Robustness of Light-Transport Processes to Bending Deformations in Graded-Index Multimode Waveguides

Space-time wave packets in multimode optical fibers with controlled dynamic motions and tunable group velocities

Space-time wave packets (STWPs) with correlated spatial and frequency degrees of freedom exhibit time-dependent spatial interference, thereby giving rise to interesting dynamic evolution behaviors. While versatile spatiotemporal phenomena have been demonstrated in freely propagating fields, coupling spatiotemporal light into multimode fibers remains a fundamental experimental challenge. Whereas synthesizing freely propagating STWPs typically relies on a continuum of plane-wave modes, their multimode-fiber counterparts must be constructed from the discrete set of fiber modes whose propagation constants depend on fiber structures. Here, we demonstrate STWPs with axially controllable motion of the transverse profile and reconfigurable group velocity in graded-index multimode fibers. This is accomplished by introducing a linear association between frequency comb lines and corresponding fiber modes. The synthesized STWPs present dynamic rotation and translation with a 4.8-ps period. Simultaneously, the group velocity can be tuned from positive subluminal and superluminal to negative values (e.g., 0.870, 1.35, 10, and -3.3 × 108 m/s, respectively).

Polarization-resolved transmission matrices of specialty optical fibers

Transmission matrix measurements of multimode fibers are now routinely performed in numerous laboratories, enabling control of the electric field at the distal end of the fiber and paving the way for the potential application to ultrathin medical endoscopes with high resolution. The same concepts are applicable to other areas, such as space division multiplexing, targeted power delivery, fiber laser performance, and the general study of the mode coupling properties of the fiber. However, the process of building an experimental setup and developing the supporting code to measure the fiber's transmission matrix remains challenging and time consuming, with full details on experimental design, data collection, and supporting algorithms spread over multiple papers or lacking in detail. Here, we outline a complete and self-contained description of the specific experiment we use to measure fully polarization-resolved transmission matrices, which enable full control of the electric field, in contrast to the more common scalar setups. Our exact implementation of the full polarization experiment is new and is easy to align while providing flexibility to switch between full-polarization and scalar measurements if desired. We utilize a spatial light modulator to measure the transmission matrix using linear phase gratings to generate the basis functions and measure the distal electric field using phase-shifting interferometry with an independent reference beam derived from the same laser. We introduce a new method to measure and account for the phase and amplitude drift during the measurement using a Levenberg-Marquardt nonlinear fitting algorithm. Finally, we describe creating distal images through the multimode fiber using phase-to-amplitude shaping techniques to construct the correct input electric field through a superposition of the basis functions with the phase-only spatial light modulator. We show that results are insensitive to the choice of phase-to-amplitude shaping technique as quantified by measuring the contrast of a razor blade at the distal end of the fiber, indicating that the simplest but most power efficient method may be the best choice for many applications. We also discuss some of the possible variations on the setup and techniques presented here and highlight the details that we have found key in achieving high fidelity distal control. Throughout the paper, we discuss applications of our setup and measurement process to a variety of specialty fibers, including fibers with harsh environment coatings, coreless fibers, rectangular core fibers, pedestal fibers, and a pump-signal combiner based on a tapered fiber bundle. This demonstrates the usefulness of these techniques across a variety of application areas and shows the flexibility of our setup in studying various fiber types.

"There's plenty of room at the bottom": deep brain imaging with holographic endo-microscopy

Significance

Over more than 300 years, microscopic imaging keeps providing fundamental insights into the mechanisms of living organisms. Seeing microscopic structures beyond the reach of free-space light-based microscopy, however, requires dissection of the tissue-an intervention seriously disturbing its physiological functions. The hunt for low-invasiveness tools has led a growing community of physicists and engineers into the realm of complex media photonics. One of its activities represents exploiting multimode optical fibers (MMFs) as ultra-thin endoscopic probes. Employing wavefront shaping, these tools only recently facilitated the first peeks at cells and their sub-cellular compartments at the bottom of the mouse brain with the impact of micro-scale tissue damage.

Aim

Here, we aim to highlight advances in MMF-based holographic endo-microscopy facilitating microscopic imaging throughout the whole depth of the mouse brain.

Approach

We summarize the important technical and methodological prerequisites for stabile high-resolution imaging in vivo.

Results

We showcase images of the microscopic building blocks of brain tissue, including neurons, neuronal processes, vessels, intracellular calcium signaling, and red blood cell velocity in individual vessels.

Conclusions

This perspective article helps to understand the complexity behind the technology of holographic endo-microscopy, summarizes its recent advances and challenges, and stimulates the mind of the reader for further exploitation of this tool in the neuroscience research.

Spectral-temporal-spatial customization via modulating multimodal nonlinear pulse propagation

Multimode fibers (MMFs) are gaining renewed interest for nonlinear effects due to their high-dimensional spatiotemporal nonlinear dynamics and scalability for high power. High-brightness MMF sources with effective control of the nonlinear processes would offer possibilities in many areas from high-power fiber lasers, to bioimaging and chemical sensing, and to intriguing physics phenomena. Here we present a simple yet effective way of controlling nonlinear effects at high peak power levels. This is achieved by leveraging not only the spatial but also the temporal degrees of freedom during multimodal nonlinear pulse propagation in step-index MMFs, using a programmable fiber shaper that introduces time-dependent disorders. We achieve high tunability in MMF output fields, resulting in a broadband high-peak-power source. Its potential as a nonlinear imaging source is further demonstrated through widely tunable two-photon and three-photon microscopy. These demonstrations provide possibilities for technology advances in nonlinear optics, bioimaging, spectroscopy, optical computing, and material processing.

