Erratum: Resonant-state-expansion Born approximation for waveguides with dispersion [Phys. Rev. A 
<b>93</b>
, 023835 (2016)]

Doost, Mark

doi:10.1103/physreva.95.049902

Cited by 8 publications

(26 citation statements)

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“…Looking at the dependence of the error on the basis size, presented in Fig. 4(b), we see that the error decreases by roughly an order as the basis size doubles, which is close to the 1/N 3 dependence observed for ef- fective 1D systems treated by the RSE [26,27,30]. This demonstrates a high efficiency of the PC-RSE.…”

Section: Verification Of the Pc-rsesupporting

confidence: 74%

“…11(b) and (c), we see that the RSE in the k-representation quickly converges to the exact solution. The relative error scales as 1/N 3 , which is typical for effective 1D systems, see [17,26,27,30,31].…”

Section: Rse In K-representationmentioning

confidence: 99%

“…So far the RSE has been applied to finite open optical systems of different geometry and dimensional-ity [27,30,31], as well as to homogeneous [17,32] and inhomogeneous planar waveguides [14]. Recently, the RSE was generalized to systems with frequency dispersion of the permittivity [33] and later on to magnetic, chiral and bi-anisotropic optical systems [34], enabling its further application to metamaterials.…”

Section: Introductionmentioning

confidence: 99%

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Resonant-state expansion for planar photonic crystal structures

Neale

Muljarov

2020

Phys. Rev. B

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We present a new paradigm in the field of photonic crystals and metamaterials, applying the resonant-state expansion (RSE) to planar photonic-crystal structures. The RSE allows us to understand and quantify optical resonances in photonic-crystal structures in terms of the analytic resonant states of a homogeneous planar waveguide. The RSE provides an efficient and reliable tool for accurate calculation of a complete set of the resonant states of a photonic-crystal slab, which is required for the correct description and a better understanding of its optical spectra. For the proof of principle, numerical verification of the RSE, and demonstration of its unprecedented accuracy and convergence, an infinite planar photonic crystal slab periodic in one dimension is taken as an example. To illustrate the power of the present approach, we consider the mode evolution with the amplitude of the periodic modulation, revealing the role of the guided modes in the formation of bound states in the continuum. arXiv:1908.06916v1 [physics.optics]

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Section: Verification Of the Pc-rsesupporting

confidence: 74%

Section: Rse In K-representationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Resonant-state expansion for planar photonic crystal structures

Neale

Muljarov

2020

Phys. Rev. B

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“…Following the procedure de- scribed in Ref. 8, we extrapolate the new wave numbers to infinite k max yielding k (∞) . We find that this extrapolation provides 1 to 2 orders of magnitude further reduction of the error, see Fig.…”

Section: A Homogeneous Sphere Perturbationmentioning

confidence: 99%

“…5 the wave number of this RS, and compare it with the results of the RSE using the VSC or the VC basis, as functions of k max , as well as with their extrapolated values including errors (see Ref. 8 for the extrapolation procedure). We find that the convergence is somewhat different for the VC and VSC static basis, but the extrapolated values are equal within the estimated errors.…”

Section: Sphere To Cylinder Perturbationmentioning

confidence: 99%

Resonant-state expansion applied to three-dimensional open optical systems: Complete set of static modes

2019

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We present two alternative complete sets of static modes of a homogeneous dielectric sphere, for their use in the resonant-state expansion (RSE), a rigorous perturbative method in electrodynamics. Physically, these modes are needed to correctly describe the static electric field of a charge redistribution within the optical system due to a perturbation of the permittivity. We demonstrate the convergence of the RSE towards the exact result for a perturbation describing a size reduction of the basis sphere. We then revisit the quarter-sphere perturbation treated in [Doost et al., Phys. Rev. A 90, 013834 (2014)], where only a single static mode per each angular momentum was introduced, and show that using a complete set of static modes leads to a small, though non-negligible correction of the RSE result, improving the agreement with finite-element simulations. As another example of applying the RSE with a complete set of static modes, we calculate the resonant states of a dielectric cylinder, also comparing the result with a finite-element simulation.

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Resonant-state-expansion Born approximation with a correct eigen-mode normalisation

Doost¹

2016

J. Opt.

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The Born approximation (Born 1926 Z.Phys.38.802) is a fundamental result in physics, it allows the calculation of weak scattering via the Fourier transform of the scattering potential. As was done by previous authors (Ge et al 2014 New J. Phys. 16 113048) the Born approximation is extended by including in the formula the resonant-states (RSs) of the scatterer. However in this study unlike previous studies the included eigen-modes are correctly normalised with dramatic positive consequences for the accuracy of the method. The normalisation of the RSs used in the previous RSE Born approximation or resonant-state-expansion Born approximation made in Ge et al (2014 New J. Phys. 16 113048) has been shown to be numerically unstable in Muljarov et al (2014 arXiv:1409.6877) and by analytics here. The RSs of the system can be calculated using my recently discovered RSE perturbation theory for dispersive electrodynamic scatterers (Muljarov et al 2010 Europhys. Lett. 92 50010; Doost et al 2012 Phys, Rev. A 89; Doost et al 2014 Phys. Rev. A 90 013834) and normalised correctly to appear in the spectral Green's functions and hence the RSE Born approximation via the flux-volume normalisation which I recently rigorously derived in Armitage et al (2014 Phys. Rev. A 89), Doost et al (2014 Phys. Rev. A 90 013834)(2016 Phys. Rev. A 93 023835). In the case of effectively one-dimensional systems I find an RSE Born approximation alternative to the scattering matrix method.

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Erratum: Resonant-state-expansion Born approximation for waveguides with dispersion [Phys. Rev. A 93 , 023835 (2016)]

Cited by 8 publications

References 0 publications

Resonant-state expansion for planar photonic crystal structures

Resonant-state expansion for planar photonic crystal structures

Resonant-state expansion applied to three-dimensional open optical systems: Complete set of static modes

Resonant-state-expansion Born approximation with a correct eigen-mode normalisation

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