Abstract
The explosive rise of silicon photonics has led to renewed interest in the electro-optic (EO) or Pockels effect due to its potential uses in many next generation device applications. To find materials with a strong EO response in thin film form, which are essential for low power and small footprint devices, one needs to find a general design rule for strong Pockels materials. To elucidate what makes the Pockels effect strong, we study the effect in LiB3O5 (LBO) and CsB3O5 (CBO) and use these materials as prototypical examples of where conventional wisdom breaks down. We find the Pockels tensor components to be extremely small in both materials, despite the large degree of anharmonicity in the crystals, which has been used as a proxy for the presence of nonlinear electronic effects. We relate the lack of EO response to the large optical phonon frequencies (despite the relatively large Raman susceptibility) in LBO and to the small Raman susceptibility (despite the low phonon frequencies) in CBO, respectively. We shed light on the underlying physical phenomena behind the Raman susceptibility, which we find to be intimately linked to the electron–phonon coupling strength of the near-edge electronic states, and identify a route to discovering new strong EO materials.
Highlights
The remarkable ability of a noncentrosymmetric crystal to change its index of refraction in response to an applied electric field, known as the Pockels effect[1], has been the subject of increasing study in recent years due to its potential to facilitate high-speed, low-power electro-optical modulation in integrated photonics applications[2,3,4,5,6], including intrachip data transmission, neuromorphic logic optical chips[7], and photonic integrated circuits for quantum computing[8,9]
In these materials, the Pockels effect is dominated by the lattice, the appropriate figure of merit is the ratio of the Raman susceptibility and square of the phonon frequency
All calculations are performed within density functional theory (DFT) using ABINIT45–51 and follow the theoretical framework developed by Veithen et al.[49]
Summary
The remarkable ability of a noncentrosymmetric crystal to change its index of refraction in response to an applied electric field, known as the Pockels effect[1], has been the subject of increasing study in recent years due to its potential to facilitate high-speed, low-power electro-optical modulation in integrated photonics applications[2,3,4,5,6], including intrachip data transmission, neuromorphic logic optical chips[7], and photonic integrated circuits for quantum computing[8,9]. It is of paramount importance to find materials with large Pockels responses in order to decrease the power consumption and/or size of integrated EO devices. Paillard et al.[20] reported similar behavior in the EO response of strained PbTiO3 (PTO) These crystals all have in common soft phonons and large crystal anharmonicity. BTO, STO, and PTO all have large thermal expansion coefficients, as do many other strong Pockels materials. Though there are no reported Pockels measurements of LBO (Fig. 1), it is a commonly used nonlinear optical crystal[38] with many favorable optical properties[39,40] and it boasts a thermal expansion coefficient an order of magnitude larger[41,42] than that of BTO, STO, or PTO
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