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 report the measurement of a large optical reflection matrix (RM) of a highly disordered medium. Incident optical fields onto a turbid sample are controlled by a spatial light modulator, and the corresponding fields reflected from the sample are measured using full-field Michelson interferometry. The number of modes in the measured RM is set to exceed the number of resolvable modes in the scattering media. We successfully study the subtle intrinsic correlations in the RM which agrees with the theoretical prediction by random-matrix theory when the effect of the limited numerical aperture on …
In this work we present a theoretical study on the propagation of light in heterogeneous systems with fluctuating optical properties. To understand the consequences of the fluctuations we perform numerical calculations with uniform and non uniforms systems using Monte Carlo simulations. We consider two distributions to represent a non-uniform medium: delta function and an exponential negative distributions.The results show that even with finite moments distributions, may require a large number of interactions for a convergence towards Gaussian statistics. This can be important when estimating …
In this Letter we present experimental results concerning the retrieval of images of absorbing objects immersed in turbid media via differential ghost imaging (DGI) in a backscattering configuration. The method has been applied, for the first time to our knowledge, to the imaging of small thin black objects located at different depths inside a turbid solution of polystyrene nanospheres and its performances assessed via comparison with standard imaging techniques. A simple theoretical model capable of describing the basic optics of DGI in turbid media is proposed.
Focusing light through turbid media presents a highly fascinating challenge in modern biophotonics. The unique capability of optoacoustics for high resolution imaging of light absorption contrast in deep tissues can provide a natural and efficient feedback to control light delivery in scattering medium. While basic feasibility of using optoacoustic readings as a feedback mechanism for wavefront shaping has been recently reported, the suggested approaches may require long acquisition times making them challenging to be translated into realistic tissue environments. In an attempt to significantl…
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 show that the Kubelka-Munk equations for the description of the intensity transfer of light in turbid media are equivalent to a one-dimensional diffusion equation, which is obtained by averaging the three-dimensional diffusion equation over the lateral directions. This enables us to identify uniquely the Kubelka-Munk parameters and derive expressions for diffuse reflection and transmission coefficients including the effect of internal reflections. Without internal reflections we recover the Kubelka-Munk formulas for these coefficients. We show that the Kubelka-Munk equations are the proper …
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 discuss the far-field spatio-temporal cross-correlations of waves multiple-scattered in a turbid medium in which is embedded a hidden heterogeneous region (inclusion) characterized by a distinct scatterer dynamics (as compared to the rest of the medium). We show that the spatio-temporal correlation is affected by the inclusion which suggests a new method of imaging in turbid media. Our results allow qualitative interpretation in terms of diffraction theory: the cross-correlation of scattered waves behaves similarly to the intensity of a wave diffracted by an aperture.
Imaging with optical resolution through highly scattering media is a long sought-after goal with important applications in deep tissue imaging. Although being the focus of numerous works, this goal was considered impractical until recently. Adaptive-optics techniques which are effective in correcting weak wavefront aberrations, were deemed inadequate for turbid samples, where complex speckle patterns arise and light is scattered to a large number of modes that greatly exceeds the number of degrees of control. This conception changed after the demonstration of focusing coherent light through tu…
Brillouin microscopy has recently emerged as powerful technique to characterize the mechanical properties of biological tissue, cell and biomaterials. However, the potential of Brillouin microscopy is currently limited to transparent samples, because Brillouin spectrometers do not have sufficient spectral extinction to reject the predominant non-Brillouin scattered light of turbid media. To overcome this issue, we developed a spectrometer composed of a two VIPA stages and a multi-pass Fabry-Perot interferometer. The Fabry-Perot etalon acts as an ultra-narrow band-pass filter for Brillouin ligh…
We present a theoretical and experimental study of light transport in disordered media with strongly heterogeneous distribution of scatterers formed via non-scattering regions. Step correlations induced by quenched disorder are found to prevent diffusivity from diverging with increasing heterogeneity scale, contrary to expectations from annealed models. Spectral diffusivity is measured for a porous ceramic where nanopores act as scatterers and macropores render their distribution heterogeneous. Results agree well with Monte Carlo simulations and a proposed analytical model.
