Would you mind providing more details? The following papers may be helpful.

https://doi.org/10.1016/j.infrared.2018.07.015

https://doi.org/10.1364/AO.32.002606

Jingrun Zhu Sir i am having dipole LSPR peak for core material in UV region (at about 200 nm) and another peak for shell/coating material at about 400 nm, all for a single core-shell nanoparticle. Hope this is more clarified.

Thankyou for your suggestion

LSPRs depend on the material (1), the dimensions (2) and the shape (3).

1) If you have nanospheres with the same diameter but some made of silver and others made of gold, the former would exhibit the LSPR peak at higher energy (lower wavelength).

2) If you have nanospheres made of the same material but some with diameter d1 and others with diameter d2, with d2>d1, the LSPR peak of d1 nanospheres would appear at higher energy (lower wavelength).

3) If you have a collection of identical aligned nanorods made of the same material, you would have two LSPR peaks depending on the light polarization: one along the rod axis and another along the perpendicular direction; the latter would appear at higher energy (lower wavelength).

So, in the case of your core-shell nanostructures, we need additional information to give an answer. If those nanostructures have spherical shape and the core material and the shell material are optically very different, one could assume that one LSPR peak is due to the shell and another to the core. But if those core-shell structures have a rod-like shape and the materials are optically similar, the peaks can be attributted to the resonances along the axis and along the perpendicular-to-axis directions.

Jose-Miguel Garcia-Martin Sir thankyou for the justified answer and the question was about core-shell nanosphere with core showing optical response in UV region and coating (silver) material having optical response in visible region.