Significance of Bloch impedance over wave impedance in photonic crystal waveguides

Abstract

The impedance of a medium carrying electromagnetic waves had been one of the important metrics for designing devices. However, the conclusions of wave impedance in periodic media like photonic crystal (PhC) waveguides fail to describe different wave propagation phenomena. Instead, Bloch impedance fits more appropriately in such a case. However, the existing definition of Bloch impedance by Boscolo et al. [J. Lightwave Technol. 20, 304 (2002)JLTEDG0733-872410.1109/50.983245] is also unable to encounter some typical characteristics of wave propagation. This work brings out these discrepancies by providing a detailed comparison between the wave impedance, and the said Bloch impedance in rods-in-air-type and holes-in-dielectric-type PhC (hole-type) structures. The theoretical analysis shows that the nature of wave propagation in a rods-in-air-type PhC waveguide can be successfully described by this Bloch impedance in the whole band, whereas the wave impedance fails in it at and beyond the point of transition (from positive to negative) in group velocity. Conversely, this Bloch impedance is unable to characterize the wave propagation at the point of transition in group velocity within a hole-type PhC. Thereby, a procedural change in the calculation of Bloch impedance is proposed, and the supremacy of this proposed calculation over existing ones has been established for both the types of PhC waveguides. Moreover, the unexplored odd mode of the hole-type PhC waveguide has also been examined along with its even band in order to signify the importance of Bloch impedance over wave impedance.