Dynamics light scattering (DLS) is a widely used techniques to characterize dynamics in soft phases. Evanescent Wave DLS refers to the case of total internal reflection DLS that probes near interface dynamics. We here investigate the use of EWDLS for turbid sample. Using combination of ray-tracing simulation and experiments, we show that a significant fraction of the detected photons are scattered once and has phase shifts distinct from the multiple scattering fraction. It follows that the measured correlation can be separated into two contributions: a single scattering one arising from the ev…
In Polarization Discrimination Imaging, the amplitude of a sinusoid from a rotating analyzer, representing residual polarized light and carrying information on the object, is detected with the help of a lock-in amplifier. When turbidity increases beyond a level, the lock-in amplifier fails to detect the weak sinusoidal component in the transmitted light. In this work we have employed the principle of Stochastic Resonance and used a 3-level quantizer to detect the amplitude of the sinusoids, which was not detectable with a lock-in amplifier. In using the three level quantizer we have employed t…
Optical coherence tomography (OCT) is a powerful biomedical imaging technology that relies on the coherent detection of backscattered light to image tissue morphology in vivo. As a consequence, OCT is susceptible to coherent noise (speckle noise), which imposes significant limitations on its diagnostic capabilities. Here we show a method based purely on light manipulation that is able to entirely remove the speckle noise originating from turbid samples without any compromise in resolution. We refer to this method as Speckle-Free OCT (SFOCT). Using SFOCT, we succeeded in revealing small structu…
We present a probabilistic theory of random walks in turbid media with non-scattering regions. It is shown that important characteristics such as diffusion constants, average step lengths, crossing statistics and void spacings can be analytically predicted. The theory is validated using Monte Carlo simulations of light transport in heterogeneous systems in the form of random sphere packings, and good agreement is found. The role of step correlations is discussed, and differences between unbounded and bounded systems are investigated. Our results are relevant to the optics of heterogeneous syst…
We provide a new analytic expression and an innovative experimental method to isolate the effect of multiple scattering (MS) in Brillouin investigation of highly turbid media. On the one hand, an analytic model is given to describe the spectrum in case of ill-defined exchanged wave-vector. On the other hand, a new experimental method, named Polarization Gated Brillouin Spectroscopy (PG-BS), is proposed for selecting the MS contribution through light polarization. Both experimental and analytic methods are tested against a benchmark material, milk, demonstrating their capability to extract reli…
The efficiency of using intensity modulated light for estimation of scattering properties of a turbid medium and for ballistic photon discrimination is theoretically quantified in this article. Using the diffusion model for modulated photon transport and considering a noisy quadrature demodulation scheme, the minimum-variance bounds on estimation of parameters of interest are analytically derived and analyzed. The existence of a variance-minimizing optimal modulation frequency is shown and its evolution with the properties of the intervening medium is derived and studied. Furthermore, a metric…
Gwangju Institute of Science and Technology（光州科学技术院）；Korea University（高丽大学）
The input numerical aperture (NA) of multimode fiber (MMF) can be effectively increased by placing turbid media at the input end of the MMF. This provides the potential for high-resolution imaging through the MMF. While the input NA is increased, the number of propagation modes in the MMF and hence the output NA remains the same. This makes the image reconstruction process underdetermined and may limit the quality of the image reconstruction. In this paper, we aim to improve the signal to noise ratio (SNR) of the image reconstruction in imaging through MMF. We notice that turbid media placed i…
