Eigenstates and scattering solutions for billiard problems: A boundary wall approach

Zanetti, F. M.; Vicentini, Eduardo; Luz, M. G. E. da

doi:10.1016/j.aop.2008.01.008

Cited by 25 publications

(21 citation statements)

References 80 publications

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“…Then the profiles are obtained by numerically integrating jψrj 2 over the volume of the input and output channels, respectively. Appendix A gives a brief description of the boundary wall method, and for a more detailed definition we refer the reader to the works by da Luz et al [25] and Zanetti et al [26,27].…”

Section: Open Spherical Resonatormentioning

confidence: 99%

Scalar wave scattering in spherical cavity resonator with conical channels

Garcia-Gracia

Gutiérrez-Vega

2014

J. Opt. Soc. Am. A

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We study the scalar wave scattering off the spherical cavity resonator with two finite-length conical channels attached. We use the boundary wall method to explore the response of the system to changes in control parameters, such as the size of the structure and the angular width of the input and output channels, as well as their relative angular position. We found that the system is more sensitive to changes in the input channel, and a standing wave phase distribution occurs within the cavity for nontransmitting values of the incident wave number. We also saw that an optical vortex can travel unaffected through the system with aligned channels.

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Section: Open Spherical Resonatormentioning

confidence: 99%

Scalar wave scattering in spherical cavity resonator with conical channels

Garcia-Gracia

Gutiérrez-Vega

2014

J. Opt. Soc. Am. A

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“…In this section we give a brief summary of the BWM, also discussing how it can be used to calculate electromagnetic fields in photonic crystal structures. A full account of the BWM can be found in the original work [7], as well as in a very recent technical review [11].…”

Section: The Boundary Wall Methodsmentioning

confidence: 99%

“…As proved in details in [7], any plane wave of wavenumber k, incident perpendicular to the point s on C, has the probability 4k 2 /(4k 2 + γ (s) 2 ) to be transmitted through and γ (s) 2 /(4k 2 + γ (s) 2 ) to be reflected from s. If for any s we take the limit γ (s) → ∞, the probability of transmission goes to zero. This is equivalent to a vanishing wave on C, thus leading to the usual Dirichlet impenetrable boundary condition [7,11]. The Neumann and mixing boundary conditions can be implemented by a direct extension of the method [7].…”

Section: The Bwm Formulationmentioning

confidence: 99%

Resonant scattering states in 2D nanostructured waveguides: a boundary wall approach

Zanetti¹,

Lyra²,

Moura³

et al. 2008

J. Phys. B: At. Mol. Opt. Phys.

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We determine resonant scattering states of two-dimensional photonic crystal nanostructures with defects. To do so, we use the boundary-wall method originally introduced to obtain the scattering eigenstates of one electron moving in a medium with arbitrary boundaries. We investigate geometries including beam bending and interferometer-like waveguides, as well as waveguides connected by resonant cavities. We are able to identify the electromagnetic modes that, due to the special resonance condition attained in the vicinity of defects, provide optimal transmission of an incoming plane wave. Based on the generality of the boundary wall technique and its numerical simplicity and efficiency to identify resonant scattering modes, we briefly discuss further possible applications of this method in analysing the performance of general photonic band-gap devices.

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“…We tested our approach for a rectangular domain, whose eigenenergies are known analytically, and for the quarter square Sinai billiard, which has been studied by different means in Ref. [24]. We found excellent agreement in both cases when the same number of basis functions as in the scattering calculations were included.…”

Section: Introductionmentioning

confidence: 91%

Bound states in the continuum in two-dimensional serial structures

Cattapan

Lotti

2008

Eur. Phys. J. B

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We investigate the occurrence of bound states in the continuum (BIC's) in serial structures of quantum dots coupled to an external waveguide, when some characteristic length of the system is changed. By resorting to a multichannel scattering-matrix approach, we show that BIC's do actually occur in two-dimensional serial structures, and that they are a robust effect. When a BIC is produced in a two-dot system, it also occurs for several coupled dots. We also show that the complex dependence of the conductance upon the geometry of the device allows for a simple picture in terms of the resonance pole motion in the multi-sheeted Riemann energy surface.Finally, we show that in correspondence to a zero-width state for the open system one has a multiplet of degenerate eigenenergies for the associated closed serial system, thereby generalizing results previously obtained for single dots and two-dot devices.

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Eigenstates and scattering solutions for billiard problems: A boundary wall approach

Cited by 25 publications

References 80 publications

Scalar wave scattering in spherical cavity resonator with conical channels

Scalar wave scattering in spherical cavity resonator with conical channels

Resonant scattering states in 2D nanostructured waveguides: a boundary wall approach

Bound states in the continuum in two-dimensional serial structures

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