Polarization-Tailored Fano Interference in Plasmonic Crystals: A Mueller Matrix Model of Anisotropic Fano Resonance

Abstract

We present a simple yet elegant Mueller matrix approach for controlling the Fano interference effect and engineering the resulting asymmetric spectral line shape in anisotropic optical system. The approach is founded on a generalized model of anisotropic Fano resonance, which relates the spectral asymmetry to two physically meaningful and experimentally accessible parameters of interference, namely, the Fano phase shift and the relative amplitudes of the interfering modes. The differences in these parameters between orthogonal linear polarizations in an anisotropic system are exploited to desirably tune the Fano spectral asymmetry using pre-and post-selection of optimized polarization states. We begin with a phenomenological model where a Fano-type spectral asymmetry in the scattered intensity naturally arises due to the interference of the complex Lorentzian field ( ( )) of a narrow resonance with a broad spectrum of relative field amplitude ( ) assumed to be independent of frequency (ideal continuum):Here, = ( ) = −The resulting expression for the scattered intensity becomes The first term represents the Fano-type asymmetric line shape with an effective asymmetry parameter = ⁄ . The second term corresponds to a Lorentzian background, widely reported in Fano resonance from diverse optical systems [6,25]. It is

Tunable Fano resonance using weak-value amplification with asymmetric spectral response as a natural pointer

“…The waveguided plasmonic crystal is an interesting nano optical system that exhibits prominent Fano resonance [16][17][18], and has been studied for numerous potential applications [17,18]. Such systems usually comprise of a periodic array of noble metal nanostructures on top of a dielectric waveguiding layer [16][17][18].…”

“…The intensity corresponding to Eq. 1 comprises of a Fano resonant term exhibiting the asymmetric spectral line shape and a Lorentzian background [18] (Supporting information, Eq. S1) and the frequencies corresponding to the minimum and the maximum of Fano resonance are ;…”

Natural weak value amplification in Fano resonance and giant Faraday rotation in magneto-plasmonic crystal

“…We now demonstrate this concept in a realistic Fano resonant system, namely, the waveguided magnetoplasmonic crystals [28][29][30][31][32] . The waveguided plasmonic crystal system usually comprises of a periodic array of noble metal nanostructures (e.g., a metal grating in the system investigated here) on top of a dielectric waveguiding layer [16][17][18]20 . The coupling of the surface plasmons in the metallic nanostructures or the photon continuum with the narrow quasi-guided photonic modes in the waveguiding layer leads to Fano resonance 17,20,[26][27][28] .…”

“…states 2,3 . Here, we demonstrate that due to the common interferometric origin, weak value amplification of an appropriate weak interaction parameter can naturally evolve in a universal wave interference phenomenon, namely, Fano resonance [16][17][18][19][20] . Fano resonance exhibits a characteristic asymmetric spectral line shape which emerges due to the interference of a discrete excited state with continuum of states 16 .…”

“…Investigations on Fano resonances in wide range of micro and nano scale optical systems have attracted particular attention due to their numerous potential application such as in sensing, switching, lasing, filters, color display, nonlinear and slow-light devices and in invisibility cloaking etc 16,[21][22][23][24][25][26][27] . The waveguided plasmonic crystal is one such nano-optical system that exhibit prominent Fano resonances and has already shown a number of interesting fundamental optical effects and demonstrated promising applications [16][17][18]20,26,27 . Taking example of Fano resonance in such a waveguided magneto-plasmonic crystal system [28][29][30][31] , we show that spectral domain interference between a continuum mode and a narrow resonance mode having slightly different polarization response can indeed provide a natural interferometric WVA of weak polarization rotation effect.…”