An explanation of SRS beam cleanup in graded-index fibers and the absence of SRS beam cleanup in step-index fibers

Theoretical study of graded-index fiber for beam quality improvement and SRS suppression

A confined-doped graded-index fiber model was established with reference to Nufern's 42C ytterbium-doped fiber. The core NA of the fiber is ∼0.06; the doping/core/cladding diameter is 30/42/250 µm; and the gain ion doping distribution is double parabolic. Based on a forward tandem-pumped amplifier structure, the numerical simulation was carried out on the physics characters of the fiber model. The fourth-order Runge-Kutta method was used to solve the boundary value problem during the numerical simulation. The differences between the graded-index fiber (GIF) and the step-index fiber (SIF) were studied theoretically, and the results illuminated that the beam quality of the GIF was better than the SIF. The stimulated Raman scattering (SRS) power in the GIF was lower than that in the SIF. These results show that the GIF has great potential for increasing the laser output power while maintaining good beam quality and can provide theoretical guidance and reference to experimental research of the high-power fiber laser.

Three octave visible to mid-infrared supercontinuum generation seeded by multimode silica fiber pumped at 1064 nm

Hyperspectral spectroscopy requires light sources with wide spectral ranges from the visible to the mid-infrared. Here, we demonstrate the first fiber-based mid-infrared supercontinuum covering three octaves of frequency by leveraging 1-µm laser technology. The process consists in spectral broadening of a 1064-nm pump toward 0.48-2.5 µm in a graded-index multimode fiber, followed by a fluoro-indate fiber used to reach deeper into the near infrared (4.3 µm). Finally, an arsenic selenide chalcogenide fiber allows us to reach the 6-µm wavelength region, providing a 0.75-6-µm supercontinuum. We illustrate the potential of this light source by recording mid-infrared absorption spectra of organic compounds.

Spatial beam narrowing in multimode graded-index fiber amplifiers: an analytic approach

Doped and optically pumped graded-index (GRIN) fibers can be used to amplify an optical beam such that its spatial quality is improved at the output end of the fiber compared with that of the unamplified beam. We develop a simple model of the amplification process in such GRIN fiber amplifiers and show that the resulting equations can be solved analytically with suitable approximations. The solution shows that the width of the amplifying beam oscillates but also becomes narrower because of the radial dependence of the optical gain. The main advantage of our simplified approach is that it provides an analytic expression for the damping distance of beam-width oscillations that shows clearly the role played by various physical parameters.

Nonlinear dynamics of beam self-cleaning on LP11 mode in multimode fibers

We investigate the modal energy flow of the femtosecond-pulsed beam self-cleaning on LP₁₁ mode with the influence of different factors such as the initial fraction of LP₁₁ mode, initial peak power, distribution of high-order modes and the numerical aperture of the fiber. It is interesting that there is a critical value of the initial peak power, Pcr, which is the watershed, not only in the quantitatively dominant transverse mode converting from LP₁₁ mode to LP₀₁ mode, but also in the behavior of HOMs of the transition from Attractor to chaos. Our simulation results may provide a novel perspective to understanding the beam self-cleaning on LP₁₁ mode.

Mechanism of brightness enhancement in multimode LD-pumped graded-index fiber Raman lasers: numerical modeling

We develop a comprehensive theory for describing the experimental beam profiles from multimode fiber Raman lasers. We take into account the presence of random linear mode coupling, Kerr beam self-cleaning and intra-cavity spatial filtering. All of these factors play a decisive role in shaping the Stokes beam, which has a predominant fundamental mode content. Although the highly multimode pump beam is strongly depleted, it remains almost insensitive to the different physical effects. As a result, the intensity of the output Stokes beam is an order of magnitude higher than the pump intensity at its maximum, in quantitative agreement with the experimental results and in contrast with the simplified balance model.

