Wavefront shaping is a powerful method to refocus light through a scattering medium. Its application to large spectral bandwidths or multiple wavelengths refocusing for nonlinear bio-imaging in-depth is however limited by spectral decorrelations. In this work, we demonstrate ways to access a large spectral memory of a refocus in thin scattering media and thick forward-scattering biological tissues. First, we show that the accessible spectral bandwidth through a scattering medium involves an axial spatio-spectral coupling, which can be minimized when working in a confocal geometry. Second, we show that this bandwidth can be further enlarged when working in a broadband excitation regime. These results open important prospects for multispectral nonlinear imaging through scattering media.
Metalenses have shown great promise in their ability to function as ultracompact optical systems for focusing and imaging. Remarkably, several designs have been recently demonstrated that operate over a large range of frequencies with minimized chromatic aberrations, potentially paving the way for ultrathin achromatic optics. Here, we derive fundamental bandwidth limits that apply to broadband optical metalenses, regardless of their implementation. Specifically, we discuss how the product between achievable time delay and bandwidth is limited in any time-invariant system, and we apply well-est…
We demonstrate that polarization modulation of an illumination beam can effectively control the spatial profile of the light transmitted through turbid media. Since the transmitted electric fields are completely mingled in turbid media, polarization states of an illumination beam can be effectively used to control the propagation of light through turbid media. Numerical simulations were performed which agree with experimental results obtained using a commercial in-plane switching liquid-crystal display for modulating the input polarization states.
We show that an azimuthally-periodically-modulated bright ring "necklace" beam can self-trap in self-focusing Kerr media and can exhibit stable propagation for very large distances. These are the first bright (2+1) D beams to exhibit stable self-trapping in a system described by the cubic (2+1) D Nonlinear Schrodinger Equation (NLSE).
A general method for tight focusing of waves, based on compensation of the angular spectrum, is established. We apply the method to monochromatic, polychromatic and diffusive waves. Diffusive and monochromatic waves may form spatially localized waves in free space, whereas polychromatic waves form light sheets or non-decaying traveling evanescent modes confined to subwavelength regions in media where the frequency depends on the wave vector. We suggest an analogy between our compensation method and the transformation of frequencies between inertial, relativistic coordinate systems.
We review the properties of nonlinear, multidimensional localized waves whose stationary propagation is sustained by a dynamic equilibrium between self-focusing and nonlinear losses. Their finite-energy versions preserve light bullet behavior well-beyond the characteristic diffraction or dispersion distances, and rebuild after obstacles. There exists a preferential lossy light bullet with maximum intensity and losses, defined solely by the optical properties of the medium, which is the most stable, non-conical localized wave supported by a medium with self-focusing nonlinearity and nonlinear l…
We demonstrate feedback-optimized focusing of spatially coherent polychromatic light after transmission through strongly scattering media, and describe the relationship between optimized focus intensity and initial far-field speckle contrast. Optimization is performed using a MEMS spatial light modulator with camera-based or spectrometer-based feedback. We observe that the spectral bandwidth of the optimized focus depends on characteristics of the feedback signal. We interpret this dependence as a modification in the number of spectral modes transmitted by the sample, and introduce a simple mo…
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…
We reveal the relevance between the nonlocality and the focusing/defocusing states in nonlocally nonlinear media, and predict a novel phenomenon that the self-focusing/self-defocusing property of the optical beam in the nonlocally nonlinear medium with a sine-oscillation response function depends on its degree of nonlocality. The transition from the focusing nonlinearity to the defocusing nonlinearity of the nonlinear refractive index will happen when the degree of nonlocality of the system goes cross a critical value, and vise verse. Bright and dark soliton solutions are obtained, respectivel…
We report a method to characterize the propagation of an ultrashort pulse of light through a multiple scattering medium by measuring its time-resolved transmission matrix. This method is based on the use of a spatial light modulator together with a coherent time-gated detection of the transmitted speckle field. Using this matrix, we demonstrate the focusing of the scattered pulse at any arbitrary position in space and time after the medium. Our approach opens new perspectives for both fundamental studies and applications in imaging and coherent control in disordered media.