Wavefront shaping improves the transparency of the scattering media: a review

Significance

Wavefront shaping (WFS) can compensate for distortions by optimizing the wavefront of the input light or reversing the transmission matrix of the media. It is a promising field of research. A thorough understanding of principles and developments of WFS is important for optical research.

Aim

To provide insight into WFS for researchers who deal with scattering in biomedicine, imaging, and optical communication, our study summarizes the basic principles and methods of WFS and reviews recent progress.

Approach

The basic principles, methods of WFS, and the latest applications of WFS in focusing, imaging, and multimode fiber (MMF) endoscopy are described. The practical challenges and prospects of future development are also discussed.

Results

Data-driven learning-based methods are opening up new possibilities for WFS. High-resolution imaging through MMFs can support small-diameter endoscopy in the future.

Conclusion

The rapid development of WFS over the past decade has shown that the best solution is not to avoid scattering but to find ways to correct it or even use it. WFS with faster speed, more optical modes, and more modulation degrees of freedom will continue to drive exciting developments in various fields.

Spatially resolved readout of a Fabry-Perot ultrasound sensor interrogated through a multimode optical fiber using wavefront shaping

The spatially resolved interrogation of a Fabry-Perot ultrasound sensor using a laser beam focused through a multimode fiber is demonstrated. To scan the beam across the sensor as required to read it out, optical wavefront shaping was employed to compensate for the scrambling of light in the fiber. By providing a means to map ultrasound through inexpensive, lightweight fibers, this could lead to new ultrasonic and photoacoustic imaging systems, such as endoscopes and flexible handheld probes.

Referenceless characterization of complex media using physics-informed neural networks

In this work, we present a method to characterize the transmission matrices of complex scattering media using a physics-informed, multi-plane neural network (MPNN) without the requirement of a known optical reference field. We use this method to accurately measure the transmission matrix of a commercial multi-mode fiber without the problems of output-phase ambiguity and dark spots, leading to up to 58% improvement in focusing efficiency compared with phase-stepping holography. We demonstrate how our method is significantly more noise-robust than phase-stepping holography and show how it can be generalized to characterize a cascade of transmission matrices, allowing one to control the propagation of light between independent scattering media. This work presents an essential tool for accurate light control through complex media, with applications ranging from classical optical networks, biomedical imaging, to quantum information processing.

Imaging through a square multimode fiber by scanning focused spots with the memory effect

The existence of a shift-shift memory effect in square waveguides, whereby any translation of the input field induces translations in the output field in four symmetrical directions, has been previously observed by correlation measurements. Here we demonstrate that this memory effect is also observed in real space and can be put to use for imaging purposes. First, a focus is created at the output of a square-core multimode fiber, by wavefront shaping based on feedback from a guide-star. Then, because of the memory effect, four symmetrical spots can be scanned at the fiber output by shifting the wavefront at the fiber input. We demonstrate that this property can be exploited to perform fluorescence imaging through the multimode fiber, without requiring the measurement of a transmission matrix.

Speckle-correlation imaging through a kaleidoscopic multimode fiber

Speckle-correlation imaging techniques are widely used for noninvasive imaging through complex scattering media. While light propagation through multimode fibers and scattering media share many analogies, reconstructing images through multimode fibers from speckle correlations remains an unsolved challenge. Here, we exploit a kaleidoscopic memory effect emerging in square-core multimode fibers and demonstrate fluorescence imaging with no prior knowledge on the fiber. Experimentally, our approach simply requires to translate random speckle patterns at the input of a square-core fiber and to measure the resulting fluorescence intensity with a bucket detector. The image of the fluorescent object is then reconstructed from the autocorrelation of the measured signal by solving an inverse problem. This strategy does not require the knowledge of the fragile deterministic relation between input and output fields, which makes it promising for the development of flexible minimally invasive endoscopes.

Mechanically loaded GRIN lens for endoscopy

Endoscopic techniques are broadly used in medicine. Small diameter endoscopes are either made as fiber bundles or, beneficially, as graded index lenses. Fiber bundles can withstand a mechanical load during their use but the GRIN lens's performance can be affected by its deflection. Here, we analyze the effect of deflection on the image quality and unwanted associated effects with relation to the eye endoscope we designed and built. We also present the result of our effort to make a reliable model of a bent GRIN lens in the OpticStudio software.

110 μm thin endo-microscope for deep-brain in vivo observations of neuronal connectivity, activity and blood flow dynamics

Light-based in-vivo brain imaging relies on light transport over large distances of highly scattering tissues. Scattering gradually reduces imaging contrast and resolution, making it difficult to reach structures at greater depths even with the use of multiphoton techniques. To reach deeper, minimally invasive endo-microscopy techniques have been established. These most commonly exploit graded-index rod lenses and enable a variety of modalities in head-fixed and freely moving animals. A recently proposed alternative is the use of holographic control of light transport through multimode optical fibres promising much less traumatic application and superior imaging performance. We present a 110 μm thin laser-scanning endo-microscope based on this prospect, enabling in-vivo volumetric imaging throughout the whole depth of the mouse brain. The instrument is equipped with multi-wavelength detection and three-dimensional random access options, and it performs at lateral resolution below 1 μm. We showcase various modes of its application through the observations of fluorescently labelled neurones, their processes and blood vessels. Finally, we demonstrate how to exploit the instrument to monitor calcium signalling of neurones and to measure blood flow velocity in individual vessels at high speeds.