Spatio-spectral beam control in multimode diode-pumped Raman fibre lasers via intracavity filtering and Kerr cleaning

Multimode fibres provide a promising platform for boosting the capacity of fibre links and the output power of fibre lasers. The complex spatiotemporal dynamics of multimode beams may be controlled in spatial and temporal domains via the interplay of nonlinear, dispersive and dissipative effects. Raman nonlinearity induces beam cleanup in long graded-index fibres within a laser cavity, even for CW Stokes beams pumped by highly-multimode laser diodes (LDs). This leads to a breakthrough approach for wavelength-agile high-power lasers. However, current understanding of Raman beam cleanup is restricted to a small-signal gain regime, being not applicable to describing realistic laser operation. We solved this challenge by experimentally and theoretically studying pump-to-Stokes beam conversion in a graded-index fibre cavity. We show that random mode coupling, intracavity filtering and Kerr self-cleaning all play a decisive role for the spatio-spectral control of CW Stokes beams. Whereas the depleted LD pump radiation remains insensitive to them.

Cascaded Generation in Multimode Diode-Pumped Graded-Index Fiber Raman Lasers

We review our recent experimental results on the cascaded Raman conversion of highly multimode laser diode (LD) pump radiation into the first- and higher-order Stokes radiation in multimode graded-index fibers. A linear cavity composed of fiber Bragg gratings (FBGs) inscribed in the fiber core is formed to provide feedback for the first Stokes order, whereas, for the second order, both a linear cavity consisting of two FBGs and a half-open cavity with one FBG and random distributed feedback (RDFB) via Rayleigh backscattering along the fiber are explored. LDs with different wavelengths (915 and 940 nm) are used for pumping enabling Raman lasing at different wavelengths of the first (950, 954 and 976 nm), second (976, 996 and 1019 nm) and third (1065 nm) Stokes orders. Output power and efficiency, spectral line shapes and widths, beam quality and shapes are compared for different configurations. It is shown that the RDFB cavity provides higher slope efficiency of the second Stokes generation (up to 70% as that for the first Stokes wave) with output power up to ~30 W, limited by the third Stokes generation. The best beam quality parameter of the second Stokes beam is close to the diffraction limit (M2~1.3) in both linear and half-open cavities, whereas the line is narrower (<0.2 nm) and more stable in the case of the linear cavity with two FBGs. However, an optimization of the FBG reflection spectrum used in the half-open cavity allows this linewidth value to be approached. The measured beam profiles show the dip formation in the output pump beam profile, whereas the first and second Stokes beams are Gaussian-shaped and almost unchanged with increasing power. A qualitative explanation of such behavior in connection with the power evolution for the transmitted pump and generated first, second and third Stokes beams is given. The potential for wavelength tuning of the cascaded Raman lasers based on LD-pumped multimode fibers is discussed.

Seeing the beam cleanup effect in a high-power graded-index-fiber Raman amplifier based on mode decomposition

Due to the beam cleanup effect, brightness enhancement (BE) can be achieved in a Raman fiber amplifier (RFA) based on multimode (MM) graded-index (GRIN) fiber. In this Letter, a novel, to the best of our knowledge, diagnostic tool of mode decomposition (MD) based on a stochastic parallel gradient descent algorithm is demonstrated to observe the beam cleanup effect in a GRIN-fiber-based RFA for the first time, to our knowledge. During output power boosting up to 405 W at 1130 nm, the output beam quality factor M² improves from 3.45 to 2.88, with a BE factor of 10.5. The MD results based on the near-field beam profiles from RFA indicate that the modal weight of the fundamental mode increases from 74.5% to 87%, confirming that the fundamental mode dominates with higher Raman gain. Moreover, the beam quality is found to be limited by the existence of a higher-order (Laguerre-Gaussian) LG₁₀ mode, which is insensitive to the beam cleanup effect. The correlation coefficient reaches over 0.98 for all MD results. Thus, the accuracy of the MD method is high enough to provide further valuable insight into the physics of spatiotemporal beam dynamics in MM GRIN fiber.

Conditions for walk-off soliton generation in a multimode fiber

It has been recently demonstrated that multimode solitons are unstable objects which evolve, in the range of hundreds of nonlinearity lengths, into stable single-mode solitons carried by the fundamental mode. We show experimentally and by numerical simulations that femtosecond multimode solitons composed by non-degenerate modes have unique properties: when propagating in graded-index fibers, their pulsewidth and energy do not depend on the input pulsewidth, but only on input coupling conditions and linear dispersive properties of the fiber, hence on their wavelength. Because of these properties, spatiotemporal solitons composed by non-degenerate modes with pulsewidths longer than a few hundreds of femtoseconds cannot be generated in graded-index fibers.