We propose and demonstrate a system for wavefront shaping which generates optical foci through complex disordered media and achieves an enhancement factor of greater than 100,000. To exploit the 1 Megapixel capacity of a digital micro-mirror device and its fast frame rate, we developed a fast and efficient method to handle the heavy matrix algebra computation involved in optimizing the focus. We achieved an average enhancement factor of 101,391 within an optimization time of 73 minutes. This unprecedented enhancement factor may open new possibilities for realistic image projection and the effi…
We implement the photoacoustic transmission-matrix approach on a two-dimensional photoacoustic imaging system, using a 15 MHz linear ultrasound array. Using a black leaf skeleton as a complex absorbing structure, we demonstrate that the photoacoustic transmission-matrix approach allows to reveal structural features that are invisible in conventional photoacoustic images, as well as to selectively control light focusing on absorbing targets, leading to a local enhancement of the photoacoustic signal.
Optical imaging deep inside scattering media remains a fundamental problem in bio-imaging. While wavefront shaping has been shown to allow focusing of coherent light at depth, achieving it non-invasively remains a challenge. Various feedback mechanisms, in particular acoustic or non-linear fluorescence-based, have been put forward for this purpose. Non-invasive focusing at depth on fluorescent objects with linear excitation is, however, still unresolved. Here we report a simple method for focusing inside a scattering medium in an epi-detection geometry with a linear signal: optimizing the spat…
The ability to steer light propagation inside scattering media has long been sought-after due to its potential widespread applications. To form optical foci inside scattering media, the only feasible strategy is to guide photons by using either implanted or virtual guide stars. However, all of these guide stars must be introduced extrinsically, either invasively or by physical contact, limiting the scope of their application. Here, we focus light inside scattering media by employing intrinsic dynamics as guide stars. By time-reversing the perturbed component of the scattered light adaptively, …
We experimentally and numerically study the potential of photoacoustic-guiding for light focusing through scattering samples via wavefront-shaping and iterative optimization. We experimentally demonstrate that the focusing efficiency on an extended absorber can be improved by iterative optimization of the high frequency components of the broadband photoacoustic signal detected with a spherically focused transducer. We demonstrate more than 8-fold increase in the photoacoustic signal generated by a 30 microns wire using a narrow frequency band around 60MHz. We numerically confirm that such opti…
Focusing light inside scattering media in a freely addressable fashion is challenging, as the wavefront of the scattered light is highly disordered. Recently developed ultrasound-guided wavefront shaping methods are addressing this challenge, albeit with relatively low modulation efficiency and resolution limitations. In this paper, we present a new technique, time-reversed ultrasound microbubble encoded (TRUME) optical focusing, which is able to focus light with improved efficiency and sub-ultrasound wavelength resolution. This method ultrasonically destructs microbubbles, and measures the wa…
Light scattering inhibits high-resolution optical imaging, manipulation and therapy deep inside biological tissue by preventing focusing. To form deep foci, wavefront-shaping and time-reversal techniques that break the optical diffusion limit have been developed. For in vivo applications, such focusing must provide high gain, high speed, and a large number of spatial modes. However, none of the previous techniques meet these requirements simultaneously. Here, we overcome this challenge by rapidly measuring the perturbed optical field within a single camera exposure followed by adaptively time-…
Light scattering in inhomogeneous media induces wavefront distortions which pose an inherent limitation in many optical applications. Examples range from microscopy and nanosurgery to astronomy. In recent years, ongoing efforts have made the correction of spatial distortions possible by wavefront shaping techniques. However, when ultrashort pulses are employed scattering induces temporal distortions which hinder their use in nonlinear processes such as in multiphoton microscopy and quantum control experiments. Here we show that correction of both spatial and temporal distortions can be attaine…
Focusing light into opaque random or scattering media such as biological tissue is a much sought-after goal for biomedical applications such as photodynamic therapy, optical manipulation, and photostimulation. However, focusing with conventional lenses is restricted to one transport mean free path in scattering media, limiting both optical penetration depth and resolution. Focusing deeper is possible by using optical phase conjugation or wavefront shaping to compensate for the scattering. For practical applications, wavefront shaping offers the advantage of a robust optical system that is less…