Sub-diffraction computational imaging via a flexible multicore-multimode fiber

An ultra-thin multimode fiber is an ideal platform for minimally invasive microscopy with the advantages of a high density of modes, high spatial resolution, and a compact size. In practical applications, the probe needs to be long and flexible, which unfortunately destroys the imaging capabilities of a multimode fiber. In this work, we propose and experimentally demonstrate sub-diffraction imaging through a flexible probe based on a unique multicore-multimode fiber. A multicore part consists of 120 Fermat's spiral distributed single-mode cores. Each of the cores offers stable light delivery to the multimode part, which provides optimal structured light illumination for sub-diffraction imaging. As a result, perturbation-resilient fast sub-diffraction fiber imaging by computational compressive sensing is demonstrated.

Securing Data in Multimode Fibers by Exploiting Mode-Dependent Light Propagation Effects

Multimode fibers hold great promise to advance data rates in optical communications but come with the challenge to compensate for modal crosstalk and mode-dependent losses, resulting in strong distortions. The holographic measurement of the transmission matrix enables not only correcting distortions but also harnessing these effects for creating a confidential data connection between legitimate communication parties, Alice and Bob. The feasibility of this physical-layer-security-based approach is demonstrated experimentally for the first time on a multimode fiber link to which the eavesdropper Eve is physically coupled. Once the proper structured light field is launched at Alice's side, the message can be delivered to Bob, and, simultaneously, the decipherment for an illegitimate wiretapper Eve is destroyed. Within a real communication scenario, we implement wiretap codes and demonstrate confidentiality by quantifying the level of secrecy. Compared to an uncoded data transmission, the amount of securely exchanged data is enhanced by a factor of 538. The complex light transportation phenomena that have long been considered limiting and have restricted the widespread use of multimode fiber are exploited for opening new perspectives on information security in spatial multiplexing communication systems.

Bendable long graded index lens microendoscopy

Graded index (GRIN) lens endoscopy has broadly benefited biomedical microscopic imaging by enabling accessibility to sites not reachable by traditional benchtop microscopes. It is a long-held notion that GRIN lenses can only be used as rigid probes, which may limit their potential for certain applications. Here, we describe bendable and long-range GRIN microimaging probes for a variety of potential micro-endoscopic biomedical applications. Using a two-photon fluorescence imaging system, we have experimentally demonstrated the feasibility of three-dimensional imaging through a 500-µm-diameter and ∼11 cm long GRIN lens subject to a cantilever beam-like deflection with a minimum bend radius of ∼25 cm. Bend-induced perturbation to the field of view and resolution has also been investigated quantitatively. Our development alters the conventional notion of GRIN lenses and enables a range of innovative applications. For example, the demonstrated flexibility is highly desirable for implementation into current and emerging minimally invasive clinical procedures, including a pioneering microdevice for high-throughput cancer drug selection.

A method for single particle tracking through a multimode fiber

Multimode optical fiber (MMF) endoscopes have recently gained widespread attention as a novel tool for imaging deep within tissue using light microscopy. We here present a method for particle tracking through the MMF, which overcomes the lack of a fast enough wide-field fluorescence imaging modality for this type of endoscope, namely a discrete implementation of orbital particle tracking. We achieve biologically relevant tracking speeds (up to 1.2 μm/s) despite using a slow SLM for the wavefront shaping. We demonstrate a tracking accuracy of λ/50 for a 0.3 NA fiber and show tracking of a pinhole moving to mimic Brownian motion with diffusion rates of up to 0.3 μm²/s.

Spin-Wave Channeling in Magnetization-Graded Nanostrips

Magnetization-graded ferromagnetic nanostrips are proposed as potential prospects to channel spin waves. Here, a controlled reduction of the saturation magnetization enables the localization of the propagating magnetic excitations in the same way that light is controlled in an optical fiber with a varying refraction index. The theoretical approach is based on the dynamic matrix method, where the magnetic nanostrip is divided into small sub-strips. The dipolar and exchange interactions between sub-strips have been considered to reproduce the spin-wave dynamics of the magnonic fiber. The transition from one strip to an infinite thin film is presented for the Damon-Eshbach geometry, where the nature of the spin-wave modes is discussed. An in-depth analysis of the spin-wave transport as a function of the saturation magnetization profile is provided. It is predicted that it is feasible to induce a remarkable channeling of the spin waves along the zones with a reduced saturation magnetization, even when such a reduction is tiny. The results are compared with micromagnetic simulations, where a good agreement is observed between both methods. The findings have relevance for envisioned future spin-wave-based magnonic devices operating at the nanometer scale.

