Matrix method for tunneling in heterostructures: Resonant tunneling in multilayer systems

Ko, D. Y. K.; Inkson, J C

doi:10.1103/physrevb.38.9945

Cited by 268 publications

(119 citation statements)

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“…Using these relations and the S-matrix approach [30], we find the S-MatrixŜ of the whole system, which relates the incoming ( b + 1 and d − L ) and outgoing ( b − 1 and d + L ) amplitudes, in the left (l = 1) and the right (l = L) layers just at their interfaces:…”

Section: Discussionmentioning

confidence: 99%

Resonant-state expansion of light propagation in nonuniform waveguides

et al. 2017

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A new rigorous approach for precise and efficient calculation of light propagation along nonuniform waveguides is presented. Resonant states of a uniform waveguide, which satisfy outgoingwave boundary conditions, form a natural basis for expansion of the local electromagnetic field. Using such an expansion at fixed frequency, we convert the wave equation for light propagation in a non-uniform waveguide into an ordinary second-order matrix differential equation for the expansion coefficients depending on the coordinate along the waveguide. We illustrate the method on several examples of non-uniform planar waveguides and evaluate its efficiency compared to the aperiodic Fourier modal method and the finite element method, showing improvements of one to four orders of magnitude. A similar improvement can be expected also for applications in other fields of physics showing wave phenomena, such as acoustics and quantum mechanics.

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Section: Discussionmentioning

confidence: 99%

Resonant-state expansion of light propagation in nonuniform waveguides

et al. 2017

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“…At the boundary surface of the cylindrical waveguide, the stress components σ rr and σ rz are equal to zero: To avoid numerical instabilities the scattering matrix approach is used [27,28]. For a N -layer structure, the coefficients a N and b 0 of the outgoing modes are related to the coefficients a 0 and b N of the incoming modes via the scattering matrix S(0, N )…”

Section: Acknowledgmentsmentioning

confidence: 99%

“…2(b)] and forward-and backwardpropagating modes with coefficients a i and b i at each interface i, respectively. We use here a scattering-matrix method which provides great numerical stability [27,28], where the coefficients of the outgoing modes (a N…”

Section: Theorymentioning

confidence: 99%

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Acoustic confinement in superlattice cavities

García-Sánchez

Deléglise²,

Thomas

et al. 2016

Phys. Rev. A

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The large coupling rate between the acoustic and optical fields confined in GaAs/AlAs superlattice cavities makes them appealing systems for cavity optomechanics. We have developed a mathematical model based on the scattering matrix that allows the acoustic guided modes to be predicted in nano and micropillar superlattice cavities. We demonstrate here that the reflection at the surface boundary considerably modifies the acoustic quality factor and leads to significant confinement at the micropillar center. Our mathematical model also predicts unprecedented acoustic Fano resonances on nanopillars featuring small mode volumes and very high mechanical quality factors, making them attractive systems for optomechanical applications.

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“…The interface relation (47a) is unstable in the sense that its direct use for sequential elimination of field amplitudes leads to large round-off errors (Ko and Inkson, 1988;Li, 1996a;Pisarenco et al, 2011). To avoid instability, we use an S-matrix representation.…”

Section: Non-homogeneous S-matrix Algorithm For Repeating Slicesmentioning

confidence: 99%