Scalable optical learning operator

Today's heavy machine learning tasks are fueled by large datasets. Computing is performed with power-hungry processors whose performance is ultimately limited by the data transfer to and from memory. Optics is a powerful means of communicating and processing information, and there is currently intense interest in optical information processing for realizing high-speed computations. Here we present and experimentally demonstrate an optical computing framework called scalable optical learning operator, which is based on spatiotemporal effects in multimode fibers for a range of learning tasks including classifying COVID-19 X-ray lung images, speech recognition and predicting age from images of faces. The presented framework addresses the energy scaling problem of existing systems without compromising speed. We leverage simultaneous, linear and nonlinear interaction of spatial modes as a computation engine. We numerically and experimentally show the ability of the method to execute several different tasks with accuracy comparable with a digital implementation.

Over 400 W graded-index fiber Raman laser with brightness enhancement

The power scaling on all-fiberized Raman fiber oscillator with brightness enhancement (BE) based on multimode graded-index (GRIN) fiber is demonstrated. Thanks to beam cleanup of GRIN fiber itself and single-mode selection properties of the fiber Bragg gratings inscribed in the center of GRIN fiber, the efficient BE is realized. For the laser cavity with single OC FBG, continuous-wave power of 334 W with an M² value of 2.8 and BE value of 5.6 were obtained at a wavelength of 1120 nm with an optical-to-optical efficiency of 49.6%. Furthermore, the cavity reflectivity is increased by employing two OC FBGs to scale the output power up to 443 W, while the corresponding M² is 3.5 with BE of 4.2. To our best knowledge, it is the highest power in Raman oscillator based on GRIN fiber.

Multimode LD-pumped all-fiber Raman laser with excellent quality of 2nd-order Stokes output beam at 1019 nm

A multimode all-fiber Raman laser enabling cascaded generation of high-quality 1019-nm output beam at direct pumping by highly-multimode (M²>30) 940-nm laser diodes has been demonstrated. The laser is made of a 100/140 graded-index fiber with special in-fiber Bragg gratings which secure sequential generation of the 1^st (976 nm) and 2^nd (1019 nm) Stokes orders. Comparing different 1019-nm cavity structures shows that the half-open cavity with one FBG and distributed feedback via random Rayleigh backscattering provides excellent quality (M²∼1.3) with higher slope efficiency of pump-to-2^nd Stokes conversion than in the conventional 2-FBG cavity. The maximum achieved slope efficiency amounts to about 40% at output powers of up to 12 W limited by the 3^rd Stokes generation.

Brightness enhancement in random Raman fiber laser based on a graded-index fiber with high-power multimode pumping

A brightness-enhanced random Raman fiber laser (RRFL) with maximum power of 306 W at 1120 nm is demonstrated. A half-open cavity is built based on a graded-index (GRIN) passive fiber and single high-reflective fiber Bragg grating written in it directly. Due to the beam cleanup effect in the GRIN fiber enhanced in the half-open RRFL cavity, the output beam quality factor M² is improved from 9.15 (pump) to 1.76-2.35 (Stokes) depending on power, while the pump-Stokes brightness enhancement (BE) factor increases proportionally to output power reaching 6.1 at maximum. To the best of our knowledge, this is the highest power GRIN RRFL with BE.

Efficient low-brightness-pumped Raman amplification of a single high-order Bessel mode in 335-m of 70-µm-diameter silica-core step-index fiber

We experimentally demonstrate Raman amplification of signal pulses in a high-order Bessel mode (LP₀₆) at a wavelength of 1121 nm in a 335-m step-index fiber with a 70-µm diameter, 0.227-NA pure-silica core. This was pumped by 5-ns multimode pulses at 1065 nm from a Yb-doped fiber master oscillation power amplifier. The mode purity of the amplified pulses is well preserved to 23 dB of average-power gain, to 774 W of peak power in 2 ns pulses at a 20 kHz repetition rate, when pumped with a peak power of 942 W. The pump depletion as averaged over the signal pulses reaches 59%. We believe, to the best of our knowledge, that this is the first demonstration of stable mode propagation and Raman amplification of a single Bessel-like higher-order mode in a fiber of hundreds of meters. This shows the potential for efficient power scaling of a single signal mode with low-brightness pumping, comparable with that from continuous-wave multimode diode lasers.

