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arXiv 1004.0135physics.optics
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表面等离子体激元自发发射和受激发射的量子理论

Quantum theory of spontaneous and stimulated emission of surface plasmons

Alexandre Archambault, François Marquier, Christophe Arnold, Jean-Jacques Greffet

摘要:

我们介绍了一个量子化方案,可以应用于表面波沿平面界面传播。一个重要的结果是色散无损耗介质的表面波的能量的推导,而不调用任何特定的模型的介电常数。在库仑规范中,我们使用场的模态表示。每个模式可以与量子谐振子相关联。我们应用该方法从量子力学的角度导出了二能级系统表面等离子体的自发发射率。结果是在非常好的协议与格林张量方法在无损耗的情况下。格林的方法也允许考虑损失,因此表面等离子体激元的量子方法的局限性被清楚地定义。最后,讨论了受激发射与自发发射的问题。由于在色散关系的渐近线附近态密度增加,定量地表明在这个频率区域受激发射几率太小而不能获得增益。

英文摘要:

We introduce a quantization scheme that can be applied to surface waves propagating along a plane interface. An important result is the derivation of the energy of the surface wave for dispersive non-lossy media without invoking any specific model for the dielectric constant. Working in Coulomb's gauge, we use a modal representation of the fields. Each mode can be associated with a quantum harmonic oscillator. We have applied the formalism to derive quantum-mechanically the spontaneous emission rate of surface plasmon by a two-level system. The result is in very good agreement with Green's tensor approach in the non-lossy case. Green's approach allows also to account for losses, so that the limitations of a quantum approach of surface plasmons are clearly defined. Finally, the issue of stimulated versus spontaneous emission has been addressed. Because of the increasing density of states near the asymptote of the dispersion relation, it is quantitatively shown that the stimulated emission probability is too small to obtain gain in this frequency region.

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