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High-Order Sideband Generation for Creating Optical Frequency Combs and Probing Bloch Wavefunctions


High-order sideband generation (HSG) is a recently discovered phenomenon in semiconductors simultaneously driven by a weak near infrared (NIR) laser and a strong THz electric field. The NIR field excites electrons out of the valence band into the conduction band, leaving behind holes. The strong THz field can then accelerates the electrons and holes apart before it switches directions to drive the electrons and holes back towards each other. If an electron and a hole recollide, they emit a photon. Since both particles gained energy from the THz field, the emitted photons are typically higher in energy than the original NIR photon. The narrow linewidth of both lasers result in these emitted photons being equally spaced from the NIR photon energy and each other by twice the THz frequency to generate frequency combs. More than 130 orders have been observed.

The intensities of the sidebands is typically difficult to simulate theoretically. However, a simple scaling law for the THz frequency and field strength can be used to predict the widths of the frequency combs. This provides greater tunability and control of HSG frequency combs than previously, opening technological applications of these combs. This scaling relation is complicated, however, by the motion of holes as they travel within a complicated Brillouin zone. Berry’s Curvature mixes the Bloch wavefunctions in momentum space, causing a hole to evolve into new states as it is accelerated by the THz field. When an electron recollides with a hole, these different wavefunctions are imprinted onto the intensity and polarization of the emitted sidebands. With careful polarimetry of the sidebands, information can be extracted about the material structure. For example, strain can be introduced to modify the band structure of the material, which significantly alters the measured polarizations of the sidebands. These techniques could lead to all-optical measurements of the band structure, and Berry Curvature of material systems.

In order to apply these techniques to understand novel material systems, HSG must first be observed in these materials. Any new material must be a semiconductor with a band gap near the NIR photon energy where electrons and holes can be created. However, finding systems with suitably small scattering rates and large enough coherence times remains a challenge.

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