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We study the reflectivity spectra of photonic crystal slab cavities using an extension of the scattering matrix method that allows treating finite sizes of the spot of the excitation beam. The details of the implementation of the method are presented and then we show that Fano resonances arise as a consequence of the electromagnetic interference between the discrete contribution of the fundamental cavity mode and the continuum contribution of the light scattered by the photonic crystal pattern. We control the asymmetry lineshape of the Fano resonance through the polarization of the incident field, which determines the relative phase between the two electromagnetic contributions to the interference. We analyse the electric field profile inside and outside of the crystal to help in the understanding of the dependence on polarization of the reflectivity lineshape. We also study with our implementation the dependence of the Fano resonances on the size of the incident radiation spot.

We investigate the reflectivity spectra of photonic crystal cavities using the polarization of the incoming exciting light to tune the Fano interference between the radiation reflected by the polarized cavity mode and the light scattered by the photonic crystal pattern. The reflectivity is controlled by the polarization of the incident radiation, with the change from symmetrical to asymmetrical lineshapes well described by the Fano resonance formula. We use the scattering matrix formalism to obtain the reflectivity lineshapes by relating the electromagnetic field incident on the cavity to the radiation that is reflected in qualitative good agreement with the experimental results.

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