Competing Turing and Faraday Instabilities in Longitudinally Modulated Passive Resonators

Self-assembled micro-patterns in uphill-diffusion solution system

In this work we present self-organized regular patterns in a solution system through uphill-diffusion. Micrometer thick organic semiconductor solution is sandwiched between a substrate and cover-plate. Self-assembled regular patterns can be observed on the substrate after solvent evaporation. Different micro-patterns and pattern defects were displayed and analyzed. Mechanisms of defect formation, mode selection process during patten generation, and pattern sedimentation onto substrate from solution were proposed. Organic thin film transistors were fabricated with the assembled line patterns which demonstrate a promising way to produce patterned micro/nano materials.

Observation of modulation instability in a coherently driven active fiber ring resonator at 2 μm wavelength

We report the first, to our knowledge, observation of the nonlinear phenomenon known as modulation instability (MI) in a coherently driven fiber resonator pumped at 1972 nm. To compensate for the very high losses in this spectral region, we have integrated a thulium-doped fiber amplifier inside the cavity. Lower losses allow a lower MI threshold, leading to the observation of this phenomenon at a moderate input power. The results align closely with the numerical simulations of the system. Our study shows that active compensation of loss can be implemented in the 2 µm wavelength range to construct fiber ring cavities with high finesse. It paves the way to the observation of more complex nonlinear effects optical frequency comb through cavity soliton generation.

Hybrid Patterns and Solitonic Frequency Combs in Non-Hermitian Kerr Cavities

We unveil a new scenario for the formation of dissipative localized structures in nonlinear systems. Commonly, the formation of such structures arises from the connection of a homogeneous steady state with either another homogeneous solution or a pattern. Both scenarios, typically found in cavities with normal and anomalous dispersion, respectively, exhibit unique fingerprints and particular features that characterize their behavior. However, we show that the introduction of a periodic non-Hermitian modulation in Kerr cavities hybridizes the two established soliton formation mechanisms, embodying the particular fingerprints of both. In the resulting novel scenario, the stationary states acquire a dual behavior, playing the role that was unambiguously attributed to either homogeneous states or patterns. These fundamental findings have profound practical implications for frequency comb generation, introducing unprecedented reversible mechanisms for real-time manipulation.

Impact of pump pulse duration on modulation instability Kerr frequency combs in fiber Fabry-Pérot resonators

We report an experimental investigation on the impact of the pump pulse duration on the modulation instability process in fiber Fabry-Pérot resonators. We demonstrate that cross-phase modulation between the forward and the backward waves alters significantly the modulation instability process. By varying the pump pulse duration, we show the modification of the modulation instability threshold and frequency. These experimental observations are in excellent agreement with theoretical predictions.

Coexistence of gain-through-filtering and parametric instability in a fiber ring cavity

We experimentally and numerically investigate the dynamics of a fiber ring cavity in which two different instability can be excited: gain-through-filtering and parametric instability. We demonstrate that they can be triggered individually or collectively depending on the two main control parameters offered by the cavity, namely the pump power and the cavity detuning. The experimental observations are in good agreement with numerical simulations.

Observation of modulation instability Kerr frequency combs in a fiber Fabry-Pérot resonator

We report the experimental observation of a modulation instability induced Kerr frequency comb in an all fiber Fabry-Pérot resonator. We fully characterized, in intensity and phase, the frequency comb using a commercial 10 MHz resolution heterodyne detection system to reveal more than 125 comb teeth within each of the modulation instability sidelobes. Moreover, we were able to reveal the fine temporal structure in phase and intensity of the output Turing patterns. The experimental results are generally in good agreement with numerical simulations.

Turing patterns with high-resolution formed without chemical reaction in thin-film solution of organic semiconductors

Regular patterns can form spontaneously in chemical reaction-diffusion systems under non-equilibrium conditions as proposed by Alan Turing. Here, we found that regular patterns can be generated in uphill-diffusion solution systems without a chemical reaction process through both in-situ and ex-situ observations. Organic semiconductor solution is confined between two parallel plates with controlled micron/submicron-meter distance to minimize convection of the liquid and avoid spinodal precipitation at equilibrium. The solvent evaporation concentrates the solution gradually into an oversaturated non-equilibrium condition, under which a phase-transition occurs and ordered concentration-waves are generated. By proper tuning of the experimental parameter, multiple regular patterns with micro/nano-meter scaled features (line, square-grid, zig-zag, and fence-like patterns etc.) were observed. We explain the observed phenomenon as Turing-pattern generation resulted from uphill-diffusion and solution oversaturation. The generated patterns in the solutions can be condensed onto substrates to form structured micro/nanomaterials. We have fabricated organic semiconductor devices with such patterned materials to demonstrate the potential applications. Our observation may serve as a milestone in the progress towards a fundamental understanding of pattern formation in nature, like in biosystem, and pave a new avenue in developing self-assembling techniques of micro/nano structured materials.

