Impact of third-order dispersion on the dynamics of dissipative solitons in an ultrafast fiber laser.

Dissipative solitons (DSs), due to the complex interplay among dispersion, nonlinear, gain and loss, illustrate abundant nonlinear dynamics behaviors. Especially, dispersion plays an important role in the research of DS dynamics in ultrafast fiber lasers. Previous studies have mainly focused on the effect of even-order dispersion, i.e., group velocity dispersion (GVD) and fourth-order dispersion. In fact, odd-order dispersions, such as third-order dispersion (TOD), also significantly influences the dynamics of DSs. However, due to the lack of dispersion engineering tools, few experimental researches in this domain have been reported. In this work, by employing a pulse shaper in ultrafast fiber laser, an in-depth exploration of the DS dynamics influenced by TOD was conducted. With the increase of TOD value, the stable single DS undergoes a splitting into two solitons and then enters explosion state, and ultimately evolves into a chaotic state. The laser operation state is correlated to dispersion profile, which could be controlled by TOD. Here, the positive dispersion at long-wavelength side will be gradually shifted to negative dispersion by increasing the TOD, where soliton effect will drive the transitions. These findings offer valuable insights into the nonlinear dynamics of ultrafast lasers and may also foster applications involving higher-order dispersion.

Anti-phase pulsation of counter-propagating dissipative solitons in a bidirectional fiber laser.

Due to its unique geometric structure, the bidirectional ultrafast fiber laser is an excellent light source for dual-comb applications. However, sharing the same gain between the counter-propagating solitons also gives rise to complex dynamics. Herein, we report the anti-phase pulsation of counter-propagating dissipative solitons in a bidirectional fiber laser. The in-phase and anti-phase soliton pulsation can be manipulated by adjusting the intracavity birefringence. The periodic modulation of polarization-dependent gain (PDG) caused by polarization hole burning (PHB) in the gain fiber can be responsible for anti-phase pulsation of bidirectional dissipative solitons. These findings offer new, to the best of our knowledge, insights into the complex dynamics of solitons in dissipative optical systems and performance improvement of bidirectional ultrafast fiber lasers.

Projecting colorful images through scattering media via deep learning.

The existence of scatterers in the optical path has been the major obstacle that prohibits one from projecting images through solid walls, turbid water, clouds, and fog. Recent developments in wavefront shaping and neural networks demonstrate effective compensation for scattering effects, showing the promise to project clear images against strong scattering. However, previous studies were mainly restricted to projecting greyscale images using monochromatic light, mainly due to the increased complexity of simultaneously controlling multiple wavelengths. In this work, we fill this blank by developing a projector network, which enables the projection of colorful images through scattering media with three primary colors. To validate the performance of the projector network, we experimentally demonstrated projecting colorful images obtained from the MINST dataset through two stacked diffusers. Quantitatively, the averaged intensity Pearson's correlation coefficient for 1,000 test colorful images reaches about 90.6%, indicating the superiority of the developed network. We anticipate that the projector network can be beneficial to a variety of display applications in scattering environments.

Single-exposure ultrasound-modulated optical tomography with a quaternary phase encoded mask.

Ultrasound-modulated optical tomography (UOT) is a deep-tissue imaging modality that provides optical contrast with acoustic resolution. Among existing implementations, camera-based UOT improves modulation depth through parallel detection but suffers from a low camera frame rate. The condition prohibits this technique from being applied to in vivo applications where speckles decorrelate on a time scale of 1 ms or less. To overcome this challenge, we developed single-exposure camera-based UOT by employing a quaternary phase encoded mask (QPEM). As a proof of concept, we demonstrated imaging of an absorptive target buried inside a dynamic scattering medium with a speckle correlation time as short as 0.49 ms, typical of living biological tissues. Benefiting from the QPEM-enabled single-exposure wavefront measurement (5.5 ms) and GPU-assisted wavefront reconstruction (0.97 ms), the point scanning and result update speed can reach up to 150 Hz. We envision that the QPEM-enabled single-exposure scheme paves the way for in vivo UOT imaging, which holds promise for a variety of medical and biological applications.

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.

Multimode fiber-based greyscale image projector enabled by neural networks with high generalization ability.

