We generalize the projection to orthogonal function basis (including polarization modes) method for nonlinear (Kerr medium) fiber and use this method in a case of two-mode waveguide. We consider orthogonal Bessel functions basis that fit the choice of cylindrical geometry of a fiber. The coupled nonlinear Schrödinger equations (CNLS) are derived. Analytic expressions and numerical results for coupling coefficients are given; the fiber parameters dependence is illustrated by plots.
We experimentally study polarization dynamics of Kerr beam self-cleaning in a graded-index multimode optical fiber. We show that spatial beam cleaning is accompanied by nonlinear polarization rotation, and a substantial increase of the degree of linear polarization.
We theoretically and experimentally demonstrate a novel mode-locked ytterbium-doped fiber laser with a saturable absorber based on nonlinear Kerr beam cleanup effect. The saturable absorber was formed by a 2-m graded-index multimode fiber and a single-mode fiber segment served as a diaphragm. With an all-normal-dispersion-fiber configuration, the laser generated dissipative soliton pulses with pulse duration of 26.38 ps and pulse energy more than 0.25 nJ; output pulses could be compressed externally to 615.7 fs. Moreover, the self-starting mode-locking operation of this laser exhibited a high …
We experimentally study the competition between Kerr beam self-cleaning and Raman beam cleanup in a multimode air-silica microstructure optical fiber. Kerr beam self-cleaning of the pump is observed for a certain range of input powers only. Raman Stokes beam generation and cleanup lead to both depletion and degradation of beam quality for the pump. The interplay of modal four-wave mixing and Raman scattering in the infrared domain lead to the generation of a multimode supercontinuum ranging from 500 nm up to 1800 nm.
We report experimental results, showing that the Kerr beam self-cleaning of many low-order modes in a graded-index multimode fiber can be controlled thanks to optimized wavefront shaping of the coherent excitation beam. Adaptive profiling of the transverse input phase was utilized for channeling the launched power towards a specific low-order fiber mode, by exploiting nonlinear coupling among all guided modes. Experiments were carried out with 7 ps pulses at 1064 nm injected in a five meters long multimode fiber operating in the normal dispersion regime. Optimized Kerr beam self-cleaning of fi…
We derive coupled nonlinear Schrödinger equation (CNLSE) for arbitrary polarized light propagation in a single-mode fiber. We introduce a basis of transverse eigen modes with the appropriate projecting hence solutions depend on the waveguide geometry. Considering a weak nonlinearity which is connected with Kerr effect, we give explicit expressions for nonlinear constants via integrals of Bessel functions. We compare numerical results for the nonlinear constant extracted from experimental observations of a soliton for the nonlinear Schrödinger equation (NLSE) (single-mode one). The method of pr…
We report the experimental observation of Kerr beam self-cleaning in a graded-index multimode fiber, leading to output beam profiles different from a bell shape, close to the $LP_{01}$ mode. For specific coupling conditions, nonlinear coupling among the guided modes can reshape the output speckle pattern generated by a pulsed beam into the low order $LP_{11}$ mode. This was observed in a few meters long multimode fiber with 750 ps pulses at 1064 nm in the normal dispersion regime. The power threshold for $LP_{11}$ mode self-cleaning was about three times larger than that required for Kerr nonl…
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 with 120-fs pulse durations in fiber Kerr resonators based on stretched-pulse solitons. Through matching numerical …
We study a re-configurable nonreciprocal fiber ring cavity setup to generate tunable optical frequency combs. Coherent combs can be obtained by finely exploiting bi-chromatic Brillouin lasing and cascaded four-wave mixing in the nonlinear fiber cavity. We introduce a numerical model of the cavity system, which is validated by comparisons with experiments. Our work shows the importance of the mode pulling effect, controlled by the pump laser detuning, in setting the dynamics of the comb. This effect along with the impact of multimode lasing had been overlooked in previous fiber experiments. We …
In this paper, we numerically investigate the process of beam self-cleaning in a graded-index multimode optical fiber, by using the coupled-mode model. We introduce various models of random linear coupling between spatial modes, including coupling between all modes, or only between degenerate ones, and investigate the effects of random mode coupling on the beam self-cleaning process. The results of numerical investigations are in complete agreement with our experimental data.
