Multimode fibers (MMFs) are an example of a highly scattering medium, which scramble the coherent light propagating within them to produce seemingly random patterns. Thus, for applications such as imaging and image projection through an MMF, careful measurements of the relationship between the inputs and outputs of the fiber are required. We show, as a proof of concept, that a deep neural network can learn the input-output relationship in a 0.75 m long MMF. Specifically, we demonstrate that a deep convolutional neural network (CNN) can learn the nonlinear relationships between the amplitude of the speckle pattern (phase information lost) obtained at the output of the fiber and the phase or the amplitude at the input of the fiber. Effectively, the network performs a nonlinear inversion task. We obtained image fidelities (correlations) as high as ~98% for reconstruction and ~94% for image projection in the MMF compared with the image recovered using the full knowledge of the system transmission characterized with the complex measured matrix. We further show that the network can be trained for transfer learning, i.e., it can transmit images through the MMF, which belongs to another class not used for training/testing.

The last decade has seen the development of a wide set of tools, such as wavefront shaping, computational or fundamental methods, that allow to understand and control light propagation in a complex medium, such as biological tissues or multimode fibers. A vibrant and diverse community is now working on this field, that has revolutionized the prospect of diffraction-limited imaging at depth in tissues. This roadmap highlights several key aspects of this fast developing field, and some of the challenges and opportunities ahead.

In this Letter, we demonstrate, to the best of our knowledge, the first spatiotemporally mode-locked fiber laser with self-similar pulse evolution. The multimode fiber oscillator generates parabolic amplifier similaritons at 1030 nm with 90 mW average power, 2.3 ps duration, and 37.9 MHz repetition rate. Remarkably, we observe experimentally a near-Gaussian beam quality (M 2 <1.4) at the output of the highly multimode fiber. The output pulses are compressed to 192 fs via an external grating compressor. Numerical simulations are performed to investigate the cavity dynamics which confirm experimental observations of selfsimilar pulse propagation. The reported results open a new direction to investigate new types of pulse besides beam shaping and nonlinear dynamics in spatiotemporal mode-locked fiber lasers.

No abstract

The performance of fiber mode-locked lasers is limited due to the high nonlinearity induced by the spatial confinement of the single-mode fiber core. To massively increase the pulse energy of the femtosecond pulses, amplification is performed outside the oscillator. Recently, spatiotemporal mode-locking has been proposed as a new path to fiber lasers. However, the beam quality was highly multimode, and the calculated threshold pulse energy (>100 nJ) for nonlinear beam self-cleaning was challenging to realize. We present an approach to reach high energy per pulse directly in the mode-locked multimode fiber oscillator with a near single-mode output beam. Our approach relies on spatial beam self-cleaning via the nonlinear Kerr effect, and we demonstrate a multimode fiber oscillator with M 2 < 1.13 beam profile, up to 24 nJ energy, and sub-100 fs compressed duration. Nonlinear beam self-cleaning is verified both numerically and experimentally for the first time in a mode-locked multimode laser cavity. The reported approach is further power scalable with larger core sized fibers up to a certain level of modal dispersion and could benefit applications that require high-power ultrashort lasers with commercially available optical fibers.

No abstract

Spatiotemporal nonlinear interactions in multimode fibers are of interest for beam shaping and frequency conversion by exploiting the nonlinear propagation of different pump regimes from quasi-continuous wave to ultrashort pulses centered around visible to infrared pump wavelengths. The nonlinear effects in multi-mode fibers depend strongly on the excitation condition, however relatively little work has been reported on this subject. Here, we present the first machine learning approach to learn and control the nonlinear frequency conversion inside multimode fibers by tailoring the excitation condition via deep neural networks. Trained with experimental data, deep neural networks are adapted to learn the relation between the spatial beam profile of the pump pulse and the spectrum generation. For different user-defined target spectra, network-suggested beam shapes are applied and control over the cascaded Raman scattering and supercontinuum generation processes are achieved. Our results present a novel method to tune the spectra of a broadband source.

