Nonreciprocal second harmonic generation in CuB₂O₄

In a matter with broken time-reversal and space-inversion symmetries, optical responses can differ for the photons propagating in the opposite directions. The so-called nonreciprocal optical effect has been observed ranging from GHz to X-ray. Especially, CuB₂O₄ is known to show huge nonreciprocal effects for the linear optical response, such as absorption, luminescence and refraction. In this study, we have investigated nonreciprocity of second harmonic generation. It is demonstrated that such gigantic nonreciprocal effects can show up for not only linear optical responses but also for nonlinear optical responses.
CuB₂O₄ shows nonreciprocal absorption at 1.405 eV, which corresponds to the intratomic transition of Cu²⁺ hole [1]. In addition, it has been reported that the large second harmonic signal appears at this transition [2]. Therefore, we expect nonreciprocal second harmonic generation at this photon energy. By carefully tuning the amplitude and phase of electric-dipole and magnetic-dipole transitions, we realize very large nonreciprocal signal reaching 97 %. The temperature dependence and magnetic-field dependence will also be discussed in the presentation.
[1] S. Toyoda et al., PRL 115, 267207 (2015)
[2] R. V. Pisarev et al., PRL 93, 037204 (2004)