We demonstrate a novel approach to achieve wavelength-tunable ultrashort pulses from an all-fiber mode-locked laser with a saturable absorber based on nonlinear Kerr beam clean-up effect. This saturable absorber was formed by a single-mode fiber spliced to a graded-index multimode fiber, and its tunable band-pass filter effect is studied by a numerical model. By adjusting the bending condition of graded-index multimode fiber, the laser could produce dissipative soliton pulses with their central wavelength tunable from1040 nm to 1063 nm. The pulse width of output laser could be compressed exter…
We experimentally demonstrate Kerr beam self-cleaning in the anomalous dispersion regime of graded-index multimode optical fibers. By using 90 ps duration, highly chirped (2 nm bandwidth at -3dB) optical pulses at 1562 nm, we demonstrate a 2 decades reduction, with respect to previous experiments in the normal dispersion regime, of threshold peak power for beam self-cleaning into the fundamental mode of the fiber, accompanied by more than 65% nonlinear increase of intensity correlation into the fundamental mode. Highly efficient self-selection of the LP11 mode is also observed. Self-cleaned be…
In this letter, we investigate a Yb-doped mode-locked fiber oscillator that uses coherent pulse division and recombination to avoid excessive nonlinear phase shifts. The mode-locking mechanism of the laser is based on the accumulation of a differential nonlinear phase between orthogonal polarization modes in the polarization-maintaining fiber segment. The inserted coherent pulse divider, based on YVO4-crystals rotated successively by 45°, enables stable and undistorted mode-locked steady-states. The output pulse energy is increased from 89 pJ in the non-divided operation by ~6.5 dB to more tha…
We report the suppression of intermodal modulation instability peaks as a consequence of Kerr induced self beam-cleaning in a 90m long graded-index multimode optical fiber under various specific launching conditions. The output spectrum and the modal beam profiles for three modes (LP01, LP11, and LP21) have been recorded for several values of pump pulse energy. Experimental findings establish that the nonlinear coupling among the guided modes leads to reshaping the output speckle pattern into a bell shape or higher-order spatially clean beam profile as the pump peak power increases, whereas in…
Forward stimulated Brillouin scattering (F-SBS) is a third-order nonlinear-optical mechanism that couples between two co-propagating optical fields and a guided acoustic mode in a common medium. F-SBS gives rise to nonlinear wave mixing along optical fibers, which adds up with four-wave mixing induced by the Kerr effect. In this work, we report the distributed mapping of nonlinear wave mixing processes involving both mechanisms along standard single-mode fiber, in analysis, simulation and experiment. Measurements are based on a multi-tone, optical time-domain reflectometry setup, which is high…
We demonstrate an all-optical phase regeneration technique based on Kerr soliton combs, which can realize degraded quaternary phase shift keying (QPSK) signal regeneration through phase-sensitive amplification. A Kerr soliton comb is generated at the receiver side of optical communication systems based on a carrier recovery scheme and is used as coherent dual pumps to achieve phase regeneration. Our study will enhance the relay and reception performance of all-optical communication systems.
Multimode fiber systems are desirable for industrial and scientific applications. As an interesting effect for the laser beam propagation in a multimode fiber, nonlinear Kerr beam cleanup has attracted considerable research interest due to the spatial beam compressing. However, its physical mechanisms, especially the influences of input conditions on its performances, remain unclear. Here, we report a new self-organized regime for the multimode beam propagation in a graded-index multimode fiber: when the input laser has a dominant mode in which most of the laser energy is concentrated, the bea…
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 intra-cavity birefringence. Depending on the amount of birefringence, the temporal patterns generated via PMI are found to be either statio…
Phase-locking of large mode area Yb photonic crystal fiber amplifiers via stimulated Brillouin scattering phase conjugation is analyzed. The wavefront reversing mirrors are proposed for chirped pulse fiber laser networks. The chirp control via both nonresonant Kerr and resonant index is considered.
