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T. Hansson

Publications and source records attributed to T. Hansson.

16 recordsLinked to original sources
arXiv2022

Modeling of dual frequency combs and bistable solitons in third-harmonic generation

Phase-matching of the third-harmonic generation process can be used to extend the emission of radiation from Kerr microresonators into new spectral regions far from the pump wavelength. Here, we present a theoretical mean-field model for optical frequency combs in a dissipative and nonlinear $\chi^{(3)}$-based cavity system with parametric coupling between fundamental and third-harmonic waves. We investigate temporally dispersive dual-comb generation of phase-matched combs with broad bandwidth, and report conditions for accessing a multistable regime that simultaneously supports two types of coupled bright cavity solitons. These bistable cavity solitons coexist for the same pump power and frequency detuning, while featuring dissimilar amplitudes of their individual field components. Third-harmonic generation frequency combs can permit telecom pump laser sources to simultaneously directly access both the near-infrared and the visible regions, which may be advantageous for the development of optical clocks and sensing applications.

physics.optics↗
arXiv2021

Efficient Kerr soliton comb generation in micro-resonator with interferometric back-coupling

Nonlinear Kerr micro-resonators have enabled fundamental breakthroughs in the understanding of dissipative solitons, as well as in their application to optical frequency comb generation. However, the conversion efficiency of the pump power into a soliton frequency comb typically remains below a few percent. We introduce a hybrid Mach-Zehnder ring resonator geometry, consisting of a micro-ring resonator embedded in an additional cavity with twice the optical path length of the ring. The resulting interferometric back coupling enables to achieve an unprecedented control of the pump depletion: pump-to-frequency comb conversion efficiencies of up to 98\% of the usable power is experimentally demonstrated with a soliton crystal comb. We assess the robustness of the proposed on-chip geometry by generating a large variety of dissipative Kerr soliton combs, which require a lower amount of pump power to be accessed, when compared with an isolated micro-ring resonator with identical parameters. Micro-resonators with feedback enable accessing new regimes of coherent soliton comb generation, and are well suited for comb applications in astronomy, spectroscopy and telecommunications.

physics.optics↗
arXiv2020

Localized structures formed through domain wall locking in cavity-enhanced second-harmonic generation

We analyze the formation of localized structures in cavity-enhanced second-harmonic generation. We focus on the phase-matched limit, and consider that fundamental and generated waves have opposite sign of group velocity dispersion. We show that these states form due to the locking of domain walls connecting two stable homogeneous states of the system, and undergo collapsed snaking. We study the impact of temporal walk-off on the stability and dynamics of these localized states.

nlin.PS↗
arXiv2020

Optical frequency combs in quadratically nonlinear resonators

Optical frequency combs are one of the most remarkable inventions of the last decades. Originally conceived as the spectral counterpart of the train of short pulses emitted by mode-locked lasers, frequency combs have also been subsequently generated in continuously pumped microresonators, through third-order parametric processes. Quite recently, direct generation of optical frequency combs has been demonstrated in continuous-wave laser-pumped optical resonators with a second-order nonlinear medium inside. Here, we presents a concise introduction to such quadratic combs and the physical mechanism that underlies their formation. We mainly review our recent experimental and theoretical work on formation and dynamics of such quadratic frequency combs. We experimentally demonstrated comb generation in two configurations: a cavity for second harmonic generation, where combs are generated both around the pump frequency and its second harmonic, and a degenerate optical parametric oscillator, where combs are generated around the pump frequency and its sub-harmonic. The experiments have been supported by a thorough theoretical analysis, aimed at modelling the dynamics of quadratic combs, both in frequency and time domains, providing useful insights into the physics of this new class of optical frequency comb synthesizers. Quadratic combs establish a new class of efficient frequency comb synthesizers, with unique features, which could enable straightforward access to new spectral regions and stimulate novel applications.

