Lifetime and nonlinearity of modulated surface plasmon for black phosphorus sensing application

Black phosphorus surface plasmon (BPSP) is a new promising candidate material for electromagnetic field confinement at the subwavelength scale. Here, we theoretically investigated the light confinement, second-order nonlinearity and lifetimes of tunable surface plasmons in nanostructured black phosphorus nanoflakes with superstrates. The grating structure can enhance the local optical field of the fundamental wave (FW) and second harmonic wave (SHW) due to the surface plasmon resonance. Based on the coupled mode theory (CMT), a theoretical model for the nanostructured black phosphorus was established to study the spectrum features of FW. The lifetimes of the plasmonic resonant modes were investigated with the finite difference time domain (FDTD) simulations and CMT. Since the permittivity of black phosphorus depends on its Fermi energy and electron scattering rate, the lifetimes of plasmonic absorption modes are tunable with both the Fermi energy and scattering rate. The intensity, wavelengths and spectral width of BPSP resonance modes and their lifetimes can be precisely controlled with the Fermi energy, scattering rate, side length and refractive index of the superstrate. The sensitivity is described by varying the refractive index of the superstrate such as an aqueous solution. We have introduced a second-order nonlinear source to investigate the SHW of nanostructured black phosphorus. This paper presents the corner/edge energy distribution and the tunable lifetime of BPSP as well as their unprecedented capability of photon manipulation for second-order nonlinearity within the deep subwavelength scale. The configuration and method are useful for research of the absorption, lifetime of light and nonlinear optical processes in black phosphorus-based optoelectronic devices, especially the modulation and sensing applications.