Wavefront shaping can tailor multipath interference to control multiple scattering of waves in complex optical systems. However, full-wave simulations that capture multiple scattering are computationally demanding given the large system size and the large number of input channels. Recently, an "augmented partial factorization" (APF) method was proposed to significantly speed-up such full-wave simulations. In this tutorial, we illustrate how to perform wavefront shaping simulations with the APF method using the open-source frequency-domain electromagnetic scattering solver MESTI. We present the foundational concepts and then walk through four examples: computing the scattering matrix of a slab with random permittivities, open high-transmission channels through disorder, focusing inside disorder with phase conjugation, and reflection matrix computation in a spatial focused-beam basis. The goal is to lower the barrier for researchers to use simulations to explore the rich phenomena enabled by wavefront shaping.
Light scattering is the main limitation for optical imaging. However, light can be focused through or inside turbid media by spatially shaping the incident wavefront. Wavefront shaping is ultimately limited by the available photon budget. We developed a new `dual reference' wavefront shaping algorithm that optimally uses the available light. Our method allows for multi-target wavefront shaping, making it suitable for transmission matrix measurements or transmitting images. We experimentally confirmed the improvement of the focus intensity compared to existing methods.
We show that customized optical patterns can be generated by employing feedback-based wavefront shaping without prior knowledge of the transmission matrix of optical systems. To control the spatial distribution of intensity within the target region, the overlap coefficient is employed as the key feedback signal for wavefront shaping, and the optimal phase pattern for generating the customized optical pattern is reached when the overlap coefficient converges to unity. By using the overlap-coefficient optimized wavefront shaping, we generate customized optical patterns such as multiple focused s…
Focusing light through dynamically varying heterogeneous media is a sought-after goal with important applications ranging from free-space communication to nano-surgery. The underlying challenge is to control the optical wavefront with a large number of degrees-of-freedom (DOF) at timescales shorter than the medium dynamics. Recently, many advancements have been reported following the demonstration of focusing through turbid samples by wavefront-shaping, using spatial light modulators (SLMs) having >1000 DOF. Unfortunately, SLM-based wavefront-shaping requires feedback from a detector/camera an…
A random medium can serve as a controllable arbitrary spectral filter with spectral resolution determined by the inverse of the interaction time of the light in the medium. We use wavefront shaping to implement an arbitrary spectral response at a particular point in the scattered field. We experimentally demonstrate this technique by selecting either a narrow band or dual bands with a width of 5.5nm each.
We demonstrate that simultaneous application of optical clearing agents (OCAs) and complex wavefront shaping in optical coherence tomography (OCT) can provide significant enhancement of the penetration depth and imaging quality. OCA reduces optical inhomogeneity of a highly scattering sample, and the wavefront shaping of illumination light controls multiple scattering, resulting in an enhancement of the penetration depth and signal-to-noise ratio. A tissue phantom study shows that concurrent applications of OCA and wavefront shaping successfully operate in OCT imaging. The penetration depth en…
We show that the polarization state of coherent light propagating through an optically thick multiple-scattering medium, can be controlled by wavefront shaping, i.e. by controlling only the spatial phase of the incoming field with a spatial light modulator. Any polarization state of light at any spatial position behind the scattering medium can be attained with this technique. Thus, transforming the random medium to an arbitrary optical polarization component becomes possible.
We introduce a non-invasive approach for optogenetic regulation in biological cells through highly scattering skull tissue using wavefront shaping. The wavefront of the incident light was systematically controlled using a spatial light modulator in order to overcome multiple light-scattering in a mouse skull layer and to focus light on the target cells. We demonstrate that illumination with shaped waves enables spatiotemporal regulation of intracellular Ca2+ level at the individual-cell level.
Scattering prevents light from being focused in turbid media. The effect of scattering can be negated through wavefront shaping techniques when a localized form of feedback is available. Even in the absence of such a localized reporter, wavefront shaping can blindly form a single diffraction-limited focus when the feedback response is nonlinear. We developed and experimentally validated a model that accurately describes the statistics of this blind focusing process. We show that maximizing the nonlinear feedback signal does not always result in the formation of a focus. Using our model, we can…
One of the main limitations of utilizing optimal wavefront shaping in imaging and authentication applications is the slow speed of the optimization algorithms currently being used. To address this problem we develop a micro-genetic optimization algorithm ($μ$GA) for optimal wavefront shaping. We test the abilities of the $μ$GA and make comparisons to previous algorithms (iterative and simple-genetic) by using each algorithm to optimize transmission through an opaque medium. From our experiments we find that the $μ$GA is faster than both the iterative and simple-genetic algorithms and that both…
Wavefront shaping has revolutionized imaging deep in scattering media, being able to spatially and temporally refocus light through or inside the medium. However, wavefront shaping is not compatible yet with polarization-resolved microscopy given the need of polarizing optics to refocus light with a controlled polarization state. Here, we show that wavefront shaping is not only able to restore a focus, but it can also recover the injected polarization state without using any polarizing optics at the detection. This counter-intuitive effect occurs up to several transport mean free path thick sa…
Light scattering limits the penetration depth of non-invasive Raman spectroscopy in biological media. While safe levels of irradiation may be adequate to analyze superficial tissue, scattering of the pump beam reduces the Raman signal to undetectable levels deeper within the tissue. Here we demonstrate how wavefront shaping techniques can significantly increase the Raman signal at depth, while keeping the total irradiance constant, thus increasing the amount of Raman signal available for detection.