physics.optics↗
arXiv2018

Quadratic Soliton Combs in Doubly-Resonant Second-Harmonic Generation

We report a theoretical investigation of quadratic frequency combs in a dispersive second-harmonic generation cavity system. We identify different dynamical regimes and demonstrate that the same system can exhibit both bright and dark localized cavity solitons in the absence of a temporal walk-off.

physics.optics↗
arXiv2018

Modulation Instability Induced Frequency Comb Generation in a Continuously Pumped Optical Parametric Oscillator

Continuously pumped passive nonlinear cavities can be harnessed for the creation of novel optical frequency combs. While most research has focused on third-order "Kerr" nonlinear interactions, recent studies have shown that frequency comb formation can also occur via second-order nonlinear effects. Here, we report on the formation of quadratic combs in optical parametric oscillator (OPO) configurations. Specifically, we demonstrate that optical frequency combs can be generated in the parametric region around half of the pump frequency in a continuously-driven OPO. We also model the OPO dynamics through a single time-domain mean-field equation, identifying previously unknown dynamical regimes, induced by modulation instabilities, which lead to comb formation. Numerical simulation results are in good agreement with experimentally observed spectra. Moreover, the analysis of the coherence properties of the simulated spectra shows the existence of correlated and phase-locked combs. Our results reveal previously unnoticed dynamics of an apparently well assessed optical system, and can lead to a new class of frequency comb sources that may stimulate novel applications by enabling straightforward access to elusive spectral regions, such as the mid-infrared.

physics.optics↗
arXiv2018

Modulational instability of nonlinear polarization mode coupling in microresonators

We investigate frequency comb generation in the presence of polarization effects induced by nonlinear mode coupling in microresonator devices. A set of coupled temporal Lugiato-Lefever equations are derived to model the propagation dynamics, and an in-depth study is made of the modulational instability of their multistable homogeneous steady-state solutions. It is shown that new kinds of instabilities can occur for co-propagating fields that interact through nonlinear cross-phase modulation. These instabilities display properties that differ from their scalar counterpart, and are shown to result in the generation of new types of incoherently coupled frequency comb states.

physics.optics↗
arXiv2016

Frequency comb formation in doubly resonant second-harmonic generation

We theoretically study the generation of optical frequency combs and corresponding pulse trains in doubly resonant intracavity second-harmonic generation (SHG). We find that, despite the large temporal walk-off characteristic of realistic cavity systems, the nonlinear dynamics can be accurately and efficiently modelled using a pair of coupled mean-field equations. Through rigorous stability analysis of the system's steady-state continuous wave solutions, we demonstrate that walk-off can give rise to a new, previously unexplored regime of temporal modulation instability (MI). Numerical simulations performed in this regime reveal rich dynamical behaviours, including the emergence of temporal patterns that correspond to coherent optical frequency combs. We also demonstrate that the two coupled equations that govern the doubly resonant cavity behaviour can, under typical conditions, be reduced to a single mean-field equation akin to that describing the dynamics of singly resonant cavity SHG [F. Leo et al., Phys. Rev. Lett. 116, 033901 (2016)]. This reduced approach allows us to derive a simple expression for the MI gain, thus permitting to acquire significant insight into the underlying physics. We anticipate that our work will have wide impact on the study of frequency combs in emerging doubly resonant cavity SHG platforms, including quadratically nonlinear microresonators.

physics.optics↗
arXiv2016

Single envelope equation modelling of multi-octave comb arrays in microresonators with quadratic and cubic nonlinearity

We numerically study, by means of the single envelope equation, the generation of optical frequency combs ranging from the visible to the mid-infrared spectral regions in resonators with quadratic and cubic nonlinearities. Phase-matched quadratic wave-mixing processes among the comb lines can be activated by low-power continuous wave pumping in the near infrared of a radially poled lithium niobate whispering gallery resonator (WGR). We examine both separate and co-existing intra-cavity doubly resonant second-harmonic generation and parametric oscillation processes, and find that modulation instabilities may lead to the formation of coupled comb arrays extending over multiple octaves. In the temporal domain, the frequency combs may correspond to pulse trains, or isolated pulses.

