Reconstruction of structured laser beams through a multimode fiber based on digital optical phase conjugation

Neural network enabled fringe projection through scattering media

The projection of fringes plays an essential role in many applications, such as fringe projection profilometry and structured illumination microscopy. However, these capabilities are significantly constrained in environments affected by optical scattering. Although recent developments in wavefront shaping have effectively generated high-fidelity focal points and relatively simple structured images amidst scattering, the ability to project fringes that cover half of the projection area has not yet been achieved. To address this limitation, this study presents a fringe projector enabled by a neural network, capable of projecting fringes with variable periodicities and orientation angles through scattering media. We tested this projector on two types of scattering media: ground glass diffusers and multimode fibers. For these scattering media, the average Pearson's correlation coefficients between the projected fringes and their designed configurations are 86.9% and 79.7%, respectively. These results demonstrate the effectiveness of the proposed neural network enabled fringe projector. This advancement is expected to broaden the scope of fringe-based imaging techniques, making it feasible to employ them in conditions previously hindered by scattering effects.

Space-time wave packets with reduced divergence and tunable group velocity generated in free space after multi-mode fiber propagation

Previously, space-time wave packets (STWPs) have been generated in free space with reduced diffraction and a tunable group velocity by combining multiple frequency comb lines each carrying a single Bessel mode with a unique wave number. It might be potentially desirable to propagate the STWP through fiber for reconfigurable positioning. However, fiber mode coupling might degrade the output STWP and distort its propagation characteristics. In this Letter, we experimentally demonstrate STWP generation and propagation over 1-m graded-index multi-mode fiber. Fiber mode coupling is mitigated by pre-distortion according to the inverse matrix of the fiber mode coupling matrix. Measurement of the STWP at the fiber output shows that its group velocity can vary from 1.0042c to 0.9967c by tuning the wave number of the Bessel mode on each frequency. The measured time-averaged intensity profiles show that the beam radius remains similar after 150-mm free-space propagation after exiting the fiber.

Optical focusing inside scattering media with iterative time-reversed ultrasonically encoded near-infrared light

Focusing light inside scattering media is a long-sought goal in optics. Time-reversed ultrasonically encoded (TRUE) focusing, which combines the advantages of biological transparency of the ultrasound and the high efficiency of digital optical phase conjugation (DOPC) based wavefront shaping, has been proposed to tackle this problem. By invoking repeated acousto-optic interactions, iterative TRUE (iTRUE) focusing can further break the resolution barrier imposed by the acoustic diffraction limit, showing great potential for deep-tissue biomedical applications. However, stringent requirements on system alignment prohibit the practical use of iTRUE focusing, especially for biomedical applications at the near-infrared spectral window. In this work, we fill this blank by developing an alignment protocol that is suitable for iTRUE focusing with a near-infrared light source. This protocol mainly contains three steps, including rough alignment with manual adjustment, fine-tuning with a high-precision motorized stage, and digital compensation through Zernike polynomials. Using this protocol, an optical focus with a peak-to-background ratio (PBR) of up to 70% of the theoretical value can be achieved. By using a 5-MHz ultrasonic transducer, we demonstrated the first iTRUE focusing using near-infrared light at 1053 nm, enabling the formation of an optical focus inside a scattering medium composed of stacked scattering films and a mirror. Quantitatively, the size of the focus decreased from roughly 1 mm to 160 µm within a few consecutive iterations and a PBR up to 70 was finally achieved. We anticipate that the capability of focusing near-infrared light inside scattering media, along with the reported alignment protocol, can be beneficial to a variety of applications in biomedical optics.

Light-field focusing and modulation through scattering media based on dual-polarization-encoded digital optical phase conjugation

Digital optical phase conjugation (DOPC) can be applied for light-field focusing and imaging through or within scattering media. Traditional DOPC only recovers the phase but loses the polarization information of the original incident beam. In this Letter, we propose a dual-polarization-encoded DOPC to recover the full information (both phase and polarization) of the incident beam. The phase distributions of two orthogonal polarization components of the speckle field coming from a multimode fiber are first measured by using digital holography. Then, the phase distributions are separately modulated on two beams and their conjugations are superposed to recover the incident beam through the fiber. By changing the phase difference or amplitude ratio between the two conjugate beams, light fields with complex polarization distribution can also be generated. This method will broaden the application scope of DOPC in imaging through scattering media.

Self-focusing propagation characteristics of a radially-polarized beam in nonlinear media

In this study, an analytical formula for the self-focusing length of a radially polarized beam (RPB) is first derived, which has a similar behavior to the semi-empirical Marburger formula of a Gaussian beam, and is beneficial to quantitatively and qualitatively analyze practical experimental scenarios. However, the relation of the self-focusing length with the states of polarization (SoPs) was evaluated, and it was found that RPB with spatially inhomogeneous SoP at the field cross-section can retain a further self-focusing length compared to a beam with a spatially homogeneous one. The influence of the topological charge on the self-focusing length is explored, which shows that RPB with a low topological charge can achieve a high-power density at a relatively further receiver plane. Therefore, it is demonstrated that the RPB as a laser source not only extends the self-focusing length, but also improves the power density of the target. With the help of RPB, it is possible to realize a controllable self-focusing length and a high target optical power density, which may have potential applications in fine optical manipulation, optical communication, high-power long-range laser atmospheric propagation, and related areas.

