The paper investigates the quasiparticle band gap, excitons, and anisotropic optical responses of few-layer black phosphorus (phosphorene). The authors use first-principles GW-Bethe-Salpeter Equation (BSE) simulations to study the electronic and optical properties of phosphorene. Key findings include: 1. **Many-Electron Effects**: The electronic structures of phosphorene are quasi-one-dimensional, leading to significant self-energy corrections and enhanced excitonic effects. For monolayer phosphorene, the band gap increases from 0.8 eV to 2 eV, and the lowest-energy optical absorption peak shifts to 1.2 eV due to a large exciton binding energy of around 800 meV. 2. **Anisotropic Optical Responses**: Phosphorene exhibits strong absorption of light polarized along the armchair direction and transparency to light polarized along the zigzag direction. This anisotropy makes phosphorene an ideal candidate for linear optical polarizers, covering a wide range of energies from the infrared to part of the visible light spectrum. 3. **Tunable Properties**: The number of stacked layers controls the band gap, optical absorption spectrum, and anisotropic polarization energy window. The band gap decreases from 2 eV in monolayer to 0.3 eV in bulk phosphorene, and the optical absorption peaks and exciton binding energies follow similar scaling laws with the stacking layer number. 4. **Bulk Limit**: In the bulk limit, the optical absorption spectrum is nearly unchanged by electron-hole interactions, with an upper limit for exciton binding energy of 30 meV. The bulk phosphorene has weaker excitonic effects due to stronger interlayer interactions and reduced perpendicular quantum confinement. 5. **Wavefunction Analysis**: The spatial distribution of exciton wave functions is anisotropic, extending along the armchair direction. This anisotropy is consistent with the anisotropic band dispersion and results in striped patterns in the optical absorption spectra. 6. **Interlayer Distance Impact**: The interlayer distance has a minor effect on the band gap and intralayer excitons in suspended few-layer phosphorene, but it significantly affects the bulk limit, where a small change in interlayer distance can shift the band gap and exciton energy by 150 meV. The study highlights the potential of phosphorene for various applications, including optical polarizers and electronic devices, due to its unique many-electron effects and tunable properties.The paper investigates the quasiparticle band gap, excitons, and anisotropic optical responses of few-layer black phosphorus (phosphorene). The authors use first-principles GW-Bethe-Salpeter Equation (BSE) simulations to study the electronic and optical properties of phosphorene. Key findings include: 1. **Many-Electron Effects**: The electronic structures of phosphorene are quasi-one-dimensional, leading to significant self-energy corrections and enhanced excitonic effects. For monolayer phosphorene, the band gap increases from 0.8 eV to 2 eV, and the lowest-energy optical absorption peak shifts to 1.2 eV due to a large exciton binding energy of around 800 meV. 2. **Anisotropic Optical Responses**: Phosphorene exhibits strong absorption of light polarized along the armchair direction and transparency to light polarized along the zigzag direction. This anisotropy makes phosphorene an ideal candidate for linear optical polarizers, covering a wide range of energies from the infrared to part of the visible light spectrum. 3. **Tunable Properties**: The number of stacked layers controls the band gap, optical absorption spectrum, and anisotropic polarization energy window. The band gap decreases from 2 eV in monolayer to 0.3 eV in bulk phosphorene, and the optical absorption peaks and exciton binding energies follow similar scaling laws with the stacking layer number. 4. **Bulk Limit**: In the bulk limit, the optical absorption spectrum is nearly unchanged by electron-hole interactions, with an upper limit for exciton binding energy of 30 meV. The bulk phosphorene has weaker excitonic effects due to stronger interlayer interactions and reduced perpendicular quantum confinement. 5. **Wavefunction Analysis**: The spatial distribution of exciton wave functions is anisotropic, extending along the armchair direction. This anisotropy is consistent with the anisotropic band dispersion and results in striped patterns in the optical absorption spectra. 6. **Interlayer Distance Impact**: The interlayer distance has a minor effect on the band gap and intralayer excitons in suspended few-layer phosphorene, but it significantly affects the bulk limit, where a small change in interlayer distance can shift the band gap and exciton energy by 150 meV. The study highlights the potential of phosphorene for various applications, including optical polarizers and electronic devices, due to its unique many-electron effects and tunable properties.