Scattering-matrix approach to multilayer diffraction

Cotter, N. P. K.; Preist, T. W.; Sambles, J. R.

doi:10.1364/josaa.12.001097

Cited by 156 publications

(76 citation statements)

References 14 publications

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“…2a is TE polarization, we can not find that the resonance absorption in the thin dielectric coating layer arises in the diffraction efficiency as TM polarization. Also, the numerical results(ρ r 0 ) by T-matrix method with R-matrix expression in the paper are confirmed in good agreement with the results by S-matrix method [4] in the special case of a sinusoidal profile (γ = 0) with incident angle (θ inc = 42 • ), however, the figures are omitted here.…”

Section: Numerical Examples and Discussionsupporting

confidence: 81%

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T-Matrix Analysis of Electromagnetic Wave Diffraction From a Dielectric Coated Fourier Grating

Ohki¹,

Sato²,

Matsumoto³

et al. 2005

PIER

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Abstract-This paper describes exactly a new formulation of the Tmatrix method with R-matrix expression for the electromagnetic wave diffraction efficiency from dielectric coated metallic Fourier grating. We found that the parameters of numerical calculation are widely applied by using R-matrix expression in dielectric coating media whose thickness or depth groove on the Fourier grating is large. The absorption phenomena of diffraction efficiency in particular incident angle are observed in the two cases. One of the factor is a guided mode in the dielectric coated layer. Other factor is resonance absorption that occurs by plasmon anomalies on the substrate for the TM polarization.

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Section: Numerical Examples and Discussionsupporting

confidence: 81%

“…For the sinusoidal metallic grating with dielectric coating media, the rigorous solution of differential method [4], the mode matching method [3] have already been done, however, the sufficient analysis for the Fourier grating with dielectric coating media has not yet carried out by T-matrix method with R-matrix expression.…”

Section: Introductionmentioning

confidence: 99%

T-Matrix Analysis of Electromagnetic Wave Diffraction From a Dielectric Coated Fourier Grating

Ohki¹,

Sato²,

Matsumoto³

et al. 2005

PIER

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“…The method used in this code has been reported in more detail elsewhere. 11 In all of the following work the permittivity of the metal gratings is modeled as that of silver, being described by a Drude model with a plasma frequency of p ϭ1.32 ϫ10 16 s Ϫ1 , and a relaxation time of ϭ1.45ϫ10 Ϫ14 s.…”

Section: The Modeling Codementioning

confidence: 99%

Surface plasmon polaritons on narrow-ridged short-pitch metal gratings

Hooper

Sambles

2002

Phys. Rev. B

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The reflectivity of short pitch metal gratings consisting of a series of narrow Gaussian ridges in the classical mount has been modeled as a function of frequency and in-plane wave vector ͑the plane of incidence containing the grating vector͒ for various ridge heights. Surface plasmon polaritons ͑SPP's͒ are found to be excited even in the zero-order region of the spectrum. These may result in strong absorption of radiation polarized with its electric field in the plane of incidence ͑transverse magnetic͒. For zero in-plane wave vector the SPP modes consist of a symmetric charge distribution on either side of the grating ridges, a family of these modes existing with different numbers of field maxima per grating period. Because of the charge symmetry these modes may only be coupled to at angles away from normal incidence where strong resonant absorption may then occur. The dispersion of these SPP modes as a function of the in-plane wave vector is found to be complex arising from the formation of very large band gaps due to the harmonic content of the grating profile, the creation of a pseudo high-energy mode, and through strong interactions between different SPP bands.

