1. Introduction

Polarization is an intrinsic property of light that has found use in both imaging [1] and manipulation schemes [2–6]. Light polarization is crucial in several optical phenomena including fluorescence resonance energy transfer, circular dichroism, birefringence, and nonlinear optical effects such as second harmonic generation. Since multiple light scattering scrambles the polarization state of light, these useful optical techniques based on light polarization have been effectively employed in direct in vivo studies. This limitation is unfortunate because light polarization has much to offer to the world of in vivo studies of biological phenomena with its unique contrast modalities, its molecular structure dependency, and avoidance of radiation damage by light.

The traditional way of obtaining a highly polarized light field is to place polarizing optical components in the beam path prior to the sample. This method, however, is only applicable for ex vitro studies where there is no scattering layer between the probe and sample since multiple light scattering significantly scrambles polarization and light paths. Scattering is routinely observed in many systems displaying an inhomogeneous refractive index map and is one of the main limiting factors in accurately delivering light through or inside scattering media. In this work we choose a random nanostructure as a model system for scattering in biological tissues and control the relative phases of the scattering paths to achieve full manipulation of the polarization properties of a focused beam after multiple scattering events. This demonstrates that the scattering layer itself can be used as an optical relay system with unique polarization controlling functionalities.

It has been commonly understood that light scattering scrambles the polarization properties of the incident wavefront. However, the present approach demonstrates controlling the polarization of light utilizing multiple light scattering in highly scattering media by optimizing the incident wavefront upon the scattering media. The polarization of an optimized focus beyond a scattering layer can be actively controlled with no constraints on the polarization of the incident beam. The resulting polarized state is independent of the incident beam’s polarization and has no spatial restrictions. We show that a random nanostructure can be used as a dynamic wave plate by controlling the phase of combined orthogonal polarization states. Although previous works in wavefront shaping have shown that optimizing a focus beyond turbid layers is possible [7], the polarization of the optimized focus had not been considered [8–10] or has only been regarded as a method to enhance the optimizing procedure [11–15]. Our results may directly be applied to various applications such as photothermal therapy [16] and the transfer of angular momentum in optical manipulation of biological systems [4–6].

2. Theory

The concept of the polarization specific optimizing process is illustrated in Figs. 1(a) -1(c). An incident beam with a predefined polarization is multiply scattered through the scattering medium. After each scattering event, the polarization and outgoing direction of the scattered wave are significantly changed, and thus strongly mix the information of the initial wavefront and polarization states. This random combination of different paths with different polarization and phase coherently add up to become the speckle that we typically observe [Fig. 1(a)]. Wavefront shaping without considering the polarization degree of freedom results in randomly polarized focuses with the dominant polarization direction decided by the polarization bias of the original speckle due to the enpolarization of the reference beam [17,18] [Fig. 1(b)].

 

Fig. 1 Experimental scheme for controlling polarization in turbid media. (a) Scrambling of polarization and propagation paths through multiple scattering. (b) Shaping the wavefront to make constructive interference at a focus point without polarization control. (c) With polarization taken into account, both polarization control and spatial focusing of light can be achieved. The different polarization states of light paths are illustrated with different colors for ease of visualization.

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In this work, the polarization states of the multiple scattering paths are considered during the optimization process. During multiple light scattering, a single optimizing channel, a spatial frequency vector k, is divided into numerous paths with different complex weights before arriving at a target point. We can express the vector field components of the electromagnetic field using and orthogonal basis of circular polarized beams

3. Experimental setup

The experimental configuration is shown in Fig. 2 . Light from a frequency doubled 532 nm ND:Yag laser is expanded through a telescopic relay system before passing through a ND filter and a polarizer. The expanded beam is reflected off a SLM and imaged onto the scattering sample. The SLM(X10468-01, Hamamatsu Photonics Inc. Japan) is placed at a conjugate image plane of the scattering sample (a 10 µm layer of commercial white spray paint (Pingo General, Noroo Paint) sprayed on a 170 µm cover slip). The SEM image in the inset of Fig. 2 shows the scatterers with an average size of 200 nm aggregated in a random manner. A mask at the back focal plane of the condenser blocks high order diffracted beams from SLM pixels. The object plane 0.1mm above the surface of the other side of the sample is imaged onto a CMOS camera. The CMOS camera (INFINITY lite C, Lumenera corp.) is used as the detector for the optimizing feedback control during wavefront shaping. The rotatable analyzer in front of the camera is used to choose the polarization state during the optimization process as well as to check the polarization of the optimized focus.

 

Fig. 2 Experimental setup. L1,L2:plano-convex lens. BS: non-polarizing beam splitter. (inset) Scanning electron micrograph of scattering particles. Scale bar 1 µm.

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In order to realize a stable and efficient optimization process, we utilized the entire area of the SLM for optimizing each channel by using different wave vectors k as the orthogonal basis. Since the SLM is directly projected onto the scattering sample, each SLM pixel has a one-to-one correspondence to a single position on the sample. By applying a phase ramp with the specific k vector on the SLM, a plane wave with a different angle of incidence can be impinged onto the same lateral position of the scattering sample corresponding to a single optimizing channel. This technique is advantageous in terms of attaining higher signal sensitivity since the entire wavefront is modulated during the optimization process and gives a higher signal to noise ratio allowing us to use an affordable 8 bit CMOS camera. After finding the optimized phase for each k vector, linear superposition of k vectors with their optimized phases generates a coherent intense focus at the target position.

