Polarization control of multiply scattered light through random media by wavefront shaping

Construction of vector vortex beams on hybrid-order Poincaré sphere through highly scattering media

Vector vortex beams (VVBs) have attracted extensive attention due to their unique properties and their wide applications in fields such as optical manipulation and optical imaging. However, the wavefronts of the vector vortex beams are highly scrambled when they encounter highly scattering media (HSM), such as thick biological tissues, which greatly prevents the applications of VVBs behind HSM. To address this issue, we propose a scheme to construct VVBs of freewill position on the surface of hybrid-order Poincaré sphere (HyOPS) through HSM. With the measurement of two orthogonal scalar transmission matrices, the conjugated wavefronts for constructing orbital angular momentum beams with arbitrary topological charge in right and left circularly polarized states through HSM can be calculated, respectively. When an input wavefront superimposed by the two conjugated wavefronts with an appropriate ratio and phase delay, impinges on the HSM, the desired VVB can be created through HSM. To demonstrate the viability of our scheme, a series of VVBs on different locations of various HyOPSs have been reconstructed through a ZnO scattering layer experimentally. Furthermore, to characterize the polarization distribution of the generated beams, the polarization maps of these beams are derived by measuring the four Stokes parameters, which agree well with the theoretical distributions. This work will promote the applications of VVBs in highly scattering environments.

Generation of flattop beams from a distorted optical field by the wavefront shaping technique

Uniform laser beams with controllable patterns are crucial for various applications, including laser processing and inertial confinement fusion. While some methods have been proposed to generate flattop beams, they often require complex optical systems that can become ineffective because of the misalignment of the system or the imperfection of optical elements. To overcome these issues, we utilized feedback-based wavefront shaping (FWS) technology to generate flattop beams with desired patterns from a disordered light. To solve the multi-goal optimization problem, we propose some modifications based on the Non-dominated Sorting Genetic Algorithm II (NSGA2) and successfully generate focal beams with a uniform intensity distribution and controllable beam shape from the disordered light field.

Focusing through scattering media by a single polarization transmission matrix with binary polarization modulation

Wavefront distortion induced by scattering media seriously affects optical focusing. Wavefront shaping based on a transmission matrix (TM) is useful in controlling light propagation in highly scattering media. Traditional TM generally studies amplitude and phase, but the stochastic nature of the light propagation in the scattering medium also affects its polarization. Based on the binary polarization modulation, we propose a single polarization transmission matrix (SPTM) and achieve single-spot focusing through scattering media. We anticipate that the SPTM will be widely used in wavefront shaping.

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.

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.

Gradient-assisted focusing light through scattering media

Focusing light through a scattering medium is a longstanding challenge in biomedical optics, to which wavefront shaping is a powerful solution. The state-of-the-art feedback-based approach is the widely used genetic algorithm method. However, it can only achieve relatively low enhancement of the focus, and the genetic algorithm is known to be time-consuming. To tackle those issues, we propose a gradient-assisted strategy for wavefront shaping. The proposed method conducts optimization in the function distribution space. Specifically, when optimizing the parameters along each iteration, the consequent function distribution changes within a distance as measured by the Kullback-Leibler divergence. Taking advantage of the gradient information, the proposed method is over 60× faster to obtain the same peak-to-background ratio (PBR) level. Compared with the genetic algorithm that is able to optimize a number of 64×64 phase segments, the proposed gradient strategy is able to optimize 256×256 phase segments, and gives 20× higher focus enhancement as quantified by the PBR.

Single pixel polarimetric imaging through scattering media

Polarimetric imaging can provide valuable information about biological samples in a wide range of applications. Detrimental tissue scattering and depolarization however currently hamper in vivo polarization imaging. In this work, single pixel imaging is investigated as a means of reconstructing polarimetric images through scattering media. A theoretical imaging model is presented, and the recovery of the spatially resolved Mueller matrix of a test object behind a scattering phantom is demonstrated experimentally.