We experimentally and theoretically study self-phase modulation by Kerr effect in a liquid filled hollow core photonic crystal fiber. We perform a complete characterization of the linear optical properties of the hollow core photonic band gap fiber filled with deuterated acetone to determine all the characteristics of the propagation mode. The nonlinear coefficient of the fiber is determined by fitting the output spectra broadened by self-phase modulation with a new analytical expression giving the spectra of a secant hyperbolic pulse transmitted through a Kerr media. The experiment allows a p…
We introduce a mechanism of stable spatiotemporal soliton formation in a multimode fiber laser. This is based on spatially graded dissipation, leading to distributed Kerr-lens mode-locking. Our analysis involves solutions of a generalized dissipative Gross-Pitaevskii equation. This equation has a broad range of applications in nonlinear physics, including nonlinear optics, spatiotemporal patterns formation, plasma dynamics, and Bose-Einstein condensates. We demonstrate that careful control of dissipative and non-dissipative physical mechanisms results in the self-emergence of stable (2+1)-dime…
Optical fibers have been enabling numerous distinguished applications involving the operation and generation of light, such as soliton transmission, light amplification, all-optical switching and supercontinuum generation. The active function of optical fibers in the quantum regime is expected to be applicable to ultralow-power all-optical signal processing and quantum information processing. Here we demonstrate the first experimental observation of optical nonlinearity at the single-photon level in an optical fiber. Taking advantage of large nonlinearity and managed dispersion of a photonic c…
THz oscillators generated via frequency-multiplication of microwaves are facing difficulty in achieving low phase noise. Photonics-based techniques, in which optical two tones are translated to a THz wave through opto-electronic conversion, are promising if the relative phase noise between the two tones is well suppressed. Here, a THz ($\approx$ 560 GHz) wave with a low phase noise is provided by a frequency-stabilized, dissipative Kerr microresonator soliton comb. The repetition frequency of the comb is stabilized to a long fiber in a two-wavelength delayed self-heterodyne interferometer, sig…
We overview recent advances in the research on spatiotemporal beam shaping in nonlinear multimode optical fibers. An intense light beam coupled to a graded index (GRIN) highly multimode fiber undergoes a series of complex nonlinear processes when its power grows larger. Among them, the lowest threshold effect is the Kerr-induced beam self-cleaning, that redistributes most of the beam energy into a robust bell-shaped beam close to the fundamental mode. At higher powers a series of spectral sidebands is generated, thanks to the phase matching induced by the long period grating due to the periodi…
We demonstrate the first compact photonic flywheel with sub-fs time jitter (averaging times up to 10 μs) at the quantum-noise limit of a monolithic fiber resonator. Such quantum-limited performance is accessed through novel two-step pumping scheme for dissipative Kerr soliton (DKS) generation. Controllable interaction between stimulated Brillouin lasing and Kerr nonlinearity enhances the DKS coherence and mitigate the thermal instability challenge, achieving a remarkable 22-Hz intrinsic comb linewidth and an unprecedented phase noise of -180 dBc/Hz at 945 MHz carrier at free running. The schem…
In this Letter, we show theoretically that the nonlinear photoionisation process of a noble gas inside a hollow-core photonic crystal fibre can be exploited in obtaining broadband supercontinuum generation via pumping close to the mid-infrared regime. The interplay between the Kerr and photoionisation nonlinearities is strongly enhanced in this regime. Photoionisation continuously modifies the medium dispersion, in which the refractive index starts to significantly decrease and approach the epsilon-near-zero regime. Subsequently, the self-phase modulation induced by the Kerr effect is boosted …
Kerr optical frequency combs generated in a coherently driven Kerr nonlinear resonator has the potential for a wide range of applications. However, in a single cavity which is a widely adopted configuration for Kerr optical frequency combs generation, modulation instability is suppressed in normal dispersion regime and the pump-to-comb conversion efficiency is extremely low for a single dissipative Kerr soliton in anomalous dispersion regime. Dual-coupled cavities have been proposed to generate Kerr optical frequency combs in normal dispersion regime, and have potential to remarkably increase …
A bidirectional mode-locked fiber laser producing two correlated frequency combs of the same repetition rate is demonstrated. The intensity dependence of pulse and phase velocities are measured simultaneously. As expected, the phase delay is determined by the linear and nonlinear indices of refraction. The nonlinear Kerr effect contribution to the pulse velocity is dwarfed by a contribution from saturable gain dynamics.