physics.optics↗
arXiv2016

Walk-off-induced modulation instability, temporal pattern formation, and frequency comb generation in cavity-enhanced second-harmonic generation

We derive a time-domain mean-field equation to model the full temporal and spectral dynamics of light in singly resonant cavity-enhanced second-harmonic generation systems. We show that the temporal walk-off between the fundamental and the second-harmonic fields plays a decisive role under realistic conditions, giving rise to rich, previously unidentified nonlinear behaviour. Through linear stability analysis and numerical simulations, we discover a new kind of quadratic modulation instability which leads to the formation of optical frequency combs and associated time-domain dissipative structures. Our numerical simulations show excellent agreement with recent experimental observations of frequency combs in quadratic nonlinear media [Phys. Rev. A 91, 063839 (2015)]. Thus, in addition to unveiling a new, experimentally accessible regime of nonlinear dynamics, our work enables predictive modeling of frequency comb generation in cavity-enhanced second-harmonic generation systems.

physics.optics↗
arXiv2014

Dual pumped microresonator frequency combs

A study is made of the nonlinear dynamics of dual pumped microresonator Kerr frequency combs described by a driven and damped nonlinear Schrödinger equation, with an additional degree of freedom in the form of the modulation frequency. A truncated four wave model is derived for the pump modes and the dominant sideband pair which is found to be able to describe much of the essential dynamical behaviour of the full equation. The stability of stationary states within the four wave model is investigated and numerical simulations are made to demonstrate that a large range of solutions, including cavity solitons, are possible beyond previously considered low intensity patterns.

physics.optics↗
arXiv2013

On the numerical simulation of Kerr frequency combs using coupled mode equations

It is demonstrated that Kerr frequency comb generation described by coupled mode equations can be numerically simulated using Fast Fourier Transform methods. This allows broadband frequency combs spanning a full octave to be efficiently simulated using standard algorithms, resulting in orders of magnitude improvements in the computation time.

physics.optics↗
arXiv2013

Dynamics of the Modulational Instability in Microresonator Frequency Combs

A study is made of frequency comb generation described by the driven and damped nonlinear Schrödinger equation on a finite interval. It is shown that frequency comb generation can be interpreted as a modulational instability of the continuous wave pump mode, and a linear stability analysis, taking into account the cavity boundary conditions, is performed. Further, a truncated three-wave model is derived, which allows one to gain additional insight into the dynamical behaviour of the comb generation. This formalism describes the pump mode and the most unstable sideband and is found to connect the coupled mode theory with the conventional theory of modulational instability. An in-depth analysis is done of the nonlinear three-wave model. It is demonstrated that stable frequency comb states can be interpreted as attractive fixed points of a dynamical system. The possibility of soft and hard excitation states in both the normal and the anomalous dispersion regime is discussed. Investigations are made of bistable comb states, and the dependence of the final state on the way the comb has been generated. The analytical predictions are verified by means of direct comparison with numerical simulations of the full equation and the agreement is discussed.

physics.optics↗
arXiv2012

A Scalar Wigner Theory for Polarized Light in Nonlinear Kerr Media

A scalar Wigner distribution function for describing polarized light is proposed in analogy with the treatment of spin variables in quantum kinetic theory. The formalism is applied to the propagation of circularly polarized light in nonlinear Kerr media and an extended phase space evolution equation is derived along with invariant quantities. We further consider modulation instability as well as the extension to partially coherent fields.

physics.optics↗
arXiv2011

Multi--hump soliton--like structures in interactions of lasers and Bose--Einstein condensates

An investigation is made of multi-hump and periodic solutions of the semi-classical coupled equations describing laser radiation copropagating with a Bose-Einstein condensate. Solutions reminiscent of optical vector solitons have been found and have been used to gain understanding of the dynamics observed in the numerical simulations, in particular to shed light on the phenomenon of jet emission from a condensate interacting with a laser.

nlin.PS↗