Elimination of polarization degeneracy in circularly symmetric bianisotropic waveguides: a decoupled case

Xu, Jing; Wu, Bing; Chen, Yuntian

doi:10.1364/oe.23.011566

Cited by 9 publications

(6 citation statements)

References 36 publications

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“…As such, the total degree of freedom of unknows is halved [30]. We note that GCMT can also be applied to bianisotropic waveguides [33]. …”

Section: [E E E(r R R) H H H(r R R)] T Where E E E(r R R) = E E E(mentioning

confidence: 96%

General coupled mode theory in non-Hermitian waveguides

Xu¹,

Chen²

2015

Opt. Express

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Abstract:In the presence of loss and gain, the coupled mode equation on describing the mode hybridization of various waveguides or cavities, or cavities coupled to waveguides becomes intrinsically non-Hermitian. In such non-Hermitian waveguides, the standard coupled mode theory fails. We generalize the coupled mode theory with a properly defined inner product based on reaction conservation. We apply our theory to the non-Hermitian parity-time symmetric waveguides, and obtain excellent agreement with results obtained by finite element fullwave simulations. The theory presented here is typically formulated in space to study coupling between waveguides, which can be transformed into time domain by proper reformulation to study coupling between non-Hermitian resonators. Our theory has the strength of studying non-Hermitian optical systems with inclusion of the full vector fields, thus is useful to study and design non-Hermitian devices that support asymmetric and even nonreciprocal light propagations.

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“…As such, the total degree of freedom of unknows is halved [30]. We note that GCMT can also be applied to bianisotropic waveguides [33]. …”

Section: [E E E(r R R) H H H(r R R)] T Where E E E(r R R) = E E E(mentioning

confidence: 96%

General coupled mode theory in non-Hermitian waveguides

Xu¹,

Chen²

2015

Opt. Express

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“…Apparently, the paring-β argument still applies. And the modal index decreases for larger ∆χ, see detailed explanation in Xu's work 54 .…”

Section: B Bianisotropic Waveguidementioning

confidence: 77%

Generalized coupled-mode formalism in reciprocal waveguides with gain, loss, anisotropy, or bianisotropy

Chen

Xiong

et al. 2019

Phys. Rev. B

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In anisotropic or bianisotropic waveguides, the standard coupled mode theory fails due to the broken link between the forward and backward propagating modes, which together form the dual mode sets that are crucial in constructing couple mode equations. We generalize the coupled mode theory by treating the forward and backward propagating modes on the same footing via a generalized eigenvalue problem that is exactly equivalent to the waveguide Hamiltonian. The generalized eigenvalue problem is fully characterized by two operators, i.e., (L,B), whereinL is a self-adjoint differential operator, whileB is a constant antisymmetric operator. From the properties ofL andB, we establish the relation between the dual mode sets that are essential in constructing coupled mode equations in terms of forward and backward propagating modes. By perturbation, the generalized coupled mode equation can be derived in a natural way. Our generalized coupled mode formalism can be used to study the mode coupling in waveguides that may contain gain/loss, anisotropy or bianisotropy. We further illustrate how the generalized coupled theory can be used to study the modal coupling in anisotropy and bianisotropy waveguides through a few concrete examples.

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“…(2) Applying standard FEM procedure leads to the unbalanced formulation of weak form in bianisotropic media as used in reference [27], which gives rise to artificial numerical errors due to the spatial differentiation of constitutive parameters, i.e., giving rise to the unusual imaginary part of the propagation constant of bianisotropic waveguides;…”

Section: Modelmentioning

confidence: 99%

Finite element modeling of electromagnetic properties in photonic bianisotropic structures

Xiong

Chen

Wang

et al. 2021

Front. Optoelectron.

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Given a constitutive relation of the bianisotropic medium, it is not trivial to study how light interacts with the photonic bianisotropic structure due to the limited available means of studying electromagnetic properties in bianisotropic media. In this paper, we study the electromagnetic properties of photonic bianisotropic structures using the finite element method. We prove that the vector wave equation with the presence of bianisotropic is selfadjoint under scalar inner product. we propose a balanced formulation of weak form in the practical implementation, which outperforms the standard formulation in finite element modeling. Furthermore, we benchmark our numerical results obtained from finite element simulation in three different scenarios. These are bianisotropydependent reflection and transmission of plane waves incident onto a bianisotropic slab, band structure of bianisotropic photonic crystals with valley-dependent phenomena, and the modal properties of bianisotropic ring resonators. The first two simulated results obtained from our modified weak form yield excellent agreements either with theoretical predictions or available data from the literature, and the modal properties in the last example, i.e., bianisotropic ring resonators as a polarizationdependent optical insulator, are also consistent with the theoretical analyses.

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Elimination of polarization degeneracy in circularly symmetric bianisotropic waveguides: a decoupled case

Cited by 9 publications

References 36 publications

General coupled mode theory in non-Hermitian waveguides

General coupled mode theory in non-Hermitian waveguides

Generalized coupled-mode formalism in reciprocal waveguides with gain, loss, anisotropy, or bianisotropy

Finite element modeling of electromagnetic properties in photonic bianisotropic structures

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