4. Results and discussion

As a first demonstration of polarization control through turbid media, we place an analyzer in front of the CMOS camera imaging the back side of the scattering sample. We use a parallel aligned nematic liquid crystal SLM (800 × 600 pixels) that only changes the phase of the reflected wavefront without any rotation of the polarization state. By using the polarizer prior to the SLM, only p polarized light was shaped by the SLM and incident on the sample during the entire experiment. The results for the specific polarized focuses are shown in Fig. 3 . By simply rotating the analyzer prior to the optimizing process, an arbitrary polarized focus and its corresponding wavefront information could be obtained. Figure 3(b) shows the resulting p polarized focus while Fig. 3(f) shows an s polarized focus at the same position beyond the scattering sample. The enhancement factors were approximately × 400 compared to the average background speckle using 1681 optimized channels. The intensity of the polarized focus detected at the opposite orthogonal polarization state show comparable value with the average speckle background, indicating no significant effects in the opposite orthogonally polarized output channel during the polarization sensitive optimization procedure. This also demonstrates that the degree of polarization is proportional to the enhancement factor. The collected wavefront information [Fig. 3(a), 3(e)] for each focus can be used at any time after the experiment as long as the experimental setup has not significantly drifted (several hours). This directly allows us to dynamically switch between orthogonally polarized focuses at a target position beyond the scattering media. These results imply that there exist multiple wavefronts which give the same optimized focus but with different polarizations. However, due to the randomness of the sample, a simple relation between the different wavefronts resulting in different polarizations cannot be obtained. The randomness of the scattering sample also ensures that there is no sensitivity or restriction on the position where we place the polarized focus and prohibit bias from the initial polarization state of the incoming wavefront on the final result.

 

Fig. 3 Demonstration of polarization control in optimized focusing. (a),(e), Phase maps of the complex wavefront displayed on the SLM resulting in optimized (b-d) p polarized and (f-h) s polarized focuses, respectively. (b-c), Images of an optimized p-pol focus taken with the analyzer oriented in horizontal (b) and vertical (c) directions. (f-g), Images of an optimized s-pol focus taken with the analyzer oriented in horizontal (f) and vertical (g) directions. (d),(h) Normalized intensity as a function of analyzer angle for the polarized focuses and a random background speckle. Solid blue lines are theoretical curves of cos²ϕ and sin²ϕ, respectively. Solid red lines are sinusoidal fits to the data. Scale bar, 2 µm.

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Our approach where we obtain and record the complex wavefront for a specific polarized focus also allows us to control the phase of the polarized focus. This can be accomplished by simply applying an arbitrary phase delay to the previously acquired wavefront. This will preserve the shape of the wavefront while delaying its overall propagation through the turbid media. After having recorded the libraries of the wavefronts resulting in optimized focuses at the same point with orthogonal polarizations, the relative phases of the orthogonally polarized focuses can be controlled to produce arbitrary combinations of the two polarized beams.

Figure 4 demonstrates that shifting the phase of the p polarized focus while keeping the phase of the s polarized focus constant results in a shift from linear to circular (elliptical due to experimental limitations) polarized focuses. The phase shift can be given any arbitrary value which is equivalent to using the scattering random nanostructure as a dynamic wave plate without any moving mechanical parts. This demonstrates for the first time that turbid media can be used as a miniature on chip optical device performing the simultaneous functions of a high NA objective lens as well as a polarizer or multifunctional wave plate.

 

Fig. 4 Using the linear combination of two orthogonally polarized focuses to achieve full control of polarization states. (a) Intensity of the coherent sum of p- and s-polarized focuses as a function of phase shift given to the p-polarized focus. Analyzer is placed at + 45 degrees. (b) Intensity plot for the various polarization states as a function of the analyzer angle. (c) Polar plot clearly demonstrates the transition from linear to circular polarization and the reversal in linear polarization direction. Solid lines in (a), (b), are sinusoidal fits to the data.

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To demonstrate the expandability of the method, we demonstrate that a linear combination of wavefronts can simultaneously optimize multiple focuses at different points with p, s, and circular polarizations, respectively [Fig. 5 ]. The number of different polarized focuses is only limited by the conservation of energy [11] and the diffraction efficiency of the SLM and is shown to be independently controllable.

 

Fig. 5 Multiple focuses with differently controlled polarization states. Image (a) without analyzer, (b) with horizontally and (c) vertically aligned analyzer. (d), Normalized intensity plot for each focus as a function of analyzer angle. Solid lines are sinusoidal fits to the data. Scale bar, 2 µm.

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5. Conclusion

Our work demonstrates that it is possible to achieve a high degree of control of light polarization utilizing multiple light scattering. Albeit the small number of optimized input channels (~10³) compared to the maximum number of independent incident modes that the transmission matrix of the turbid media can support [7], $N_{\max }=2\pi A/{\lambda }^2$ (~10⁸) where A is the illuminated surface area and is the wavelength of incident light, orthogonal states of a high degree of polarization could be achieved at the same output position. Due to this large degree of freedom of the transmission matrix, arbitrary combination of differently polarized outputs could be obtained simultaneously with a single input wavefront.

The present technique of controlling light polarization may be particularly useful in cases where multiple light scattering is inevitable. The method is expected to be easily adapted to the current state-of-the art technologies which include holographic polarization field measurement [19], perfect focusing [9,10], spectral filtering [20] and temporal control of light through scattering media [21,22]. Recent interests in photothermal therapy also require the focused delivery of light through scattering skin layers. Our technique will significantly enhance the efficient transfer of energy to anisotropic target nanoparticles [23,24] using skin layers as a dynamic wave plate. By adding the polarization degree of freedom to in situ optical manipulation [25], the role of various perturbations in real biological systems can be studied. Future work using the independent polarization and phase control will also allow us to generate nontrivial beams such as optical vortices [4,26] through scattering media. In addition, optical imaging and manipulating of highly birefringent biological objects such as polymerized hemoglobin fibers in sickle cell disease is now directly accessible [27,28].