tweak to materials docs

doc/docs/Materials.md

@@ -98,7 +98,7 @@ Conductivity and Complex ε
 
 Often, you only care about the absorption loss in a narrow bandwidth, where you just want to set the imaginary part of $\varepsilon$ (or $\mu$) to some known experimental value, in the same way that you often just care about setting a dispersionless real $\varepsilon$ that is the correct value in your bandwidth of interest.
 
-One approach to this problem would be allowing you to specify a constant, frequency-independent, imaginary part of $\varepsilon$, but this has the disadvantage of requiring the simulation to employ complex fields which double the memory and time requirements, and also tends to be numerically unstable. Instead, the approach in Meep is for you to set the conductivity $\sigma_D$ (or $\sigma_B$ for an imaginary part of $\mu$), chosen so that $\mathrm{Im}\, \varepsilon = \varepsilon_\infty \sigma_D / \omega$ is the correct value at your frequency $\omega$ of interest. Note that, in Meep, you specify $f = \omega/2\pi$ instead of $\omega$ for the frequency, however, so you need to include the factor of $2\pi$ when computing the corresponding imaginary part of $\varepsilon$. Conductivities can be implemented with purely real fields, so they are not nearly as expensive as implementing a frequency-independent complex $\varepsilon$ or $\mu$.
+One might hope that Meep would allow you to specify a constant, frequency-independent, imaginary part of $\varepsilon$, but this is inherently unstable: $\omega \mathrm{Im}\, \varepsilon < 0$ corresponds to gain (exponential growth), but every time-domain simulation will include both positive and negative frequencies ω so there is no way to choose nonzero frequency-independent $\mathrm{Im}\, \varepsilon$ that does not yield gain at some ω.  Instead, a simple approach in Meep is for you to set the conductivity $\sigma_D$ (or $\sigma_B$ for an imaginary part of $\mu$), chosen so that $\mathrm{Im}\, \varepsilon = \varepsilon_\infty \sigma_D / \omega$ is the correct value at your frequency $\omega$ of interest. Note that, in Meep, you specify $f = \omega/2\pi$ instead of $\omega$ for the frequency, however, so you need to include the factor of $2\pi$ when computing the corresponding imaginary part of $\varepsilon$. Conductivities are absorptive at all frequencies (and are more computationally efficient than Lorentzian models).
 
 For example, suppose you want to simulate a medium with $\varepsilon = 3.4 + 0.101i$ at a frequency 0.42 (in your Meep units), and you only care about the material in a narrow bandwidth around this frequency (i.e. you don't need to simulate the full experimental frequency-dependent permittivity). Then, in Meep, you could use `meep.Medium(epsilon=3.4, D_conductivity=2*math.pi*0.42*0.101/3.4)` in Python or `(make medium (epsilon 3.4) (D-conductivity (* 2 pi 0.42 0.101 (/ 3.4))))` in Scheme; i.e. $\varepsilon_\infty = \mathrm{Re}[\varepsilon] = 3.4$ and $\sigma_D = \omega \, \mathrm{Im}[\varepsilon] / \varepsilon_\infty = (2\pi \, 0.42) \, 0.101 / 3.4$.