Why is Sellmeier's equation an even function of $lambda$?

Question

According to Sellmeier's formula, the dispersion formula of a transparent material can be written as
$$n^2(lambda) = 1 +sum_ifrac{B_i lambda^2}{lambda^2 - C_i},$$ where $B_i$ and $C_i$ are empirically-determined  material constants. When written this way the formula assumes explicitly that the function $n^2(lambda)$ is even. What justifies this assumption?

Buzz · Answer

What would a negative value of the wavelength mean?  Well, frequently we define
$$lambda=frac{2pi}{left|vec{k}right|},$$
in terms of the wave vector $vec{k}$, which would make $lambda$ nonnegative by defintion.  However, if we restrict attention to waves propagating along a single axis, say $vec{k}=khat{z}$, we can allow for either positive or negative values of $lambda$,
according to
$$lambda=frac{2pi}{k}.$$
This means that a negative value of $lambda$ just corresponds to a wave propagating in the opposite direction relative to a positive $lambda$. In an isotropic material, the index of refraction does not depend on the direction.*  So the formula for $n(lambda)$ is necessarily going to give an even function, so that the speed is the same in the $z$-direction or the $-z$-direction.
*It is, of course, possible to have asymmetric media, but the Sellmeier formula does not apply to those cases.

Why is Sellmeier's equation an even function of $lambda$?

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