Modified nonlinear optical effects in exciton–plasmon hybrid systems have been extensively studied, demonstrating that their optical properties can be tuned by controlling key system parameters. Notably, the pump–probe response has already been investigated in a hybrid structure consisting of a two-level semiconductor quantum dot (SQD) and a spherical gold metal nanoparticle (MNP) under strong pump and weak probe fields [1]. The present study extends this work by examining first-order absorption and gain while modifying the orientation and eccentricity of the MNP [2-4]. Using the Liouville equation under the rotating wave and dipole approximations, we perform a first-order expansion of the density matrix elements with respect to the weak probe field and numerically solve the resulting equations in the steady state. We compute the first-order optical susceptibilities of both the SQD and the MNP, focusing on how the absorption/gain spectral profile is influenced by the geometrical parameters of the nanostructure. We show that, for an exactly resonant pump field, the SQD shows a higher absorption peak in the Dark metastate than in the Bright one. Also, in the Dark region, both components display only absorption across a wider spectral range. These results highlight the tunability of the optical responses, offering new perspectives for sensing, energy harvesting and quantum technologies. A dressed-state framework supports our analysis of the pump–probe response.

[1] S. G. Kosionis and E. Paspalakis, J. Appl. Phys. 124, 223104 (2018).

[2] A. Hatef, S. M. Sadeghi, and M. R. Singh, Nanotechnology 23, 205203 (2012).

[3] M. R. Singh, D. G. Schindel, and A. Hatef, Appl. Phys. Lett. 99,181106 (2011).

[4] A. M. Abd-Elsamie, S. Abd-Elnabi, and K. I. Osman, Plasmonics 23, 02101–02107 (2023).