Abstract
Potential-based formulation with generalized Lorenz gauge can be used in the quantization of electromagnetic fields in inhomogeneous media [1]. However, one often faces the redundancy of modes when finding eigenmodes from potential-based formulation. In free space, this can be explained by the connection to the well-known Helmholtz decomposition. In this work, the Helmholtz decomposition is generalized to its generalized form, echoing the use of generalized Lorenz gauge in inhomogeneous media [2]. Electromagnetics eigenvalue problems are formulated using vector potential formulation which is often used in numerical quantization [1]. The properties of the differential operators are mathematically analyzed. Orthogonality relations between the two classes of modes are proved in both continuous and discrete space. Completeness of two sets of modes and the orthogonality relations are numerically validated in inhomogeneous anisotropic media. This work serves as a foundation for numerical quantization of electromagnetic fields in inhomogeneous media with potential-based formulation.
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.