Disordered Optics: Exploiting Multiple Light Scattering and Wavefront Shaping for Nonconventional Optical Elements

Advances in diverse areas such as inspection, imaging, manufacturing, telecommunications, and information processing have been stimulated by novel optical devices. Conventional material ingredients for these devices are typically made of homogeneous refractive or diffractive materials and require sophisticated design and fabrication, which results in practical limitations related to their form and functional figures of merit. To overcome such limitations, recent developments in the application of disordered materials as novel optical elements have indicated great potential in enabling functionalities that go beyond their conventional counterparts, while the materials exhibit potential advantages with respect to reduced form factors. Combined with wavefront shaping, disordered materials enable dynamic transitions between multiple functionalities in a single active optical device. Recent progress in this field is summarized to gain insight into the physical principles behind disordered optics with regard to their advantages in various applications as well as their limitations compared to conventional optics.

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.

Controlling light in complex media beyond the acoustic diffraction-limit using the acousto-optic transmission matrix

Studying the internal structure of complex samples with light is an important task but a difficult challenge due to light scattering. While the complex optical distortions induced by scattering can be effectively undone if the medium’s scattering-matrix is known, this matrix generally cannot be retrieved without the presence of an invasive detector or guide-star at the target points of interest. To overcome this limitation, the current state-of-the-art approaches utilize focused ultrasound for generating acousto-optic guide-stars, in a variety of different techniques. Here, we introduce the acousto-optic transmission matrix (AOTM), which is an ultrasonically-encoded, spatially-resolved, optical scattering-matrix. The AOTM provides both a generalized framework to describe any acousto-optic based technique, and a tool for light control and focusing beyond the acoustic diffraction-limit inside complex samples. We experimentally demonstrate complex light control using the AOTM singular vectors, and utilize the AOTM framework to analyze the resolution limitation of acousto-optic guided focusing approaches.

Various techniques combine light and ultrasound to study the inside of strongly scattering samples, beyond the reach of purely optical imaging. Here, Katz et al. introduce the acousto-optic transmission matrix framework that allows to control and focus light beyond the acoustic diffraction limit.

Mode conversion via wavefront shaping

In recent years, wavefront shaping has been utilized to control and correct distorted light for enhancing a bright spot, generation of a Bessel beam or darkening a complete area at the output of a scattering system. All these outcomes can be thought of as enhancing a particular mode of the output field. In this letter, we study the relation between the attainable enhancement factor, corresponding to the efficiency of mode conversion, and the field distribution of the target mode. Working in the limit of a thin diffuser enables not only a comparison between experimental and simulated results, but also allows for derivation of an analytic formula. These results shed light on the ability to use a scattering medium as a mode converter and on the relationship between the desired shape and the efficiency.

Complete polarization control in multimode fibers with polarization and mode coupling

Multimode optical fibers have seen increasing applications in communication, imaging, high-power lasers, and amplifiers. However, inherent imperfections and environmental perturbations cause random polarization and mode mixing, causing the output polarization states to be different from the input polarization states. This difference poses a serious issue for employing polarization-sensitive techniques to control light-matter interactions or nonlinear optical processes at the distal end of a fiber probe. Here, we demonstrate complete control of polarization states for all output channels by only manipulating the spatial wavefront of a laser beam into the fiber. Arbitrary polarization states for individual output channels are generated by wavefront shaping without constraining the input polarization. The strong coupling between the spatial and polarization degrees of freedom in a multimode fiber enables full polarization control with the spatial degrees of freedom alone; thus, wavefront shaping can transform a multimode fiber into a highly efficient reconfigurable matrix of waveplates for imaging and communication applications.

Simulated annealing optimization in wavefront shaping controlled transmission

In this research, we present results of simulated annealing (SA), a heuristic optimization algorithm, for focusing light through a turbid medium. Performance of the algorithm on phase and amplitude modulations has been evaluated. A number of tips to tune the optimization parameters are provided. The effect of measurement noise on the performance of the SA algorithm is explored. Additionally, SA performance is compared with continuous sequential and briefly with other optimization algorithms.

Powder sum-frequency generation as a versatile method for infrared optical alignment

The sum-frequency generation (SFG) in potassium dihydrogen phosphate (KDP) powder with μm-grade particle size is successfully demonstrated under various experimental conditions. Two focused beams of 870 nm and 1369 nm are used for SFG excitation. SFG is observed under different excitation energies. The SFG intensity shows isotropy with different observation azimuths. The intersection angle between two excitation beams is not limited by conventional phase-matching conditions, and it owns the flexibility of a very large allowed range, e.g., it can be 0°∼100° in this work. The polarization combination of excitation beams is not limited either. Thanks to the non-toxicity, low price, and low SFG threshold properties of KDP material and the optical flexibility, this powder SFG technology is a versatile method and is expected to be applied to various situations of optical alignment, e.g., surface SFG, four-wave mixing, coherent anti-Stokes Raman spectroscopy, multi-color laser excitation, etc. The effect of potential powder SFG-assisted optical alignments is also discussed. Extension of this method to multi-beams, tight focusing beams, and plasmonic polariton devices is proposed.

