On 12/19/2017 02:21 AM, Hirokazu Kubota wrote:
Sorry if this question was already asked.
I'm confused on the relationship between n_2 and chi(3).
The relation given in "Units and Nonlinearity" page is
n_2 = 3 chi(3)/4 n^2,
https://meep.readthedocs.io/en/latest/Units_and_Nonlinearity/
while we usually write chi = chi(1)+3 chi(3)/4 |E|^2 and n = sqrt(1+chi)
so the relation is
n_2 = 3 chi(3) / 8 n.
Why this difference occurs
The definition of n_2 depends on whether it relates to |E|^2 or the
time-averaged intensity of the optical field I = 2n|E|^2.
Meep uses the latter convention which give rises to the expression shown
in the documentation. The derivation for this expression is shown in
R.W. Boyd's Nonlinear Optics book (3rd edition) as equation 4.1.19.
The former convention yields n_2 = 3 chi(3) / 4 n. This is equation
4.1.11 in the book.
We will update the documentation to make this point clearer.
_______________________________________________
meep-discuss mailing list
meep-discuss@ab-initio.mit.edu
http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/meep-discuss
