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

• Published in: The European physical journal. B, Condensed matter physics Condensed matter physics, 2017-11, Vol.90 (11), p.1-10, Article 203
• Main Authors: Margulis, Vladimir A., Muryumin, Evgeny E., Gaiduk, Evgeny A.
• Format: Article
• Language: English
• Subjects: Complex Systems; Condensed Matter Physics; Crystallography; Efficiency; Energy conversion efficiency; Fluid- and Aerodynamics; Incident radiation; Infrared spectra; Near infrared radiation; Nonlinear optics; Nonlinear response; Phosphorene; Phosphorus; Photonics; Physics; Physics and Astronomy; Polarization; Radiation (Physics); Regular Article; S parameters; Solid State Physics
• ISSN: 1434-6028; 1434-6036
• DOI: 10.1140/epjb/e2017-80420-1

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 3 ω . 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.