Frequency Comb of Electric-Polarization Waves

Abstract

Frequency combs are a spectrum of equally spaced frequency components with very high time-frequency accuracy, which have been widely used in the optical and microwave frequency ranges. We propose the realization of a frequency comb operating at the terahertz regime in terms of the nonlinear dynamics of electric-polarization waves, or ferrons as their quanta, in the ferroelectric materials. The efficiency of the frequency comb of the electric-polarization waves is exactly proportional to the static electric polarization carried by the ferron modes, which thereby offers new opportunities for the direct observation and application of the intrinsic properties of ferrons.

Figures (3)

• Figure 1: Efficient modulation of electric-polarization waves of frequency $\omega_d$ to a frequency comb by a focused electric field of frequency $\omega_0$ in a ferroelectric thin film with a spontaneous polarization ${\bf P}_0$ along the $\hat{\bf y}$-direction. The spacing of the comb frequency components in the comb is $\omega_0$.
• Figure 2: Band structures of ferrons of high-frequency $\omega_{+}({\bf k})$ [(a)] and low-frequency $\omega_{-}({\bf k})$ [(b)] modes and their carried static electric polarizations [(c) and (d)].
• Figure 3: Frequency comb spectra of coherent ferrons. (a) and (b): frequency comb of mode $\{\lambda_0=+,{\bf k}_0=(3,0)~\mu{\rm m}^{-1}\}$ modulated by electric fields of $\{0.5,3\}$ MV/cm. (c) and (d): frequency comb of mode $\{\lambda_0=-,{\bf k}_0=(0,10)~\mu {\rm m}^{-1}\}$. (e) and (f): tomography of ferron electric polarization by the frequency comb teeth number as a function of mode wavevector ${\bf k}$ for the $\omega_+$ [(e)] branch and $\omega_-$ [(f)] ferron branch.