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Report

Teaser, summary, work performed and final results

Periodic Reporting for period 1 - QuadraComb (Quadratic dispersive resonators for optical frequency comb generation)

Teaser

Summary

\"Optical frequency combs are made of thousands of equally spaced spectral lines, each an ultra-stable laser in its own right. They act as â€œspectral rulersâ€ 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

Workpackage 1:
We have theoretically uncovered novel localised structures in quadratic resonators. We found LDSs similar to that of Kerr resonators as well as a new kind, formed through the locking of domains of different phases. In both cases, we are investigating, both analytically and numerically, the system\'s bifurcations to better understand the physics at play.
We also worked intensely on the theory of second harmonic generation in IIIV semiconductors waveguides and ring resonators. Preliminary results of work package 2b (see below) highlighted the need for detailed modelling. In these semiconductors, the physics of nonlinear coupling though a quadratic response was not fully understood.
We performed full vectorial modelling of nonlinear coupling in subwavelength IIIV-on-insulator waveguides and uncovered new wave mixing schemes involving the longitudinal component of the field. Furthermore, we applied our results to ring resonators and developed a novel mean field model that accounts for the fact that the nonlinearity is not constant over one roundtrip.

Workpackage 2a:
We have built a ring cavity made of our special quadratic fiber. Preliminary results in a single pass configuration (parametric down conversion) predict strong nonlinear gain. We built a novel source of nanosecond pulses to reach the threshold for frequency comb formation.

Workpackage 2b:
As in workpackage 2a, we started working on frequency conversion in a single passe configurations (second harmonic generation). We found that longitudinal field components play a surprisingly important role in the process. We experimentally and theoretically characterised second harmonic generation through the mixing of transverse and longitudinal field components for the fist time.
We have decided to develop a new experimental platform as efficient conversion will be hampered by multi photon absorption in our current one. We are collaborating with Rennes university as well as the laboratoire de photonique et de nanostructure in Paris to fabricate gallium phosphide nanowaveguides.

Final results

All our advances listed above go beyond the state of the art. Next we plan to focus on nonlinear coupling in resonators, specifically frequency comb formation which is the main goal of the project.
We have already identified suitable configuration in workpackage 1. Both our platforms (fiber and integrated) are on pace to generate frequency combs by the end of the project

As we progress on experimental platforms, we realise that the higher order (cubic) nonlinearity will most often not be negligible. Hence we are planning on investigating both experimentally and theoretically, competing nonlinearities in resonators.