Accurate characterization using static light scattering (SLS) and dynamic light scattering (DLS) methods mandates the measurement and analysis of singly-scattered light. In turbid samples, the suppression of multiple scattering is therefore required to obtain meaningful results. One powerful technique for achieving this, known as 3D cross-correlation, uses two simultaneous light scattering experiments performed at the same scattering vector on the same sample volume in order to extract only the single scattering information common to both. Here we present a significant improvement to this meth…
Duke University（杜克大学）；Tsinghua University（清华大学）；Lund University（隆德大学）；Tsinghua Shenzhen International Graduate School（清华大学深圳国际研究生院）
Noninvasive optical imaging through dynamic scattering media has numerous important biomedical applications but still remains a challenging task. While standard diffuse imaging methods measure optical absorption or fluorescent emission, it is also well-established that the temporal correlation of scattered coherent light diffuses through tissue much like optical intensity. Few works to date, however, have aimed to experimentally measure and process such temporal correlation data to demonstrate deep-tissue video reconstruction of decorrelation dynamics. In this work, we utilize a single-photon …
Purpose: Visualization and monitoring of capillary loops in dermis and mucosa are interesting for various clinical applications, including rheumatology, early cancer, and shock detection. However, the limitations of existing imaging technologies are not well understood. Therefore, this study aimed to elucidate peculiarities of the subsurface defect visualization in realistic skin imaging geometries. Methods: We used a perturbation approach for the light propagation in turbid tissues with mismatched boundaries. Defects were considered as negative light sources immersed in homogeneous media, whi…
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 propose a new method to image fluorescent objects through turbid media base on Airy beam scanning. This is achieved by using the non-diffractive nature of Airy beams, namely their ability to maintain their shape while penetrating through a highly scattering medium. We show, that our technique can image fluorescent objects immersed in turbid media with higher resolution and signal to noise than confocal imaging. As proof-of-principle, we demonstrate imaging of 1$μ$m sized fluorescent beads through a dense suspension of yeast cells with an attenuation coefficient of 51cm$^{-1}$ at a depth of …
In turbid media, scattering of light scrambles information of the incident beam and represents an obstacle to optical imaging. Noninvasive imaging through opaque layers is challenging for dynamic and wide-field objects due to unreliable image reconstruction processes. We here propose a new perspective to solve these problems: rather than using the full point-spread-function (PSF), the wave distortions in scattering layers can be characterized with only the phase of the optical-transfer-function (OTF, the Fourier transform of PSF), with which diffraction-limit images can be analytically solved.…
One challenge that has long held the attention of scientists is that of clearly seeing objects hidden by turbid media, as smoke, fog or biological tissue, which has major implications in fields such as remote sensing or early diagnosis of diseases. Here, we combine structured incoherent illumination and bucket detection for imaging an object completely embedded in a turbid medium. A sequence of low-intensity microstructured light patterns is launched onto the object, whose image is accurately reconstructed through the light fluctuations measured by a single-pixel detector. Our technique is non…
The propagation of monochromatic light through a scattering medium produces speckle patterns in reflection and transmission, and the apparent randomness of these patterns prevents direct imaging through thick turbid media. Yet, since elastic multiple scattering is fundamentally a linear and deterministic process, information is not lost but distributed among many degrees of freedom that can be resolved and manipulated. Here we demonstrate experimentally that the reflected and transmitted speckle patterns are correlated, even for opaque media with thickness much larger than the transport mean f…
We study theoretically and experimentally the modulational instability of broad optical beams in photorefractive nonlinear media. We demonstrate the impact of the anisotropy of the nonlinearity on the growth rate of periodic perturbations. Our findings are confirmed by experimental measurements in a strontium barium niobate photorefractive crystal.
