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Here, we develop the first full-polarization DOPC system which records and phase-conjugates scattered light along two orthogonal polarizations. When focusing light through thick scattering media, such as 2 mm and 4 mm thick chicken breast tissue, our full-polarization DOPC system on average doubles the focal peak-to-background ratio achieved by single-polarization DOPC systems and improves the phase conjugation fidelity. Focusing light through or within scattering media is critically important in many applications, such as high-resolution optical imaging, photodynamic therapy, and optical manipulation.

To break this fundamental limit, various methods have been developed, including iterative wavefront shaping [ 4 — 6 ], transmission matrix measurement [ 7 ], and optical phase conjugation OPC [ 8 — 21 ]. Among all these approaches, OPC, which is based on the principle of time reversal, determines the optimum wavefront without time-consuming iterations. First, unlike analog OPC systems, which work with a narrow wavelength range dictated by the properties of the nonlinear crystals, the specific wavelength used by DOPC systems can be tuned in a relatively large range without modifying the system.

Second, DOPC has much higher phase conjugation reflectivity. When the scattering medium is optically thick, the polarization of the scattered light becomes spatially randomized and its representation on the Poincare sphere is distributed randomly and evenly.

Principles of Phase Conjugation (Paperback)

Thus, in any OPC experiment, it is ideal to first record all the information about the scattered light, including its phase, amplitude, and polarization at all positions. Next, to rigorously follow the time-reversal principle, scattered light needs to be phase conjugated with the original position-dependent polarizations maintained.

Using a nonlinear crystal, a full-polarization analog OPC system has been developed to restore images through multimode fibers [ 9 ]. However, in practice, the SLMs used in DOPC systems can modulate only linearly polarized light along a fixed direction, and thus are incapable of faithfully phase-conjugating scattered light with different polarization states.

To address this problem, we have developed the first full-polarization DOPC system which is able to record and phase-conjugate light with random polarizations. In the recording step [ Fig.

Chapter 1 - Overview of Phase Conjugation

In general, the speckle patterns corresponding to the two orthogonal polarizations bear little resemblance, and the polarizations at two arbitrary positions that are not within the same speckle grain, i. Next, in the playback step [ Fig. After they pass through the scattering medium, an output collimated beam that is phase-conjugated to the input beam is obtained.

Schematic of the processes in full-polarization DOPC. We theoretically studied full-polarization DOPC by extending the existing scalar-field-based random matrix theory [ 23 ]. The input light field E 1 x, y is expressed as a Jones column vector concatenated by two components E H 1 x, y and E V 1 x, y :. In practice, only a fraction of the transmitted light is measured. Under this condition, the elements in each T AB can be approximated by the corresponding circular Gaussian distributions [ 23 ]. The playback OPC field is phase-conjugated to the recorded field:. This field is sent back to pass through the scattering medium again.

Combining Eqs.

An Intuitive Explanation of Phase Conjugation

Here, the first term on the right-hand side of Eq. For most scattering media, these two values are very close.

The 1st Phase Conjugate of Pythagoras Tuning

So, the full-polarization DOPC process faithfully produces the phase-conjugated field of the input light. However, if the DOPC process phase-conjugates scattered light only along the horizontal polarization direction referred to as single-polarization DOPC , the output field is calculated as.

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Again, the first term on the right hand side of Eq. To compare the performance of full-polarization DOPC and single-polarization DOPC, we performed numerical simulations based on the above matrix analysis. In the simulation, N was set to be , and the input light was chosen to be horizontally polarized with the central pixel being 1 for the electric field amplitude and the other pixels being 0.

An intuitive explanation is that in the full polarization scenario, the peak intensity is enhanced by a factor of 4 due to constructive interference, while the background is doubled by summing the background intensities corresponding to the two orthogonal polarizations.

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Based on the above analysis, it is highly desired to develop a full-polarization DOPC system. The performance of such a system is not sensitive to the properties of the scattering media, and the system can always achieve a higher PBR than that achieved by single-polarization DOPC systems. Discrete data points are from numerical simulation results, while the lines are plotted using analytical expressions. Based on the positive results from the numerical simulations, we developed a full-polarization DOPC system schematically shown in Fig. In the phase recording step, the input light was split into a planar reference beam R and a sample beam S by a polarizing beamsplitter PBS ; R was vertically polarized and S was horizontally polarized.

Each beam was subsequently modulated by an acoustooptic modulator to induce a 12 Hz frequency difference between R and S. The polarization direction of R was then rotated by a half wave plate HWP to 45 degrees. In the sample arm, S illuminated an ex vivo chicken breast tissue slice, and its polarization state became spatially inhomogeneous after tissue scattering.

Then, the two beams were combined by a beamspliter BS for interferometry. Since the scattered light took various polarization states, we used a PBS to spatially separate it into components with horizontal and vertical polarizations. Each component then impinged on the surface of an SLM whose pixels displayed all zeros at this step. Schematic of the full-polarization DOPC set-up. Polarization states are indicated by the red arrows. In the playback step, the conjugate phase maps were displayed on the respective SLMs.

The sample beam was blocked by a mechanical shutter in this step, and the planar reference beam illuminated the two SLMs to acquire the conjugate phase map. The two branches of phase conjugated light were then combined by PBS3 and were directed to the scattering sample. After they passed through the sample, a bright focus was formed on the focal plane of lens L5. To observe the focus, a BS was inserted to create a copy of the focus, which was captured by a charge-coupled device CCD camera.

Specifically, Fig. All three images are shown using the same intensity scale.

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  6. Moreover, the PBRs for the three images are , , and , respectively. To better visualize the shape of the focus, each image is zoomed in and is normalized by its own peak intensity, as shown in Fig. It can be seen that all three foci maintain nearly circular shapes, which shows that when the sample is not too thick, single-polarization DOPC can still achieve high OPC fidelity. For the 4 mm thick chicken tissue, the images of the foci achieved by horizontal polarization, vertical polarization, and full polarization DOPC are shown in Fig. Due to the increased thickness, the PBRs for the three images are lower and are calculated to be 21, 18, and Among all three foci, the one achieved by full-polarization DOPC has a nearly circular shape that most closely resembles the shape of the input focus.

    We note that the increased size of the foci for 4 mm thick chicken tissue is due to different experimental conditions. Images of the foci achieved by single-polarization and full-polarization DOPC. To better visualize the shape of the focus, each image is normalized by its own peak intensity.

    Again, to better visualize the shape of the focus, each image is normalized by its own peak intensity. Here, we briefly discuss the polarization states of the OPC field in our experiments. Currently, the two SLMs in the set-up modulate only the phase but not the amplitude of light. Thus, the SLM-generated OPC field before illuminating the sample does not have the same polarization as that of the scattered light.

    Nonetheless, compared with the ideal case when both phase and amplitude are modulated, due to the scrambling nature of the thick scattering medium, the phase-modulated light still constructively interferes in the same polarization state as that of the recording-phase input light though the amplitude is reduced , while there is no constructive interference in the orthogonal polarization state.

    Thus, after the SLM-generated OPC field passes through the scattering medium, the polarization of the electric field at the focus is approximately the same as that of the input field. In our experiments, the input electric field at the focus was set to be horizontally polarized. Using a polarizer, we confirmed that the electric field at the focus achieved by full-polarization DOPC was also horizontally polarized. In conclusion, we developed the first DOPC system that can record and phase-conjugate the scattered light with various polarization states.

    When the scattering sample is optically thick, our system doubles the PBR achieved by single-polarization DOPC systems, improves the OPC fidelity, and maintains the polarization of the input light field. The method described here can be easily applied to existing DOPC systems to improve their performance.