Flexible-type ultrathin holographic endoscope for microscopic imaging of unstained biological tissues

Ultrathin lensless fibre endoscopes offer minimally invasive investigation, but they mostly operate as a rigid type due to the need for prior calibration of a fibre probe. Furthermore, most implementations work in fluorescence mode rather than label-free imaging mode, making them unsuitable for general medical diagnosis. Herein, we report a fully flexible ultrathin fibre endoscope taking 3D holographic images of unstained tissues with 0.85-μm spatial resolution. Using a bare fibre bundle as thin as 200-μm diameter, we design a lensless Fourier holographic imaging configuration to selectively detect weak reflections from biological tissues, a critical step for label-free endoscopic reflectance imaging. A unique algorithm is developed for calibration-free holographic image reconstruction, allowing us to image through a narrow and curved passage regardless of fibre bending. We demonstrate endoscopic reflectance imaging of unstained rat intestine tissues that are completely invisible to conventional endoscopes. The proposed endoscope will expedite a more accurate and earlier diagnosis than before with minimal complications.

Ultrathin, high-speed, all-optical photoacoustic endomicroscopy probe for guiding minimally invasive surgery

Photoacoustic (PA) endoscopy has shown significant potential for clinical diagnosis and surgical guidance. Multimode fibres (MMFs) are becoming increasingly attractive for the development of miniature endoscopy probes owing to their ultrathin size, low cost and diffraction-limited spatial resolution enabled by wavefront shaping. However, current MMF-based PA endomicroscopy probes are either limited by a bulky ultrasound detector or a low imaging speed that hindered their usability. In this work, we report the development of a highly miniaturised and high-speed PA endomicroscopy probe that is integrated within the cannula of a 20 gauge medical needle. This probe comprises a MMF for delivering the PA excitation light and a single-mode optical fibre with a plano-concave microresonator for ultrasound detection. Wavefront shaping with a digital micromirror device enabled rapid raster-scanning of a focused light spot at the distal end of the MMF for tissue interrogation. High-resolution PA imaging of mouse red blood cells covering an area 100 µm in diameter was achieved with the needle probe at ∼3 frames per second. Mosaicing imaging was performed after fibre characterisation by translating the needle probe to enlarge the field-of-view in real-time. The developed ultrathin PA endomicroscopy probe is promising for guiding minimally invasive surgery by providing functional, molecular and microstructural information of tissue in real-time.

Wavefront shaping: A versatile tool to conquer multiple scattering in multidisciplinary fields

Optical techniques offer a wide variety of applications as light-matter interactions provide extremely sensitive mechanisms to probe or treat target media. Most of these implementations rely on the usage of ballistic or quasi-ballistic photons to achieve high spatial resolution. However, the inherent scattering nature of light in biological tissues or tissue-like scattering media constitutes a critical obstacle that has restricted the penetration depth of non-scattered photons and hence limited the implementation of most optical techniques for wider applications. In addition, the components of an optical system are usually designed and manufactured for a fixed function or performance. Recent advances in wavefront shaping have demonstrated that scattering- or component-induced phase distortions can be compensated by optimizing the wavefront of the input light pattern through iteration or by conjugating the transmission matrix of the scattering medium. This offers unprecedented opportunities in many applications to achieve controllable optical delivery or detection at depths or dynamically configurable functionalities by using scattering media to substitute conventional optical components. In this article, the recent progress of wavefront shaping in multidisciplinary fields is reviewed, from optical focusing and imaging with scattering media, functionalized devices, modulation of mode coupling, and nonlinearity in multimode fiber to multimode fiber-based applications. Apart from insights into the underlying principles and recent advances in wavefront shaping implementations, practical limitations and roadmap for future development are discussed in depth. Looking back and looking forward, it is believed that wavefront shaping holds a bright future that will open new avenues for noninvasive or minimally invasive optical interactions and arbitrary control inside deep tissues. The high degree of freedom with multiple scattering will also provide unprecedented opportunities to develop novel optical devices based on a single scattering medium (generic or customized) that can outperform traditional optical components.

Repeated imaging through a multimode optical fiber using adaptive optics

Multimode optical fibers (MMF) have shown considerable potential for minimally invasive diffraction-limited fluorescence imaging of deep brain regions owing to their small size. They also look to be suitable for imaging across long time periods, with repeated measurements performed within the same brain region, which is useful to assess the role of synapses in normal brain function and neurological disease. However, the approach is not without challenge. Prior to imaging, light propagation through a MMF must be characterized in a calibration procedure. Manual repositioning, as required for repeated imaging, renders this calibration invalid. In this study, we provide a two-step solution to the problem consisting of (1) a custom headplate enabling precise reinsertion of the MMF implant achieving low-quality focusing and (2) sensorless adaptive optics to correct translational shifts in the MMF position enabling generation of high-quality imaging foci. We show that this approach achieves fluorescence imaging after repeated removal and reinsertion of a MMF.

Learning to image and compute with multimode optical fibers

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].

Side-view holographic endomicroscopy via a custom-terminated multimode fibre

Microendoscopes based on optical fibres have recently come to the fore as promising candidates allowing in-vivo observations of otherwise inaccessible biological structures in animal models. Despite being still in its infancy, imaging can now be performed at the tip of a single multimode fibre, by relying on powerful holographic methods for light control. Fibre based endoscopy is commonly performed en face, resulting in possible damage of the specimen owing to the direct contact between the distal end of the probe and target. On this ground, we designed an all-fibre probe with an engineered termination that reduces compression and damage to the tissue under investigation upon probe insertion. The geometry of the termination brings the field of view to a plane parallel to the fibre's longitudinal direction, conveying the probe with off-axis imaging capabilities. We show that its focusing ability also benefits from a higher numerical aperture, resulting in imaging with increased spatial resolution. The effect of probe insertion was investigated inside a tissue phantom comprising fluorescent particles suspended in agarose gel, and a comparison was established between the novel side-view probe and the standard en face fibre probe. This new concept paves the way to significantly less invasive deep-tissue imaging.