Multimode fibers (MMFs) are emerging as promising transmission media for delivering images. However, strong mode coupling inherent in MMFs induces difficulties in directly projecting two-dimensional images through MMFs. By training two subnetworks named Actor-net and Model-net synergetically, [Nature Machine Intelligence2, 403 (2020)10.1038/s42256-020-0199-9] alleviated this issue and demonstrated projecting images through MMFs with high fidelity. In this work, we make a step further by improving the generalization ability to greyscale images. The modified projector network contains three subnetworks, namely forward-net, backward-net, and holography-net, accounting for forward propagation, backward propagation, and the phase-retrieval process. As a proof of concept, we experimentally trained the projector network using randomly generated phase maps and their corresponding resultant speckle images output from a 1-meter-long MMF. With the network being trained, we successfully demonstrated projecting binary images from MNIST and EMNIST and greyscale images from Fashion-MNIST, exhibiting averaged Pearson's correlation coefficients of 0.91, 0.92, and 0.87, respectively. Since all these projected images have never been seen by the projector network before, a strong generalization ability in projecting greyscale images is confirmed.

Coaxial interferometry for camera-based ultrasound-modulated optical tomography with paired illumination.

Ultrasound-modulated optical tomography (UOT), which combines the advantages of both light and ultrasound, is a promising imaging modality for deep-tissue high-resolution imaging. Among existing implementations, camera-based UOT gains huge advances in modulation depth through parallel detection. However, limited by the long exposure time and the slow framerate of modern cameras, the measurement of UOT signals always requires holographic methods with additional reference beams. This requirement increases system complexity and is susceptible to environmental disturbances. To overcome this challenge, we develop coaxial interferometry for camera-based UOT in this work. Such a coaxial scheme is enabled by employing paired illumination with slightly different optical frequencies. To measure the UOT signal, the conventional phase-stepping method in holography can be directly transplanted into coaxial interferometry. Specifically, we performed both numerical investigations and experimental validations for camera-based UOT under the proposed coaxial scheme. One-dimensional imaging for an absorptive target buried inside a scattering medium was demonstrated. With coaxial interferometry, this work presents an effective way to reduce system complexity and cope with environmental disturbances for camera-based UOT.

High-speed single-exposure time-reversed ultrasonically encoded optical focusing against dynamic scattering.

Focusing light deep inside live scattering tissue promises to revolutionize biophotonics by enabling deep tissue noninvasive optical imaging, manipulation, and therapy. By combining with guide stars, wavefront shaping is emerging as a powerful tool to make scattering media optically transparent. However, for in vivo biomedical applications, the speeds of existing techniques are still too slow to accommodate the fast speckle decorrelation of live tissue. To address this key bottleneck, we develop a quaternary phase encoding scheme to enable single-exposure time-reversed ultrasonically encode optical focusing with full-phase modulations. Specifically, we focus light inside dynamic scattering media with an average mode time down to 29 ns, which indicates that more than 104 effective spatial modes can be controlled within 1 millisecond. With this technique, we demonstrate in vivo light focusing in between a highly opaque adult zebrafish of 5.1 millimeters in thickness and a ground glass diffuser. Our work presents an important step toward in vivo deep tissue applications of wavefront shaping.

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.

Characterization of the spectral memory effect of scattering media.

The optical memory effect is an interesting phenomenon exploited for deep-tissue optical imaging. Besides the widely studied memory effects in the spatial domain to accelerate point scanning speed, the spectral memory effect is also important in multispectral wavefront shaping. Although being theoretically analyzed for decades, quantitative studies of spectral memory effect on a variety of scattering media including biological tissue were rarely reported. In practice, quantifying the range of the spectral memory effect is essential in efficiently shaping broadband light, as it determines the optimum spectral resolution in realizing spatiotemporal focus through scattering media. In this work, we analyze the spectral memory effect based on a diffusion model. An explicit analytical expression involves the illumination wavelength, the diffusion constant, and the sample thickness is derived, which is consistent with the one in the literature. We experimentally quantified the range of spectral correlation for two types of biological tissue, tissue-mimicking phantoms with different concentrations, and diffusers. Specifically, for tissue-mimicking phantoms with calibrated scattering parameters, we show that a correction factor of more than 20 should be inserted, indicating that the range of spectral correlation is much larger than one would expect. This finding is particularly beneficial to multispectral wavefront shaping, as stringent requirements on the spectral resolution could be alleviated by at least one order of magnitude.

Imaging biological tissue with high-throughput single-pixel compressive holography.