We introduce the concept of spatial and spectral control of nonlinear parametric sidebands in multimode optical fibers by tailoring their linear refractive index profile. In all cases, the pump experiences Kerr self-cleaning, leading to a bell-shaped profile close to the fundamental mode. Geometric parametric instability, owing to quasi-phase-matching from the grating generated via the Kerr effect by pump self-imaging, leads to frequency multicasting of beam self-cleaning across a wideband array of sidebands. Our experiments show that introducing a gaussian dip in the refractive index profile …
Using ultrafast photonic first-order differentiator applied on a partially coherent field, we report the generation of two correlated temporal waveforms and study their correlation properties upon linear and nonlinear propagation along the two orthogonal polarization axis of a dispersive optical fiber. Temporal correlations are maintained in linear propagation whereas Kerr nonlinearity generates anti-correlated temporal intensity patterns for both partially and uncorrelated fields. Experiments are in close agreement with the theoretical analysis.
Self-referencing turns pulsed laser systems into self-referenced frequency combs. Such frequency combs allow counting of optical frequencies and have a wide range of applications. The required optical bandwidth to implement self-referencing is typically obtained via nonlinear broadening in optical fibers. Recent advances in the field of Kerr frequency combs have provided a path towards the development of compact frequency comb sources that provide broadband frequency combs, exhibit microwave repetition rates and that are compatible with on-chip photonic integration. These devices have the pote…
We demonstrate theoretically a large transverse magneto-optical Kerr effect (TMOKE) in subwavelength gratings consisting of alternating magneto-insulating and nonmagnetic dielectric nanostripes. The reflectivity of the grating reaches $96\%$ at the frequencies corresponding to the maximum of the TMOKE response. The combination of a large TMOKE response and high reflectivity is important for applications in $3$D imaging, magneto-optical data storage, and magnonics.
The origin of the Kerr type nonlinearity of the medium as a result of the interaction between photons via the Dirac delta-potential is presented in the formalism adopted from the photon wave function approach. In the view of the result the optical soliton may be treated as a bound state (cluster) of many photons.
Optical injection locking is implemented to faithfully transfer the phase noise of a dissipative Kerr microresonator soliton comb in addition to the amplification of the Kerr comb. Unlike Er-doped fiber and semiconductor optical amplifiers, the optical injection locking amplifies the comb mode without degrading the optical signal-to-noise ratio. In addition, we show that the residual phase noise of the optical injection locking is sufficiently small to transfer the relative phase noise of comb modes (equivalent to the repetition frequency) of low phase noise Kerr combs, concluding that the opt…
We introduce a novel concept for optical frequency measurement and division which employs a Kerr-lens mode-locked laser as a transfer oscillator whose noise properties do not enter the measurement process. We experimentally demonstrate, that this method opens up the route to phase-link signals with arbitrary frequencies in the optical or microwave range while their frequency stability is preserved.
We show the formation of slow optical solitons in the asymmetric coupled double quantum-wells (CQW) via a two-photon Raman resonance. With the consideration of real parameters in AlGaAs-based CQW, we indicate the possibility to have cancellation of the linear absorption and giant Kerr nonlinearities. With the controllable balance between dispersion and nonlinear effects in these solid-state based devices, this work may provide a practical platform for nonlinear optical signal processing.
