Fano resonances and band structure of two-dimensional photonic structures

Abstract

We show that the frequency spectrum of two dimensional photonic crystals is strongly influenced by Fano resonances which can be excited already in the linear array of dielectric cylinders. To support this claim, we calculate the transmission of electromagnetic wave through linear array of dielectric cylinders and show that frequencies of observed Fano resonances coincides with position of narrow frequency bands found in the spectra of corresponding two-dimensional photonic crystals. Split of frequency band or overlap of two bands, observed in the band structure of photonic structures are also associated with Fano resonances.

Photonic crystal with left-handed components

“…2(a,b). For dielectric cylinders, we identify three deep minima in T which correspond to Fano resonances excited by incident wave [16,22]. Similar resonances were found in the LH structure, but their number is much higher and resonant frequencies are located in the region of small frequencies a/λ < 0.2.…”

“…As expected, the spectrum for left-handed cylinders is more complicated. In contrast to dielectric cylinders [22], the number of guided modes is much higher. The number of modes depends on the model parameters and increases when absolute value of the refractive index increases (data not shown).…”

“…For dielectric cylinders, Fano resonances develop to narrow Fano bands discussed in details in Ref. [22]. In contrast, a high number of Fano resonances in the LH structure, completely destroy the band structure.…”

Fano resonances in dielectric, metallic and metamaterial photonic structures

“…we find the wave vector q of the EM wave propagating through the structure and, consequently, calculate the band spectrum of the two-dimensional array of cylinders [11,16].…”

Switchable invisibility of dielectric resonators

“…We can expect an interaction of the Fano-type if a spectrally narrow band virtually any origin interacts with broad spectrum (featureless background) through an interference effect constructively or destructively. It is well known that the Fano resonance has been observed across many different branches of physics [17][18][19][20] including plasmonic [21][22][23] and dielectric structures [24][25][26][27][28] . If there are no parts of background avoiding the above interaction, the Fano relation takes the form 14…”