed for the optical domain, thanks to the scaling properties of the Maxwell equations and the easier and cheaper fabrication and testing capabilities of the fabricated structures compared to their optical counterparts. This can be illustrated by the fact that the first photonic bandgap structures were developed to work at microwave frequencies. Photonic bandgap structures have also attracted interest for microwave applications in themselves, and several proposals of electromagnetic bandgap techniques and circuits aimed at improving the properties of current microwave and millimeter‐wave devices have been reported. The concept of photonic bandgap is so wide that it becomes unapproachable to summarize all the knowledge related to this field in a few pages. Thus, although a general vision of the field is offered to the reader, we have focused our efforts on passive microwave components and devices that make use of the principles of photonic bandgap. We start this chapter with a brief historical introduction and a description of photonic bandgap fundamentals. Then, we first summarize some typical functionalities employed in passive optical devices (waveguides, directional couplers, Y junctions, and interferometers), which are tested at microwave frequencies by using a photonic bandgap structure based on alumina rods. The obtained results allow us to visualize a near‐future implementation of the proposed devices using photonic bandgap technology in the optical domain. In a second step, we show how the photonic bandgap concept can be applied to a very extended microwave technology, specifically microstrip technology, and describe and experimentally demonstrate some applications such as novel filter structures and harmonic suppression in microstrip bandpass filters based on coupled rings. Finally, a brief summary of the application of photonic bandgap structures in the optical regime is drawn.

Coupling techniques between dielectric waveguides and planar photonic crystals.

“…In this case, T 23 and R 23 can also be simplified by expressing the Bloch modes in terms of forward and backward components. Moreover, it can be seen that as the interface layer of medium II is the same as that of medium I-II, the eigenmodes expansion will be the same in both media allowing us to take advantage of the orthogonality relation.…”