$\chi ^{(2)}$ Modulator With 40-GHz Modulation Utilizing BaTiO3 Photonic Crystal Waveguides

Future telecommunication and data center networks as well as quantum optical communication systems will require optical modulators with wide bandwidths, large extinction, low operating voltage, and small size. We report the first quantitative demonstration of slow light enhancement of the electro-optic (EO) coefficient in a χ
⁽²⁾
ferroelectric waveguide at microwave modulation frequencies. This is demonstrated in a compact (1 mm) photonic crystal (PC) device with a voltage-length product (Vπ·L) of 0.66 V-cm at 10 GHz and measured EO modulation out to 40 GHz. A local enhancement factor of 12 and effective EO coefficient of 900 pm/V is measured in the PC region at a wavelength of 1530 nm. By further optimizing the PC structure, devices with EO 3-dB bandwidths greater than 40 GHz and voltage-length product of 0.16 V-cm are predicted with 100-μm interaction length.