120-fs single-pulse generation from stretched-pulse fiber Kerr resonators

Fiber Kerr resonators are simple driven resonators with desirable wavelength and repetition rate flexibility for generating ultrashort pulses for applications including telecommunications, biomedicine, and materials processing. However, fiber Kerr resonators to date often generate longer pulses and require more complicated techniques for generating single pulses than would be desirable for applications. Here we address these limits by demonstrating robust single-pulse performance supporting 120-fs pulse durations in fiber Kerr resonators based on stretched-pulse solitons. Through matching numerical and experimental studies, stretched-pulse soliton performance is found to strongly depend on the total cavity length, and the optimum length is found to depend on the drive, Raman scattering, and the total pulse stretching. The bandwidth increases with decreasing net dispersion, enabled by shorter total cavity lengths. In a cavity with an optimized length and the described setup, stable stretched-pulse solitons corresponding to 120-fs duration are experimentally observed. In addition, soliton trapping is demonstrated with a pulsed drive source despite large intracavity breathing, and single-pulse performance is observed. Robust with high performance single-pulse generation is a critical step toward useful femtosecond pulse generation.

Coherent terahertz radiation with 2.8-octave tunability through chip-scale photomixed microresonator optical parametric oscillation

High-spectral-purity frequency-agile room-temperature sources in the terahertz spectrum are foundational elements for imaging, sensing, metrology, and communications. Here we present a chip-scale optical parametric oscillator based on an integrated nonlinear microresonator that provides broadly tunable single-frequency and multi-frequency oscillators in the terahertz regime. Through optical-to-terahertz down-conversion using a plasmonic nanoantenna array, coherent terahertz radiation spanning 2.8-octaves is achieved from 330 GHz to 2.3 THz, with ≈20 GHz cavity-mode-limited frequency tuning step and ≈10 MHz intracavity-mode continuous frequency tuning range at each step. By controlling the microresonator intracavity power and pump-resonance detuning, tunable multi-frequency terahertz oscillators are also realized. Furthermore, by stabilizing the microresonator pump power and wavelength, sub-100 Hz linewidth of the terahertz radiation with 10-15 residual frequency instability is demonstrated. The room-temperature generation of both single-frequency, frequency-agile terahertz radiation and multi-frequency terahertz oscillators in the chip-scale platform offers unique capabilities in metrology, sensing, imaging and communications.

Polarization modulation instability in a nonlinear fiber Kerr resonator

We report on the experimental and numerical observation of polarization modulation instability (PMI) in a nonlinear fiber Kerr resonator. This phenomenon is phased-matched through the relative phase detuning between the intracavity fields associated with the two principal polarization modes of the cavity. Our experimental investigation is based on a 12 m long fiber ring resonator in which a polarization controller is inserted to finely control the level of intracavity birefringence. Depending on the amount of birefringence, the temporal patterns generated via PMI are found to be either stationary or to exhibit a period-doubled dynamics. The experimental results are in good agreement with numerical simulations based on an Ikeda map for the two orthogonally polarized modes. This Letter provides new insights into the control of modulation instability in multimode Kerr resonators.

Nonlinear Evolution of the Locally Induced Modulational Instability in Fiber Optics

We report an optical fiber experiment in which we study the nonlinear stage of modulational instability of a plane wave in the presence of a localized perturbation. Using a recirculating fiber loop as the experimental platform, we show that the initial perturbation evolves into an expanding nonlinear oscillatory structure exhibiting some universal characteristics that agree with theoretical predictions based on integrability properties of the focusing nonlinear Schrödinger equation. Our experimental results demonstrate the persistence of the universal evolution scenario, even in the presence of small dissipation and noise in an experimental system that is not rigorously of an integrable nature.

