Excitation of cyclic Sommerfeld waves and Wood's anomalies in plane wave scattering from a dielectric cylinder at oblique incidence

Abstract

In this paper we consider a process of plane wave scattering from a single dielectric cylinder at oblique incidence under which it is possible to excite long range cyclic Sommerfeld waves (CSWs) and consequently cyclic Sommerfeld resonances (CSRs) of different orders. It is shown that the CSRs are analogous to Wood's anomalies occurred under plane wave scattering from one dimensional (1D) metallic diffraction gratings. The conditions which are necessary for an effective excitation of CSWs and CSRs with high quality factors are analyzed.

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“…Yet what do these two scattering processes in the 1D photonic crystals and the cylindrical surface have in common? In the following discussion we will use our results obtained in [8] to try to answer this question. It is known that mathematically the incident and scattering waves under plane wave scattering from a 1D diffraction grating and a cylindrical surface are expressed according to Fourier and Fourier -Bessel expansions.…”

“…The angle of incidence is θ = 0.02 rad and the refractive index of the capillary and cylinder is n = 1.444. If one calculates the differential backscattering cross section ) 0 ( d σ (ϕ = 0) [8] in the case of the TE polarized incident plane wave: It can be shown that in the case of the plane wave scattering from the dielectric cylinder at oblique incidence it is also possible to observe the anomalies with Lorentzian spectral profiles [8]. As one can see from …”

“…The propagating fields with dependencies ikz e ± become standing waves cos(kz) and sin(kz) at these values of k n due to multiple reflection from the periodic structure. It is also possible to show [11,8] that in the case of plane wave scattering from an individual capillary or cylinder analogous azimuthal standing waves called cyclic Sommerfeld waves are excited and the excitation of these waves determines the band edge formation in the waveguide structures which are periodic in the azimuthal direction. Yet what do these two scattering processes in the 1D photonic crystals and the cylindrical surface have in common?…”

“…These orders are determined by different values of the reciprocal lattice vector 2πn/d , where d is period of the grating and n is the number of the diffraction order. It is possible to show [8] that the cylindrical surface can also be considered as an azimuthal diffraction grating with diffraction orders determined by angular mode numbers in the azimuthal dependence of ϕ im e − . The second process corresponds to a standing wave formation at the band edges in the case of a 1D photonic crystal [9,10].…”

“…If one considers a 1D metallic diffraction grating with a period d the integer n (2) characterizes the linear momentum transfer by the diffraction grating to the incident wave in the tangential direction. If one considers an individual dielectric capillary or cylinder their cylindrical surface can be considered as a diffraction grating [8] and angular mode number m (3) can characterize the momentum transfer from the cylindrical surface to the incident wave in the azimuthal direction. To demonstrate the validity of our assumption let us consider such an interesting phenomenon as Wood anomalies.…”