Laguerre-Gaussian (LG) beams carrying orbital angular momentum (OAM) have shown promise in deep tissue imaging, medical diagnostics, and optical communication due to their robust propagation properties through scattering media. However, an exact model that provides a mechanism for the enhanced scattering properties of LG beams over Gaussian beams has not been established till date. Here, we examine this issue by studying the propagation of polarized vortex beams transmitted through tissue-like turbid scattering media. We demonstrate that the intensity profile has a much more profound effect on…
A simple and general formalism for mode coupling by a spatial, temporal or spatiotemporal perturbation in dispersive materials is developed. This formalism can be used for studying various linear and non-linear optical interactions involving a dynamic modulation of the interaction parameters such as non-reciprocal phenomena, time reversal of signals and spatiotemporal quasi phase matching
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…
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…
We address the existence and properties of solitons in thermal media with periodic modulation of linear refractive index. Many kinds of solitons in such optical lattices, including symmetric and antisymmetric lattices, are found under different conditions. We study the influence of the refractive index difference between two different layers on solitons. It is also found that there do not exist cutoff value of propagation constant and soliton power for shifted lattice solitons. In addition, the solitons launched away from their stationary position may propagate without oscillation when the con…
We report a method to design at will the spatial profile of transmitted coherent light after propagation through a scattering sample. We compute an operator based on the experimentally measured transmission matrix, obtained by numerically adding an arbitrary mask in the Fourier domain prior to focusing. We demonstrate the strength of the technique through several examples: propagating Bessel beams, thus generating foci smaller than the diffraction limited speckle grain, donut beams, and helical beams. We characterize the 3D profile of the achieved foci and analyze the fundamental limitations o…
We investigate the interaction of two pulses (pump and probe) scattered by a nonlinear epsilon-near-zero (ENZ) slab whose thickness is comparable with the ENZ wavelength. We show that when the probe has a narrow spectrum localized around the ENZ wavelength its transmission is dramatically affected by the intensity of the pump. Conversely, if the probe is not in the ENZ regime, its propagation is not noticeably affected by the pump. Such all-optical modulation is due to the oversensitive character of the ENZ regime and it is so efficient to even occur in a wavelength thick slab.
The dynamics of the modulation instability induced by cross phase modulation is studied by considering the influence of the walk-off and noninstantaneous response effects for two copropagating optical fields travelling in the anomalous regime of dispersion. To do so, we make use of extensions of the nonlinear Schrödinger equation jointly with the Debye model for polarization, which is shown to be effective and simplified when compared to the implementation of other methods for the noninstantaneous nonlinear response. In analyzing the sideband formation, two bands are observed with different be…
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 …
The solution of the wave equation in the envelope approximation with temporal corrections for a laser pulse propagating in a medium where the Kerr effect, field ionization, and associated absorption take place, is obtained through a first-order perturbative approach. The closed-form expressions so obtained clarify the influence of the various terms of the equation on the laser amplitude and on the frequency generation as a function of the retarded time. Furthermore, they allow extracting scaling parameters which size the nonlinear effects. The results are illustrated quantitatively on the case…
We report on new electromagnetic modes in space-time modulated dispersion-engineered media. These modes exhibit unusual dispersion relation, field profile and scattering properties. They are generated by coupled codirectional space-time harmonic pairs, and occur in space-time periodic media whose constituent materials exhibit specific dispersion. Excitation of a slab of such a medium with subluminal modulation results in periodic transfer of energy between the incident frequency and a frequency shifted by a multiple of the modulation frequency, whereas superluminal modulation generates exponen…
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…
The scattering of light observed through the turbid underwater channel is often regarded as the leading challenge when designing underwater electro-optical imaging systems. There have been many approaches to address the effects of scattering such as using pulsed laser sources to reject scattered light temporally, or using intensity modulated waveforms and matched filters to remove the scattered light spectrally. In this paper, a new method is proposed which primarily uses the backscattering asymmetry property for object detection and geometric profiling. In our approach, two parallel and ident…
