EPJ D Special issue: Theory and Applications of the Lugiato-Lefever Equation

The Lugiato-Lefever Equation (LLE) was first introduced in 1987 by Luigi Lugiato and René Lefever as a paradigm for the understanding of complex phenomena in dissipative and nonlinear optical cavities. About thirty years later, this equation has become an essential model to investigate the dynamical properties of laser fields confined in nonlinear optical resonators. The LLE has permitted the prediction and analysis of various intra-cavity structures such as solitons (bright and dark, spatial and temporal), Turing patterns (rolls, hexagons), and even spatiotemporal chaos. This equation has also been found to be the best framework for the theoretical investigation of Kerr optical frequency comb generation using whispering gallery mode cavities or integrated ring resonators. These Kerr combs are known to be useful for several applications in aerospace engineering, coherent optical fiber communications, and time-frequency metrology. A quantum version of the LLE also permits to explore phenomena such as entanglement and two-mode squeezing.

This topical issue, which celebrates the 30th anniversary of LLE, will feature an introductory article co-authored by Luigi Lugiato, and is intended to provide an overview of current research in relation with the theory and applications of the LLE.

We invite the community to submit contributions on topics including, but not limited to:

  • Kerr optical frequency combs in whispering gallery mode resonators
  • Spatial dissipative structures in optical cavities
  • Temporal dissipative structures in fiber ring resonators
  • Quantum effects in Kerr cavities
  • Mathematical analysis of the LLE
  • Applications of systems modeled by the LLE
  • Extensions of the LLE to include new effects and materials (Raman, polarization, noise, photonic crystals, non-local coupling, delayed feedback, etc.)

We invite the contributors to submit their manuscripts before the deadline directly to the EPJD Editorial Office at https://articlestatus.edpsciences.org/is/epjd. If you are a first-time author with EPJD, you will first be invited to register on the same web site. Submissions should be clearly identified as intended for the Topical Issue "Theory and applications of the Lugiato-Lefever Equation". The style for submission can be found here.

Guest Editors of the special issue:

  • Yanne K. Chembo, FEMTO-ST Institute, CNRS, France
  • Damia Gomila, IFISC, Spain
  • Mustapha Tlidi, Univ. Libre de Bruxelles, Belgium
  • Curtis R. Menyuk, Univ. Maryland Baltimore County, USA

Open calls for papers