Reply to "Comment on 'Modal expansion approach to optical-frequency-comb generation with monolithic whispering-gallery-mode resonators' "

In a Comment [Deych, Phys. Rev. A 84, 017801 (2011)] on our recent article [Chembo and Yu, Phys. Rev. A 82, 033801 (2010)] on Kerr comb generation in monolithic whispering-gallery-mode (WGM) resonators, the author claims that even though our main results "remain intact," the framework of our analysis contains some mathematical errors. In this Reply, we demonstrate that the author's criticisms and his alternative theory are incorrect, and that all the disagreeing claims come from the author's misunderstanding of the physical system under investigation. In particular, the main conceptual error in the Comment is the confusion between evanescent and radiative coupling mechanisms for WGM resonators (in terms of Q factor, this is in our case a confusion between similar to 10(9) and similar to 10(2000), respectively). This essential misconception leads for example the author to introduce a nonphysical similar to 10(2000) multiplicative correction factor for the laser pump power. We show in this Reply that our WGM resonators are radiatively closed (because of the quasi-infinite radiative Q factor), so that the Mie scattering formalism proposed by Deych, which relies on radiative coupling, can only lead to erroneous results. We also show that the modal expansion approach in our original paper is appropriate, and all our approximations are physically well justified. We therefore stand by our modeling results, which are moreover in excellent agreement with the experiments reported in [Chembo, Strekalov, and Yu, Phys. Rev. Lett. 104, 103902 (2010)].