Generation of focal pattern with controllable polarization and intensity for laser beam passing through a multi-mode fiber

Similar to coherent light passing through a scattering medium, the propagation of coherent light through a multi-mode fiber (MMF) will result in a random speckle field. For a non-polarization maintaining MMF, the randomization can be observed not only in the intensity distribution, but also in the polarization state. In this paper, we propose a new technique known as phase combination to control the optical field for the light passing through the MMF. We show that, based on this new technique, the random speckle pattern can be modulated into an intensity distribution of two bright focal spots with mutually perpendicular polarization by only one polarizer. In particular, the intensity distribution of these two focal spots can be quantitatively controlled. This technique may find applications in medical imaging, nonlinear optics and optical communication etc.

Controlled modulation of depolarization in laser speckle

A new technique based on superposition of two speckle patterns is proposed and demonstrated for controlled modulation of the spatial polarization distribution of the resultant speckle. It is theoretically and experimentally demonstrated that controlled modulation of the spatial polarization distribution of laser speckle can be achieved by proper choice of the polarization states as well as the average spatial intensity of the constituent speckles. It is shown that the proposed technique is useful to generate different speckle patterns with sinusoidal variation in their degree of polarization, which can be tuned from zero to unity. This technique can find application in sensing, biomedical studies, and in determining the rotation of an electric field vector after passing through a scattering medium.

Polarization recovery through scattering media

The control and use of light polarization in optical sciences and engineering are widespread. Despite remarkable developments in polarization-resolved imaging for life sciences, their transposition to strongly scattering media is currently not possible, because of the inherent depolarization effects arising from multiple scattering. We show an unprecedented phenomenon that opens new possibilities for polarization-resolved microscopy in strongly scattering media: polarization recovery via broadband wavefront shaping. We demonstrate focusing and recovery of the original injected polarization state without using any polarizing optics at the detection. To enable molecular-level structural imaging, an arbitrary rotation of the input polarization does not degrade the quality of the focus. We further exploit the robustness of polarization recovery for structural imaging of biological tissues through scattering media. We retrieve molecular-level organization information of collagen fibers by polarization-resolved second harmonic generation, a topic of wide interest for diagnosis in biomedical optics. Ultimately, the observation of this new phenomenon paves the way for extending current polarization-based methods to strongly scattering environments.

Lensless wide-field single-shot imaging through turbid media based on object-modulated speckles

The need to image objects through light-scattering materials is common in a range of applications. Different methods have been investigated to acquire the image of the object when diffusers are presented. In this paper, we demonstrate the object reconstruction with single-shot imaging based on the correlography principle and phase retrieval algorithm with coherent illumination. We prove the possibility of reconstructing positive and negative objects in both transmission and reflection modes with collimated and scattered light. Formulas for calculating the size of the object from the reconstructed image are presented. We also prove that the object can be retrieved from a small section of the raw speckle image. These interesting features will have broad potential applications in many areas (such as biomedicine, security and sensing).

Propagation of polarized waves through bounded composite materials

We describe a numerical model, based on a Monte Carlo algorithm, to calculate the propagation of polarized waves through highly scattering microstructured materials, and to properly account for the effect of both loss and boundaries. As an example, we investigate the impact of a strongly scattering object of air-polymer composite material on a broadband collimated source. We also calculate the depolarization of linearly polarized and circularly polarized waves escaping from the sample boundaries, especially at large scattering angles, and we show how boundaries can modify the distribution and the polarization of the scattered waves propagating out of the sample.

