From the Lugiato-Lefever equation to microresonator-based soliton Kerr frequency combs

Area of Science:

• Nonlinear optics
• Dissipative systems
• Photonics

Background:

• The Lugiato-Lefever equation (LLE) was developed in 1987 to model dissipative structures and pattern formation in nonlinear optics.
• It describes driven, detuned, and damped nonlinear Schrödinger equations, leading to spatial and temporal solitons.
• Recent experiments with continuous wave driven optical microresonators have realized the conditions described by the LLE.

Purpose of the Study:

• To highlight the Lugiato-Lefever equation's role in understanding dissipative structures.
• To connect the LLE to the emergence and properties of temporal dissipative Kerr solitons (DKS).
• To underscore the significance of DKS in microresonator-based soliton Kerr frequency combs.

Main Methods:

• Theoretical modeling using the Lugiato-Lefever equation.
• Experimental realization in continuous wave driven optical microresonators.
• Observation and characterization of temporal dissipative Kerr solitons (DKS).

Main Results:

• The LLE accurately describes Kerr frequency combs and their soliton states.
• DKS spontaneously form in crystalline microresonators, representing a preferred operational state.
• DKS enable coherent, broadband optical frequency combs with extendable bandwidth.

Conclusions:

• The LLE provides an exact description for DKS in optical microresonators.
• DKS are crucial for developing miniaturized, on-chip soliton micro-comb technology.
• Pattern formation in driven, dissipative nonlinear optical systems is central to soliton micro-comb technology.