We demonstrate numerically a method of focusing two-photon field inside one-dimensional random media. The approach is based on coherent control of backscattering achieved by adaptive spectral pulse shaping. The spectral phases of a femtosecond laser pulse are adjusted for the constructive interference of its backward-traveling components, resulting in an enhanced reflection from within the random system. A delayed forward-propagating second pulse overlaps with the controlled reflection, increasing the inter-pulse multi-photon field at a location determined by the delay between the two pulses. …
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…
Adaptive optics can focus light through opaque media by compensating the random phase delay acquired while crossing a scattering curtain. The technique is commonly exploited in many fields, including astrophysics, microscopy, biomedicine and biology. A turbid lens has the capability of producing foci with a resolution higher than conventional optics, however it has a fundamental limit: to obtain a sharp focus one has to introduce a strongly scattering medium in the optical path. Indeed a tight focusing needs strong scattering and, as a consequence, high resolution focusing is obtained only for…
We study the prospects of controlling transmission of broadband and bi-chromatic laser pulses through turbid samples. The ability to focus transmitted broadband light is limited via both the scattering properties of the medium, and the technical characteristics of the experimental set-up. There are two time scales, given by pulse stretching in the near- and far-field regions, which define the maximum bandwidth of a pulse amenable to focusing. In the geometric optics regime of wave propagation in the medium, a single set-up can be optimal for focusing light at frequencies w and nw simultaneousl…
We study the focusing of light through random photonic materials using wavefront shaping. We explore a novel approach namely binary amplitude modulation. To this end, the light incident to a random photonic medium is spatially divided into a number of segments. We identify the segments that give rise to fields that are out of phase with the total field at the intended focus and assign these a zero amplitude, whereas the remaining segments maintain their original amplitude. Using 812 independently controlled segments of light, we find the intensity at the target to be 75 +/- 6 times enhanced ov…
A fundamental challenge in physics is controlling the propagation of waves in disordered media despite strong scattering from inhomogeneities. Spatial light modulators enable one to synthesize (shape) the incident wavefront, optimizing the multipath interference to achieve a specific behavior such as focusing light to a target region. However, the extent of achievable control was not known when the target region is much larger than the wavelength and contains many speckles. Here we show that for targets containing more than $g$ speckles, where $g$ is the dimensionless conductance, the extent o…
Focusing scattered light using wavefront shaping provides interesting perspectives to image deep in opaque samples, as e.g. in nonlinear fluorescence microscopy. Applying these technics to in vivo imaging remains challenging due to the short decorrelation time of the speckle in depth, as focusing and imaging has to be achieved within the order of the decorrelation time. In this paper, we experimentally study the focus lifetime after focusing through dynamical scattering media, when iterative wavefront optimization and speckle decorrelation occur over the same timescale. We show experimental si…
The small correction volume for conventional wavefront shaping methods limits their applications in biological imaging through scattering media. We demonstrate large volume wavefront shaping through a scattering layer with a single correction by conjugate adaptive optics and remote focusing (CAORF). The remote focusing module can keep the conjugation between the AO and scattering layer during three-dimensional scanning. This new configuration provides a wider correction volume by the best utilization of the memory effect in a fast three-dimensional laser scanning microscope. Our results show t…
We present a new approach for spatiotemporal focusing through complex scattering media by wave front shaping. Using a nonlinear feedback signal to shape the incident pulsed wave front, we show that the limit of a spatiotemporal matched filter can be achieved, i.e., the wave amplitude at the intended time and focus position is maximized for a given input energy. It is exactly what is also achieved with time-reversal. Demonstrated with ultrasound experiments, our method is generally applicable to all types of waves.
