English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

This paper focuses on studying the bifurcation analysis of the eigenstructureof the $\gamma$-parameterized generalized eigenvalue problem ($\gamma$-GEP)arising in three-dimensional (3D) source-free Maxwell's equations with Pasteurmedia, where $\gamma$ is the magnetoelectric chirality parameter. For theweakly coupled case, namely, $\gamma < \gamma_{*} \equiv$ critical value, the$\gamma$-GEP is positive definite, which has been well-studied by Chern et.\al, 2015. For the strongly coupled case, namely, $\gamma > \gamma_{*}$, the$\gamma$-GEP is no longer positive definite, introducing a totally differentand complicated structure. For the critical strongly coupled case, numericalcomputations for electromagnetic fields have been presented by Huang et.\ al,2018. In this paper, we build several theoretical results on the eigenstructurebehavior of the $\gamma$-GEPs. We prove that the $\gamma$-GEP is regular forany $\gamma > 0$, and the $\gamma$-GEP has $2 \times 2$ Jordan blocks ofinfinite eigenvalues at the critical value $\gamma_{*}$. Then, we show that the$2 \times 2$ Jordan block will split into a complex conjugate eigenvalue pairthat rapidly goes down and up and then collides at some real point near theorigin. Next, it will bifurcate into two real eigenvalues, with one movingtoward the left and the other to the right along the real axis as $\gamma$increases. A newly formed state whose energy is smaller than the ground statecan be created as $\gamma$ is larger than the critical value. This stunningfeature of the physical phenomenon would be very helpful in practicalapplications. Therefore, the purpose of this paper is to clarify thecorresponding theoretical eigenstructure of 3D Maxwell's equations with Pasteurmedia.

Bifurcation Analysis of the Eigenstructure of the Discrete Single-curl Operator in Three-dimensional Maxwell's Equations with Pasteur Media