Long-GRIN-Lens Microendoscopy Enabled by Wavefront Shaping for a Biomedical Microdevice: An Analytical Investigation

We analytically investigate the feasibility of long graded-index (GRIN)-lens-based microendoscopes through wavefront shaping. Following the very well-defined ray trajectories in a GRIN lens, mode-dependent phase delay is first determined. Then, the phase compensation needed for obtaining diffraction limited resolution is derived. Finally, the diffraction pattern of the lens output is computed using the Rayleigh-Sommerfeld diffraction theory. We show that diffraction-limited resolution is obtained for a 0.5 mm diameter lens with a length over 1 m. It is also demonstrated that different imaging working distances (WDs) can be realized by modifying the phase compensation. When a short design WD is used, a large imaging numerical aperture (NA) higher than 0.4 is achievable even when a low NA lens (NA = 0.1) is used. The long- and thin-GRIN-lens-based microendoscope investigated here, which is attractive for biomedical applications, is being prioritized for use in a clinical stage microdevice that measures three-dimensional drug responses inside the body. The advance described in this work may enable superior imaging capabilities in clinical applications in which long and flexible imaging probes are favored.

Memory effect assisted imaging through multimode optical fibres

When light propagates through opaque material, the spatial information it holds becomes scrambled, but not necessarily lost. Two classes of techniques have emerged to recover this information: methods relying on optical memory effects, and transmission matrix (TM) approaches. Here we develop a general framework describing the nature of memory effects in structures of arbitrary geometry. We show how this framework, when combined with wavefront shaping driven by feedback from a guide-star, enables estimation of the TM of any such system. This highlights that guide-star assisted imaging is possible regardless of the type of memory effect a scatterer exhibits. We apply this concept to multimode fibres (MMFs) and identify a 'quasi-radial' memory effect. This allows the TM of an MMF to be approximated from only one end - an important step for micro-endoscopy. Our work broadens the applications of memory effects to a range of novel imaging and optical communication scenarios.

Focusing light through multimode fibres using a digital micromirror device: a comparison study of non-holographic approaches

Focusing light through a multimode fibre (MMF) has attracted significant research interest, mainly driven by the need for miniature endoscopes in biomedicine. In recent years, digital micromirror devices (DMD) have become increasingly popular as a high-speed alternative to liquid-crystal spatial light modulators for light focusing via wavefront shaping based on binary amplitude modulations. To exploit the potentials and limitations of the state-of-the-art DMD-based wavefront shaping methods, in this study, for the first time, we compared four representative, non-holographic and DMD-based methods that are reported so far in literature with the same experimental and simulation conditions, including a real-valued intensity transmission matrix (RVITM)-based algorithm, a complex-valued transmission matrix (TM)-based algorithm, a conditional probability algorithm and a genetic algorithm. We investigated the maximum achievable peak-to-background ratio (PBR) in comparison to theoretical expectations, and further improved the performance of the RVITM-based method. With both numerical simulations and experiments, we found that the genetic algorithm offered the highest PBR but suffered from the lowest focusing speed, while the RVITM-based algorithm provided a comparable PBR to that of the genetic algorithm, and the highest focusing speed.

Compressively sampling the optical transmission matrix of a multimode fibre

The measurement of the optical transmission matrix (TM) of an opaque material is an advanced form of space-variant aberration correction. Beyond imaging, TM-based methods are emerging in a range of fields, including optical communications, micro-manipulation, and computing. In many cases, the TM is very sensitive to perturbations in the configuration of the scattering medium it represents. Therefore, applications often require an up-to-the-minute characterisation of the fragile TM, typically entailing hundreds to thousands of probe measurements. Here, we explore how these measurement requirements can be relaxed using the framework of compressive sensing, in which the incorporation of prior information enables accurate estimation from fewer measurements than the dimensionality of the TM we aim to reconstruct. Examples of such priors include knowledge of a memory effect linking the input and output fields, an approximate model of the optical system, or a recent but degraded TM measurement. We demonstrate this concept by reconstructing the full-size TM of a multimode fibre supporting 754 modes at compression ratios down to ∼5% with good fidelity. We show that in this case, imaging is still possible using TMs reconstructed at compression ratios down to ∼1% (eight probe measurements). This compressive TM sampling strategy is quite general and may be applied to a variety of other scattering samples, including diffusers, thin layers of tissue, fibre optics of any refractive profile, and reflections from opaque walls. These approaches offer a route towards the measurement of high-dimensional TMs either quickly or with access to limited numbers of measurements.

