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dipole moment vector $\mathbf{p}$ and can be excited by an electric field in any direction, so the above equations are no longer valid.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.

  • $\begingroup$ 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


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.