The origins of strong Pockels responses

The linear electro-optic (Pockels) effect, which relates the change in the index of refraction of a crystal to an applied electric field, has been subject to increasing study in recent years due to its potential applications in integrated photonics, which include interchip optical interconnects, neuromorphic computing, and photonic chips for quantum computing. The current “gold standard” Pockels-active material is LiNbO₃, which sees wide use as an optical modulator in the telecommunications industry. However, LiNbO₃ has a small Pockels response (~30 pm/V) and does not integrate well with Si. Therefore, finding other Pockels-active materials is of great importance for their potential use in future devices. Most current studies are focused on BaTiO₃, which has an enormous response (~1600 pm/V) in bulk, and which can be epitaxially integrated on silicon (001). However, it of great technological importance to find other strong Pockels materials and to understand the underlying physical principles which drive strong Pockels responses. In this work, we calculate the Pockels response of a wide variety of materials from first principles. We show that SrTiO₃, a centrosymmetric crystal which ordinarily cannot exhibit a Pockels response, can be made to have a strong response through epitaxial strain. The phonon modes driving the large response in SrTiO₃ are very anharmonic. Noticing that other strong Pockels materials are also strongly anharmonic, we investigate whether crystal anharmonicity in non-centrosymmetric crystals is a predictor of strong Pockels responses. We do this by through an in-depth study of LiB₃O₅, which has thermal anharmonicity an order of magnitude larger than that of BaTiO₃ or SrTiO₃. We find that crystal anharmonicity (or rather, soft phonon modes) is a necessary, but not sufficient requirement for strong Pockels responses. Large Raman susceptibilities, which we associate with strong electron-phonon interactions and large deformation potentials, are also required. Finally, we summarize unpublished calculations of the Pockels response of a variety of crystals, many of which have not been considered for the electro-optical applications, and we provide suggestions for future first-principles studies of the Pockels effect