Toward improved endoscopic surveillance with multidiameter single fiber reflectance spectroscopy in patients with Barrett's esophagus

Patients with Barrett's esophagus are at an increased risk to develop esophageal cancer and, therefore, undergo regular endoscopic surveillance. Early detection of neoplasia enables endoscopic treatment, which improves outcomes. However, early Barrett's neoplasia is easily missed during endoscopic surveillance. This study investigates multidiameter single fiber reflectance spectroscopy (MDSFR) to improve Barrett's surveillance. Based on the concept of field cancerization, it may be possible to identify the presence of a neoplastic lesion from measurements elsewhere in the esophagus or even the oral cavity. In this study, MDSFR measurements are performed on non-dysplastic Barrett's mucosa, squamous mucosa, oral mucosa, and the neoplastic lesion (if present). Based on logistic regression analysis on the scattering parameters measured by MDSFR, a classifier is developed that can predict the presence of neoplasia elsewhere in the Barrett's segment from measurements on the non-dysplastic Barrett's mucosa (sensitivity 91%, specificity 71%, AUC = 0.77). Classifiers obtained from logistic regression analysis for the squamous and oral mucosa do not result in an AUC significantly different from 0.5.

High-fidelity spatial mode transmission through a 1-km-long multimode fiber via vectorial time reversal

The large number of spatial modes supported by standard multimode fibers is a promising platform for boosting the channel capacity of quantum and classical communications by orders of magnitude. However, the practical use of long multimode fibers is severely hampered by modal crosstalk and polarization mixing. To overcome these challenges, we develop and experimentally demonstrate a vectorial time reversal technique, which is accomplished by digitally pre-shaping the wavefront and polarization of the forward-propagating signal beam to be the phase conjugate of an auxiliary, backward-propagating probe beam. Here, we report an average modal fidelity above 80% for 210 Laguerre-Gauss and Hermite-Gauss modes by using vectorial time reversal over an unstabilized 1-km-long fiber. We also propose a practical and scalable spatial-mode-multiplexed quantum communication protocol over long multimode fibers to illustrate potential applications that can be enabled by our technique.

The use of long multimode fibers for multiplexed quantum communication is hindered by modal crosstalk and polarisation mixing. Here, the authors use an auxiliary laser beam sent backwards from Bob to Alice, allowing her to pre-compensate for the spatial distortions and polarisation scrambling.

Image reconstruction through a multimode fiber with a simple neural network architecture

Multimode fibers (MMFs) have the potential to carry complex images for endoscopy and related applications, but decoding the complex speckle patterns produced by mode-mixing and modal dispersion in MMFs is a serious challenge. Several groups have recently shown that convolutional neural networks (CNNs) can be trained to perform high-fidelity MMF image reconstruction. We find that a considerably simpler neural network architecture, the single hidden layer dense neural network, performs at least as well as previously-used CNNs in terms of image reconstruction fidelity, and is superior in terms of training time and computing resources required. The trained networks can accurately reconstruct MMF images collected over a week after the cessation of the training set, with the dense network performing as well as the CNN over the entire period.

Classical Rayleigh-Jeans Condensation of Light Waves: Observation and Thermodynamic Characterization

Theoretical studies on wave turbulence predict that a purely classical system of random waves can exhibit a process of condensation, which originates in the singularity of the Rayleigh-Jeans equilibrium distribution. We report the experimental observation of the transition to condensation of classical optical waves propagating in a multimode fiber, i.e., in a conservative Hamiltonian system without thermal heat bath. In contrast to conventional self-organization processes featured by the nonequilibrium formation of nonlinear coherent structures (solitons, vortices,…), here the self-organization originates in the equilibrium Rayleigh-Jeans statistics of classical waves. The experimental results show that the chemical potential reaches the lowest energy level at the transition to condensation, which leads to the macroscopic population of the fundamental mode of the optical fiber. The near-field and far-field measurements of the condensate fraction across the transition to condensation are in quantitative agreement with the Rayleigh-Jeans theory. The thermodynamics of classical wave condensation reveals that the heat capacity takes a constant value in the condensed state and tends to vanish above the transition in the normal state. Our experiments provide the first demonstration of a coherent phenomenon of self-organization that is exclusively driven by optical thermalization toward the Rayleigh-Jeans equilibrium.

Multisite cell- and neural-dynamics-resolving deep brain imaging in freely moving mice with implanted reconnectable fiber bundles

We demonstrate a reconnectable implantable ultraslim fiber-optic microendoscope that integrates a branching fiber bundle (BFB) with gradient-index fiber lenses, enabling a simultaneous fluorescence imaging of individual cells in distinctly separate brain regions, including brain structures as distant as the neocortex and hippocampus. We show that fluorescence images of individual calcium-indicator-expressing neurons in the brain of freely moving transgenic mice can be recorded, via the implanted BFB probe, in parallel with time- and cell-resolved traces of calcium signaling, thus enabling correlated circuit-dynamics studies at -multiple sites within the brain of freely moving animals.

Single-shot hybrid photoacoustic-fluorescent microendoscopy through a multimode fiber with wavefront shaping

We present a minimally-invasive endoscope based on a multimode fiber that combines photoacoustic and fluorescence sensing. From the measurement of a transmission matrix during a prior calibration step, a focused spot is produced and raster-scanned over a sample at the distal tip of the fiber by use of a fast spatial light modulator. An ultra-sensitive fiber-optic ultrasound sensor for photoacoustic detection placed next to the fiber is combined with a photodetector to obtain both fluorescence and photoacoustic images with a distal imaging tip no larger than 250 µm. The high signal-to-noise ratio provided by wavefront shaping based focusing and the ultra-sensitive ultrasound sensor enables imaging with a single laser shot per pixel, demonstrating fast two-dimensional hybrid in vitro imaging of red blood cells and fluorescent beads.