We show that in the presence of a rapidly modulated dielectric permittivity with a large modulation depth (Kapitza medium) a novel and robust regime of diffractionless electromagnetic propagation occurs. This happens when the mean value to depth ratio of the dielectric profile is comparable to the small ratio between the modulation period and the wavelength. We show that the standard effective medium theory is inadequate to describe the proposed regime and that, its occurrence is not substantially hampered by medium losses. We check the feasibility of the proposed regime by means of a large mo…
Modulational instability is a phenomenon that reveals itself as the exponential growth of weak perturbations in the presence of an intense pump beam propagating in a nonlinear medium. It plays a key role in such nonlinear optical processes as supercontinuum generation, light filamentation, and rogue waves. However, practical realization of these phenomena in the majority of available nonlinear media still relies on high-intensity optical beams. Here, we analytically and numerically show the possibility of necklace beam generation originating from low-intensity spatial modulational instability …
We demonstrate experimentally an efficient control of light intensity distribution inside a random scattering system. The adaptive wavefront shaping technique is applied to a silicon waveguide containing scattering nanostructures, and the on-chip coupling scheme enables access to all input spatial modes. By selectively coupling the incident light to open or closed channels of the disordered system, we not only vary the total energy stored inside the system by 7.4 times, but also change the energy density distribution from an exponential decay to a linear decay and to a profile peaked near the …
We report a modulational instability (MI) analysis of a mathematical model appropriate for ultrashort pulses in cascaded quadratic-cubic nonlinear media beyond the so-called slowly varying envelope approximation. Theoretically predicted MI properties are found to be in good agreement with numerical simulation. The study shows the possibility of controlling the generation of MI and formation of solitons in a cascaded quadratic-cubic media in the few cycle regimes. We also find that stable propagation of soliton-like few-cycle pulses in the medium is subject to the fulfilment of the modulation i…
We study the influence of third-harmonic generation (THG) and negative frequency polarization terms in the self-phase modulation (SPM) of short and intense pulses in Kerr media. We find that THG induces additional symmetric lobes in the SPM process. The amplitude of these new sidebands are greatly enhanced by the contributions of the negative frequency Kerr (NFK) term and the shock operator. We compare our theoretical predictions based on the analytical nonlinear phase with simulations carried out by using the full unidirectional pulse propagation equation (UPPE).
While controlling particle diffusion in a confined geometry is a popular approach taken by both natural and artificial systems, it has not been widely adopted for controlling light transport in random media, where wave interference effects play a critical role. The transmission eigenchannels determine not only light propagation through the disordered system but also the energy concentrated inside. Here we propose and demonstrate an effective approach to modify these channels, whose structures are considered to be universal in conventional diffusive waveguides. By adjusting the waveguide geomet…
We show that the velocity and thus the frequency of a signal pulse can be adjusted by the use of a control Airy pulse. In particular, we utilize a nonlinear Airy pulse which, via cross-phase modulation, creates an effective potential for the optical signal. Interestingly, during the interaction, the signal dispersion is suppressed. Importantly, the whole process is controllable and by using Airy pulses with different truncations leads to predetermined values of the frequency shifting. Such a functionality might be useful in wavelength division multiplexing networks.
We consider dynamically controllable periodic structures, called Raman induced gratings, in three- and four-level atomic media, resulting from Raman interaction in a standing-wave pump. These gratings are due to periodic spatial modulation of the Raman nonlinearity and fundamentally differ from the ones based on electromagnetically induced transparency. The transmission and reflection spectra of such gratings can be simultaneously amplified and controlled by varying the pump field intensity. It is shown that a transparent medium with periodic spatial modulation of the Raman gain can be opaque …
We introduce an elegant method which allows the application of diffusing-wave spectroscopy (DWS) to nonergodic, solid-like samples. The method is based on the idea that light transmitted through a sandwich of two turbid cells can be considered ergodic even though only the second cell is ergodic. If absorption and/or leakage of light take place at the interface between the cells, we establish a so-called "multiplication rule", which relates the intensity autocorrelation function of light transmitted through the double-cell sandwich to the autocorrelation functions of individual cells by a simpl…
