Reformulation of the Fourier–Bessel steady state mode solver

Gauthier, Robert C.

doi:10.1016/j.optcom.2016.05.006

Cited by 5 publications

(6 citation statements)

References 22 publications

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“…In order to perform the required derivatives, each field component for A  can be series expanded using Fourier-Bessel basis functions [1,4]:…”

Section: Theoretical Developmentmentioning

confidence: 99%

“…The goal is to propose the optical state and compute the material properties and geometry of the resonator that will support the desired state. The theoretical development presented here is based on the Fourier-Bessel (FB) numerical mode solver for structures that display a high degree of cylindrical symmetry [1]. The presented approach is well suited for the reverse design of numerous axially symmetric structures such as optical and photonic crystal fibers, ring resonators and whispering gallery mode configurations.…”

Section: Introductionmentioning

confidence: 99%

“…In a general coordinate system, the curl operators would need to be properly defined as detailed in [4]. Orthogonality of the basis functions utilized in the series expansions is highly desirable but is not an absolute requirement as the volume integrals can be tabulated as done in the FB numerical process [1]. Section 2 indicates the theoretical approach for determining the structure given a particular resonator state.…”

Section: Introductionmentioning

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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“…In order to perform the required derivatives, each field component for A  can be series expanded using Fourier-Bessel basis functions [1,4]:…”

Section: Theoretical Developmentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Gauthier

2018

Opt. Express

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show abstract

“…The most common application is its use in modelling fields within close proximity of circular scatterers [90]. This thesis's theoretical development is based on the FFB numerical mode solver for structures that display a high degree of cylindrical symmetry [91]. This approach is well suited for PCs, optical fibers, ring resonators, and whispering gallery mode-based resonator configurations.…”

Section: Fourier-fourier-besselmentioning

confidence: 99%

“…It has been dramatically simplified using Faraday's and Ampere's laws rather than usual wave equations. The FFB solver requires the resolution of the electric and magnetic medium properties, and only the first derivatives of the field components give this approach faster convergence properties than using the wave equations directly [96].…”

Section: Fourier-fourier-besselmentioning

confidence: 99%