Research ArticleLIGHT POLARIZATION

Polarization recovery through scattering media

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Science Advances  01 Sep 2017:
Vol. 3, no. 9, e1600743
DOI: 10.1126/sciadv.1600743
  • Fig. 1 Illustration of polarization state scrambling during propagation in a scattering medium and principle of polarization recovery via wavefront shaping.

    When light propagates in a scattering medium, the wavefront is rapidly deformed into a speckle pattern (at depths comparable to the scattering mean free path ls), but polarization scrambling occurs on a different length scale. In the forward scattering regime (as typically found in biological tissues), when the thickness L is smaller than the transport mean free path lt, forward scattering events mainly conserves the initial polarization state. (A) In the diffusive regime L > lt for an unshaped wavefront, the polarization of the speckle gradually scrambles and lacks any resemblance with the input one. The bottom panel illustrates how, during propagation, each forward scattering conserves polarization (continuous line) and how polarization is mixed when entering the diffusive regime (dashed line). (B) In contrast, we observe that an optimal wavefront shaped by a spatial light modulator (SLM) not only is able to refocus light but also recovers the original polarization state even without any polarizing optics in the detection, under broadband source illumination.

  • Fig. 2 Experimental quantification of polarization recovery.

    (A) Left: Averaged DOLP of the speckle (<DOLP>) (red squares) and refocus intensity ratio after wavefront shaping (I/I; corresponding to the same wavefront but rotated input polarization) (green circles), as a function of optical depths L/lt. Polarization scrambling of the speckle occurs for lengths of the order of lt. Nevertheless, at depths of several lt, after shaping, the refocus intensity survives a change of 90° of the input polarization. Right: Speckle image after (top) and before (bottom) the wavefront shaping procedure. The scattering media are made of 5-μm-diameter polystyrene beads. The asterisk symbol (*) in the box refers to the images shown on the right. (B) Similar experiments performed using 1-mm-thick opaque acute brain slice coronal cross section as a scattering medium. Top left: Nonanalyzed refocus intensity (green circles) upon rotation of the excitation field. Right: Images show the refocus at two input polarization states (⊥ and ∥) with the same intensity scale. Bottom left: The refocus polarization state purity is evaluated by placing an analyzer and observing an extinction (black circles). Scale bars, 1 μm.

  • Fig. 3 Experimental quantification of vectorial transmission matrix correlations and the origin of the polarization recovery.

    (A) Cross-correlation of vectorial transmission matrix elements with polarization combinations xx and yy for L/lt ≈ 6. The peak confirms strong correlation between the matrix elements, thus explaining the resilience of the refocus to a polarization state change. (B) Images of the output speckle parallel (xx) and perpendicular (yx) to the input polarization state for a monochromatic (Mono) source (left panel) and a broadband (BB) source (right panel) for L/lt ≈ 6.

  • Fig. 4 Demonstration of structural imaging through scattering media–exploiting transmission matrix correlations.

    (A) Simplified experimental layout used in the experiments. Ultrashort pulse wavefronts are shaped by an SLM and focused on the scattering medium. The speckle transmitted by the scattering medium excites the nonlinear sources (nanoKTP) placed at a plane further imaged on a complementary metal-oxide semiconductor (CMOS) camera and a photomultiplier tube (PMT). (B) Demonstration of structural imaging by polarization-resolved SHG. In the first step, the vectorial transmission matrix elements Embedded Image are acquired and used to raster-scan the refocus, thus generating the SHG images (left panel). The bottom-right inset in (A) shows the bright-field (BF) image at the same region of interest (ROI), where two particles can be seen. In the second step, only the excitation polarization is rotated, and a second scan is taken (5× rescaled) (right panel) using the very same Embedded Image elements. Scale bar, 1 μm.

  • Fig. 5 Applications of transmission matrix correlations for biological specimen SHG structural imaging.

    (A) Raster-scanning rat tail collagen tendon placed after a thin diffuser, with an unshaped wavefront, leads to a featureless SHG image (left panel). Furthermore, the SHG intensity response upon turning the input polarization (right panel) is almost isotropic, an outcome that is not representative of the molecular structure of collagen. (B) Raster-scanning using the memory effect, from a known transmission matrix, generates morphological features reminiscent of collagen fibers (left panel). By refocusing on a specific fiber, we recorded the intensity response of the SHG signal upon turning the input polarization angle (right panel). The continuous line (black) is a fit to the data (green circles) from which we retrieve the fiber-scale nonlinear susceptibility values of collagen. The retrieved nonlinear susceptibilities reveal the molecular order of the fibers and are in agreement with previous observations. In the polar plots, the radial direction represents SHG intensity. Scale bar, 1 μm.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/9/e1600743/DC1

    section S1. Polarization state evaluation

    section S2. Vectorial transmission matrix analysis under broadband conditions

    section S3. Comparison with a monochromatic transmission matrix

    section S4. Time-of-flight results

    section S5. Exclusion of ballistic hypothesis

    section S6. Model for nonanalyzed SHG response

    section S7. On the role of bandwidth

    section S8. Discussion on theoretical models

    fig. S1. Polarization state evaluation of the refocused light for the brain specimen.

    fig. S2. Polarization state evaluation of the refocused light.

    fig. S3. Effect of transmission matrix interelement coupling on cross-correlation.

    fig. S4. Cross-correlation between various transmission matrices.

    fig. S5. Comparison of different transmission matrix acquisition methods.

    fig. S6. Time-of-flight results.

    fig. S7. Size of the refocus, enhancement, contrast, and ballistic contribution versus optical thickness.

    fig. S8. Bandwidth results.

    References (4456)

  • Supplementary Materials

    This PDF file includes:

    • section S1. Polarization state evaluation
    • section S2. Vectorial transmission matrix analysis under broadband conditions
    • section S3. Comparison with a monochromatic transmission matrix
    • section S4. Time-of-flight results
    • section S5. Exclusion of ballistic hypothesis
    • section S6. Model for nonanalyzed SHG response
    • section S7. On the role of bandwidth
    • section S8. Discussion on theoretical models
    • fig. S1. Polarization state evaluation of the refocused light for the brain specimen.
    • fig. S2. Polarization state evaluation of the refocused light.
    • fig. S3. Effect of transmission matrix interelement coupling on cross-correlation.
    • fig. S4. Cross-correlation between various transmission matrices.
    • fig. S5. Comparison of different transmission matrix acquisition methods.
    • fig. S6. Time-of-flight results.
    • fig. S7. Size of the refocus, enhancement, contrast, and ballistic contribution versus optical thickness.
    • fig. S8. Bandwidth results.
    • References (44–56)

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