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“…This approach is chosen as it enables easier matching of the electromagnetic boundary conditions, and therefore the reflection and transmission of complex structures may be calculated. 8 A polynomial fitted to experimentally determined values 9 is used throughout this work to describe the frequency-dependent dielectric function of the silver: r ϭϪ255.3189ϩ1.9863ϫ10 Ϫ13 Ϫ6.0794ϫ10 Ϫ29 2 ϩ8.3810ϫ10 Ϫ45 3 Ϫ4.3004ϫ10 Ϫ61 4 , i ϭ83.2575Ϫ1.3279ϫ10 Ϫ13 ϩ9.0474ϫ10 Ϫ29 2 Ϫ3.2880 ϫ10 Ϫ44 3 ϩ6.6591ϫ10 Ϫ60 4 Ϫ7.0893ϫ10 Ϫ76 5 ϩ3.0913ϫ10 Ϫ92 6 , where is the angular frequency of the incident light. The results of these calculations for structures designed to replicate the results of Schröter and Heitmann as closely as possible with normally incident TM-polarized light as a function of frequency are shown in Fig.…”

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confidence: 99%

Surface plasmon polaritons on thin-slab metal gratings

Hooper

Sambles

2003

Phys. Rev. B

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In a recently published paper ͓U. Schröter and D. Heitmann, Phys. Rev. B 60, 4992 ͑1999͔͒ an unexpected result occurred when light was incident upon a periodically corrugated thin metal film when the corrugations on the two interfaces were identical and in phase with each other. It was observed that it was not possible to excite the surface plasmon polariton on the metal surface facing away from the incoming light, and they ascribed this to the lack of a thickness variation within the metal. In this paper a somewhat different interpretation of their results is presented, which shows that the surface plasmon polariton ͑SSP͒ is in fact very weakly excited on the transmission side of such structures. It is explained why this coupling is so weak in terms of the cancellation of the evanescent diffracted orders from the two diffractive surfaces and how, by changing the phase between the grating on either surface, this coupling becomes much stronger. An explanation for the observation that SPP excitation on such structures may lead to either transmission maxima or minima is also presented. DOI: 10.1103/PhysRevB.67.235404 PACS number͑s͒: 73.20.Mf, 42.70.Qs, 78.66.Bz, 41.20.Jb A surface plasmon polariton ͑SPP͒ is an electromagnetic excitation at the interface between a material with a negative permittivity ͑often a metal͒ and a dielectric. 1 It consists of a surface charge density oscillation coupled to electromagnetic fields, which are bound to the surface and which decay exponentially into both media. With an appropriate coupling geometry ͑in-plane momentum matching͒ SPP's may be excited by incident radiation. This results in resonant coupling and enhanced optical fields, which is one of the reasons why SPP's may be of use in such fields as surface-enhanced Raman spectroscopy or in nonlinear optics. Interest in SPP's has also been heightened in the last few years after it was discovered that they may mediate enhanced transmission of light through arrays of subwavelength apertures in classically opaque metal films. 2,3 When light is incident upon a planar metal surface SPP's cannot be excited since the wave vector parallel to the surface of the SPP is greater than that available to the incident radiation. However, by periodically corrugating the metal surface the wave vector of the incident light may effectively gain integer values of the grating vector, and therefore coupling may occur when the wave vector matching condition is satisfied. Since the increase in the wave vector of the incident light occurs due to diffraction, it is the evanescent diffracted orders of the system which excite the SPP's.If an optically thin metal film bounded by dielectrics is investigated, then it is possible that SPP's may be excited at both metal and dielectric interfaces, and in each case it is the evanescent-diffracted orders ͑corresponding to diffraction in each bounding dielectric medium͒ which excite the SPP. It is this case which Schröter and Heitmann recently investigated. 4 There is also the possibility of exciting coupled...

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Scattering-matrix approach to multilayer diffraction

Cited by 156 publications

References 14 publications

T-Matrix Analysis of Electromagnetic Wave Diffraction From a Dielectric Coated Fourier Grating

T-Matrix Analysis of Electromagnetic Wave Diffraction From a Dielectric Coated Fourier Grating

Surface plasmon polaritons on narrow-ridged short-pitch metal gratings

Surface plasmon polaritons on thin-slab metal gratings

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