Mode dynamics in high-power Yb-Raman fiber amplifier

Yb-Raman fiber amplifier (YRFA) is a compact setup that can be applied to achieve high-power narrow linewidth or special wavelength lasers. In this Letter, we realized a high-power YRFA with seed wavelengths of 1090 nm and 1150 nm, tandem-pumped by a 1018 nm fiber laser. The dynamic of mode interaction has been carefully studied. The beam cleanup effect in the large mode area, step-index fiber has been observed for the first time, to the best of our knowledge, when the pump power ranges from 800 W to 1700 W. A model taking into account the Raman mode interaction is proposed to explain this phenomenon, which agrees well with the experiments. The mode instability (MI) effect is also observed in the amplifier, and the threshold is about 2 kW, which is lower than the conventional Yb-doped fiber amplifier. Stimulated Raman scattering is attributed to the onset of MI. Finally, the 1338 W 1150 nm laser is achieved by this YRFA, which we believe to be the highest power reported at this wavelength.

Spatial Beam Self-Cleaning in Second-Harmonic Generation

We experimentally demonstrate the spatial self-cleaning of a highly multimode optical beam, in the process of second-harmonic generation in a quadratic nonlinear potassium titanyl phosphate crystal. As the beam energy grows larger, the output beam from the crystal evolves from a highly speckled intensity pattern into a single, bell-shaped spot, sitting on a low energy background. We demonstrate that quadratic beam cleanup is accompanied by significant self-focusing of the fundamental beam, for both positive and negative signs of the linear phase mismatch close to the phase-matching condition.

2 kW high-efficiency Raman fiber amplifier based on passive fiber with dynamic analysis on beam cleanup and fluctuation

In this paper, we study the power scaling in high power continuous-wave Raman fiber amplifier employing graded-index passive fiber. The maximum output power reaches 2.087 kW at 1130 nm with an optical conversion efficiency of 90.1% (the output signal power versus the depleted pump power). To the best of our knowledge, this is the highest power in the fields of Raman fiber lasers based merely on Stokes radiation. The beam quality parameter M² improves from 15 to 8.9 during the power boosting process, then beam spot distortion appears at high power level. This is the first observation and analysis on erratic dynamic properties of the transverse modes in high power Raman fiber amplifier.

High-efficiency laser wavelength conversion in deuterium-filled hollow-core photonic crystal fiber by rotational stimulated Raman scattering

We report here, to the best of our knowledge, for the first time high-efficiency laser wavelength conversion from 1.5 µm band to 1.7 µm band in deuterium-filled hollow-core photonic crystal fibers by rotational stimulated Raman scattering (SRS). Due to the special transmission properties of this low-loss hollow-core fiber, the ordinary dominant vibrational SRS is suppressed, permitting efficient conversion to the rotational stokes wave in a single-pass configuration pumped by a fiber amplified and modulated tunable 1.55 µm diode laser. Using proper pump pulse energy and gas pressure, the power conversion efficiencies over the whole output laser wavelength range from 1640 nm to 1674 nm are higher than 48%. And the maximum Raman conversion efficiency of 61.2% is achieved with 20 m fiber and 20 bar deuterium pressure pumped at 1540 nm, giving a maximum average power of about 0.8 W (pulse energy of 1.6 µJ). This work points to a new way for engineerable and compact fiber lasers operation at 1.7 µm band, which has significant applications in biological imaging, laser medical treatment, material processing and detecting.

All-fiberized transverse mode-switching method based on temperature control

In this paper, an all-fiberized transverse mode-switching method was proposed based on temperature control of few-mode (FM) fiber Bragg gratings (FBGs). Two types of fibers were selected to fabricate the FBG pair in order to match the reflection peaks of the desired mode. The temperature-dependence property of the FM FBGs has been utilized to tune the reflection spectra. Through temperature control, 20 W level output power was obtained when the output laser was switched between the LP₁₁ mode and the LP₀₁ mode in both an all-fiberized ytterbium-doped laser and a Raman laser, which is increased by ∼2 orders of magnitude compared with previous demonstrations (almost less than 100 mW).