We report on the generation of multiwavelength gain-guided soliton (GGS) in an all normal dispersion birefringent fiber laser passively mode-locked with a semiconductor saturable absorber mirror (SESAM). Determined by the cavity birefringence, we observe the stable single-, dual- and triple- wavelength mode locked GGSs, which is a natural consequence of the mutual nonlinear interaction among the normal cavity dispersion, cavity fiber nonlinear Kerr effect, laser gain saturation and bandwidth limitation resulting from the intra-cavity birefringent filter.
Impact of Stimulated Brillouin Scattering on Modulation Instability in Fiber Fabry-Perot Resonators
Laboratoire Physique des Lasers, Atomes et Molécules, UMR No. 8523, CNRS, University of Lille（里尔大学）；Service OPERA-Photonique, Université libre de Bruxelles (ULB)（布鲁塞尔自由大学）
We performed non-degenerate pump-probe experiments on a GaAs/AlAs photonic structure. We switched the photonic properties using the optical Kerr effect and free carriers excited by three photon absorption. From these measurements we extracted the non-degenerate Kerr coefficients over a broad wavelength range and we extracted the three photon absorption coefficient for GaAs at three wavelengths in the near infrared. We show that the optical Kerr effect is large enough to switch a cavity resonance with a high \emph{Q} ($Q>1000$) photonic cavity.
We investigate the various routes to spatiotemporal chaos in Kerr optical frequency combs obtained through pumping an ultra-high quality whispering-gallery mode resonator with a continuous-wave laser. The Lugiato-Lefever model is used to build bifurcation diagrams with regards to the parameters that are externally controllable, namely, the frequency and the power of the pumping laser. We show that the spatiotemporal chaos emerging from Turing patterns and solitons display distinctive dynamical features. Experimental spectra of chaotic Kerr combs are also presented for both cases, in excellent …
It has been shown that a slab of a negative index material can behave as a superlens enhancing the imaging resolution beyond the wavelength limit. We show here that if such a slab possesses in addition some magneto-optical activity, it could act as an ideal optical filter and exhibit an extraordinary transverse magneto-optical Kerr effect. Moreover, we show that losses, which spoil the imaging resolution of these lenses, are a necessary ingredient to observe this effect.
We investigate the optical Kerr nonlinearity and multi-photon absorption (MPA) properties of DSTMS excited by femtosecond pulses at a wavelengths of 1.43 μm, which is optimal for terahertz generation via difference frequency mixing. The MPA and the optical Kerr coefficients of DSTMS at 1.43 μm are strongly anisotropic indicating a dominating contribution from cascaded 2nd-order nonlinearity. These results suggest that the saturation of the THz generation efficiency is mainly related to the MPA process and to a spectral broadening caused by cascaded 2nd-order frequency mixing within DSTMS
We show that double-charged optical vortices can be generated with the help of Kerr electrooptic effect in either single crystals or isotropic media, including gaseous and liquid ones. We analyze possibilities for the vortex generation via the Kerr effect for different point group of symmetry and formulate the appropriate conditions. We prove that the crystals, textures and the isotropic media most suitable for the generation of double-charged optical vortices should belong to the symmetry groups 622, 6mm, 6/mmm, 6, 6/m, inf/m, inf, inf 2, inf mm, inf/mmm, inf/inf/mmm, and inf/inf2.