Mapping the energy density of shaped waves in scattering media onto a complete set of diffusion modes

We study the energy density of shaped waves inside a quasi-1D disordered waveguide. We find that the spatial energy density of optimally shaped waves, when expanded in the complete set of eigenfunctions of the diffusion equation, is well described by considering only a few of the lowest eigenfunctions. Taking into account only the fundamental eigenfunction, the total internal energy inside the sample is underestimated by only 2%. The spatial distribution of the shaped energy density is very similar to the fundamental eigenfunction, up to a cosine distance of about 0.01. We obtain the energy density of transmission eigenchannels inside the sample by numerical simulation of the scattering matrix. Computing the transmission-averaged energy density over all transmission channels yields the ensemble averaged energy density of shaped waves. From the averaged energy density, we reconstruct its spatial distribution using the eigenfunctions of the diffusion equation. The results of our study have exciting applications in controlled biomedical imaging, efficient light harvesting in solar cells, enhanced energy conversion in solid-state lighting, and low threshold random lasers.

Polarization modulation for imaging behind the scattering medium

We propose and experimentally demonstrate a technique, based on polarization modulation, for imaging of the polarization discriminating object hidden behind a scattering medium. This is realized by making use of the relation between the complex correlation function of the randomly scattered orthogonal polarization components in the far field and polarized source structure at the scattering plane. Full use of a polarimetric parameter at the scattering plane is realized in the object plane reconstruction behind the scattering medium using a backpropagation approach. To demonstrate application of the technique, imaging of two different objects lying behind the scattering media is presented.

Enabling focusing around the corner in multiple scattering media

We report an alternative experimental setup to laterally focus light at an angle of 90 deg relative to turbid, multiple scattering media, using preprocessing wavefront shaping. We compare the measured image quality to one obtained in the usual configuration for focusing light through turbid media, where focusing occurs behind the scattering sample. We demonstrate that the depth of focus in the lateral configuration is of the same order of the usual transversal one because both setups are designed to operate in the deep Fresnel zone. This result shows that this novel, versatile lateral configuration allows for effectively focusing around corners through multiple scattering samples.

Controlled light field concentration through turbid biological membrane for phototherapy

Laser propagation through a turbid rat dura mater membrane is shown to be controllable with a wavefront modulation technique. The scattered light field can be refocused into a target area behind the rat dura mater membrane with a 110 times intensity enhancement using a spatial light modulator. The efficient laser intensity concentration system is demonstrated to imitate the phototherapy for human brain tumors. The power density in the target area is enhanced more than 200 times compared with the input power density on the dura mater membrane, thus allowing continued irradiation concentration to the deep lesion without damage to the dura mater. Multibeam inputs along different directions, or at different positions, can be guided to focus to the same spot behind the membrane, hence providing a similar gamma knife function in optical spectral range. Moreover, both the polarization and the phase of the input field can be recovered in the target area, allowing coherent field superposition in comparison with the linear intensity superposition for the gamma knife.

Feedback-based wavefront shaping

Light scattering was thought to be the fundamental limitation for the depth at which optical imaging methods can retain their resolution and sensitivity. However, it was shown that light can be focused inside even the most strongly scattering objects by spatially shaping the wavefront of the incident light. This review summarizes recently developed feedback-based approaches for focusing light inside and through scattering objects.

Microgenetic optimization algorithm for optimal wavefront shaping

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 microgenetic optimization algorithm (μGA) for optimal wavefront shaping. We test the abilities of the μGA 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 μGA is faster than both the iterative and simple-genetic algorithms and that both genetic algorithms are more resistant to noise and sample decoherence than the iterative algorithm.

Programmable multiport optical circuits in opaque scattering materials

We propose and experimentally verify a method to program the effective transmission matrix of general multiport linear optical circuits in random multiple-scattering materials by phase modulation of incident wavefronts. We demonstrate the power of our method by programming linear optical circuits in white paint layers with 2 inputs and 2 outputs, and 2 inputs and 3 outputs. Using interferometric techniques we verify our ability to program any desired phase relation between the outputs. The method works in a deterministic manner and can be directly applied to existing wavefront-shaping setups without the need of measuring a transmission matrix or to rely on sensitive interference measurements.

Superpixel-based spatial amplitude and phase modulation using a digital micromirror device

We present a superpixel method for full spatial phase and amplitude control of a light beam using a digital micromirror device (DMD) combined with a spatial filter. We combine square regions of nearby micromirrors into superpixels by low pass filtering in a Fourier plane of the DMD. At each superpixel we are able to independently modulate the phase and the amplitude of light, while retaining a high resolution and the very high speed of a DMD. The method achieves a measured fidelity F = 0.98 for a target field with fully independent phase and amplitude at a resolution of 8 × 8 pixels per diffraction limited spot. For the LG10 orbital angular momentum mode the calculated fidelity is F = 0.99993, using 768 × 768 DMD pixels. The superpixel method reduces the errors when compared to the state of the art Lee holography method for these test fields by 50% and 18%, with a comparable light efficiency of around 5%. Our control software is publicly available.

