Black phosphorene (BP) has emerged as a promising platform for tunable nonlinear photonics due to its layer-dependent band gap, high carrier mobility, and remarkable in-plane anisotropy. In this study, we investigate the second harmonic generation (SHG) of monolayer and bilayer BP under an external static electric field. The electronic states are described by a tight-binding model, and the nonlinear optical conductivities are derived from the semiconductor Bloch equations using perturbation theory. Our results reveal that BP exhibits large second-order nonlinear optical response along the armchair direction, with significant resonant enhancement when the incident photon energy approaches half of its band gap. Under an applied electric field of ${10}^7$ V/m, the effective second-order nonlinear susceptibility of BP can be as large as ${10}^3$ pm/V, surpassing that of the conventional nonlinear crystal ${\mathrm{AgGaSe}}_2$ by more than an order of magnitude. With respect to the static electric field induced by gate voltage, we discuss the relation between the electric-field-induced second harmonic (EFISH) generation and conventional SHG—under lower gate voltage, the EFISH approach agrees well with the SHG solutions, whereas the former is no longer applicable under higher gate voltage. Specifically, as the gate voltage increases, monolayer BP exhibits the band gap expansion and the corresponding blueshift in the SHG resonant peak. In contrast, bilayer BP undergoes a semiconductor-to-semimetal transition, forming a Dirac cone and generating divergent SHG spectra as photon energy goes to zero. Additionally, the chemical potential allows for precise control over interband and intraband nonlinear responses. In this work, we provide important theoretical foundations for the development of BP-based tunable nonlinear photonic devices and expand the application potential of anisotropic two-dimensional materials in nonlinear optics.

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• Nonlinear optics
• Optical conductivity
• Semiconductor Bloch equations
• 2-dimensional systems
• Band structure methods
• Tight-binding model