Interplay of Polarization and Time-Reversal Symmetry Breaking in Synchronously Pumped Ring Resonators

Optically induced breaking of symmetries plays an important role in nonlinear photonics, with applications ranging from optical switching in integrated photonic circuits to soliton generation in ring lasers. In this work we study for the first time the interplay of two types of spontaneous symmetry breaking that can occur simultaneously in optical ring resonators. Specifically we investigate a ring resonator that is synchronously pumped with short pulses of light. In this system we numerically study the interplay and transition between regimes of temporal symmetry breaking (in which pulses in the resonator either run ahead or behind the seed pulses) and polarization symmetry breaking (in which the resonator spontaneously generates elliptically polarized light out of linearly polarized seed pulses). We find ranges of pump parameters for which each symmetry breaking can be independently observed, but also a regime in which a dynamical interplay takes place. Besides the fundamentally interesting physics of the interplay of different types of symmetry breaking, our work contributes to a better understanding of the nonlinear dynamics of optical ring cavities which are of interest for future applications including all-optical logic gates, synchronously pumped optical frequency comb generation, and resonator-based sensor technologies.

Selective generation of Kerr combs induced by asymmetrically phase-detuned dual pumping of a fiber ring cavity

We numerically and experimentally investigate the asymmetrically phase-detuned dual pumping of a passive inhomogeneous fiber ring cavity. This configuration originates from the fine control of frequency mismatch between the frequency spacing of the bichromatic pump and the free spectral range of the cavity. Multicomb states at offset frequencies can be selectively generated by means of the mismatch parameter and the coexistence of Turing and Faraday instabilities.

Gain through losses in nonlinear optics

Instabilities of uniform states are ubiquitous processes occurring in a variety of spatially extended nonlinear systems. These instabilities are at the heart of symmetry breaking, condensate dynamics, self-organisation, pattern formation, and noise amplification across diverse disciplines, including physics, chemistry, engineering, and biology. In nonlinear optics, modulation instabilities are generally linked to the so-called parametric amplification process, which occurs when certain phase-matching or quasi-phase-matching conditions are satisfied. In the present review article, we summarise the principle results on modulation instabilities and parametric amplification in nonlinear optics, with special emphasis on optical fibres. We then review state-of-the-art research about a peculiar class of modulation instabilities (MIs) and signal amplification processes induced by dissipation in nonlinear optical systems. Losses applied to certain parts of the spectrum counterintuitively lead to the exponential growth of the damped mode themselves, causing gain through losses. We discuss the concept of imaging of losses into gain, showing how to map a given spectral loss profile into a gain spectrum. We demonstrate with concrete examples that dissipation-induced MI, apart from being of fundamental theoretical interest, may pave the way towards the design of a new class of tuneable fibre-based optical amplifiers, optical parametric oscillators, frequency comb sources, and pulsed lasers.

Stimulated Raman Scattering Imposes Fundamental Limits to the Duration and Bandwidth of Temporal Cavity Solitons

Temporal cavity solitons (CS) are optical pulses that can persist in passive resonators, and they play a key role in the generation of coherent microresonator frequency combs. In resonators made of amorphous materials, such as fused silica, they can exhibit a spectral redshift due to stimulated Raman scattering. Here we show that this Raman-induced self-frequency-shift imposes a fundamental limit on the duration and bandwidth of temporal CSs. Specifically, we theoretically predict that stimulated Raman scattering introduces a previously unidentified Hopf bifurcation that leads to destabilization of CSs at large pump-cavity detunings, limiting the range of detunings over which they can exist. We have confirmed our theoretical predictions by performing extensive experiments in synchronously driven fiber ring resonators, obtaining results in excellent agreement with numerical simulations. Our results could have significant implications for the future design of Kerr frequency comb systems based on amorphous microresonators.

Modulation instability in the weak normal dispersion region of passive fiber ring cavities

We report the experimental observation of modulation instability in the weak normal dispersion region of a passive fiber ring cavity. We show that the fourth-order dispersion strongly modifies the dynamics of the cavity through the generation of new instability bands. Experimental results are in excellent agreement with theoretical predictions and numerical simulations.