A model for a non-Kerr cylindrical nematic fiber is presented. We use the multiple scales method to show the possibility of constructing different kinds of wavepackets of transverse magnetic (TM) modes propagating through the fiber. This procedure allows us to generate different hierarchies of nonlinear partial differential equations (PDEs) which describe the propagation of optical pulses along the fiber. We go beyond the usual weakly nonlinear limit of a Kerr medium and derive an extended Nonlinear Schrodinger equation (eNLS) with a third order derivative nonlinearity, governing the dynamics …
High index dielectric nanoantennas excited at Mie-type resonances have exhibited enormous enhancement of optical nonlinearity. Such nanostructures have been actively studied by researchers in the last years. The present work provides the first numerical analysis study of the optical Kerr effect of nanocomposites consisting of high refractive index (GaP) spheres at the wavelength of 532~nm. This is done by means of three-dimensional finite-difference time-domain (FDTD) simulations. The effective nonlinear refractive index of $0.8$~$μ$m thick nanocomposites and metasurfaces is evaluated. It is s…
On-chip optical nonreciprocal devices are vital components for integrated photonic systems and scalable quantum information processing. Nonlinear optical isolators and circulators have attracted considerable attention because of their fundamental interest and their important advantages in integrated photonic circuits. However, optical nonreciprocal devices based on Kerr or Kerr-like nonlinearity are subject to dynamical reciprocity when the forward and backward signals coexist simultaneously in a nonlinear system. Here, we theoretically propose a method for realizing on-chip nonlinear isolator…
Using a generalized Gaussian beam decomposition method we determine the propagation of a Laguerre-Gaussian beam that has passed through a thin nonlinear optical Kerr medium. The orbital angular momentum per photon of the beam is found to be conserved while the component beams change. As an illustration of applications, we propose and demonstrate a z-scan experiment using an $LG_0^1$ beam and a dye-doped polymer film.
We show that scattering-based interaction among nearly degenerate optical modes is the key factor in low threshold generation of Kerr frequency combs in nonlinear optical resonators possessing small group velocity dispersion (GVD). The mode interaction is capable of producing drastic change in the local GVD, resulting in either a significant reduction or increase of the oscillation threshold. It is also responsible for the majority of observed combs in resonators characterized with large normal GVD. We present results of our numerical simulations as well as supporting experimental data.
Mode interaction in silicon nitride micro-resonators is investigated. We provide clear experimental evidence of mode interaction between two family modes and mode interaction is demonstrated to be the cause of the comb generation in resonators with normal dispersion.
The possibility of generation and propagation of ultraslow bright optical solitons in asymmetric three-coupled quantum well systems is studied in this paper. These bright solitons owe their existence to Kerr and quintic nonlinearities which arise due to a probe pulse and two controlling laser beams. We also demonstrate numerically that these solitons are stable. The modulation instability of a continuous or quasi-continuous wave probe beam has been also investigated and the role of quintic nonlinearity in suppressing this instability addressed.
Kerr microresonators generate interesting and useful fundamental states of electromagnetic radiation through nonlinear interactions of continuous-wave (CW) laser light. Using photonic-integration techniques, functional devices with low noise, small size, low-power consumption, scalable fabrication, and heterogeneous combinations of photonics and electronics can be realized. Kerr solitons, which stably circulate in a Kerr microresonator, have emerged as a source of coherent, ultrafast pulse trains and ultra-broadband optical-frequency combs. Using the f-2f technique, Kerr combs support carrier-…
This chapter describes the discovery and stable generation of temporal dissipative Kerr solitons in continuous-wave (CW) laser driven optical microresonators. The experimental signatures as well as the temporal and spectral characteristics of this class of bright solitons are discussed. Moreover, analytical and numerical descriptions are presented that do not only reproduce qualitative features but can also be used to accurately model and predict the characteristics of experimental systems. Particular emphasis lies on temporal dissipative Kerr solitons with regard to optical frequency comb gen…
Using an enhanced optically heterodyned optical Kerr effect method and a theoretical description of the interactions between an optical beam, a single layer of graphene, and its substrate, we provide experimental answers to questions raised by theoretical models of graphene third-order nonlinear optical response. In particular, we measure separately the time response of the two main tensor components of the nonlinear susceptibility, we validate the assumption that the out-of plane tensor components are small, and we quantify the optical impact of the substrate on the measured coefficients. Our…
Photonic crystal fibers doped with silver nanoparticles exhibit the Kerr nonlinearity that can be positive or negative depending on wavelength and vanishes at a specific wavelength. We study numerically how the simultaneous presence of a zero-nonlinearity wavelength (ZNW) and a zero-dispersion wavelength affects evolution of soliton and supercontinuum generation inside such fibers and find a number of unique features. The existence of negative nonlinearity allows soliton formation even in the normaldispersion region of the fiber, and the ZNW acts as a barrier for the Raman-induced red shift of…
