3,874 research outputs found
Adaptive Finite Element Method for Simulation of Optical Nano Structures
We discuss realization, properties and performance of the adaptive finite
element approach to the design of nano-photonic components. Central issues are
the construction of vectorial finite elements and the embedding of bounded
components into the unbounded and possibly heterogeneous exterior. We apply the
finite element method to the optimization of the design of a hollow core
photonic crystal fiber. Thereby we look at the convergence of the method and
discuss automatic and adaptive grid refinement and the performance of higher
order elements
Analytical mode normalization and resonant state expansion for optical fibers - an efficient tool to model transverse disorder
We adapt the resonant state expansion to optical fibers such as capillary and
photonic crystal fibers. As a key requirement of the resonant state expansion
and any related perturbative approach, we derive the correct analytical
normalization for all modes of these fiber structures, including leaky modes
that radiate energy perpendicular to the direction of propagation and have
fields that grow with distance from the fiber core. Based on the normalized
fiber modes, an eigenvalue equation is derived that allows for calculating the
influence of small and large perturbations such as structural disorder on the
guiding properties. This is demonstrated for two test systems: a capillary
fiber and an endlessly single mode fiber.Comment: 10 pages, 4 figure
Non-perturbative approach to high-index-contrast variations in electromagnetic systems
We present a method that formally calculates \emph{exact} frequency shifts of
an electromagnetic field for arbitrary changes in the refractive index. The
possible refractive index changes include both anisotropic changes and boundary
shifts. Degenerate eigenmode frequencies pose no problems in the presented
method. The approach relies on operator algebra to derive an equation for the
frequency shifts, which eventually turn out in a simple and physically sound
form. Numerically the equations are well-behaved, easy implementable, and can
be solved very fast. Like in perturbation theory a reference system is first
considered, which then subsequently is used to solve another related, but
different system. For our method precision is only limited by the reference
system basis functions and the error induced in frequency is of second order
for first-order basis set error. As an example we apply our method to the
problem of variations in the air-hole diameter in a photonic crystal fiber.Comment: Accepted for Opt. Commu
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