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 projecting we use allows a direct generalization to multi-mode fiber case.
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 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…
Kerr-effect-induced changes of the polarization state of light are well known in pulsed laser systems. An example is nonlinear polarization rotation, which is critical to the operation of many types of mode-locked lasers. Here, we demonstrate that the Kerr effect in a high-finesse Fabry-Pérot resonator can be utilized to control the polarization of a continuous wave laser. It is shown that a linearly-polarized input field is converted into a left- or right-circularly-polarized field, controlled via the optical power. The observations are explained by Kerr-nonlinearity induced symmetry breaking…
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.
We demonstrate polarization multiplexed dissipative Kerr solitons in an on-chip silicon nitride micro-resonator. In our experiment, TE- and TM-polarized soliton can be individually generated and controlled, thanks to their weak mutual interaction as the result of sufficiently different repetition rates and orthogonal polarization states. Furthermore, we find that TE- and TM-polarized solitons usually exhibit uncorrelated time jitters, therefore the frequency and phase coherence between the polarization multiplexed soliton microcombs change dramatically as a function of pump laser parameters, b…
Flexible management of light polarization is necessary to develop the technologies of optical fiber communications. However, it is still a great challenge to manipulate optical polarization in all-fiberbased devices. Here we present a novel structural design of three-core fiber couplers to create arbitrary polarization management by embedding a vector mode segregated core within the conventional fiber couplers. We take advantages of these coupling structures to achieve polarization split, rotation, and exchange, as three essential polarization managements for fiber-guided modes. We study these…
Multimode optical fibers have seen increasing applications in communication, imaging, high-power lasers and amplifiers. However, inherent imperfections and environmental perturbations cause random polarization and mode mixing, making the output polarization states very different from the input one. This poses a serious issue for employing polarization sensitive techniques to control light-matter interactions or nonlinear optical processes at the distal end of a fiber probe. Here we demonstrate a complete control of polarization states for all output channels by only manipulating the spatial wa…
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…
Symmetry-Broken Cavity Solitons and Collective Polarization Conformity in Fabry-Perot Kerr Resonators
Université Bourgogne Europe（勃艮第欧洲大学）；CNRS（法国国家科学研究中心）；Max Planck Institute for the Science of Light（马克斯·普朗克光科学研究所）；Friedrich Alexander University Erlangen-Nuremberg（埃尔兰根-纽伦堡弗里德里希·阿历山大大学）；Alexandria University（亚历山大大学）；Huazhong University of Science and Technology（华中科技大学）；University of Strathclyde（思克莱德大学）；The University of Auckland（奥克兰大学）
In this paper, we demonstrate the polarization-multiplexed system capable of generating two stable optical frequency combs with tunable frequency differences and a large extinction ratio. Also, the polarization dynamics of a dual-frequency comb generated from a single mode-locked Er-doped fiber laser are experimentally studied. The obtained results will extend the application to areas such as polarization spectroscopy and dual-comb-based polarimetry.
Polarization maintaining (PM) fibers are meant to maintain linear polarization along a preferred axis. A PM fiber can be seen as the fiber version of a very high order waveplate, designed with different refractive indices along two orthogonal axes. It is shown that monitoring the polarization of initially circularly polarized light sent through a PM fiber, leads not only to new sensing methods, but also to power control, saturable absorption, and optical path stabilization. Even at peak power levels not exceeding a few mW, nonlinear transmission is detected, with time constants in the microsec…
We propose a robust spectral beam combining scheme using wavelength dependent polarisation rotators and polarization beam combiners. We successfully demonstrated the concept for two Yb-doped fiber lasers at 1064nm and 1092nm up to a total input power of 90W. The results reveal a very good combining efficiency and the potential for scaling to high power operations in this method of beam combining.
A bidirectional all polarization maintaining fiber laser as a highly sensitive sensor for rotation is presented. This sensor is based on intracavity phase interferometry with application in inertial sensing, magnetometry, displacements and nonlinear index. The bios beat note of this gyroscopic laser is lowered to 166 KHz implementing a symmetric configuration including two parts of Er-doped fibers.
Efficient slow and fast light fiber devices based on narrow band optical parametric amplification require a strict polarization control of the waves involved in the interaction. The use of high birefringence and spun fibers is studied theoretically, possible impairments evaluated, and design parameters determined.
We report on a polarization maintaining large mode area photonic crystal fiber. Unlike, previous work on polarization maintaining photonic crystal fibers, birefringence is introduced using stress applying parts. This has allowed us to realize fibers, which are both single mode at any wavelength and have a practically constant birefringence for any wavelength. The fibers presented in this work have mode field diameters from about 4 to 6.5 micron, and exhibit a typical birefringence of 1.5e-4.