Using random matrix calculations, we show that, the contrast between maximally focused intensity through random media and the background of the transmitted speckle pattern for diffusive waves is, μ_N =1 +N_{eff}, where N eff is the eigenchannel participation number for the transmission matrix. For diffusive waves, N_{eff} is the inverse of the degree of intensity correlation, κ. The profile of the focused beam relative to the ensemble average intensity is expressed in terms of the square of the normalized spatial field correlation function, F(Δr), and κ. These results are demonstrated in micro…
We design three-dimensional (3D) metallic nanowire media with different structures and numerically demonstrate that they can be homogeneous effective indefinite anisotropic media by showing that their dispersion relations are hyperbolic. For a finite slab, a nice fitting procedure is exploited to obtain the dispersion relations from which we retrieve the effective permittivities. The pseudo focusing for the real 3D wire medium agrees very well with the homogeneous medium having the effective permittivity tensor of the wire medium. Studies also show that in the long-wavelength limit, the hyperb…
We introduce a wavefront shaping protocol for focusing inside disordered media based on a generalization of the established Wigner-Smith time-delay operator. The key ingredient for our approach is the scattering (or transmission) matrix of the medium and its derivative with respect to the position of the target one aims to focus on. A specifc experimental realization in the microwave regime is presented showing that the eigenstates of a corresponding operator are sorted by their focusing strength - ranging from strongly focusing on the designated target to completely bypassing it. Our protocol…
In this paper we set forth new exact analytical Superluminal localized solutions to the wave equation for arbitrary frequencies and adjustable bandwidth. The formulation presented here is rather simple, and its results can be expressed in terms of the ordinary, so-called "X-shaped waves". Moeover, by the present formalism we obtain the first analytical localized Superluminal approximate solutions which represent beams propagating in dispersive media. Our solutions may find application in different fields, like optics, microwaves, radio waves, and so on. [PACS nos.: 03.50.De ; 41.20.Jb ; 83.50.…
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…
It is generally thought that correcting chromatic aberrations in imaging requires multiple surfaces. Here, we show that by allowing the phase in the image plane of a flat lens to be a free parameter, it is possible to correct chromatic aberrations over an almost unlimited bandwidth with a single diffractive surface. Specifically, we designed, fabricated and characterized a flat multi-level diffractive lens (MDL) that images at the wavelengths from 450nm to 850nm. We experimentally characterized the focusing efficiency, modulation-transfer function, wavefront aberrations, vignetting, distortion…
In this paper, we report on a singly resonant optical parametric oscillator (OPO) pumped by an amplified spontaneous emission (ASE) source. The pump focusing conditions allow non-collinear phasematching, which resulted in a 230 nm (190 cm$^{-1}$) spectral bandwidth. Calculations indicate that such phasematching schemes may be used to further broaden OPO spectral bandwidths.
Non-invasive optical focusing inside scattering media is still a big challenge because inhomogeneous media scatter both incoming photons for focusing and outgoing photons for observation. Various approaches, utilizing non-linear fluorescence or ultrasound, have been reported to address this difficulty. However, implementation of these methods is complicated and highly expensive, as ultrafast laser systems or photo-acoustic equipment must be employed. Here, we demonstrate a wavefront shaping technique to achieve non-invasive focusing (NiF) inside scattering media using only a linear fluorescent…
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…
Manipulating and focusing light deep inside biological tissue and tissue-like complex media has been desired for long yet considered challenging. One feasible strategy is through optical wavefront engineering, where the optical scattering-induced phase distortions are time reversed or pre-compensated so that photons travel along different optical paths interfere constructively at the targeted position within a scattering medium. To define the targeted position, an internal guidestar is needed to guide or provide a feedback for wavefront engineering. It could be injected or embedded probes such…
Optical random scattering is generally considered to be a nuisance of microscopy that limits imaging depth and spatial resolution. Wavefront shaping techniques have recently enabled optical imaging at unprecedented depth, but a remaining problem is also to attain super-resolution within complex media. To address this challenge, we introduce a new technique to focus inside of complex media by the use of a quantum reference beacon (QRB), consisting of solid-state quantum emitters with spin-dependent fluorescence. This QRB provides subwavelength guidestar feedback for wavefront shaping to achieve…
Powerful incoherent laser pulses can propagate in focusing Kerr media much longer distances than can coherent pulses, due to the fast phase mixing that prevents transverse filamentation. This distance is limited by 4-wave scattering, which accumulates waves at small transverse wavenumbers, where phase mixing is too slow to retain the incoherence and thus prevent the filamentation. However, we identify how this theoretical limit can be overcome by countering this accumulation through transverse heating of the pulse by random fluctuations of the refractive index. In these new regimes, the laser …
We study theoretically light focusing at subwavelength scale inside a disordered strongly scattering open medium. We show that broadband time reversal at a single point antenna, in conjunction with near-field interactions and multiple scattering, produces spatial focusing with a quality comparable to that obtained in an ideal closed cavity. This gives new perspectives for super-resolved optical imaging and coherent control of single nanosources or absorbers in complex media.
We present a simple scheme to determine the diffusion properties of a thin slab of strongly scattering material by measuring the speckle contrast resulting from the transmission of a femtosecond pulse with controlled bandwidth. In contrast with previous methods, our scheme does not require time measurements nor interferometry. It is well adapted to the characterization of samples for pulse shaping, non-linear excitation through scattering media and biological imaging.
We derive a nonlinear envelope equation to describe the propagation of broadband optical pulses in second order nonlinear materials. The equation is first order in the propagation coordinate and is valid for arbitrarily wide pulse bandwidth. Our approach goes beyond the usual coupled wave description of $χ^{(2)}$ phenomena and provides an accurate modelling of the evolution of ultra-broadband pulses also when the separation into different coupled frequency components is not possible or not profitable.
