## 1 Introduction  
In current studies in photonics, coupled structures formed from semiconductor quantum dots and metal particles at the nanoscale play an important role as they give, in many cases, enhanced optical properties in comparison to individual SQDs and MNPs [1]. The coupling of the excitons to plasmons is responsible for the emergence of interesting optical effects from the SQD-MNP structures, including altered excitonic Rabi oscillations [2; 3; 4], creation and control of optical bistability and multistability [5; 6; 7; 8; 9], population transfer to the exciton [10; 11; 12; 13; 14] or biexciton state with high accuracy [15; 16; 17], controlled slow light [18], creation of gain without inversion [19; 20; 21], strong enhancement of second harmonic generation [22], and strong modification of four-wave mixing, as well as self- or cross-Kerr nonlinearity [23; 24; 25; 26], control of resonance fluorescence [27; 28; 29; 30], and several others [31; 32; 33; 34; 35; 36; 37; 38]. These effects can find applications in the construction of efficient optical devices which can be implemented in the fields of nanophotonics and quantum technology. In some of these studies, the nonlinear optical effects in an SQD-MNP hybrid structure are examined under interaction with a pump field of high intensity and a tunable probe field of much lower intensity [7; 18; 23; 24; 26; 28; 34; 36]. A specific SQD nanostructure that exhibits optical properties of high importance is the asymmetric molecule consisting of a couple of SQDs [39; 40; 41; 42]. The band structures of the SQDs are considered to be different from each other, while the rate at which the tunneling effects take place is determined by the value of the applied voltage. More recently, the optical properties of a hybrid structure composed of an asymmetric double SQD molecule coupled to a MNP have been analyzed [32; 38]. In these studies, the construction of a diffraction grating, the special characteristics of which can be modified due to plasmonic mediated interaction [32], and the control and the energy absorption rate spectrum [38] were explored. Here, we analyze the response of a system of an MNP coupled to a doublet of SQDs interacting with a pump field of high intensity. Specifically, we combine the theoretical approaches presented in Refs. [36; 46] and calculate the optical susceptibility of the probe field, while a second field of much higher intensity is used for the pumping of the system. Then, we analyze the spectral profile of the real and the imaginary part of the susceptibility, for different values of the physical parameters of the structure. We find that, at the exact-resonance case with the pump field, the spectra present exact symmetry and are composed of a quartet of resonances. In the off-resonance case, the spectra exhibit six resonances and are not symmetric, for average values of the tunneling coefficient. For high interparticle distances, analytical expressions for the position of the resonances are provided based on the dressed-states analysis, which is valid in the strong intensity regime applied in the present paper. For low tunneling rates, the contribution of MNP outweighs the contribution of the coupled SQDs and it also introduces a non-negligible slope to the spectra of the total susceptibility. However, for higher values of tunneling coupling coefficient, the contribution of the double SQD molecule seems to play a more important role in the spectral profile of the total susceptibility, determining to a substantial extent the shape of its imaginary part. In every case, as the distance between the counterparts decreases, the resonances are transposed away from the center of the spectra. This study is structured as follows.