Wavefront shaping for reconfigurable beam steering in lithium niobate multimode waveguide

Reconfigurable photonic devices are important constituents for future optical integrated circuits, where electro-optic manipulation of the light field in a lithium niobate (LN) waveguide is one of the promising solutions. Herein, we demonstrate a paradigm shift of the beam steering mechanism where reconfigurable beam steering is enabled by the wavefront shaping technology. Furthermore, this strategy is fully compatible with the electro-optic tuning mechanism of the LN multimode waveguide, where microstructured serrated array electrodes are employed to fine tune the output beam upon its reconfigurable output position. Our results provide new, to the best of our knowledge, insight for molding the flow of light in multimode waveguides and shed new light on beam steering photonic devices.

Feedback-assisted transmission matrix measurement of a multimode fiber in a referenceless system

Recent development in wavefront shaping shows the promise to employ multimode fibers (MMFs) to deliver images in endoscopy. In these applications, retrieving the transmission matrix (TM) of the MMF is especially important. Among existing non-holographic approaches, feedback-based wavefront shaping requires a large number of measurements, while directly measuring the TM can be easily trapped into local optimums if the constraints are insufficient. To reduce the required number of measurements, we combine the concepts of these two approaches and develop a scheme termed feedback-assisted TM measurements. We show that under such a hybrid scheme, less than 3N intensity measurements are sufficient to accurately retrieve one row of the TM that contains N unknown complex elements. As a proof of concept, we experimentally demonstrated retrieving multiple rows of the TM of an MMF using the proposed scheme with high fidelity. In particular, a single focus and dual foci through the MMF with enhancements larger than 75% of the theoretical values were reported.

Experimental generation of perfect optical vortices through strongly scattering media

Perfect optical vortices enable the unprecedented optical multiplexing utilizing orbital angular momentum of light, which, however, suffer from distortion when they propagate in inhomogeneous media. Herein, we report on the experimental demonstration of perfect optical vortice generation through strongly scattering media. The transmission-matrix-based point-spread-function engineering is applied to encode the targeted mask in the Fourier domain before focusing. We experimentally demonstrate the perfect optical vortice generation either through a multimode fiber or a ground glass, where the numerical results agree well with the measured one. Our results might facilitate the manipulation of orbital angular momentum of light through disordered scattering media and shed new light on the optical multiplexing utilizing perfect optical vortices.

Genetic-algorithm-assisted coherent enhancement absorption in scattering media by exploiting transmission and reflection matrices

The investigations on coherent enhancement absorption (CEA) inside scattering media are critically important in biophotonics. CEA can deliver light to the targeted position, thus enabling deep-tissue optical imaging by improving signal strength and imaging resolution. In this work, we develop a numerical framework that employs the method of finite-difference time-domain. Both the transmission and reflection matrices of scattering media with open boundaries are constructed, allowing the studies on the eigenvalues and eigenchannels. To realize CEA for scattering media with local absorption, we develop a genetic-algorithm-assisted numerical model. By minimizing the total transmittance and reflectance simultaneously, different realizations of CEA are observed and, without setting internal monitors, can be differentiated with cases of light leaked from sides. By modulating the incident wavefront at only one side of the scattering medium, it is shown that for a 5-μm-diameter absorber buried inside a scattering medium of 15 μm × 12 μm, more than half of the incident light can be delivered and absorbed at the target position. The enhancement in absorption is more than four times higher than that with random input. This value can be even higher for smaller absorption regions. We also quantify the effectiveness of the method and show that it is inversely proportional to the openness of the scattering medium. This result is potentially useful for targeted light delivery inside scattering media with local absorption.

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.

Retrieving the optical transmission matrix of a multimode fiber using the extended Kalman filter

Characterizing the transmission matrix (TM) of a multimode fiber (MMF) benefits many fiber-based applications and allows in-depth studies on the physical properties. For example, by modulating the incident field, the knowledge of the TM allows one to synthesize any optical field at the distill end of the MMF. However, the extraction of optical fields usually requires holographic measurements with interferometry, which complicates the system design and introduces additional noise. In this work, we developed an efficient method to retrieve the TM of the MMF in a referenceless optical system. With pure intensity measurements, this method uses the extended Kalman filter (EKF) to recursively search for the optimum solution. To facilitate the computational process, a modified speckle-correlation scatter matrix (MSSM) is constructed as a low-fidelity initial estimation. This method, termed EKF-MSSM, only requires 4N intensity measurements to precisely solve for N unknown complex variables in the TM. Experimentally, we successfully retrieved the TM of the MMF with high precision, which allows optical focusing with the enhancement (>70%) close to the theoretical value. We anticipate that this method will serve as a useful tool for studying physical properties of the MMFs and potentially open new possibilities in a variety of applications in fiber optics.

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.

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.