Scattering and Field Enhancement of a Perfect Conducting Narrow Slit

Lin, Junshan; Zhang, Hai

doi:10.1137/16m1094464

Cited by 42 publications

(52 citation statements)

References 22 publications

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“…This constant is consistent with the one obtained for the case of a single slit perforated in a slab of infinite length (cf [23]). Now if mπ < |κ| such that Imγ(mπ, κ, d) = 0, the imaginary part of O(ε)-term of k m in (4.1) is zero.…”

Section: Asymptotic Expansions Of Resonances and Eigenvaluessupporting

confidence: 91%

“…Therefore, the following lemma follows. The following identities are proved in [23]. By applying L −1 on both sides of (3.11), we see that…”

Section: Asymptotic Expansion Of the Boundary Integral Operatorsmentioning

confidence: 89%

“…Proof The asymptotic expansion for the kernels G i ε andG i ε has been derived in [23]. See also Appendix A for the proof.…”

Section: Asymptotic Expansion Of the Boundary Integral Operatorsmentioning

confidence: 99%

“…For instance, the enhancement can be attributed to surface plasmonic resonance [17,18], non-plasmonic resonances [32,33], or even without the resonant effect (cf. [21,22,23]) Very recently, for a single narrow slit perforated in a perfect conducting slab, we have presented quantitative analysis of the field enhancement, which provides a complete picture for its enhancement mechanisms [23]. In this paper and its sequel [24], we investigate the scattering and field enhancement when the slab is patterned with a periodic array of narrow slits.…”

Section: Introductionmentioning

confidence: 99%

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Scattering by a Periodic Array of Subwavelength Slits I: Field Enhancement in the Diffraction Regime

Lin¹,

Zhang²

2018

Multiscale Model. Simul.

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This is the first part in a series of two papers that concern with the quantitative analysis of the electromagnetic field enhancement and anomalous diffraction by a periodic array of subwavelength slits. The scattering problem in the diffraction regime is investigated in this part, for which the size of the period is comparable to the incident wavelength. We distinguish scattering resonances and real eigenvalues, and derive their asymptotic expansions when they are away from the Rayleigh cut-off frequencies.Furthermore, we present quantitative analysis of the field enhancement at resonant frequencies, by quantifying both the enhancement order and the associated resonant modes. The field enhancement near the Rayleigh cut-off frequencies is also investigated. It is demonstrated that the field enhancement becomes weaker at the resonant frequency if it is close to the Rayleigh cut-off frequencies. Finally, we also characterize the embedded eigenvalues for the underlying periodic structure, and point out that transmission anomaly such as Fano resonant phenomenon does not occur for the narrow slit array.

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Section: Asymptotic Expansions Of Resonances and Eigenvaluessupporting

confidence: 91%

“…Therefore, the following lemma follows. The following identities are proved in [23]. By applying L −1 on both sides of (3.11), we see that…”

Section: Asymptotic Expansion Of the Boundary Integral Operatorsmentioning

confidence: 89%

“…Proof The asymptotic expansion for the kernels G i ε andG i ε has been derived in [23]. See also Appendix A for the proof.…”

Section: Asymptotic Expansion Of the Boundary Integral Operatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Scattering by a Periodic Array of Subwavelength Slits I: Field Enhancement in the Diffraction Regime

Lin¹,

Zhang²

2018

Multiscale Model. Simul.

Self Cite

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“…Briefly speaking, the field enhancement becomes stronger as d increases. For extremely large d that still satisfies d λ, the effect of periodicity is vanishing and enhancement behavior resembles that of the single slit considered in [22] as d → ∞. On the other hand, as d decreases, the field enhancement becomes weaker.…”

Section: Homogenization Regime (H2): Non-resonant Field Enhancementmentioning

confidence: 73%

Scattering by a Periodic Array of Subwavelength Slits II: Surface Bound States, Total Transmission, and Field Enhancement in Homogenization Regimes

Lin¹,

Zhang²

2018

Multiscale Model. Simul.

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This is the second part in a series of two papers that concern with the quantitative analysis of the electromagnetic field enhancement and anomalous diffraction by a periodic array of subwavelength slits. In this part, we explore the scattering problem in the homogenization regimes, where the size of the period is much smaller than the incident wavelength. In particular, two homogenization regimes are investigated, where the size of the pattered slits has the same order as the size of the period in the first configuration, and the size of the slit is much smaller than the size of the period in the second configuration. By presenting rigorous asymptotic analysis, we demonstrate that surface plasmonic effect mimicking that of plasmonic metals occurs in the first homogenization regime. The corresponding dispersion curve lies below the light line and the associated eigenmodes are surface bound sates. In addition, for the incident plane wave, we discover and justify a novel phenomenon of total transmission which occurs either at certain frequencies for all incident angles, or at a special incident angle but for all frequencies. For the second homogenization regime, the non-resonant field enhancement is investigated, and it is shown that the fast transition of the magnetic field in the slit induces strong electric field enhancement. Moreover, the enhancement becomes stronger when the coupling of the slits is weaker.

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