Tapered-fiber-enabled high-power, high-spectral-purity random fiber lasing

Random distributed feedback Raman fiber laser is a new kind of light source that can be applied to generate a high-power laser. In this Letter, we report on a high-power, high-spectral-purity random Raman fiber laser based on tapered fiber, in which the four-wave mixing (FWM) effect has been sufficiently suppressed. By choosing an appropriate tapered fiber length, we achieve a maximum random laser output of 491 W, and the spectral purity can reach to as high as 94%. We carefully compare the influence of different tapered fiber lengths and splicing patterns on the FWM effect by the cutting-back method and lateral-offset splicing. The results show that the transverse modes dispersion is responsible for the appearance of FWM by compensating the phase mismatch. It is believed that a kilowatt-level random laser can be obtained by further optimizing the parameters of tapered fiber.

Cascaded Raman scattering based high power octave-spanning supercontinuum generation in graded-index multimode fibers

A new method to generate multi-watt-level, octave-spanning, spectrally flat supercontinua stemmed from cascaded Raman scattering in graded-index multimode fibers is reported. Formation dynamics of supercontinua are investigated by studying the effect of fiber length and core size. High power handling capacity of the graded-index multimode fibers is demonstrated by power scaling experiments. Pump pulse repetition rate is scaled from kHz to MHz while pump pulse peak power remains same and ~4 W supercontinuum is achieved with 2 MHz pump repetition rate. To the best of our knowledge, this is the highest average power and repetition supercontinuum source ever reported based on a graded-index multimode silica fiber. Spatial properties of the generated supercontinua are measured and Gaussian-like beam profiles obtained for different wavelength ranges. Numerical simulations are performed to investigate underlying nonlinear dynamics in details and well-aligned with experimental observations.

Interplay of Kerr and Raman beam cleaning with a multimode microstructure fiber

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. Stokes Raman 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 leads to the generation of a multimode supercontinuum ranging from 500 nm up to 1800 nm.

Versatile supercontinuum generation in parabolic multimode optical fibers

We demonstrate that the pump's spatial input profile can provide additional degrees of freedom in tailoring at will the nonlinear dynamics and the ensuing spectral content of supercontinuum generation in highly multimoded optical fibers. Experiments and simulations carried out at 1550 nm indicate that the modal composition of the input beam can substantially alter the soliton fission process as well as the resulting Raman and dispersive wave generation that eventually lead to supercontinuum in such a multimode environment. Given the multitude of conceivable initial conditions, our results suggest that it is possible to pre-engineer the supercontinuum spectral content in a versatile manner.

Raman-shifted wavelength-selectable pulsed fiber laser with high repetition rate and high pulse energy in the visible

A high-pulse-energy, diffraction-limited, wavelength-selectable, visible source, based on Raman frequency shifting of a frequency-doubled Yb-doped fiber laser, has been studied. The relative length-scaling laws of Raman gain and self-phase modulation push the design towards short fiber lengths with large core size. It is experimentally demonstrated that the Raman clean-up effect in a graded-index multi-mode fiber is not sufficient to obtain diffraction-limited beam quality in the short fiber length. Thus, a large-core photonic crystal fiber is used to maintain diffraction-limited performance and output pulse energies of ~1 μJ, at a 1-MHz repetition rate and 1.3-ns pulse-width are successfully achieved. This step-tunable visible source should find applications in photoacoustic microscopy.

Spatiotemporal characterization of supercontinuum extending from the visible to the mid-infrared in a multimode graded-index optical fiber

We experimentally demonstrate that pumping a graded-index multimode fiber with sub-ns pulses from a microchip Nd:YAG laser leads to spectrally flat supercontinuum generation with a uniform bell-shaped spatial beam profile extending from the visible to the mid-infrared at 2500 nm. We study the development of the supercontinuum along the multimode fiber by the cut-back method, which permits us to analyze the competition between the Kerr-induced geometric parametric instability and stimulated Raman scattering. We also performed a spectrally resolved temporal analysis of the supercontinuum emission.

