Computationally efficient analysis of extraordinary optical transmission through infinite and truncated subwavelength hole arrays

Camacho, Miguel; Boix, Rafael R.; Medina, F.

doi:10.1103/physreve.93.063312

Cited by 24 publications

(39 citation statements)

References 32 publications

(69 reference statements)

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“…For the case of l s = 9 mm, the expected transmission peak would be near 16.7 GHz, while we find that the bound surface mode only exists below 12 GHz. We have found numerically, however, that the same set of basis functions can reliably explain the behavior of slot elements for both radiative (as shown elsewhere [28]) and bound regimes (with weights e ∞,j that will vary from one problem to the other).…”

Section: Infinite Periodic Arraysupporting

confidence: 52%

“…Note that, although in principle only an infinite number of basis functions would be an exact solution, very good convergence can be obtained when these are chosen adequately to the geometry of the problem (in this case, these will be given by Chebyshev polynomials multiplied by the edge behavior of the electric field for each polarization) [28,29]. By substituting (6) in (5) and using each of the basis functions as weighting and then projecting that expression into the domain C 00 the following system of equations is obtained…”

Section: Infinite Periodic Arraymentioning

confidence: 99%

“…These matrix elements can be calculated very efficiently by making use of the properties of the Fourier transform, which lead to quasianalytical expressions, as shown elsewhere [28]. With the addition of the in-plane momentum components (k x0 and k y0 ), the calculation of the periodic dyadic Green's function needs to be generalized but can still be efficiently calculated by means of Ewald's method [30,31].…”

Section: Infinite Periodic Arraymentioning

confidence: 99%

“…Mathematically, this can be easily introduced into the model as J as (x,y) ∝ δ(y − y cc ) for (x cc − w s /2) < x < (x cc + w s /2) and zero otherwise (where y cc and x cc are the y and x coordinates of the center of the central slot, respectively). In a very similar manner to the case of an infinite array, the matrix elements given by (12) can be efficiently calculated when rearranged in terms of cross correlations of the basis functions as explained in detail elsewhere [28]. Once these coefficients are calculated, the electric field is completely determined on the surface.…”

Section: Truncated Periodic Arraymentioning

confidence: 99%

“…In reality, when experimentally measuring the dispersion relation of the surface waves supported by an array of slots, effects due to the finite dimensions along the different directions of a rectangular array cannot be avoided. It is just these effects that are presented here and numerically reproduced by using a method of moments (MoM) technique, which is based on a previous study of some of the authors [28]. To be able to compare the behavior of infinite and finite arrays this method is first applied to the analysis of infinite periodic arrays, and the results obtained compared to those from a commercial software based on finite element method.…”

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confidence: 99%

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Theoretical and experimental exploration of finite sample size effects on the propagation of surface waves supported by slot arrays

et al. 2017

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The propagation of surface waves supported by a finite array of slots perforated on a zero thickness perfect electrically conducting screen is studied both experimentally and theoretically. To generate numerical results, the integral equation satisfied by the electric field in the slots is efficiently solved by means of Galerkin's method, treating the metal as perfectly conducting. The finite size of the array along the direction of propagation creates a family of states of higher momentum and lower amplitude than the single mode for the corresponding infinite array. These modes are spaced in momentum with a periodicity inversely proportional to the length of the array. In addition, the finite width in the transverse direction produces a set of higher frequency modes due to this additional quantization. Both effects arising from finite sample length and width are explained by the theoretical model and validated experimentally. DOI: 10.1103/PhysRevB.95.245425 The existence of strongly localized surface modes supported by corrugated metallic surfaces at frequencies varying from terahertz [1] to microwaves [2] is well established. At optical frequencies, due to the Drude-like properties of the metal, these exist even on flat surfaces, being labeled surface plasmons polaritons (SPPs) [3,4]. However, following the discovery of extraordinary optical transmission (EOT) [5] and the later theoretical calculations, these surface waves were linked to a massively enhanced transmission through subwavelength holes [6,7] due to the diffractive coupling of radiative modes with the SPPs. This theory was, however, essentially developed for optical frequencies relying on the presence of SPPs. The subsequent discovery of EOT at frequencies at which metals behave as near perfect electric conductors (PEC), such as microwaves [8,9], launched the search for a more general theory. Many workers in the field made analogies of the surface waves supported on a patterned PEC with the aforementioned SPP, and due to the similarities with the SPP dispersion, the modes became commonly known as the "spoof surface plasmons" [10][11][12]. It should be noted, however, that there has been a wealth of studies of surface waves on metals at low frequencies, dating back to the 1940s [13,14]. This connection between the surface waves supported by hole arrays and the transmission through them has given rise to much research [15,16] in which the transmission through both infinite and finite arrays of holes and slits has been studied often using a modal matching approach [17,18]. However, there is no corresponding study on the effects of finite sample size on the propagation of surface waves themselves. At microwave frequencies, these surface modes have been explored particularly using metasurfaces [19], subwavelengthstructured metallic surfaces that yield novel properties such as negative refraction [20], band gaps [21], and dispersive behavior leading to the design of surface wave lenses and antennas [22][23][24][25]. With the development of miniaturiza...