Due to the highly inhomogeneous distributions of refractive indexes, light propagation in complex media such as biological tissue experiences multiple light scattering events. The suppression and control of multiple light scattering events are investigated because they offer the possibility of optical focusing and imaging through biological tissues, and they may open new avenues for diagnosis and treatment of several human diseases. In order to provide insight into how new optical techniques can address the issues of multiple light scattering in biomedical applications, the recent progress in …
Wavefront shaping is a powerful technique that can be used to focus light through scattering media, which can be important for imaging through scattering samples such as tissue. The method is based on the assumption that the field at the output of the medium is a linear superposition of the modes traveling through different paths in the medium. However, when the scattering medium also exhibits nonlinearity, as may occur in multiphoton microscopy, this assumption is violated and the applicability of wavefront shaping becomes unclear. Here we show, using a simple model system with a scattering l…
Optical focusing through scattering media has important implications for optical applications in medicine, communications, and detection. In recent years, many wavefront shaping methods have been successfully applied to the field, among which the population optimization algorithm has achieved remarkable results. However, the current population optimization algorithm has some drawbacks: 1. the offspring do not fully inherit the good genes from the parent. 2. more efforts are needed to tune the parameters. In this paper, we propose the mutate greedy algorithm. It combines greedy strategies and r…
Scattering has usually be considered as detrimental for optical focusing or imaging. Recently, more and more research has shown that strongly scattering materials can be utilized to focus coherent light by controlling or shaping the incident light. Here, purposeful focusing of second-harmonic waves, which are generated and scattered from nonlinear turbid media via feedback-based wavefront shaping is presented. This work shows a flexible manipulation of both disordered linear and nonlinear scattering signals, indicating more controllable degrees of freedom for the description of turbid media. T…
We report the realization of a Pancharatnam-Berry phase optical element [Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. \textbf{27}, 1141 (2002)] for wavefront shaping working in the visible spectral domain, based on patterned liquid crystal technology. This device generates helical modes of visible light with the possibility of electro-optically switching between opposite helicities by controlling the handedness of the input circular polarization. By cascading this approach, fast switching among multiple wavefront helicities can be achieved, with potential applications to multi-s…
Imaging through optical multimode fibers (MMFs) has the potential to enable hair-thin endoscopes that reduce the invasiveness of imaging deep inside tissues and organs. Current approaches predominantly require active wavefront shaping and fluorescent labeling, which limits their use to preclinical applications and frustrates imaging speed. Here we present a computational approach to reconstruct depth-gated confocal images using a raster-scanned, focused input illumination. We demonstrate the compatibility of this approach with quantitative phase, dark-field, and polarimetric imaging. Computati…
In this paper, we experimentally demonstrate reversible wavefront shaping through mimicking gravitational field. A gradient-index micro-structured optical waveguide with special refractive index profile was constructed whose effective index satisfying a gravitational field profile. Inside the waveguide, an incident broad Gaussian beam is firstly transformed into an accelerating beam, and the generated accelerating beam is gradually changed back to a Gaussian beam afterwards. To validate our experiment, we performed full-wave continuum simulations that agree with the experimental results. Furth…
We demonstrate a new concept for reconfigurable nanophotonic devices exploiting ultrafast nonlinear control of shaped wavefronts in a multimode nanomaterial consisting of semiconductor nanowires. Femtosecond pulsed laser excitation of the nanowire mat is shown to provide an efficient nonlinear mechanism to control both destructive and constructive interference in a shaped wavefront. Modulations of up to 63% are induced by optical pumping, due to a combination of multimode dephasing and induced transient absorption. We show that part of the nonlinear phase dynamics can be inverted to provide a …
We introduce a simple but practical method to measure the optical transmission matrix (TM) of complex media. The optical TM of a complex medium is obtained by modulating the wavefront of a beam impinging on the complex medium and imaging the transmitted full-field speckle intensity patterns. Using the retrieved TM, we demonstrate the generation and linear combination of multiple foci on demand through the complex medium. This method will be used as a versatile tool for coherence control of waves through turbid media.
