Dynamics of localized and patterned structures in the Lugiato-Lefever equation determine the stability and shape of optical frequency combs

by Parra-Rivas, P., Gomila, D., Matías, M. A., Coen, S. and Gelens, L.
Abstract:
It has been recently uncovered that coherent structures in microresonators such as cavity solitons and patterns are intimately related to Kerr frequency combs. In this work, we present a general analysis of the regions of existence and stability of cavity solitons and patterns in the Lugiato-Lefever equation, a mean-field model that finds applications in many different nonlinear optical cavities. We demonstrate that the rich dynamics and coexistence of multiple solutions in the Lugiato-Lefever equation are of key importance to understanding frequency comb generation. A detailed map of how and where to target stable Kerr frequency combs in the parameter space defined by the frequency detuning and the pump power is provided. Moreover, the work presented also includes the organization of various dynamical regimes in terms of bifurcation points of higher codimension in regions of parameter space that were previously unexplored in the Lugiato-Lefever equation. We discuss different dynamical instabilities such as oscillations and chaotic regimes.
Reference:
Dynamics of localized and patterned structures in the Lugiato-Lefever equation determine the stability and shape of optical frequency combs Parra-Rivas, P., Gomila, D., Matías, M. A., Coen, S. and Gelens, L., Physical Review A, volume 89, pp. 043813, 2014.
Bibtex Entry:
@article{parra-rivas_dynamics_2014,
	title = {Dynamics of localized and patterned structures in the {Lugiato}-{Lefever} equation determine the stability and shape of optical frequency combs},
	volume = {89},
	url = {http://link.aps.org/doi/10.1103/PhysRevA.89.043813},
	doi = {10.1103/PhysRevA.89.043813},
	abstract = {It has been recently uncovered that coherent structures in microresonators such as cavity solitons and patterns are intimately related to Kerr frequency combs. In this work, we present a general analysis of the regions of existence and stability of cavity solitons and patterns in the Lugiato-Lefever equation, a mean-field model that finds applications in many different nonlinear optical cavities. We demonstrate that the rich dynamics and coexistence of multiple solutions in the Lugiato-Lefever equation are of key importance to understanding frequency comb generation. A detailed map of how and where to target stable Kerr frequency combs in the parameter space defined by the frequency detuning and the pump power is provided. Moreover, the work presented also includes the organization of various dynamical regimes in terms of bifurcation points of higher codimension in regions of parameter space that were previously unexplored in the Lugiato-Lefever equation. We discuss different dynamical instabilities such as oscillations and chaotic regimes.},
	number = {4},
	urldate = {2016-11-07},
	journal = {Physical Review A},
	author = {Parra-Rivas, P. and Gomila, D. and Matías, M. A. and Coen, S. and Gelens, L.},
	month = apr,
	year = {2014},
	pages = {043813},
	file = {APS Snapshot:/home/jan/.zotero/zotero/djuw86a6.default/zotero/storage/IWZIBWN3/PhysRevA.89.html:text/html}
}