Multi-resonant Lugiato-Lefever model

We introduce a new model that extends the Lugiato-Lefever equation to the description of multiple resonances in Kerr optical cavities. It perfectly agrees quantitatively (in both stationary and dynamical regimes) with the exact Ikeda map, even when using a small number of resonances. Our model predicts the onset of complex phenomena such as the recently observed super-cavity solitons and the coexistence of multiple nonlinear states. It will be of crucial importance for the analytical understanding of new nonlinear phenomena in Kerr cavities when the intensities or nonlinearities are high enough to be able to excite more than one cavity resonance.

Quasi-phase-matched multispectral Kerr frequency comb

We study a new type of Kerr frequency comb where the momentum conservation law is fulfilled by azimuthal modulation of the waveguide dispersion. The concept can expand the parametric range in which a Kerr frequency comb is obtained. In a good agreement with the theoretical analysis, we demonstrate a multispectral Kerr frequency comb covering important fiber-optic communication bands. Comb coherence and absence of a sub-comb offset are confirmed by continuous-wave heterodyne beat note and amplitude noise spectra measurements. The device can be used for achieving broadband optical frequency synthesizers and high-capacity coherent communication.

Modulation instability in the weak dispersion regime of a dispersion modulated passive fiber-ring cavity

We present a theoretical and experimental study of the modulation instability process in a dispersion oscillating passive fiber-ring resonator in the low dispersion region. Generally, the modulation of the dispersion along the cavity length is responsible for the emergence of a regime characterised by multiple parametric resonances (or Faraday instabilities). We show that, under weak dispersion conditions, a huge number of Faraday sidebands can grow under the influence of fourth order dispersion. We specifically designed a piecewise uniform fiber-ring cavity and report on experiments that confirm our theoretical predictions. We recorded the dynamics of this system revealing strong interactions between the different sidebands in agreement with numerical simulations.

Dynamics of Turing and Faraday instabilities in a longitudinally modulated fiber-ring cavity

We experimentally investigate the round-trip-to-round-trip dynamics of the modulation instability spectrum in a passive fiber-ring cavity presenting an inhomogeneous dispersion profile. By implementing a real-time spectroscopy technique, we are able to record successive single-shot spectra, which display the evolution of the system toward a stationary state. We find that the two instability regimes (Turing and Faraday) that compete in this kind of inhomogeneous cavity not only differ by their characteristic frequency but also by their dynamical behavior. The dynamic transition between those two regimes of instability is also presented.

Coherent and incoherent seeding of dissipative modulation instability in a nonlinear fiber ring cavity

We investigate the coherent or incoherent seeding of dissipative modulation instability (MI) in a nonlinear fiber ring cavity. By varying wavelength and degree of coherence of the seed signal across the MI gain band, we observe a strong sensitivity of the resulting MI sidebands in terms of bandwidth and amplification. Both spectral and temporal characterizations are performed to reveal intensity coherence properties (over a single round-trip) of the generated temporal patterns. Experimental observations are well confirmed by numerical simulations. Our results provide new insights into the control of dissipative MI through a specific seeding in optical resonators with a moderate free-spectral range. In particular, a large tunability of the subsequent Kerr comb spacing is achieved by means of the early transient stage of seeded MI growth.

Parametric instabilities in modulated fiber ring cavities

We investigate modulational instability in inhomogeneous passive cavities modeled by the Ikeda map. The cavity boundary conditions and the modulation of the fiber dispersion force the system to develop parametric instabilities, which lead to the generation of simple, as well as period-doubled, temporal patterns. The analytical results obtained by means of the Floquet theory are validated through numerical solution of the Ikeda map, and the limitations of the mean-field Lugiato-Lefever model are highlighted.

Mode-locking via dissipative Faraday instability

Emergence of coherent structures and patterns at the nonlinear stage of modulation instability of a uniform state is an inherent feature of many biological, physical and engineering systems. There are several well-studied classical modulation instabilities, such as Benjamin-Feir, Turing and Faraday instability, which play a critical role in the self-organization of energy and matter in non-equilibrium physical, chemical and biological systems. Here we experimentally demonstrate the dissipative Faraday instability induced by spatially periodic zig-zag modulation of a dissipative parameter of the system-spectrally dependent losses-achieving generation of temporal patterns and high-harmonic mode-locking in a fibre laser. We demonstrate features of this instability that distinguish it from both the Benjamin-Feir and the purely dispersive Faraday instability. Our results open the possibilities for new designs of mode-locked lasers and can be extended to other fields of physics and engineering.