Eur. Phys. J. B (2017) 90: 203
https://doi.org/10.1140/epjb/e2017-80420-1

Regular Article

Coherent nonlinear optical response of single-layer black phosphorus: third-harmonic generation

¹ Department of Physics, Mordovian Ogarev State University, Saransk 430005, Russia
² Department of Chemistry, Mordovian Ogarev State University, Saransk 430005, Russia

^a e-mail: 612033@inbox.ru

Received: 14 July 2017
Received in final form: 1 August 2017
Published online: 1 November 2017

Abstract

We theoretically calculate the nonlinear optical (NLO) response of phosphorene (a black phosphorus monolayer) to a normally incident and linearly polarized coherent laser radiation of frequency ω, resulting in the generation of radiation at frequency 3ω. We derive explicit analytic expressions for four independent nonvanishing elements of the third-order NLO susceptibility tensor, describing the third-harmonic generation (THG) from phosphorene. The final formulas are numerically evaluated for typical values of the system’s parameters to explore how the efficiency of the THG varies with both the frequency and the polarization direction of the incident radiation. The results obtained show a resonant enhancement of the THG efficiency when the pump photon energy ℏω approaches a value of one third of the bandgap energy E_g (≈1.5 eV) of phosphorene. It is also shown that the THG efficiency exhibits a specific polarization dependence, allowing the THG to be used for determining the orientation of phosphorene’s crystallographic axes. Our findings highlight the material’s potential for practical application in nanoscale photonic devices such as frequency convertors operating in the near-infrared spectral range.