arXiv:0805.2257v2 [cond-mat.mtrl-sci] 21 May 2008 Optically induced relaxation modes in a nanoparticle of a uniformly charged electret S.I. Bastrukov 1 ,2 , I.V. Molodtsova 2 , Pik-Yin Lai 3 1 National Tsing Hua University, Hsinchu, Taiwan 2 Joint Institute for Nuclear Research, Dubna, Russia 3 National Central University, Chungli, Taiwan Abstract The electromagnetic response of a nanoparticle of an ion-doped polymeric elastic insulator, commonly called as an electret, is considered in the continuum model of a uniformly charged elastic sphere. The spectral formulae for the frequency of optically induced spheroidal and torsional shear oscillations driven by bulk force of dielectric stresses are obtained in analytic form. Particular attention is given to relaxation na- ture of the electrostriction modes unique to ultrafine particles of electrets capable of accumulating likely-charged inclusions uniformly dispersed over the spherical volume of an elastic matrix. PACS: 72.15.Nj, 74.25.Nf, 77.65.-j Key words: nanoparticle, ion-doped polymeric electret, biolabels 1 Introduction The phenomenological continuum-mechanical models of vibrating liquid drop and solid globe provide proper account of gross features of resonance-like excitations in electromagnetic re- sponse of ultra fine particles. The spectra of these excitations are currently measured by methods of Raman scattering and inelastically scattered neutrons. The physical idea under- lying these models is to identify the frequency of AC field incident on a nanoparticle with frequency of material oscillations in the particle regarded as a spherical piece of either liq- uid or solid continuous medium. A canonical example is fluid-mechanically computed Mie’s spectral formula for the frequency of surface plasmons in nanoparticles of highly conducting metals like silver and gold [1-5]. Another example is the solid-mechanically calculated fre- quency spectra of optically induced elastic oscillations, acoustic phonons, in a nanoparticle of a dielectric solid [6-9]. In this work we consider a model of resonant response of a nanoparticle of charged elec- tret (insulating elastic matrix doped by likely-charged ions homogeneously distributed over 1 Corresponding author, e-mail: bast@jinr.ru