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 report on experimental observations of coexistence and interactions between nonlinear states with different polarizations in a passive Kerr resonator driven at a single carrier frequency. Using a fiber ring resonator with adjustable birefringence, we partially overlap nonlinear resonances of two orthogonal polarization modes, achieving coexistence between different nonlinear states by locking the driving laser frequency at various points within the overlap region. In particular, we observe coexistence between temporal cavity solitons and modulation instability patterns, as well as coexisten…
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…
An extensive study of the alignment between the pump, the signal and the polarization dependent gain (PDG) vectors in stimulated Brillouin amplification in randomly birefringent fibers is realized by numerically integrating the equations governing the propagation. At the fiber output, the signal tends to align to the PDG vector for large pump power because of the nonlinear polarization pulling effect. The PDG vector, for large random birefringence, aligns to a state that has the same linear component of the pump but opposite circular component.
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…
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…
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…
In this paper, we demonstrate that it is possible to combine both Raman amplification and polarization attraction of a signal wave in a single optical fiber by means of a counterpropagating scheme. Experiments were performed near 1550 nm in a continuous wave regime and by means of a 10 Gbit / s return-to-zero signal injected in a 20 kmlong low polarization mode dispersion optical fiber. Complete repolarization and 6.7 dB amplification of the signal wave was achieved by injecting a 850 mW, 1480 nm counterpropagating polarized pump wave.
Investigation of internal polarization dynamics of vector dissipative-soliton-resonance (DSR) pulses in a mode-locked fiber laser is presented. Stable vector DSR pulses are experimentally ob- served. Using a waveplate-analyzer configuration, we find that polarization is not uniform across a resonant dissipative soliton. Specifically, although the central plane wave of the resonant dissi- pative soliton acquires nearly a fixed polarization, the fronts feature polarization states that are different and spatially varying. This distinct polarizaiton distribution is maintained while the whole solit…
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…
We study continuous-wave light propagation through a twisted birefringent single-mode fiber amplifier with saturable nonlinearity. The corresponding coupled-mode system is isomorphic to a non-Hermitian nonlinear dimer, and gives rise to analytic polarization-mode dynamics. It provides an optical simulation of the semi-classical non-Hermitian Bose-Hubbard model, and suggests its use for the design of polarization circulators and filters, as well as sources of polarized light.
In this paper, we report the observation and exploitation of the capability of light to self-organize its state-of-polarization, upon propagation in optical fibers, by means of a device called Omnipolarizer. The principle of operation of this system consists in a counter-propagating four-wave mixing interaction between an incident signal and its backward replica generated at the fiber output thanks to a reflective fiber loop. We have exploited this self-induced polarization tracking phenomenon for all-optical data processing and successfully demonstrated the spontaneous repolarization of a 40-…
We examine properties of an ultrashort laser pulse propagating through an artificial Saturable Absorber based on Nonlinear Polarization Evolution device which has been realized with Polarization Maintaining fibers only (PM NPE). We study and compare in-line and Faraday Mirror geometries showing that the latter is immune to errors in the PM NPE construction. Experimental results for the transmission measurements of the PM NPE setup for different input linear polarization angles and various input pulse powers are presented. We show that PM NPE topology is of crucial importance for controlling th…
Our aim is to transpose the polarization control by mechanical stress usually applied to single mode fibers, to the (TM01, TE01,HEev21,HEod21) annular mode family. Nevertheless, the quasi degeneracy of these four modes makes the situation more complex than with the fundamental mode HE11. We propose a simple device based on periodic perturbation and mode coupling to produce the radially polarized TM01 mode or at least one single of the four modes at the extremity of an arbitrarily long fiber, the conversion to TM01 mode being achievable by classical crystalline plates.
In this letter, to the best of our knowledge, a new type of hollow-core anti-resonant fiber (HC-ARF) design using hybrid silica/chalcogenide cladding is presented for single-polarization, high-birefringence, and endlessly single-mode operation at 2 $μ$m wavelength. We show that the inclusion of a chalcogenide layer in the cladding allows strong suppression of $x$-polarization, while maintaining low propagation loss and single-mode propagation for $y$-polarization. The optimized HC-ARF design includes a combination of low propagation loss, high-birefringence, and polarization-extinction ratio (…
We present a theoretical model and its efficient numerical implementation for the simulation of wavelength-swept waveform propagation in fiber systems such as Fourier domain mode-locked (FDML) lasers, fully accounting for the polarization dynamics in fiber spools and further polarization dependent optical components in the setup. This approach enables us to perform long-time simulations of the FDML laser dynamics over more than 100000 cavity roundtrips, as required for some FDML configurations to ensure convergence to the steady state operating regime. The model is validated against experiment…
We demonstrated an all polarization-maintaining fiber (PMF) laser which could offer selective transverse mode emission. Offset and cross splicing between PMF sections was used to generate higher order mode and to yield a birefringence induced mode filter. Polarization rotation technique (PRT) was used to select the output beam profile. Both linear cavity and ring cavity were explored. Experimentally, 360° rotating LP11 mode and OAM vortex beam with plus and minus 1 topological charges have been realized from an all PMF linear cavity laser and a ring cavity laser respectively.
The dynamics of the state of polarization in single mode and multimode fiber amplifiers are presented. The experimental results reveal that although the state of polarizations at the output can vary over a large range when changing the temperatures of the fiber amplifiers, the variations are significantly reduced when resorting to the principal states of polarization in single mode fiber amplifiers and principal modes in multimode fiber amplifiers.
