Electro-optic crystals—capable of efficient refractive index modulation via external electric fields—are essential components in modern optoelectronics. However, in wide band gap insulators, the electronic contribution to the electro-optic effect is typically modest. We propose that terahertz field–driven ionic displacements $\stackrel{\rightharpoonup }{u}\left(t\right)$ can effectively modulate the refractive index through the quadratic electro-optic effect $\beta {|\stackrel{\rightharpoonup }{u}\left(t\right)|}^2$, which circumvents the phase-matching condition required for the linear electro-optic effect. Taking the nonlinear optical crystal guanidinium tetrafluoroborate [$\mathrm{C}{\left(\mathrm{N}{\mathrm{H}}_2\right)}_3\mathrm{B}{\mathrm{F}}_4$]—composed of alternating layers of ${\left[\mathrm{C}{\left(\mathrm{N}{\mathrm{H}}_2\right)}_3\right]}^{+}$ and ${\left[\mathrm{B}{\mathrm{F}}_4\right]}^{-}$—as a prototype, our density functional perturbation theory calculations demonstrate that hydrogen (H) atomic displacements can be significantly enhanced via resonant absorption of terahertz photons. Specifically, terahertz-driven H atomic displacement efficiently tunes the refractive index through the quadratic electro-optic mechanism. Our work illustrates that in certain wide-band-gap insulators where the electronically contributed electro-optic effect is negligible, the quadratic electro-optic effect induced by terahertz-driven ionic motion offers an efficient approach for optical phase manipulation and frequency comb generation.

Close

PrevNext

View figure in article

• Electro-optic effects
• Electron-phonon coupling
• Optical phonons
• First-principles calculations