Anisotropic resonator analysis using the Fourier–Bessel mode solver

Gauthier, Robert C.

doi:10.1016/j.optcom.2017.10.009

Cited by 3 publications

(3 citation statements)

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“…The solution to (13) is to yield the material properties which are the elements of the 6 X 6 matrix on the right hand side. Therefore the spacial variations of the 6 field component vector on the RHS is proposed and from these the curls can be computed using the series expansions (7) to generate the 6 component vector on the left hand side. The angular frequency, ω , is chosen for the proposed state, can be complex, enabling the selection of the state's wavelength and quality factor.…”

Section: Theoretical Developmentmentioning

confidence: 99%

“…, , x y z coordinates and diagonal may not be represented by a diagonal relative permittivity tensor in cylindrical coordinates. Please consult the following when considering anisotropy in general cylindrical resonator configurations [7]. The numerical process will be more involved but the set of equations can be solved for the unknowns provided there are an equal number of equations as unknowns.…”

Section: Comments On the Techniquementioning

confidence: 99%

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Defining cylindrical space optical resonators through supported mode properties: inverse numerical process

Gauthier

2018

Opt. Express

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Faraday's and Ampere's laws are converted to matrix operator form and rearranged such that the unknown relative permittivity and relative permeability tensors can be determined. The material and geometry of cylindrically symmetric optical resonator structures are determined through the electric and magnetic field component profiles and complex angular frequency of a proposed localized state. This differs from the usual utilization of the electromagnetic wave equations, solving for states given the material properties and geometry. Thus the technique presented here is an inverse numerical process. The theoretical expressions are provided based on a Fourier-Bessel numerical approach which is highly suitable for cylindrical geometry resonators. Without loss of the generality of the technique, examples of resonant structure determination are presented for non-magnetic and diagonal relative permittivity tensor. Axial field propagation is included to demonstrate the design capabilities related to optical fiber and photonic crystal fiber structures.

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Section: Theoretical Developmentmentioning

confidence: 99%

Section: Comments On the Techniquementioning

confidence: 99%

Defining cylindrical space optical resonators through supported mode properties: inverse numerical process

Gauthier

2018

Opt. Express

Self Cite

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show abstract

“…These expressions utilize the inverse of the relative permittivity and permeability tensors when anisotropy is included and, in general, contain nine elements that must be specified at every point in the computational domain [97].…”

Section: Theoretical Developmentmentioning

confidence: 99%