A COST 240 benchmark test for beam propagation methods applied to an electrooptical modulator based on surface plasmons

Hoekstra, H.J.W.M.; Lambeck, Paul; Krijnen, Gijs; Ctvroky, J.; Minicis, H. De; Sibilia, C.; Conradi, O.; Helfert, S.; Pregla, R.

doi:10.1109/50.721081

Cited by 8 publications

(8 citation statements)

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“…An FFT-based BPM program including the reflection operator of Equation (9) has been implemented in Fortran to calculate the reflected power in TE and TM cases. The numerical values of the FFT-BPM algorithm are as follows: Number of sampling points along x-axis N = 2 16 , sampling interval along the x-axis ∆x = 0.0003 · λ o /n re f , propagation step-size ∆z = 1 nm. The dielectric waveguide core thickness h varies from 1 to 900 nm, the core refractive index is n co = 3.6, the cladding refractive index is expressed as a percentage δ of the core refractive index: n cl = n co (1 − δ) (where δ = 3%, and 10%), and the free space wavelength λ o = 0.86 µm.…”

Section: Dielectric Waveguide Facetmentioning

confidence: 99%

“…The main essence of the BPM is simple: propagation in a reference homogenous medium over a small distance ∆z followed by phase correction that takes into account the spatial dependence of the refractive index of the medium. However, three major problems should be considered carefully when dealing with step discontinuity and plasmonic devices: The transverse magnetic nature of modes, the abrupt index change in the transverse direction and in the propagation direction at the junction plane [15].Two remedies are used to circumvent the first two problems: the TM nature of the propagated mode is transformed to an equivalent TE field propagating in an equivalent refractive index medium [16,17]. Concerning the step-like transverse variation of the refractive index of the dielectric and plasmonic guides, we used a sigmoid-like function to approximate such abrupt index changes.…”

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confidence: 99%

“…Concerning the step-like transverse variation of the refractive index of the dielectric and plasmonic guides, we used a sigmoid-like function to approximate such abrupt index changes. It is worthy to note that many smoothing functions could be used [10,13,16]. We adopted the sigmoid function because of its simplicity in the analytical and numerical evaluation of the second derivative of the inverse index profile in the TM wave equation.The third problem concerning the reflected field at the junction plane, we adopted a well-established, combined spatial-spectral operator formalism [12,14].In this paper, a dielectric waveguide with its end facet terminated by air is considered in two cases: with and without coating layer.…”

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confidence: 99%

“…Two remedies are used to circumvent the first two problems: the TM nature of the propagated mode is transformed to an equivalent TE field propagating in an equivalent refractive index medium [16,17]. Concerning the step-like transverse variation of the refractive index of the dielectric and plasmonic guides, we used a sigmoid-like function to approximate such abrupt index changes.…”

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confidence: 99%

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confidence: 99%

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Extension of an FFT-Based Beam Propagation Method to Plasmonic and Dielectric Waveguide Discontinuities and Junctions

Shaaban

Gomaa

2019

Applied Sciences

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We adapted a fast Fourier transform-based Beam Propagation Method (FFT-BPM) to investigate waveguide discontinuities in plasmonic waveguides. The adaptation of the FFT-BPM to treat transverse magnetic (TM) fields requires the circumvention of two major difficulties: the mixed derivatives of the magnetic field and waveguide refractive index profile in the TM wave equation and the step-like index change at the transverse metal-dielectric boundary of the plasmonic guide and the transverse boundaries of the dielectric waveguide as well. An equivalent-index method is adopted to transform TM fields to transverse electric (TE) ones, thus enabling the benefit of the full power and simplicity of the FFT-BPM. Moreover, an appropriate smoothing function is used to approximate the step-like refractive index profile in the transverse direction. At the junction plane, we used an accurate combined spatial-spectral reflection operator to calculate the reflected field. To validate our proposed scheme, we investigated the modal propagation in a silicon waveguide terminated by air (like a laser facet in two cases: with and without a coating layer). Then we considered a subwavelength plasmonic waveguide (metal-insulator-metal MIM) butt-coupled with a dielectric waveguide, where the power transmission efficiency has been calculated and compared with other numerical methods. The comparison reveals good agreement.Waals materials layers (like graphene) or through multilayered heterostructures. This leads to strong nonlinearities, large photonic forces, and enhanced emission and absorption probabilities. A practical approach toward nanoscale light trapping and manipulation is offered by interfaces separating media with permittivities of opposite signs [5]. Graphene plasmons are very promising to be the best alternative to noble-metal plasmons as they exhibit much tighter confinement and relatively long propagation distances, with the advantage of being highly tunable via electrostatic gating [6].The integration of plasmonic-based devices and photonic devices will eventually lead to an interfacing between plasmomic and photonic guides. Especially, butt-coupling plasmonic and dielectric guides is one of the most efficient ways for light transmission between highly confined modes and low-loss guided wave structures [7]. It is worthy to note that subwavelength optical confinement modes, allows the efficient and beneficial use of compact photonic devices like nanoscale photodetectors; thus, improving noise immunity, response speed and power dissipation in optical communication devices [8,9].The versatility of the FFT-BPM in the simulation of wide range of photonic devices is well understood [10][11][12][13][14]. In this paper, for the sake of simplicity, we shall consider two-dimensional structures invariant in the y-direction. The main essence of the BPM is simple: propagation in a reference homogenous medium over a small distance ∆z followed by phase correction that takes into account the spatial dependence of the refractive index of the me...

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Section: Dielectric Waveguide Facetmentioning

confidence: 99%

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confidence: 99%

mentioning

confidence: 99%

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confidence: 99%

mentioning

confidence: 99%

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