Performance of real-time adaptive optics compensation in a turbulent channel with high-dimensional spatial-mode encoding

The orbital angular momentum (OAM) of photons is a promising degree of freedom for high-dimensional quantum key distribution (QKD). However, effectively mitigating the adverse effects of atmospheric turbulence is a persistent challenge in OAM QKD systems operating over free-space communication channels. In contrast to previous works focusing on correcting static simulated turbulence, we investigate the performance of OAM QKD in real atmospheric turbulence with real-time adaptive optics (AO) correction. We show that even though our AO system provides a limited correction, it is possible to mitigate the errors induced by weak turbulence and establish a secure channel. The crosstalk induced by turbulence and the performance of AO systems is investigated in two configurations: a lab-scale link with controllable turbulence, and a 340 m long cross-campus link with dynamic atmospheric turbulence. Our experimental results suggest that an advanced AO system with fine beam tracking, reliable beam stabilization, precise wavefront sensing, and accurate wavefront correction is necessary to adequately correct turbulence-induced error. We also propose and demonstrate different solutions to improve the performance of OAM QKD with turbulence, which could enable the possibility of OAM encoding in strong turbulence.

Velocity measurements with structured light transmitted through a multimode optical fiber using digital optical phase conjugation

Lensless fiber microendoscopes enable optical diagnostics and therapy with minimal invasiveness. Because of their small diameters, multimode fibers are ideal candidates, but mode scrambling hinders the transmission of structured light fields. We present the generation of a localized fringe system at variable distances from the distal fiber end by exploiting digital optical phase conjugation. The replayed fringe system was used for quantitative metrology. Velocity measurements of a microchannel flow in the immediate proximity of the fiber end without the use of any imaging lenses are shown. Lensless multimode fiber systems are of interest especially for biomedical imaging and stimulation as well as technical inspection and flow measurements.

Physical Layer Security in Multimode Fiber Optical Networks

The light propagation through a multimode fiber is used to increase information security during data transmission without the need for cryptographic approaches. The use of an inverse precoding method in a multimode fiber-optic communication network is based on mode-dependent losses on the physical layer. This leads to an asymmetry between legitimate (Bob) and illegitimate (Eve) recipients of messages, resulting in significant SNR advantage for Bob. In combination with dynamic mode channel changes, there are defined hurdles for Eve to reconstruct a sent message even in a worst-case scenario in which she knows the channel completely. This is the first time that physical layer security has been investigated in a fiber optical network based on measured transmission matrices. The results show that messages can be sent securely using traditional communication techniques. The technology introduced is a step towards the development of cyber physical systems with increased security.

Structured light beams created through a multimode fiber via virtual Fourier filtering based on digital optical phase conjugation

Digital optical phase conjugation (DOPC) is a newly developed technique in wavefront shaping to control light propagation through complex media. Currently, DOPC has been demonstrated for the reconstruction of two- and three-dimensional targets and enabled important applications in many areas. Nevertheless, the reconstruction results are only phase conjugated to the original input targets. Herein, we demonstrate that DOPC could be further developed for creating structured light beams through a multimode fiber (MMF). By applying annular filtering in the virtual Fourier domain of the acquired speckle field, we realize the creation of the quasi-Bessel and donut beams through the MMF. In principle, arbitrary amplitude and/or phase circular symmetry filtering could be performed in the Fourier domain, thus generating the corresponding point spread functions. We expect that the reported technique can be useful for super-resolution endoscopic imaging and optical manipulation through MMFs.

Non-linear label-free imaging through a multimode graded index optical fibre

In recent years, great advances have been made in developing minimal footprint micro-endoscopes using multimode optical fibres (MMF) [1]. By employing wavefront shaping methods the seemingly random speckle pattern resulting from the guiding of coherent light through an MMF can be formed into a diffraction limited spot. This enables the implementation of multiple laser scanning techniques. In this work we show that this approach can be employed to realize label-free non-linear microscopy techniques such as coherent anti-Stokes Raman scattering (CARS) and second harmonic generation (SHG). Backscattered light makes epi-detection possible even though these processes preferably emit light in the direction of beam propagation [2].

Control of the temporal and polarization response of a multimode fiber

Control of the spatial and temporal properties of light propagating in disordered media have been demonstrated over the last decade using spatial light modulators. Most of the previous studies demonstrated spatial focusing to the speckle grain size, and manipulation of the temporal properties of the achieved focus. In this work, we demonstrate an approach to control the total temporal impulse response, not only at a single speckle grain but over all spatial degrees of freedom (spatial and polarization modes) at any arbitrary delay time through a multimode fiber. Global enhancement or suppression of the total light intensity exiting a multimode fibre is shown for arbitrary delays and polarization states. This work could benefit to applications that require pulse delivery in disordered media.

