I'm having some conceptual trouble understanding the extinction efficiency, usually denoted as $Q_{\rm ext}$, in Mie theory. I know that $Q_{\rm ext} = Q_{\rm sca} + Q_{\rm abs}$ where $Q_{\rm sca}$ and $Q_{\rm abs}$ are scattering and absorption efficiencies respectively. I'm confused why $Q_{\rm ext}$ should approach $2$ as the particle size increases. Doesn't that mean that the extinction cross section approaches $2$x the geometric cross section? For large particles (orders of magnitude larger than the wavelength), shouldn't the extinction cross section simply be the geometric cross section? Is there a transition to geometric optics not described by Mie theory? Or am I misunderstanding something about the extinction efficiency and cross section?
1 Answer
You're definitely not alone in this. What you're referring to is often called the "extinction paradox" (https://en.wikipedia.org/wiki/Extinction_paradox). It is actually a non-trivial conceptual problem, even if the analytical solution is rigorous and uncontroversial.
I first encountered this in Bohren & Huffman (p. 107), where the authors attribute this to diffraction around the edges of large particles. The general idea is that the particle itself extinguishes light with a cross section of $\pi a^2$, and its shadow diffracts the rest with an identical cross section of $\pi a^2$, thus leading to a total efficiency of 2. This type of explanation, which is similar to other proposed solutions, has been challenged by a more complex approach (M. J. Berg et al., JQSRT 112 (2011) 1170–1181, http://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1109&context=usarmyresearch). It is definitely a problem worth checking out.
