Massless Dirac electrons in graphene and on the surface of 3D topological insulators such as Bi2Se3 demonstrate strong nonlinear optical response and support tightly confined surface plasmon modes. Although both systems constitute an isotropic medium for low-energy in-plane electron excitations, their second-order nonlinear susceptibility becomes non-zero when its spatial dispersion is taken into account. In this case the anisotropy is induced by in-plane wave vectors of obliquely incident or in-plane propagating electromagnetic waves. In this work we develop a rigorous quantum theory of the second-order nonlinear response and apply it to the parametric amplification of mid-infrared and Thz radiation. We show that a strong near-infrared or mid-infrared laser beam obliquely incident on graphene can experience a parametric instability with respect to decay into lower-frequency (idler) photons and THz surface plasmons. The parametric gain leads to efficient generation of THz plasmons. Furthermore, the parametric decay process gives rise to quantum entanglement of idler photon and surface plasmon states. This enables diagnostics and control of surface plasmons by detecting idler photons. A similar parametric process can be implemented in topological insulator thin films.
Alexey A. Belyanin, Mikhail Tokman, Yongrui Wang, Ivan Oladyshkin, and A. Ryan Kutayiah, "Laser-driven parametric generation of coherent THz radiation in graphene and topological insulators (Conference Presentation)," Proc. SPIE 10123, Novel In-Plane Semiconductor Lasers XVI, 101231I (Presented at SPIE OPTO: February 02, 2017; Published: 20 April 2017); https://doi.org/10.1117/12.2255940.5398643867001.
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