Quadratic dispersive resonators for optical frequency comb generation

Project Information

QuadraComb

Grant agreement ID: 757800

DOI

10.3030/757800

Project closed

EC signature date 16 October 2017

Start date 1 January 2018

End date 31 December 2022

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 579 213,00

EU contribution

€ 1 579 213,00

Coordinated by

UNIVERSITE LIBRE DE BRUXELLES
Belgium

Periodic Reporting for period 4 - QuadraComb (Quadratic dispersive resonators for optical frequency comb generation)

Reporting period: 2022-07-01 to 2022-12-31

Summary of the context and overall objectives of the project

Optical frequency combs are made of thousands of equally spaced spectral lines, each an ultra-stable laser in its own right. They act as “spectral rulers” against which unknown optical frequencies can be measured, and they have had a revolutionary impact on numerous fields ranging from the detection of extra-solar planets to precision metrology, winning its inventors a Nobel prize in 2005. Traditionally, frequency combs have been generated by ultrashort pulsed lasers, but in 2007 an important observation changed the research landscape: a continuous-wave laser coupled into a microscopic resonator was shown to spontaneously transform into thousands of comb lines via third-order nonlinear optical effects. I believe that yet another revolution lies at the horizon. Specifically, recent experiments have alluded to the possibility of realizing optical frequency combs purely through second order (quadratic) nonlinear effects. The intrinsic features of the second order nonlinearity hold promise to deliver access to new regions of the electro-magnetic spectrum beyond all conventional frequency comb technologies. But unfortunately, experimental investigations are scarce and the physics that underlie frequency comb formation in quadratic resonators is poorly understood. The goal of the QuadraComb project is to pursue a complete characterization of frequency comb generation in dispersive quadratically nonlinear resonators. I plan to (i) develop theoretical models to describe quadratic frequency combs, and (ii) develop novel platforms for the experimental realization of quadratic frequency combs.

The work is split in two main work packages, a theoretical one and an experimental one.
Frequency combs most often correspond in the time domain to stable pulse trains. One way to generate them is to excite "localised dissipative structures (LDSs)" in optical resonators. LDSs are well known in nonlinear science and appear in systems where gain balances loss and the nonlinearity balances a diffusion like process. They have been studied in many fields such as chemistry, by the Nobel Prize winner Ilya Prygogine among many others, and hydrodynamics.
In optics, LDSs correspond to short pulses propagating unperturbed in a cavity. A "copy" of the pulse exits every roundtrip, forming a stable pulse tain at the output of the resonator.
They have been first evidenced in long fibre resonators and are now commonly observed in microresonators, forming so called micro combs.
Our work aims at uncovering similar dynamics in quadratic resonators, where micro combs would naturally form optical rulers, as opposed to cubic microcombs that requite complicated stabilisations steps.

The first workpackage aims at theoretically uncovering nonlinear stationary solutions of quadratic nonlinear resonators. While the dynamics of cubic ("Kerr") resonators is very well known, the same cannot be said of quadratic resonators.
The system can be described by so called "mean field equations" that describes the dynamics in the resonator round trip after roundtrip. By looking, both analytically and numerically, for stable solutions of these equations, we hope to uncover previoulsy unknown localised dissipative structures.
The second workpackage is dedicated to the development of novel experimental platforms to observe LDSs.
(a) We will use a special kind of optical fibres, fabricated at the university of Southampton, that display a quadratic nonlinearity. We plan to build a fiber loop such that the loss can be balanced by parametric gain. The quadratic nonlinearity on the other hand, will be balanced by the dispersion of the fiber.
(b) In collaboration with Ghent university and others, we will fabricate microring resonators with suitable semiconductors, specifically IIIV alloys that display a strong quadratic nonlinearity.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

We have investigated, theoretically and experimentally the nonlinear dynamics of quadratic resonators.
Theoretically, we uncovered many novel configurations for frequency comb generation that were prevoioulsy unknown.
To confirm these experimentally, we built two novel experimental platforms for frequency comb generation, namely acivte fiber resonators and gallium phosphide-on-insulator.
The first was achived earlier in the project and has been used for several important advances in the field of frequency comb generation and soliton formation

• N. Englebert, C. Mas Arabí, P. Parra-Rivas, S.-P. Gorza, and F. Leo, Temporal Solitons in a Coherently Driven Active Resonator, Nature Photonics 15, 536 (2021).
• N. Englebert, F. De Lucia, P. Parra-Rivas, C. M. Arabí, P.-J. Sazio, S.-P. Gorza, and F. Leo, Parametrically Driven Kerr Cavity Solitons, Nat. Photon. 15, 857 (2021).
• N. Englebert, N. Goldman, M. Erkintalo, N. Mostaan, S.-P. Gorza, F. Leo, and J. Fatome, Bloch Oscillations of Driven Dissipative Solitons in a Synthetic Dimension, to appear in Nat. Phys (2023)

The second was more challenging but we recently achieved the fabrication of high quality waveguides and resonators which will be suitable for frequency comb generation.

• M. Billet et al., Gallium Phosphide-on-Insulator Integrated Photonic Structures Fabricated Using Micro-Transfer Printing, Opt. Mater. Express 12, 3731 (2022).

We are currently actively working on both platforms to further advance the field of optical frequency combs.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

The team has published 17 papers (+ 2 accepted papers). All these results go beyond the state of the art.
The active fiber platform in particular is a significant achievement in the field of nonlinear photonics.
The results from the project have been published in high impact journals (Nature Physics and twice in Nature Photonics) and attracted significant interest from the photonics community, leading to strong visibility and external collaborations.

Schematic illustration of frequency comb generation in a quadratic resonator.