Multimode fibers (MMF) were initially developed to transmit digital information encoded in the time domain. There were few attempts in the late 60s and 70s to transmit analog images through MMF. With the availability of digital spatial modulators, practical image transfer through MMFs has the potential to revolutionize medical endoscopy. Because of the fiber’s ability to transmit multiple spatial modes of light simultaneously, MMFs could, in principle, replace the millimeters-thick bundles of fibers currently used in endoscopes with a single fiber, only a few hundred microns thick. That, in turn, could potentially open up new, less invasive forms of endoscopy to perform high-resolution imaging of tissues out of reach of current conventional endoscopes. Taking endoscopy by its general meaning as looking into, we review in this paper novel ways of imaging and transmitting images using a machine learning approach. Additionally, we review recent work on using MMF to perform machine learning tasks. The advantages and disadvantages of using machine learning instead of conventional methods is also discussed. Methods of imaging in scattering media and particularly MMFs involves measuring the phase and amplitude of the electromagnetic wave, coming out of the MMF and using these measurements to infer the relationship between the input and the output of the MMF. Most notable techniques include analog phase conjugation [A. Yariv, “On transmission and recovery of three-dimensional image information in optical waveguides,” J. Opt. Soc. Am., vol. 66, no. 4, pp. 301–306, 1976; A. Gover, C. Lee, and A. Yariv, “Direct transmission of pictorial information in multimode optical fibers,” J. Opt. Soc. Am., vol. 66, no. 4, pp. 306–311, 1976; G. J. Dunning and R. Lind, “Demonstration of image transmission through fibers by optical phase conjugation,” Opt. Lett., vol. 7, no. 11, pp. 558–560, 1982; A. Friesem, U. Levy, and Y. Silberberg, “Parallel transmission of images through single optical fibers,” Proc. IEEE, vol. 71, no. 2, pp. 208–221, 1983], digital phase conjugation [I. N. Papadopoulos, S. Farahi, C. Moser, and D. Psaltis, “Focusing and scanning light through a multimode optical fiber using digital phase conjugation,” Opt. Express, vol. 20, no. 10, pp. 10583–10590, 2012; I. N. Papadopoulos, S. Farahi, C. Moser, and D. Psaltis, “High-resolution, lensless endoscope based on digital scanning through a multimode optical fiber,” Biomed. Opt. Express, vol. 4, no. 2, pp. 260–270, 2013] or the full-wave holographic transmission matrix method. The latter technique, which is the current gold standard, measures both the amplitude and phase of the output patterns corresponding to multiple input patterns to construct a matrix of complex numbers relaying the input to the output [Y. Choi, et al., “Scanner-free and wide-field endoscopic imaging by using a single multimode optical fiber,” Phys. Rev. Lett., vol. 109, no. 20, p. 203901, 2012; A. M. Caravaca-Aguirre, E. Niv, D. B. Conkey, and R. Piestun, “Real-time resilient focusing through a bending multimode fiber,” Opt. Express, vol. 21, no. 10, pp. 12881–12887; R. Y. Gu, R. N. Mahalati, and J. M. Kahn, “Design of flexible multi-mode fiber endoscope,” Opt. Express, vol. 23, no. 21, pp. 26905–26918, 2015; D. Loterie, S. Farahi, I. Papadopoulos, A. Goy, D. Psaltis, and C. Moser, “Digital confocal microscopy through a multimode fiber,” Opt. Express, vol. 23, no. 18, pp. 23845–23858, 2015]. This matrix is then used for imaging of the inputs or projection of desired patterns. Other techniques rely on iteratively optimizing the pixel value of the input image to perform a particular task (such as focusing or displaying an image) [R. Di Leonardo and S. Bianchi, “Hologram transmission through multi-mode optical fibers,” Opt. Express, vol. 19, no. 1, pp. 247–254, 2011; T. Čižmár and K. Dholakia, “Shaping the light transmission through a multimode optical fibre: complex transformation analysis and applications in biophotonics,” Opt. Express, vol. 19, no. 20, pp. 18871–18884, 2011; T. Čižmár and K. Dholakia, “Exploiting multimode waveguides for pure fibre-based imaging,” Nat. Commun., vol. 3, no. 1, pp. 1–9, 2012; S. Bianchi and R. Di Leonardo, “A multi-mode fiber probe for holographic micromanipulation and microscopy,” Lab Chip, vol. 12, no. 3, pp. 635–639, 2012; E. R. Andresen, G. Bouwmans, S. Monneret, and H. Rigneault, “Toward endoscopes with no distal optics: video-rate scanning microscopy through a fiber bundle,” Opt. Lett., vol. 38, no. 5, pp. 609–611, 2013].