PBG structures have been explored as a way of reducing harmonics.
Vincente Rodríguez-Pereyra, Ph.D., ETS-Lindgren
The concept of photonic structures has recently been applied to the study of the microwave frequency (MW) range [1, 2]. Photonic bandgap (PBG) structures are analogous to a crystal lattice. It is known that in natural crystals there are certain non-occurring or “impossible” energy levels. At these particular energy levels, electrons simply cannot exist. The observations derived from these electronic bandgaps can be extrapolated into the electromagnetic realm. Within the photonic crystals, there are certain energy levels at which, as in natural crystals, certain photon energies cannot exist.  Photon energies are related to frequencies by Plank’s constant, E = hf.
This equation indicates that since some energy levels for the photons in the photonic crystal are not possible, then the frequencies associated with these energy levels cannot propagate within the photonic crystal.
Just how are these photonic crystals built? The analogous structure of natural crystals is instructive. In a natural crystal, ions are located in the sides or vertices of a geometrical lattice. Yablonovitch  tried locating dielectric spheres supported by foam, but his “dielectric crystals” failed to exhibit PBG characteristics (Figure 1a). The opposite approach was followed, and holes were made in a dielectric block (Figure 1b). This geometrical “Swiss cheese” does exhibit PBG properties.
A much simpler PBG structure is introduced by Maradudin and McGurn in . Maradudin’s PBG is a two dimensional Bravais lattice. Dielectric rods are introduced in a different dielectric background. The structure is placed between two conductive plates (Figure 2). This structure forbids the propagation of certain frequency bands.
APPLICATIONS TO MW AND RF
As noted above, these structures have been utilized in the field of optics—e.g., as mirrors in lasers. Only recently have these concepts been applied to the lower spectrum frequencies. Filtering was one of the first applications. Since they block certain bands, these structures can be used to block undesired frequencies. In some instances, [1,2,5] the idea of the two-dimensional Bravais type lattice is borrowed. Rasidic et al.  construct their lattice by drilling holes in the dielectric substrate along a microstrip line (Figure 3). A two-dimensional lattice works well since we know the direction in which the electromagnetic (EM) energy propagates. In Rasidic et al.,  the PBG structure is placed on the output of an amplifier to filter undesired noise and harmonics. In Rasidic et al.,  another approach for creating a PBG structure along microstrip lines is introduced. Figure 4 shows that, in this case, the holes are etched on the ground plane of the structure. The measured results reported  are corroborated by numerical analysis in Figure 4 .
In Rumsey et al.,  three different PBG structures are lined together to create a broadband filter; Figure 5 shows these structures.
USES IN EMC
The use in EMC of PBG structures is not yet very widespread. In Rodriguez et al.,  the possibility of using a PBG to reduce crosstalk in a microstrip line was introduced. The authors demonstrated that if a line carries a known frequency that could be coupled to a nearby line, the use of a PBG structure under the passive line reduces the coupling and consequentially improves transmission on the active line (Figure 6). The results for a series of cross-talk reducing techniques are compared.
Also, PBG structures have been explored at a way of reducing harmonics in printed microstrip antennas. Specifically, a three0dimensional PBG is used as the substrate of the antenna. The use of these structures in EMC antennas is a totally new idea. These structures are virtually invisible at some frequencies, and behave like conductors (not allowing certain frequencies to propagate through) at other frequencies, so their use in broadband antennas appears quite promising.
EMC antennas are usually very broadband. Designing broadband antennas is a challenge. When certain parts of the antenna are modified to improve performance, performance at certain other frequencies may degrate. Figure 7 shows how PBGs’ structure could be used as beam-forming strucutures at certain operating frequencies without affecting other frequencies at which they would be virtually invisible. The horn antenna in Figure 7 operates at a given low frequency. As the frequency increases, higher order modes are launched from the feed cavity. These modes may not radiate or may do so with a split beam. Locating a PBG structure in the cavity could reduce higher order modes and could allow for an effective pattern at higher frequencies, hence increasing the band of the horn without affecting low frequency behavior.
LIMITATIONS OF PBG STRUCTURES
As with every technology, PBG structures have their limitations. Although two-dimensional PBGs are rather easy to construct, three-dimensional PBGs are not easy to manufacture. Also, prior knowledge of the antenna fields is needed for using PBGs effectively in the design of EMC antennas. (Still, this can be obtained via numerical simulation). Another limitation of PBGs relates to their size. To stop the propagation of energy effectively, the PBG must be “electrically large” (ideally infinite). A small PBG structure will attenuate the propagating wave but will not totally stop its propagation. This limitation is especially significant in printed circuit design where the PBG may occupy a much larger area than a filter made up of lumped elements.
The present work has explored the basic principles of PBGs and has demonstrated some of their applications. A great deal of work remains to be done in this area, especially to determine if these structures can be utilized efficiently to increase the performance of broadband antennas vital to EMC. Some of the limitations of PBG structures have been explored as well.
1. Rasidic et al. “Broad-Band Amplifier Using Dielectric Photonic Bandgap Structure.” IEEE Microwave Guided Wave Letters, Vol. 8, No. 1, January 1998. p. 13.
2. Rasidic et al. “Novel 2D Photonic Bandgap Structure for Microstrip Lines.” IEEE Microwave Guided Wave Letters, Vol. 8, No. 2, February 1998. p. 69.
3. Yablonovitch. “Photonic Bandgap Strucutres.” J. Opt. Soc. Am. B., Vol. 10, No. 2, February 1993, pp.283-295.
4. Maradudin et al. “Photonic Band Structure of a Truncated, 2D, Periodic Dielectric Medium.” J. Opt. Soc. Am. B., Vol. 10, No. 2, February 1993, pp. 307-313.
5. Rumsey et al. “Photonic Bandgap Structures Used as Filters in Microstrip Circuits.” IEEE Microwave Guided Wave Letters, Vol. 8, No. 10, October 1998.
6. V. Rodriguez-Pereyra, A. Z. Elsherbeni, and C. E. Smith. “Photonic Bandgap Structures for Minimizing the Coupling Between Microstrip Lines.” 1999 IEEE AP-S International Symposium and USNC/URSI National Radio Science Meeting, Orlando, Florida, July 1999.
Vincente Rodríguez-Pereyra attended the University of Mississippi, where he obtained his BSEE, MS, and Ph.D. in 1994, 1996 and 1999, respectively. Beginnnig in 1994, he was a research assistant at the Electrical Engineering Department at the University of Mississippi. From August 1999 to May 2000, he was a Visiting Assistant Professor of Electrical Engineering and Computer Science at Texas A&M University-Kingsville. In May 2000, he joined ETS-Lindgren as an RF and electromagnetics engineer.
Dr. Rodríguez’ primary interest is Numerical Methods in Electromagnetics—especially as applied to antenna and RF/MW absorber design. Dr. Rodriguez is the author of more than 15 publications, including journal and conference papers, as well as contributions to texts. Dr. Rodríguez is a member of the ACES and the IEEE and several of its technical societies. He can be reached at [email protected]