Single-pixel holography (SPH) is capable of generating holographic images with rich spatial information by employing only a single-pixel detector. Thanks to the relatively low dark-noise production, high sensitivity, large bandwidth, and cheap price of single-pixel detectors in comparison to pixel-array detectors, SPH is becoming an attractive imaging modality at wavelengths where pixel-array detectors are not available or prohibitively expensive. In this work, we develop a high-throughput single-pixel compressive holography with a space-bandwidth-time product (SBP-T) of 41,667 pixels/s, realized by enabling phase stepping naturally in time and abandoning the need for phase-encoded illumination. This holographic system is scalable to provide either a large field of view (~83 mm2) or a high resolution (5.80 µm × 4.31 µm). In particular, high-resolution holographic images of biological tissues are presented, exhibiting rich contrast in both amplitude and phase. This work is an important step towards multi-spectrum imaging using a single-pixel detector in biophotonics.

Single-shot ultrasound-modulated optical tomography with enhanced speckle contrast.

Ultrasound-modulated optical tomography (UOT) images optical contrast deep inside biological tissue. Among existing approaches, camera-based parallel detection is beneficial in modulation depth but is limited to the relatively slow framerate of cameras. This condition prevents such a scheme from achieving maturity to image live animals with sub-millisecond speckle correlation time. In this work, we developed on-axis single-shot UOT by investigating the statistics of speckles, breaking the restriction imposed by the slow camera framerate. As a proof of concept, we experimentally imaged a one-dimensional absorptive object buried inside a moving scattering medium with speckle correlation time down to 0.48 ms. We envision that this single-shot UOT is promising to cope with live animals with fast speckle decorrelation.

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.

Delivering targeted color light through a multimode fiber by field synthesis.

Recent developments of wavefront shaping make the multimode fiber (MMF) as a promising tool to deliver images in endoscopy. However, previous studies using the MMF were limited to monochromatic light or polychromatic light with narrow bandwidth. The desires for colored imaging stimulate us to deliver multi-wavelength light that covers the entire visible spectrum through the MMF. In this work, we demonstrated delivering targeted color light through the MMF by mixing three primary colors (red, green, and blue) with a single spatial light modulator. The optimum phase map that considers all three colors was generated through field synthesis (FS), which requires every pixel of the SLM to partially account for all colors. With both theoretical and numerical approaches, we showed that FS exhibited much better performance than the previously developed spatial segmentation method that employs different pixels to represent different colors. Moreover, by computationally adjusting the compositions of the weight for each color, the colors of the delivered focus can be switched at video framerate. We anticipate that our work paves a way for future applications of delivering color images through the MMF in endoscopy.

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.

Efficient glare suppression with Hadamard-encoding-algorithm-based wavefront shaping.

In this Letter, we explore the effectiveness of a Hadamard encoding algorithm (HEA) for efficiently suppressing glare. Both numerical simulations and experimental data show that light intensity decays exponentially with respect to the number of HEA measurements. Specifically, we applied the HEA to reduce the intensity of a single speckle to 4.1% of its original value within only 16 measurements. In contrast, the commonly used genetic algorithm (GA) can reduce the speckle intensity only to 0.2 of its original value even after 1200 measurements. Therefore, the HEA greatly outperforms the previously adopted GA in terms of efficiency. We further show that the HEA is also applicable to suppress the integrated intensity of many speckles.

Ultrafast polarization bio-imaging based on coherent detection and time-stretch techniques.

Optical polarization imaging has played an important role in many biological and biomedical applications, as it provides a label-free and non-invasive detection scheme to reveal the polarization information of optical rotation, birefringence, and photoelasticity distribution inherent in biological samples. However, the imaging speeds of the previously demonstrated polarization imaging techniques were often limited by the slow frame rates of the arrayed imaging detectors, which usually run at frame rates of several hundred hertz. By combining the optical coherent detection of orthogonal polarizations and the optical time-stretch imaging technique, we achieved ultrafast polarization bio-imaging at an extremely fast record line scanning rate up to 100 MHz without averaging. We experimentally demonstrated the superior performance of our method by imaging three slices of different kinds of biological samples with the retrieved Jones matrix and polarization-sensitive information including birefringence and diattenuation. The proposed system in this paper may find potential applications for ultrafast polarization dynamics in living samples or some other advanced biomedical research.