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Let us consider a quantum emitter with a transitional dipole moment $\mathbf{p}$ and transitional frequency $\omega_0$ which is placed in an inhomogeneous environment. Its spontaneous decay rate is enhanced by the Purcell effect and can be described mathematically as [Principle of Nano-Optics, L. Novotny and B. Hecht, page 247]: \begin{equation} \gamma = \frac{\pi \omega_0}{3\hbar\epsilon_0}|\mathbf{p}|^2\rho_{\text{p}}(\mathbf{r}_0,\omega_0) \end{equation} \begin{equation} \rho_{\text{p}}(\mathbf{r}_0,\omega_0)=\frac{6\omega_0}{\pi c^2 |\mathbf{p}|^2}\left[ \mathbf{p} \cdot \text{Im} \left[\overleftrightarrow{\mathbf{G}}(\mathbf{r}_0,\mathbf{r}_0;\omega_0) \right] \cdot\mathbf{p} \right] \end{equation} How does this apply to a semi-conductor quantum dot (QD)? If I understand correctly, a (spherical) QD does not have a well-defined transitional dipole moment vector $\mathbf{p}$ and can be excited by an electric field in any direction, so the above equations are no longer valid. Thank you for the answers.

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  • $\begingroup$ Please define your notation. For example, what the heck is $\overleftrightarrow{\mathbf{G}}$? $\endgroup$
    – DanielSank
    Commented Sep 7, 2017 at 20:49
  • $\begingroup$ Thank you. It is the dyadic green's function of the electromagnetic field of the system. Please see link $\endgroup$
    – ErwinNK
    Commented Sep 11, 2017 at 17:09

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