On the generation of stable Kerr frequency combs in the Lugiato–Lefever model of periodic optical waveguides∗

HAKKAEV S. A., Stanislavova M., Stefanov A. G.

SIAM Journal on Applied Mathematics, cilt.79, sa.2, ss.477-505, 2019 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 79 Sayı: 2
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1137/18m1192767
  • Dergi Adı: SIAM Journal on Applied Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.477-505
  • Anahtar Kelimeler: Kerr frequency combs, Lugiato–Lefever, Periodic waveguides, Stability
  • Trakya Üniversitesi Adresli: Hayır

Özet

We consider the Lugiato–Lefever (LL) model of optical fibers. We construct a two parameter family of steady state solutions, i.e., Kerr frequency combs, for small pumping parameter h > 0 and the correspondingly (and necessarily) small detuning parameter, α > 0. These are O(1) waves, as they are constructed as a bifurcation from the standard dnoidal solutions of the cubic nonlinear Schrödinger equation. We identify the spectrally stable ones, and more precisely, we show that the spectrum of the linearized operator contains the eigenvalues 0,−2α, while the rest of it is a subset of {µ : <µ = −α}. This is in line with the expectations for effectively damped Hamiltonian systems, such as the LL model.