Azimuthally controlled nonlinear optical response in germanium-vacancy color centers

We investigate theoretically the spatially dependent linear and nonlinear optical properties of a four-level germanium-vacancy center system in diamond, driven by coherent laser fields under electromagnetically induced transparency conditions. In our model, one of the strong coupling fields carries orbital angular momentum (OAM) and is treated as a composite vortex beam. By numerically solving the steady-state equations of the motion, we demonstrate that both linear and third-order nonlinear optical susceptibilities are highly sensitive to the OAM value of the coupling field. Our results reveal that increasing the OAM induces spectral splitting, enhances Kerr nonlinearity, and enables the emergence of structured absorption and dispersion profiles with characteristic 2l-fold azimuthal symmetry. Notably, we identify the formation of nonlinear islands—localized spatial regions where strong Kerr nonlinearity coincides with minimal absorption. These islands are tunable via the OAM number and detuning parameters, providing a powerful mechanism for spatial control of light–matter interactions. This work offers new insights into OAM-mediated coherence effects in solid-state quantum systems and points toward promising applications in nonlinear photonics, optical information processing, and spatially structured quantum devices.