▎ 摘　　要

Theoretical demonstration of large enhancement of surface plasmon-assisted energy transfer interactions near graphenecoated, gain-assisted nanomatryoshka (GCGAN) is presented. Closed form expressions have been derived for energy transfer rate enhancement factor (eta), donor decay rate (gamma(D)), FRET rate (gamma(FRET)), and FRET efficiency (gamma). It is shown that the loss compensation through precisely calculated critical gain incorporation leads to enormous enhancement of energy transfer rate and substantial reduction of spectral width. Present investigations indicate that the loss compensation leads to an enhancement of eta similar to 10(8), gamma(D)similar to 10(2)-10(3), gamma(FRET)similar to 108, and the reduction in FWHM similar to 10(5). In order to widen the choice of plasmonic material, the investigations are focused on ZrN, a refractory transition metal, and graphene-based nanomatryoshka, namely, -SiO2/ZrN/graphene (SZG). The choice of nanomatryoshka is inspired from its wider spectral tunability, in ViS-NIR region, and resulting usefulness in biomedical and sensing. The sensing characteristics of SZG-based FRET sensor are estimated. Simple but insightful fitting expressions for designing efficient plasmonic systems for molecular energy exchange, graphene-assisted sensing, etc., and these can be employed for designing efficient plasmonic systems. The article can motivate experimentalists to synthesize refractory nitride-based nanomatryoshka systems for energy transfer and sensing.