## 1 Introduction  
Light manipulation by semiconductor devices in the terahertz (THz) regime remains a challenge, despite its technological importance. In the visible and infrared regimes, surface plasmon polariton optics (\"plasmonics\") based on nanostructures led to breakthrough applications in biosensing and optoelectronics. Advances in nanotechnology have allowed for the fabrication of various types of nanostructures with novel physical properties, including quasi-one- and quasi-two-dimensional nanostructures [1; 2; 3; 4; 5; 6], radial superlattices [7; 8; 9], quantum rings [10], quantum dots [11; 12], and nanoshells [13; 14; 15; 16; 17; 18; 19]. Nanostructures are recognized as the promising future basis of nanoelectronics. Metallic nanoshells have attracted attention due to the tunability of their optical properties [14; 15; 16; 20; 21; 22; 23; 24; 25], [PERSON] et al. [20] and [PERSON] et al. [21] investigated optical properties of nanoshells with a core diameter ranging from 120 to 340 nm and metallic shell thickness from 14 to 48 nm. The resonant maxima of the extinction coefficient in Au/Au\({}_{2}\)S nanoshells were experimentally observed for wavelengths between 600 and 900 nm [20]. Theoretical analysis showed that it was possible to shift the optical resonance to wavelengths up to 10 um by changing the ratio between core and shell radii [21]. [PERSON] and [PERSON] [22; 23] developed a quantum-mechanical description of the interaction between light and plasmons in a metallic shell. This description took into account the resonant interaction of light with surface plasmon modes at the two surfaces of the metallic shell. It was shown that the resonant peaks were red-shifted in comparison with the peaks predicted by classical electrodynamics. [PERSON] et al. [24] studied nanoshells in a dielectric medium and with a dielectric core using time-dependent local density approximation. A comparison of the calculated absorption peak positions with Mie theory [26] confirmed the conclusions of [23]. Investigation of the optical properties of Au nanoshells with Cu\({}_{2}\)O, SiO\({}_{2}\), or iron oxide core [15] demonstrated that a change in the core dielectric constant significantly affected both plasmon energies and absorption efficiency. Surface phonon resonance in doped semiconductors was proposed for Raman and infrared spectroscopy, and biomedical and gas-sensing applications [27; 28; 29; 30]. [PERSON] [31] investigated the effect of the electron-phonon coupling on the optical properties for three types of nanospheres: (i) a nanosphere made from an intrinsic (undoped) polar semiconductor, (ii) a nanosphere made from a doped polar semiconductor, and (iii) a metallic nanosphere. In all three cases, the confinement introduced a significant correction to the absorption coefficients at relatively small sphere radii \(R\sim\) 1.5-5 nm. With increasing radius, the correction decreased, and for radii \(R>20\) nm it became very small. In the spherical multilayer structures investigated in [20; 21; 22; 23; 24; 31], a response to electromagnetic radiation was determined by treating electrons in the metallic shell as an incompressible fluid. A high concentration of electrons led to an enhanced response in the plasmon energy range \(\sim\) 1.5-2 eV. There has been recent interest [32; 33; 34; 35; 36] in nanophotonic devices for the THz range from 10 to 100 meV, which is of importance for applications. These frequencies correspond to the dynamics of ions in the crystal lattice. A large ion mass and strong binding to the crystal lattice sites lead to small ionic displacements, low dipole moments, and a weak interaction of lattice vibrations with light. In the present paper, we demonstrate that the interaction of phonons with electromagnetic radiation can be resonantly enhanced in a strongly coupled interface phonon-plasmon system. We consider two types of spherical polar nanostructures (see Figure 1a). The first structure has a doped core of InAs, surrounded by an undoped GaAs shell, and placed in hexane (d-InAs/u-GaAs/Hexane).