Programming balanced optical beam splitters in white paint

Wavefront shaping allows for ultimate control of light propagation in multiple-scattering media by adaptive manipulation of incident waves. We shine two separate wavefront-shaped beams on a layer of dry white paint to create two enhanced output spots of equal intensity. We experimentally confirm by interference measurements that the output spots are almost correlated like the two outputs of an ideal balanced beam splitter. The observed deviations from the phase behavior of an ideal beam splitter are analyzed with a transmission matrix model. Our experiments demonstrate that wavefront shaping in multiple-scattering media can be used to approximate the functionality of linear optical devices with multiple inputs and outputs.

Coherent control of total transmission of light through disordered media

We demonstrate order of magnitude coherent control of total transmission of light through random media by shaping the wave front of the input light. To understand how the finite illumination area on a wide slab affects the maximum values of total transmission, we develop a model based on random matrix theory that reveals the role of long-range correlations. Its predictions are confirmed by numerical simulations and provide physical insight into the experimental results.

Harnessing randomness to control the polarization of light transmitted through highly scattering media

We show that the multiple scattering events taking place inside a highly scattering medium, in conjunction with wavefront shaping, can be used to control the state of polarization of the light transmitted through a highly scattering medium. This control is achieved by using the intensity, phase, and polarization changing behavior of a scattering medium captured by a vector transmission matrix (VTM). We use a single beam incident upon a scattering medium to measure the absolute value of the VTM elements, in contrast to the multiple beams required in our previously reported approach. Further, the phase-only spatial light modulator based on a low-cost (< US$600) deformable micro-mirror array used in our work will make similar experiments accessible to other researchers.

Digital optical phase conjugation for delivering two-dimensional images through turbid media

Optical transmission through complex media such as biological tissue is fundamentally limited by multiple light scattering. Precise control of the optical wavefield potentially holds the key to advancing a broad range of light-based techniques and applications for imaging or optical delivery. We present a simple and robust digital optical phase conjugation (DOPC) implementation for suppressing multiple light scattering. Utilizing wavefront shaping via a spatial light modulator (SLM), we demonstrate its turbidity-suppression capability by reconstructing the image of a complex two-dimensional wide-field target through a highly scattering medium. Employing an interferometer with a Sagnac-like ring design, we successfully overcome the challenging alignment and wavefront-matching constraints in DOPC, reflecting the requirement that the forward- and reverse-propagation paths through the turbid medium be identical. By measuring the output response to digital distortion of the SLM write pattern, we validate the sub-wavelength sensitivity of the system.

Increasing the imaging capabilities of multimode fibers by exploiting the properties of highly scattering media

We present a design that exploits the focusing properties of scattering media to increase the resolution and the working distance of multimode fiber (MMF)-based imaging devices. Placing a highly scattering medium in front of the distal tip of the MMF enables the formation of smaller sized foci at increased working distances away from the fiber tip. We perform a parametric study of the effect of the working distance and the separation between the fiber and the scattering medium on the focus size. We experimentally demonstrate submicrometer focused spots as far away as 800 μm with 532 nm light.

Image restoration through thin turbid layers by correlation with a known object

A method to recover the image of an object behind thin turbid layers is developed by wavefront shaping technique. The optimized wavefront is generated by modulating the scattering light of a known object with a spatial light modulator. A Pearson Correlation Coefficient is introduced as a cost function for the optimization. A beam scanning method based on optical memory effect is proposed to further enlarge the Field-of-View (FOV). The experimental results show good fidelity and large FOV of the recovered image.

Optimal control of light propagation through multiple-scattering media in the presence of noise

We study the control of coherent light propagation through multiple-scattering media in the presence of measurement noise. In our experiments, we use a two-step optimization procedure to find the optimal incident wavefront that generates a bright focal spot behind the medium. We conclude that the control of coherent light propagation through a multiple-scattering medium is only determined by the number of photoelectrons detected per optimized segment. The prediction of our model agrees well with the experimental results. Our results offer opportunities for imaging applications through scattering media such as biological tissue in the shot noise limit.