Range of validity of the Rayleigh hypothesis

Watanabe, Takaoki; Choyal, Y.; Minami, Kazuo; Granatstein, V. L.

doi:10.1103/physreve.69.056606

Cited by 37 publications

(18 citation statements)

References 10 publications

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“…(6) and (7). To this end, we will adapt the method of the reduced Rayleigh equation, which is an approximative technique suitable of accurately describing the scattering from surfaces of not too steep slopes [21,22]. We note that even if the approach is not rigorous, it is still a multiple scattering technique.…”

Section: Reduced Rayleigh Equationmentioning

confidence: 99%

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Enhanced back and forward scattering in the reflection of light from weakly rough random metal surfaces

Simonsen

2010

Physica Status Solidi (b)

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Ingve.Simonsen@ntnu.no, Phone: þ47 73 59 34 17, Fax: þ47 73 59 77 10The scattering of light from a weakly rough random silver surface characterized by a double rectangular power spectrum is studied by numerical simulations. This power spectrum can support both the enhanced back and forward scattering phenomena, which for weakly rough surfaces, are both related to the excitation of surface plasmon polaritons. Here we review these phenomena and present new results from a numerical study of the dependence of the diffuse scattering on the amplitudes (g i , i ¼ 1, 2) of the two rectangular portions of the power spectrum. It is found that there exist an optimal range of ratios, g 2 /g 1 , over which forward scattering peaks can be observed. By just changing the correlations along the interface, while keeping all other parameters like roughness, polarization, and angle of incidence unchanged, the fraction of the incident light that is scattered diffusely can be as large as 16%, while for other parameters as small as 1%. Moreover, a change in the correlation function only, can result in a 3.5 times increase in the amount of light that is absorbed at the weakly rough metal interface (s ¼ 10 nm).ß 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1 Introduction Electromagnetic wave scattering from randomly rough surface has been a field of intensive research for more then a century [1][2][3][4][5]. During this time period significant progress has been made, but still open questions remains, in particular when it comes to dealing with effects of multiple scattering and two-dimensional surfaces. The continuous interest in this problem is not only due to the fundamental scientific issues involved, but is equally prompted by the wide range of applications that depends upon it. Such applications include radar and telecommunication technology, remote sensing, astrophysics, photovoltaics, medical applications, as well as more recently nanotechnology, and plasmonics.A number of perturbative approaches has been developed for the scattering from randomly rough surface, and so have various computer simulation approaches [4]. Even if a formally exact solution to the two-dimensional scattering problem exists (in the form of integral equations), it is very computational demanding to utilize directly. However, for one-dimensional roughness, such rigorous computer simulation approaches can readily be used with confidence [4,6] often without too much demand on computer time. With such

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Section: Reduced Rayleigh Equationmentioning

confidence: 99%

“…(6) and (7), can be used to satisfy the boundary conditions at the rough interface. This assumption is known as the Rayleigh hypothesis after Lord Rayleigh that used it to study the scattering from sinusoidal surfaces [1,4,5,21].…”

Section: Reduced Rayleigh Equationmentioning

confidence: 99%

Enhanced back and forward scattering in the reflection of light from weakly rough random metal surfaces

Simonsen

2010

Physica Status Solidi (b)

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“…Such a profile can be easily treated by the analysis presented in Section 2, if we eliminate the rectangular groove (i.e., D and b tend to R in and zero, respectively) and select the function R w (z) of the smoothings properly. Figure 2 shows the convergence of the dispersion curve of the first TM mode with the number of spatial harmonics used to describe the field in Region I for a waveguide with L=15 mm, R 0 =10 mm and ɛ=0.025 (2πR 0 ɛ/L ≈ 0.105, i.e., this case is enough below the Rayleigh criterion [13]). Obviously, even with seven spatial harmonics (N max =3) the convergence is very satisfactory and the numerical results are identical to those of previous works [14].…”

Section: Sinusoidal Corrugation Profilementioning

confidence: 99%

Dispersion Characteristics of Arbitrary Periodic Structures with Rectangular Grooves

Tigelis

Raguin

Ioannidis

et al. 2008

Int J Infrared Milli Waves

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The dispersion characteristics of a circular cylindrical waveguide with periodic surface corrugations consisting of rectangular grooves with smoothing are examined using the Space Harmonic Method (SHM). The whole structure is divided into two regions, one describing the propagation volume and one inside the grooves. In the first region, the Floquet theorem is applicable and the field distribution is expressed as a summation of spatial Bloch components, whereas in the second one an appropriate Fourier expansion of standing waves is used. Applying the boundary conditions an infinite system of equations is obtained, which is solved numerically by truncation. Several cases are considered, including the limiting cases of a sinusoidal and a rectangular corrugation profile, to check the accuracy of the method proposed as well as its dependence on the corrugation profile.Numerical results are presented only for transverse magnetic modes, although the formalism can be easily extended to include all kinds of waves that can in principle propagate in such a structure.

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“…Most of them are dealing with the dispersion properties of the azimuthally symmetric TM modes in waveguides with sinusoidal periodic surface [10][11][12][13][14][15][16][17][18][19][20], but there are also published works for rectangular corrugation profiles [21][22][23][24]. The mathematical formulations used to study the sinusoidal [18] and rectangular [23,25] surface corrugations can be easily combined in a more general way to include also smoothing.…”

mentioning

confidence: 99%

TE Waves in Arbitrary Periodic Slow-wave Structures with Rectangular Grooves

Mallios

Latsas

Tigelis

2009

J Infrared Milli Terahz Waves

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The dispersion characteristics of the transverse electric modes in a waveguide with circular cross-section and periodic rectangular surface corrugations with smoothed edges are examined by the space harmonic method. The whole structure is divided into two regions, one in the propagation area and one inside the grooves. In the first region, the Floquet theorem is applied and the field distribution is expressed as a summation of spatial Bloch components, while an appropriate Fourier expansion of standing waves is used inside the grooves. Applying the appropriate interface conditions, an infinite system of equations is obtained, which is solved numerically by truncation. Numerical results are presented for several cases to check the convergence and the accuracy of the method, as well as its dependence on the corrugation profile. This formalism could be easily expanded to include all kind of waves that can in principle propagate in such slow-wave structures.

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Range of validity of the Rayleigh hypothesis

Cited by 37 publications

References 10 publications

Enhanced back and forward scattering in the reflection of light from weakly rough random metal surfaces

Enhanced back and forward scattering in the reflection of light from weakly rough random metal surfaces

Dispersion Characteristics of Arbitrary Periodic Structures with Rectangular Grooves

TE Waves in Arbitrary Periodic Slow-wave Structures with Rectangular Grooves

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