Optical imaging through scattering media is a fundamental challenge in many applications. Recently, substantial breakthroughs such as imaging through biological tissues and looking around corners have been obtained by the use of wavefront-shaping approaches. However, these require an implanted guide-star for determining the wavefront correction, controlled coherent illumination, and most often raster scanning of the shaped focus. Alternative novel computational approaches that exploit speckle correlations, avoid guide-stars and wavefront control but are limited to small two-dimensional objects…
A perfectly collimated beam can be spread out by multiple scattering, creating a speckle pattern and increasing the etendue of the system. Standard optical systems conserve etendue, and thus are unable to reverse the process by transforming a speckle pattern into a collimated beam or, equivalently, into a sharp focus. Wavefront shaping is a technique that is able to manipulate the amplitude and/or phase of a light beam, thus controlling its propagation through such media. Wavefront shaping can thus break the conservation of etendue and, in principle, reduce it. In this work we study how much o…
Three-photon (3P) microscopy is getting traction due to its superior performance in deep tissues. Yet, aberrations and light scattering still pose one of the main limitations in the attainable depth ranges for high-resolution imaging. Here, we show scattering correcting wavefront shaping with a simple continuous optimization algorithm, guided by the integrated 3P fluorescence signal. We demonstrate focusing and imaging behind scattering layers and investigate convergence trajectories for different sample geometries and feedback non-linearities. Furthermore, we show imaging through a mouse skul…
We demonstrate focusing and imaging through a scattering medium noninvasively by using wavefront shaping. Our concept is based on utilizing the spatial fluorescence contrast which naturally exists in the hidden target object. By scanning the angle of incidence of the illuminating laser beam and maximizing the variation of the detected fluorescence signal from the object, as measured by a bucket detector at the front of the scattering medium, we are able to generate a tightly focused excitation spot. Thereafter, an image is obtained by scanning the focus over the object. The requirements for ap…
Multiple light scattering in tissue limits the penetration of optical coherence tomography (OCT) imaging. Here, we present in-vivo OCT imaging of a live mouse using wavefront shaping to enhance the penetration depth. A digital micro-mirror device (DMD) was used in a spectral-domain OCT system for complex wavefront shaping of an incident beam which resulted in the optimal delivery of light energy into deep tissue. Ex-vivo imaging of chicken breasts and mouse ear tissues showed enhancements in the strength of the image signals and the penetration depth, and in-vivo imaging of the tail of a live …
We demonstrate the control of entanglement of a single photon between several spatial modes propagating through a strongly scattering medium. Measurement of the scattering matrix allows the wavefront of the photon to be shaped to compensate the distortions induced by multiple scattering events. The photon can thus be directed coherently to a single or multi-mode output. Using this approach we show how entanglement across different modes can be manipulated despite the enormous wavefront disturbance caused by the scattering medium.
Photonic devices rarely provide both elaborate spatial control and sharp spectral control over an incoming wavefront. In optical metasurfaces, for example, the localized modes of individual meta-units govern the wavefront shape over a broad bandwidth, while nonlocal lattice modes extended over many unit cells support high quality-factor resonances. Here, we experimentally demonstrate nonlocal dielectric metasurfaces in the near-infrared that offer both spatial and spectral control of light, realizing metalenses focusing light exclusively over a narrowband resonance while leaving off-resonant f…
Sorbonne Université, CNRS, Institut des NanoSciences de Paris（索邦大学，法国国家科学研究中心，巴黎纳米科学研究所）；University of the Witwatersrand（威特沃特斯兰德大学）；Università degli Studi di Napoli Federico II（那不勒斯费德里科二世大学）；Scuola Superiore Meridionale（南方高等学院）
Recent advances in iterative wavefront shaping (WFS) techniques have made it possible to manipulate the light focusing and transport in scattering media. To improve the optimization performance, various optimization algorithms and improved strategies have been utilized. Here, a novel guided mutation (GM) strategy is proposed to improve optimization efficiency for iterative WFS. For both phase modulation and binary amplitude modulation, considerable improvements in optimization effect and rate have been obtained using multiple GM-enhanced algorithms. Due of its improvements and universality, GM…
We present an optical wavefront shaping approach that allows tracking and localization of signal hidden inside or behind a scattering medium. The method combines traditional feedback based wavefront shaping together with a switch function, controlled by two different signals. A simple, in transmission imaging system is used with two detectors: one monitors the speckle signature and the other tracks the fully hidden signal (e.g., fluorescent beads). The algorithm initially finds the optimal incident wavefront to maximize light transmission to generate a focus in the scattering medium. This modu…
