Width Dependent Two-Photon Absorption in Monolayer Black Phosphorus Nanoribbons

Abstract

We analytically study the electronic structures and optical properties of zigzag-edged black phosphorene nanoribbons (ZPNRs) utilizing the tight-binding (TB) Hamiltonian and Kubo formula. By solving the discrete Schordinger equation directly, we obtain the energy spectra and wavefunctions for a N-ZPNR with N number of transverse zigzag atomic chains, and classify the eigenstates according to the lattice symmetry. We then obtain the optical transition selection rule of ZPNRs based on the symmetry analysis and the analytical expressions of the optical transition matrix elements. Under an incident light linearly-polarized along the ribbon, importantly, we find that the optical transition selection rule for the N-ZPNR with even-or odd-N is qualitatively different. In specification, for even-N ZPNRs the inter-(intra-) band selection rule is ∆n =odd (even), since the parity of the wavefunction corresponding to the nth subband in the conduction (valence) band is (−1) n [(−1) (n+1) ] due to the presence of the C 2x symmetry. In contrast, all optical transitions are possible among all subbands due to the absence of the C 2x symmetry. Our findings provide a further understanding on the electronic states and optical properties of ZPNRs, which are useful in the explanation of the optical experiment data on ZPNR samples. *

Unusual anisotropic behaviour of free-carrier-induced third-harmonic generation in phosphorene at microwave frequencies

“…The experimental research activity has been directed to the use of BP layers for ultrafast optical switching and laser pulse generation in optical fibers [27][28][29][30][31][32][33][34][35] (for a review of the field, see [36]). There are also a few theoretical works [37,38,39,[40][41][42] dealing with nonlinear optical properties of phosphorene. In our work [37], it has been shown that the output THG power P(3ω) from undoped monolayer phosphorene strongly depends on the polarization direction of the incident radiation of frequency ω: the P(3ω) is maximum when the radiation is polarized along the 'armchair'(AC) direction, and the P(3ω) vanishes when the radiation is polarized along the 'zigzag' (ZZ) direction (see figure 1, where those directions are chosen as the x and y axes, respectively).…”