THESIS
2021
1 online resource (xvii, 97 pages) : illustrations (some color)
Abstract
The optical eigenstates are the quasi time-steady states of electromagnetic fields
in the dielectric systems. As the electromagnetic fields evolve according to
Maxwell’s equations, energy of the system keeps radiating to infinity. This makes
the physical system non-Hermitian and the boundary condition for the eigen
problem exponentially growing at infinity. In this thesis, a numerical method
and a perturbation method are developed for computing the optical eigenstates
in dielectric systems.
The numerical approach is developed based on the perfectly-matched-layer method
by introducing the complex stretching technique to transform the original eigen
problem into its equivalent damping one, which can be solved by the finite element
method. The numerical method is validated by successful ap...[
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The optical eigenstates are the quasi time-steady states of electromagnetic fields
in the dielectric systems. As the electromagnetic fields evolve according to
Maxwell’s equations, energy of the system keeps radiating to infinity. This makes
the physical system non-Hermitian and the boundary condition for the eigen
problem exponentially growing at infinity. In this thesis, a numerical method
and a perturbation method are developed for computing the optical eigenstates
in dielectric systems.
The numerical approach is developed based on the perfectly-matched-layer method
by introducing the complex stretching technique to transform the original eigen
problem into its equivalent damping one, which can be solved by the finite element
method. The numerical method is validated by successful applications
to the whispering-gallery eigenstates in circular disks. The numerical method
is applied to investigate the eigenstates transitions near exceptional points, to
study the symmetries of eigenstates in axial-symmetric cavities and to inspect
the evolution of a pair of degenerate eigenstates as cavity shape deforming from
circle to square.
The perturbation approach is developed by splitting the original eigen problem into a summation of perturbation orders, which can be solved one by one in ascending
orders. The analytical perturbation approximation is applied to calculate
the optical eigenstates in different types of deformed cavities. The perturbation
method also successfully explains the splitting of clockwise and counter-clockwise
degeneracy in whispering-gallery modes.
The numerical method and perturbation method presented in this thesis are
able to facilitate the research of the inverse problem: engineering the optical
eigenstates by manipulating the dielectric distributions.
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