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Section: Infinite Periodic Arraysupporting

confidence: 52%

Section: Infinite Periodic Arraymentioning

confidence: 99%

Section: Infinite Periodic Arraymentioning

confidence: 99%

Section: Truncated Periodic Arraymentioning

confidence: 99%

mentioning

confidence: 99%

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Theoretical and experimental exploration of finite sample size effects on the propagation of surface waves supported by slot arrays

et al. 2017

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Extraordinary THz Transmission with a Small Beam Spot: The Leaky Wave Mechanism

Navarro‐Cía

Pacheco‐Peña

Kuznetsov

et al. 2018

Advanced Optical Materials

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plate has been crucial for the development of plasmonics, which is now a central part of nanophotonics technology, opening new avenues toward high performance devices such as color filters [1] and sensing platforms. [2] However, a typical drawback of EOT hole arrays compared to other 2D structures such as metasurfaces [3] is the relatively large number of holes necessary to get a well-defined resonance peak with high amplitude. [4] Indeed, this strong dependence of EOT on the number of holes was identified since the first experiments dealing with the phenomenon [5] and was explained invoking surface plasmons. Experimental results at infrared [5] already showed noticeable differences between large and small arrays. More systematic studies dealing with the enhancement of transmission as the size of the array was gradually increased were reported in the millimeter-wave regime [4,6,7] and it was found that with 961 holes (31 × 31) total transmission was reached. [7] Afterward, theoretical [8] and experimental [9] works arrived at the same conclusion.It is nowadays well established that the EOT resonance in subwavelength hole arrays (and also in an aperture flanked by periodic corrugations as discussed later) relies on surface electromagnetic modes that arise due to the coupling between holes (whose shape and size modulate slightly the EOT peak as long as the holes remain subwavelength, i.e., cut-off regime [4,7,[10][11][12][13][14][15] ), regardless the precise origin of these surface modes. [16][17][18][19][20][21][22][23][24] In real metals at visible frequencies, coupling is possible through surface plasmon polaritons as well as diffraction modes. [22] In contrast, metals at terahertz are generally considered as good conductors, and they fit in a high conductivity model which is a good approximation to a perfect conductor. In this regime, surface plasmons cannot be supported and all the coupling is through diffraction. [19] Then, the surface modes responsible for the coupling are leaky waves, [17,22,23,[25][26][27] i.e., complex waves [27] that radiate power away from the surface as they propagate along it. Leaky waves were already invoked in the prominent work by Ulrich [26] to explain the salient features of metal meshes in the far infrared, principally strong peaks in the transmittance that are directly related to the so-called resonant Wood's anomalies of reflection gratings [17,25,26] and that emerge as a result of the interference between the direct beam and the leakage beams.Aside from this, other models have been proposed to explain EOT, which can be classified into three main frames: (i) theory based on surface plasmons, [5,16,18] and (ii) full-wave diffraction models [8,17,19,24,28] discussed above, and (iii) theory based on The discovery of extraordinary optical transmission (EOT) through patterned metallic foils in the late 1990s was decisive for the development of plasmonics and cleared the path to employ small apertures for a variety of interesting applications all along the electromagnetic spectrum....

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Acoustic Surface Waves on Metasurfaces

Starkey,

Ward

2024

Springer Series in Materials Science

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Computationally efficient analysis of extraordinary optical transmission through infinite and truncated subwavelength hole arrays

Cited by 24 publications

References 32 publications

Theoretical and experimental exploration of finite sample size effects on the propagation of surface waves supported by slot arrays

Theoretical and experimental exploration of finite sample size effects on the propagation of surface waves supported by slot arrays

Extraordinary THz Transmission with a Small Beam Spot: The Leaky Wave Mechanism

Acoustic Surface Waves on Metasurfaces

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