Label-free CARS microscopy through a multimode fiber endoscope

Multimode fibres have recently been employed as high-resolution ultra-thin endoscopes, capable of imaging biological structures deep inside tissue in vivo. Here, we extend this technique to label-free non-linear microscopy with chemical contrast using coherent anti-Stokes Raman scattering (CARS) through a multimode fibre endoscope, which opens up new avenues for instant and in-situ diagnosis of potentially malignant tissue. We use a commercial 125 µm diameter, 0.29 NA GRIN fibre, and wavefront shaping on an SLM is used to create foci that are scanned behind the fibre facet across the sample. The chemical selectivity is demonstrated by imaging 2 µm polystyrene and 2.5 µm PMMA beads with per pixel integration time as low as 1 ms for epi-detection.

Wavelength dependent characterization of a multimode fibre endoscope

Multimode fibres have recently shown promise as miniature endoscopic probes. When used for non-linear microscopy, the bandwidth of the imaging system limits the ability to focus light from broadband pulsed lasers as well as the possibility of wavelength tuning during the imaging. We demonstrate that the bandwidth is limited by the dispersion of the off-axis hologram displayed on the SLM, which can be corrected for, and by the limited bandwidth of the fibre itself. The selection of the fibre is therefore crucial for these experiments. In addition, we show that a standard prism pulse compressor is sufficient for material dispersion compensation for multi-photon imaging with a fibre endoscope.

Transmission of natural scene images through a multimode fibre

The optical transport of images through a multimode fibre remains an outstanding challenge with applications ranging from optical communications to neuro-imaging. State of the art approaches either involve measurement and control of the full complex field transmitted through the fibre or, more recently, training of artificial neural networks that however, are typically limited to image classes belong to the same class as the training data set. Here we implement a method that statistically reconstructs the inverse transformation matrix for the fibre. We demonstrate imaging at high frame rates, high resolutions and in full colour of natural scenes, thus demonstrating general-purpose imaging capability. Real-time imaging over long fibre lengths opens alternative routes to exploitation for example for secure communication systems, novel remote imaging devices, quantum state control processing and endoscopy.

A light-in-flight single-pixel camera for use in the visible and short-wave infrared

Single-pixel cameras reconstruct images from a stream of spatial projection measurements recorded with a single-element detector, which itself has no spatial resolution. This enables the creation of imaging systems that can take advantage of the ultra-fast response times of single-element detectors. Here we present a single-pixel camera with a temporal resolution of 200 ps in the visible and short-wave infrared wavelengths, used here to study the transit time of distinct spatial modes transmitted through few-mode and orbital angular momentum mode conserving optical fiber. Our technique represents a way to study the spatial and temporal characteristics of light propagation in multimode optical fibers, which may find use in optical fiber design and communications.

Soft-glass imaging microstructured optical fibers

We demonstrate the fabrication of multi-core (imaging) microstructured optical fiber via soft-glass preform extrusion through a 3D printed titanium die. The combination of extrusion through 3D printed dies and structured element (capillary) stacking allows for unprecedented control of the optical fiber geometry. We have exploited this to demonstrate a 100 pixel rectangular array imaging microstructured fiber. Due to the high refractive index of the glass used (n = 1.62), such a fiber can theoretically have a pixel pitch as small as 1.8 µm. This opens opportunities for ultra-small, high-resolution imaging fibers fabricated from diverse glass types.

Compressive imaging through a multimode fiber

We propose and experimentally demonstrate a new concept of endo-microscopy: compressive multimode (MM) fiber imaging. We show that the speckle patterns generated in a MM fiber represent an excellent basis for compressive sensing. We demonstrate high-resolution compressive imaging through a fiber probe with the total number of measurements 20 times less than what is required for the standard raster scanning approach to endo-microscopy. Moreover, we show that the inherent optical sectioning of a MM fiber can help to overcome the main problem of compressive sensing and can be used for the imaging of bulk structures. Compressive MM fiber imaging does not require complex wavefront shaping and significantly increases the pre-calibration and imaging speed, creating a new approach to endo-microscopy.

Hermite-Gaussian mode sorter

The Hermite-Gaussian (HG) modes, sometimes referred to as transverse electromagnetic modes in free space, form a complete and orthonormal basis that have been extensively used to describe optical fields. In addition, these modes have been shown to be helpful in enhancing information capacity of optical communications as well as achieving super-resolution imaging in microscopy. Here we propose and present the realization of an efficient, robust mode sorter that can sort a large number of HG modes based on the relation between HG modes and Laguerre-Gaussian (LG) modes. We experimentally demonstrate the sorting of 16 HG modes, and our method can be readily extended to a higher-dimensional state space in a straightforward manner. We expect that our demonstration will have direct applications in a variety of fields including fiber optics, classical and quantum communications, as well as super-resolution imaging.

Transmission of a polychromatic electromagnetic multi-Gaussian Schell-model beam in an inhomogeneous gradient-index fiber

We derive analytical expressions for the cross-spectral density matrix of polychromatic electromagnetic multi-Gaussian Schell-model (EMGSM) beam transmission through a gradient-index fiber. The space-spectrum evolution properties for the spectral density, spectral shift, degree of polarization, and electromagnetic coherence state of a polychromatic EMGSM beam with Lorentzian line type spectrum and central wavelength λ₀=1550  nm propagation in a silica-clad germania core inhomogeneous graded-index fiber are studied in detail. We show that these statistical properties exhibit periodicity in the fiber, caused by the focusing property of square-law media, which can be reminiscent of the self-imaging effect of optical fields. The effects of the nonconventional correlation functions of the polychromatic EMGSM beam on the transmission properties are also investigated.