We report experimental results, showing that the Kerr beam self-cleaning of many low-order modes in a graded-index multimode fiber can be controlled thanks to optimized wavefront shaping of the coherent excitation beam. Adaptive profiling of the transverse input phase was utilized for channeling the launched power towards a specific low-order fiber mode, by exploiting nonlinear coupling among all guided modes. Experiments were carried out with 7 ps pulses at 1064 nm injected in a five meters long multimode fiber operating in the normal dispersion regime. Optimized Kerr beam self-cleaning of fi…
Optical logic gates are fundamental blocks of optical computing to accelerate information processing. While significant progress has been achieved in recent years, existing implementations typically rely on dedicated structures that are predesigned to modulate the phases and intensities of optical beams accurately for specific logic functions. Thus, these optical gates usually lack reconfigurability and are incapable within or through dynamic complex media/environment, such as fog and turbid water. In this work, as a conceptual demonstration, we propose reconfigurable optical logic operations …
Wavefront shaping techniques allow the control of the transport of light through many types of scattering or complex media, among them multimode fibers. The case of a multimode fiber which is also a gain medium presents further intriguing prospects for control, due to the possibility of wavefront shaping not only the signal light amplified by the medium, but also the pump light absorbed within it. Provided that the lightwave used for pumping is coherent, its shaping prior to injection will affect the complex, speckle-like spatial patterns of excitation within the amplifier volume, which in tur…
Non-invasively focusing light into strongly scattering media, such as biological tissue, is highly desirable but challenging. Recently, wavefront shaping technologies guided by ultrasonic encoding or photoacoustic sensing have been developed to address this limitation. So far, these methods provide only acoustic diffraction-limited optical focusing. Here, we introduce nonlinear photoacoustic wavefront shaping (PAWS), which achieves optical diffraction-limited (i.e. single-speckle-grain) focusing in scattering media. We develop an efficient dual-pulse excitation approach to generate strong nonl…
Converting spin angular momentum to orbital angular momentum has been shown to be a practical and efficient method for generating optical beams carrying orbital angular momentum and possessing a space-varying polarized field. Here, we present novel liquid crystal devices for tailoring the wavefront of optical beams through the Pancharatnam-Berry phase concept. We demonstrate the versatility of these devices by generating an extensive range of optical beams such as beams carrying $\pm200$ units of orbital angular momentum along with Bessel, Airy and Ince-Gauss beams. We characterize both the ph…
Controlling the propagation and interaction of light in complex media has sparked major interest in the last few years. Unfortunately, spatial light modulation devices suffer from limited speed that precludes real-time applications such as imaging in live tissue. To address this critical problem we introduce a phase-control technique to characterize complex media based on the use of fast 1D spatial light modulators and a 1D-to-2D transformation performed by the same medium being analyzed. We implement the concept using a micro-electro-mechanical grating light valve (GLV) with 1088 degrees of f…
We study the three-dimensional (3D) spatially-resolved distribution of the energy density of light in a 3D scattering medium upon the excitation of open transmission channels. The open transmission channels are excited by spatially shaping the incident optical wavefronts. To probe the local energy density, we excite isolated fluorescent nanospheres distributed inside the medium. From the spatial fluorescent intensity pattern we obtain the position of each nanosphere, while the total fluorescent intensity gauges the energy density. Our 3D spatially-resolved measurements reveal that the local en…
Optical focusing at depths in tissue is the Holy Grail of biomedical optics that may bring revolutionary advancement to the field. Wavefront shaping is a widely accepted approach to solve this problem, but most implementations thus far have only operated with stationary media which, however, are scarcely existent in practice. In this article, we propose to apply a deep convolutional neural network named as ReFocusing-Optical-Transformation-Net (RFOTNet), which is a Multi-input Single-output network, to tackle the grand challenge of light focusing in nonstationary scattering media. As known, de…
Coherent Anti Stokes Raman Scattering (CARS) offers many advantages for nonlinear bio-imaging, thanks to its sub-cellular spatial resolution and unique chemical specificity. Its working principle requires two incident pulsed laser beams with distinct frequencies to be focused in space and time, which focus quality however rapidly deteriorates when propagating at large depths in biological tissues. The depth limits of CARS and the capability of wavefront correction to overcome these limits are currently unknown. In this work we exploit the spectral correlation properties of the transmission mat…
Bessel beams are non-diffracting light structures, which can be produced with simple tabletop optical elements such as axicon lenses or ring spatial filters and coherent laser beams. One of their main characteristic is that Bessel beams maintain their spatial characteristics after meters of propagation. In this paper we demonstrate a system and method for generating Bessel beams from amorphous speckle patterns, exploiting adaptive optimization by a spatial light modulator. These speckles are generated by light modes transmitted through a scattering curtain and selected by a ring shaped filter.…
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 250um. The high signal-to-noise rati…