Near-infrared multispectral photoacoustic microscopy using a graded-index fiber amplifier

We demonstrate optical resolution photoacoustic microscopy (OR-PAM) of lipid-rich tissue using a multi-wavelength pulsed laser based on nonlinear fiber optics. 1047 nm laser pulses are converted to 1098, 1153, 1215, and 1270 nm pulses via stimulated Raman scattering in a graded-index multimode fiber. Multispectral PAM of a lipid phantom is demonstrated with our low-cost and simple technique.

Kerr self-cleaning of femtosecond-pulsed beams in graded-index multimode fiber

We observe a nonlinear spatial self-cleaning process for femtosecond pulses in graded-index (GRIN) multimode fiber (MMF). Pulses with ∼80 fs duration at 1030 nm are launched into GRIN MMF with 62.5 μm core. The near-field beam profile at the output end of the fiber evolves from a speckled pattern to a centered, bell-shaped transverse structure with increasing pulse energy. The experimental observations agree well with numerical simulations, which show that the Kerr nonlinearity underlies the process. This self-cleaning process may find applications in ultrafast pulse generation and beam-combining.

Temperature dependence of sapphire fiber Raman scattering

Anti-Stokes Raman scattering in sapphire fiber has been observed for the first time. Temperature dependence of Raman peaks' intensity, frequency shift, and linewidth were also measured. Three anti-Stokes Raman peaks were observed at temperatures higher than 300°C in a 0.72-m-long sapphire fiber excited by a second-harmonic Nd YAG laser. The intensity of anti-Stokes peaks are comparable to that of Stokes peaks when the temperature increases to 1033°C. We foresee the combination of sapphire fiber Stokes and anti-Stokes measurement in use as a mechanism for ultrahigh temperature sensing.

Spatiotemporal dynamics of multimode optical solitons

As optical fiber communications and fiber lasers approach fundamental limits there is considerable interest in multimode fibers. In nonlinear science, they represent an exciting environment for complex nonlinear waves. As in single-mode fiber, solitons may be particularly important. Multimode solitons consist of synchronized, non-dispersive pulses in multiple spatial modes, which interact via the Kerr nonlinearity of the fiber. They are expected to exhibit novel spatiotemporal characteristics, dynamics and, like single-mode solitons, may provide a convenient intuitive tool for understanding more complex nonlinear phenomena in multimode fibers. Here we explore experimentally and numerically basic properties and spatiotemporal behaviors of these solitons: their formation, fission, and Raman dynamics.

High-power and highly efficient operation of wavelength-tunable Raman fiber lasers based on volume Bragg gratings

Highly efficient and high-power operation of Raman fiber lasers in fixed-wavelength and wavelength-tunable cavity configurations based on a graded-index multimode fiber is reported. Fixed-wavelength and wavelength tunable operating regimes are achieved using volume Bragg gratings (VBGs) with center wavelengths of 1658 nm and 1750 nm, respectively. The fixed-wavelength laser yielded a maximum output power of 10.5 W at 1658.3 nm with a FWHM linewidth of ~0.1 nm for the launched pump power of 23.4 W, corresponding to a slope efficiency of 82.7% with respect to the launched pump power. The measured beam quality in the form of M² factor is ~1.35, corresponding to the fundamental mode of the fiber. For the wavelength-tunable Raman fiber laser, a wavelength tuning range of 37 nm from 1638.5 to 1675.1 nm is obtained with a maximum output power of 3.6 W at 1658.5 nm for the launched pump power of 13.0 W.

Cascaded random distributed feedback Raman fiber laser operating at 1.2 μm

We demonstrate a CW random distributed feedback Raman fiber laser operating in a 1.2 μm spectral band. The laser generates up to 3.8 W of the quasi-CW radiation at 1175 nm with the narrow spectrum of 1 nm. Conversion efficiency reaches 60%. Up to 1 W is generated at the second Stokes wavelength of 1242 nm. It is shown that the generation spectrum of RDFB Raman fiber laser is much narrower than the spectrum in the system without a weak random feedback.