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Modeling of optical microresonator frequency combs

Supervisor: Tobias Hansson

Level: Adaptable to Bachelor or Master level

Prerequisites: Electromagnetic Field Theory


Optical frequency combs are a novel type of laser sources whose frequency spectrum consists of a large number of highly resolved spectral lines that are equidistantly spaced. Frequency combs have revolutionized precision frequency metrology as recognized by the 2005 Nobel Prize, and are now finding multiple applications in fields such as spectroscopy, optical clocks and telecommunications [1].


Frequency combs can be generated through intensity dependent nonlinear processes when a continuous wave laser pumps a microresonator filled with a nonlinear Kerr medium. Of particular interest is the generation of stable mode-locked frequency combs states that in the temporal domain correspond to dissipative cavity soliton pulses that propagate without changing their form.


The dynamics of optical frequency combs has been studied mostly using a mean-field model known as the Lugiato-Lefever equation [2]. However, new types of solutions and instabilities have been found to appear beyond its limits of applicability [3]. In this diploma project we aim to investigate comb formation using a more general model based on a cavity map that couple the fields between each round-trip of the resonator. The work will involve investigating the nonlinear dynamics of comb generation, including Turing pattern and cavity soliton formation, using numerical simulations based on the split-step Fourier method.


The student will learn the fundamentals of nonlinear wave propagation and optical frequency combs, and gain proficiency in studying their dynamics by using analytical and numerical methods.


[1] T. J. Kippenberg, et al., Science 332, 555–559 (2011).

[2] S. Coen et al., Opt. Lett. 38, 37–39 (2013).

[3] T. Hansson and S. Wabnitz, J. Opt. Soc. Am. B 32, 1259-1266 (2015).

Responsible for this page: Fei Wang

Last updated: 01/10/19