Theoretical demonstration of large enhancement of surface plasmon-assisted energy transfer interactions near graphene-coated, 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 \(\eta\) ~ 10⁸, \({\gamma }_{D}\) ~ 10²–10³, \({\gamma }_{FRET}\) ~ 10⁸, and the reduction in FWHM ~ 10⁵. 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.

提出了在石墨烯涂覆的增益辅助纳米矩阵 (GCGAN) 附近大幅增强表面等离子体辅助能量转移相互作用的理论证明。已推导出能量转移率增强因子（\(\eta\)）、供体衰减率（\({\gamma }_{D}\)）、FRET 率（\({\gamma }_{ FRET}\)）和 FRET 效率（\(\gamma\)）。结果表明，通过精确计算的临界增益并入进行的损耗补偿导致能量传输速率的极大提高和谱宽的显着减小。目前的调查表明，损失补偿导致\(\eta\)  ~ 10 ⁸的增强，\({\gamma }_{D}\)  ~ 10 ² –10 ³，\({\gamma }_{FRET}\)  ~ 10 ⁸，以及 FWHM ~ 10 ⁵的减少。为了拓宽等离子体材料的选择范围，研究集中在 ZrN（一种难熔过渡金属）和基于石墨烯的 nanomatryoshka，即 SiO ₂/ZrN/石墨烯（SZG）。nanomatryoshka 的选择受到其在 ViS-NIR 区域更广泛的光谱可调性以及在生物医学和传感方面的有用性的启发。估计了基于 SZG 的 FRET 传感器的传感特性。简单但有见地的拟合表达式，用于设计用于分子能量交换、石墨烯辅助传感等的高效等离子体系统，这些可用于设计高效等离子体系统。这篇文章可以激励实验者合成用于能量转移和传感的耐火氮化物基纳米套娃系统。