Optical properties of photonic crystal slabs with an asymmetrical unit cell

Abstract

Using the unitarity and reciprocity properties of the scattering matrix, we analyse the symmetry and resonant optical properties of the photonic crystal slabs (PCS) with complicated unit cell. We show that the reflectivity is not changed upon the 180 • -rotation of the sample around the normal axis, even in PCS with asymmetrical unit cell. Whereas the transmissivity becomes asymmetrical if the diffraction or absorption are present. The PCS reflectivity peaks to unity near the quasiguided mode resonance for normal light incidence in the absence of diffraction, depolarisation, and absorptive losses. For the oblique incidence the full reflectivity is reached only in symmetrical PCS.PACS numbers: 42.70. Qs, 42.25.Bs The physics of photonic crystal slabs (PCS) [1,2,3] receives much attention in recent years because of many interesting possibilities they open to control the light interaction with matter. The tendency is toward the PCS sophistication: nanostructured metals or semiconductors are included, and the unit cell geometry, using modern technology, becomes more complicated. As a result, new tools for photonic engineering become available. A well known example is the extraordinary optical transmission through sub-wavelength hole arrays in metal films [4,5]. Another promising example are polaritonic crystal slabs with nanostructured semiconductors [6,7,8]. The physics behind is the coupling between photonic and different electronic resonances in such structures. They manifest themselves via pronounced resonant Wood's anomalies [9,10,11] in the optical spectra, due to the excitation of quasiguided [2,3,12,13,14,15] or surface plasmon [4,16,17,18] or both [19] modes. On the other hand, making complicated unit cells, e.g., characterized by a lack of 180 o -rotational symmetry in the PCS plane [17,20] adds new ways to control the interaction with light.Thus, the understanding of the symmetry and resonance properties of the optical response in PCS with a complicated unit cell becomes important, also for their optical characterization. Measuring reflection from asymmetric structure appears to be not a promising method for the PCS optical characterization, and a question arises, which optical properties are more sensitive to the PCS structure? Meanwhile, notwithstanding a long history of the investigations (see, e.g., in [11,21]), starting actually from the optical gratings, which can be understood as one-dimensional (1D) PCS, their properties look sometime amazing and even contradictory.One example is the nontrivial symmetry properties of reflection and transmission from asymmetric PCS. Namely, it was demonstrated [17] experimentally and numerically that the reflectivity from 180 o -rotationally non-invariant (in the PCS plane) metal gratings on a dielectric substrate is always symmetric, whereas the transmission is not. However, the transmission appears to be independent on the side of the illumination, whether it is from the air or from the substrate (see also in Refs. 4, 5). The authors [17] find this astonishing...

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