We study the catastrophic stationary self-focusing (collapse) of laser beam in nonlinear Kerr media. The width of a self-similar solutions near collapse distance $z=z_c$ obeys $(z_c-z)^{1/2}$ scaling law with the well-known leading order modification of loglog type $\propto (\ln|\ln(z_c-z)|)^{-1/2}$. We show that the validity of the loglog modification requires double-exponentially large amplitudes of the solution $\sim {10^{10}}^{100}$, which is unrealistic to achieve in either physical experiments or numerical simulations. We derive a new equation for the adiabatically slow parameter which d…
We report results for solitons in models of waveguides with focusing or defocusing saturable nonlinearity and a parity-time(PT )-symmetric complex-valued external potential of the Scarf-II type. The model applies to the nonlinear wave propagation in graded-index optical waveguides with balanced gain and loss. We find both fundamental and multipole solitons for both focusing and defocusing signs of the saturable nonlinearity in such PT -symmetric waveguides. The dependence of the propagation constant on the soliton's power is presented for different strengths of the nonlinearity saturation, S. …
Using a variational approach, we obtain the self-focusing critical power for a single and for any number of interacting Laguerre-Gauss beams propagating in a Kerr nonlinear optical medium. As is known, the critical power for freely propagating higher-order modes is always greater than that of the fundamental Gaussian mode. Here, we generalize that result for an arbitrary incoherent superposition of Laguerre-Gauss beams, adding interactions between them. This leads to a vast and rich spectrum of self-focusing phenomena, which is absent in the single-beam case. Specifically, we find that interac…
Optical focusing through/inside scattering media, like multimode fiber and biological tissues, has significant impact in biomedicine yet considered challenging due to strong scattering nature of light. Previously, promising progress has been made, benefiting from the iterative optical wavefront shaping, with which deep-tissue high-resolution optical focusing becomes possible. Most of iterative algorithms can overcome noise perturbations but fail to effectively adapt beyond the noise, e.g. sudden strong perturbations. Re-optimizations are usually needed for significant decorrelated medium since…
We report the first experimental demonstration of combined spatial and temporal control of light trajectories through opaque media. This control is achieved by solely manipulating spatial degrees of freedom of the incident wavefront. As an application, we demonstrate that the present approach is capable to form bandwidth-limited ultrashort pulses from the otherwise randomly transmitted light with a controllable interaction time of the pulses with the medium. Our approach provides a new tool for fundamental studies of light propagation in complex media and has potential for applications for coh…
Metasurfaces have the potential to miniaturize and improve the performance of any optical element, with applications spanning telecommunications, computing and wearable optics. However, the ability to retain functionality over a continuous, broad range of wavelengths is essential for their widespread adoption. So far, efforts to achieve this have been limited to either a reflection configuration or operation at wavelengths other than the visible. Here, we show that by judicious choice of nanostructures, one can independently control both the phase and group delay, leading to broadband transmis…
We address the existence and properties of solitons in layered thermal media made of alternating focusing and defocusing layers. Such structures support robust bright solitons even if the averaged nonlinearity is defocusing. We show that non-oscillating solitons may form in any of the focusing domains, even in those located close to the sample edge, in contrast to uniform thermal media where light beams always oscillate when not launched exactly on the sample center. Stable multipole solitons may include more than four spots in layered media.
We demonstrate that laser beam collapse in highly nonlinear media can be described, for a large number of experimental conditions, by the geometrical optics approximation within high accuracy. Taking into account this fact we succeed in constructing analytical solutions of the eikonal equation, which are exact on the beam axis and provide: i) a first-principles determination of the self-focusing position, thus replacing the widely used empirical Marburger formula, ii) a benchmark solution for numerical simulations, and iii) a tool for the experimental determination of the high-order nonlinear …
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…
In biological microscopy, light scattering represents the main limitation to image at depth. Recently, a set of wavefront shaping techniques has been developed in order to manipulate coherent light in strongly disordered materials. The Transmission Matrix approach has shown its capability to inverse the effect of scattering and efficiently focus light. In practice, the matrix is usually measured using an invasive detector or low-resolution acoustic guide stars. Here, we introduce a non-invasive and all-optical strategy based on linear fluorescence to reconstruct the transmission matrices, to a…
