Abstract
In this paper an analytical theory for arbitrary one-dimensional periodic media is presented. The analysis relies on the mathematical properties of Hill's equation. It is shown that the position of the band gaps can be obtained by quite simple expressions. As a special case, a one-dimensional multilayered medium (conventional photonic crystal) is studied. An exact formula for the location of the gap edges is derived for an infinite number of gaps, for both polarizations, at arbitrary angle of incidence. The gap closing conditions and the difference between the even- and the odd-numbered gaps are obtained. An extension for periodic structures with an arbitrary number of different layers is also presented. This method can be useful for the design of photonic crystal devices.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
