Looking for reference showing derivation of Drude equations used for FDTD index perturbation



Hi all,

I am looking for a good reference (textbook, paper, website, etc.) showing the derivation of the Drude model equations which are used for index perturbation in FDTD. Would anyone be willing to suggest one?


As a side note, I believe the delta_alpha in the “Theory behind the Drude expansion model” section of the site linked above should be proportional to lambda squared, not lambda cubed. Can anyone confirm this? Or if I am wrong, where does the extra factor of lambda come from? As a reference see equation (5) in Soref and Bennett’s original paper here:




Edited on 7/3 to fix broken link.


Dear @patrick.goley

We have used two papers for documenting this topic:

  1. Spectral dependence of the change in refractive index due to carrier injection in GaAs lasers, Henry, C. H.; Logan, R. A.; Bertness, K. A. Journal of Applied Physics, vol. 52, (1981), p. 4457-4461.

  2. Electrooptical Effects in Silicon, R. A. Soref and B. R. Bennett, SPIE Integr. Opt. Circuit Eng. 704, 32 (1987).

Second one is the one that you referred as well, and you can probably find more related topics in their references.

Based on second paper, you are right. This should be fixed in the next document release. Thank you very much for reporting this.



Thanks very much for your reply @bkhanaliloo, and for confirming the typo.

I’ve read those papers and many of the references, and was looking for more background of the theory. For others who may by interested, I did find a good resource. I’ll post the link below. I hope its helpful.


Thanks Patrick for sharing it with us.