Cyclic Sommerfeld Resonances in Nanorods at Grazing Incidences

Abstract

We investigate electromagnetic scattering from nanoscale wires and reveal the emergence of a family of exotic resonances for source waves close to grazing incidence. These grazing resonances have a much higher Q-bandwidth product and thus, a much higher Q factor and broader bandwidth than the pure plasmonic resonances found in metal nanowires. Furthermore, these grazing resonances are much less susceptible to material losses than surface plasmon resonances. Contrary to the process of exciting surface plasmon resonances, these grazing resonances can arise in both dielectric and metallic nanowires and appear near to the cutoff wavelength of the circular waveguide. This peculiar resonance effect originates from the excitation of long range guided surface waves through the interplay of coherently scattered continuum modes coupled with first-order azimuthal propagating modes of the cylindrical nanowire. These first-order cyclic Sommerfeld waves and associated cyclic Sommerfeld resonances revealed here opens up the possibility of an alternative scheme of enhanced fields with a better merit (higher Q-bandwidth product and lower loss) than conventional surface plasmon resonances in the nano-regime. This nanowire resonance phenomenon can be utilized in broad scientific areas, including: metamaterial designs, nanophotonic integration, nanoantennas, and nanosensors.

Negative curvature hollow core fibers: design, fabrication, and applications

“…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?…”

“…The formation of cyclic Sommerfeld waves occurring under the oblique incidence of the plane wave on the capillarycylinder [11,8] …”

“…As one can see from (11), the ith air core mode is characterized by one angular mode number (momentum) m in contrast to (9,10) and the process of light localization in the air core occurs due to the interference which is determined by the linear momentum k t r. In cladding (11) is transformed into a superposition of Bessel and Hankel functions in each layer of the HC BF. If the cladding is 2D photonic crystal as in the case of HC PCFs with a circular core -cladding boundary the interference in the cladding has a more complicated character but the transverse resonances in the air core are also determined by the linear momentum of cylindrical waves.…”

“…It is seen that all z -components of scattered fields (3) are standing waves in the azimuthal direction [11,8], for example, in the case of the TE polarized incident wave they are represented as [11,8]:…”

“…The cylindrical harmonics in (10) can be considered as 'propagating' in the azimuthal direction ϕ ip e − . The situation is radically changed at the cut off wavelengths of the capillary or cylinder when azimuthal standing waves (6) are excited due to coupling between the propagating helical waves (9 -10) and leaky modes of the individual capillaries of the cladding [8,11]. Standing waves (cyclic Sommerfeld waves) are not propagating in the azimuthal direction they are excited with corresponding azimuthal dependencies cos(pϕ) and sin (pϕ) (6).…”