All-optical pattern recognition and image processing on a metamaterial beam splitter

Recognition, comparison and analysis of large patterns or images are computationally intensive tasks that can be more efficiently addressed by inherently parallel optical techniques than sequential electronic data processing. However, existing all-optical image processing and pattern recognition methods based on optical nonlinearities are limited by an unavoidable trade-off between speed and intensity requirements. Here we propose and experimentally demonstrate a technique for recognition and analysis of binary images that is based on the linear interaction of light with light on a lossy metamaterial beam splitter of substantially sub-wavelength thickness. Similarities and differences between arbitrarily complex binary images are mapped directly with a camera for real-time qualitative analysis. Regarding quantitative analysis, agreement, disagreement and any other set operation between the patterns can be determined from power measurements acquired with a photodetector. In contrast to nonlinear techniques, that require high intensities to activate the nonlinear response, the image analysis method

computationally demanding and requires conversion of large quantities of optical information into electronic data. Therefore, the inherent parallelism of photonic systems has long been considered to be the route towards, faster, less complex and more energy efficient, real-time pattern recognition and image processing systems. Optical Fourier techniques and spatial light modulators, have been widely employed in image processing techniques intended for medical imaging. 1,2 However, the ultimate potential of photonic systems is revealed when alloptical logic computations come into play. [3][4][5][6] All-optical pattern recognition schemes have been realized with different types of optical correlators based on photorefractive polymers, 7 semiconductor optical amplifiers, 8 delay lines and phase shifter designs. 9 Photorefraction, 10 phase-conjugation, 11 second harmonic generation, 12 vapour atomic transitions with 4-wave mixing, 13 spatial dispersers 14 and reservoir computing 15 systems have served as the basis of reliable all-optical image processors. Nevertheless, the impact of these approaches is limited by complexity as well as fundamental speed restrictions and energy requirements due to the nonlinearities involved.
Here we report binary pattern recognition and image analysis based on the linear interaction of light with light on a beam splitter consisting of a planar metamaterial (also known as metasurface). It exploits that the light-matter interaction of a film of substantially subwavelength thickness can be controlled by counterpropagating coherent light waves, e.g. to control absorption, 16 polarization 17 or propagation direction 18 of light. Such coherent control of light with light was recently reported in two spatial dimensions as a platform for parallel all-optical logical operations based on the theory of an idealized metasurface absorber. 3 2 The theory and experiments reported here advance this concept to allow quantitative pattern recognition and image analysis on beam splitters of arbitrary loss. In our experiments, similarities and differences between binary dot patterns are recognized and satellite images analyzed by projecting reference and test images onto opposite sides of the metamaterial beam splitter using coherent light, see Fig. 1(b,c). We demonstrate that quantitative measurements of image agreement and disagreement, and indeed of any set operation between the images, can be performed by imaging the beam splitter plane onto a photodetector.
This way, the relationship between any pair of binary images (containing a large amount of optical data) may be reduced all-optically to a total of 3 characteristic power values of electronic data. Furthermore, imaging onto a CCD camera reveals maps of similarities and differences. In contrast to methods based on slow and energy demanding nonlinearities and electronics, our approach is based on linear optics and therefore it is, in principle, ultrafast with up to 100 THz bandwidth 19,20 and compatible with arbitrarily low intensities down to single photons. 21 In general, a beam splitter can be either lossless or lossy and planar metamaterialsinterfaces such as plasmonic metal films of deeply sub-wavelength thickness that are structured on the sub-wavelength scale -allow the realization of beam splitters with precisely engineered transmission, reflection and absorption levels. 22 Considering illumination by a single beam of light, we define the limiting case of an ideal lossless beam splitter as an interface having 50% transmission as well as reflection, and the limiting case of an ideal lossy beam splitter as an interface having 25% transmission as well as reflection and 50% absorption, which is the maximum achievable absorption level in truly planar structures. 23 Contrary to the common belief that light beams cannot interact in linear optics, the interaction of a beam of light with a planar metamaterial beam splitter can be controlled by a second counterpropagating coherent beam of light. This becomes clear when considering two co-polarized coherent counterpropagating waves forming a standing wave with electric field nodes and anti-nodes. A planar metamaterial interacts with the electric field of a normally incident plane wave, but its interaction with the magnetic field is prohibited as in-plane magnetic dipole modes are not supported by truly planar structures. Consequently, metasurface positioning at an electric field anti-node will enable interaction with the wave, while metasurface translation to a node will prevent light-matter interaction rendering the metasurface perfectly transparent. The position of an ideal lossless beam splitter relative to the standing wave will control how the power of the incident wave is divided between the two output beams. In contrast, for an ideal lossy beam splitter both output beams will always have the same power and the metamaterial's position relative to the standing wave will control absorption, from 0% at a node to 100% at an anti-node. will lead to addition or cancellation of the corresponding fields depending on the phase difference between the illuminating light beams, where doubled field amplitudes correspond to an intensity of 4I sgl while field cancellation implies vanishing intensity. It follows that the similarity of two patterns can be quantified by measuring the phase-dependent overall power of the output beam with a photodetector. For binary reference and test images, A and B, with illuminated areas S A and S B , respectively, similarities and differences can be characterized by the area S A∩B that is illuminated by both images (agreement) and the area of S A⊕B that is illuminated by only one image (disagreement). The area of disagreement will lead to detection of phase-independent power I sgl S A⊕B . In contrast, coherent interaction of light with light in areas illuminated from opposite sides yields detection of a phase-dependent power 4I sgl S A∩B cos 2 ϕ 2 , where ϕ is the phase difference between the transmitted beam A and 4 Table 1: Set operations between images A and B based on photodetector measurements of maximum and minimum power, P max and P min , normalized by the reference power 4P A,sgl (normalized powerP max andP min , their averageP avg and difference ∆P ).

Area [S A ] Power measurement
the reflected beam B. Therefore, the detected power is It is convenient to normalize the detected output power by 4P A,sgl , where P A,sgl = I sgl S A is the total detected output power when the metamaterial is illuminated by the reference image only. The normalized output powerP (θ) = P (θ) 4P A,sgl is Normalized in this way, the size of various characteristic areas of the images relative to the area S A of the reference image can be easily determined with a photodetector by measuring only the maximumP max and minimumP min of the phase-dependent total power of one output beam. This is illustrated by Table 1 whereP avg = (P max +P min )/2 and ∆P =P max −P min .
In particular, the sum of the illuminated areas A and B corresponds to the average power, the differences between the binary images are given by the minimum power and the overlap between the images corresponds to the phase-dependent power fluctuations.
While the above holds for any beam splitter, it is interesting to consider the limiting cases of the ideal lossless (T = R = 50%) and lossy (T = R = 25%) beam splitters. For coherent illumination with co-polarized counterpropagating light beams, I A = I B , the lossless beam splitter will split the incident intensity unevenly between the output beams, while the lossy beam splitter will split the incident intensity between absorption and two identical output beams. In the lossless case, coherent transparency at the standing wave node implies that the phase ϕ is related to the phase difference θ between the waves incident on the beam splitter by ϕ = θ ± π/2. In the lossy case, vanishing intensity implies coherent perfect absorption which occurs when the ideal lossy beam splitter is placed at an electric field anti-node of the standing wave formed by the incident waves, while the maximum output intensity corresponds to coherent transparency occurring when the beam splitter is placed at a node where interaction with the wave is eliminated. For such a coherent perfect absorber, the phase ϕ is related to the phase difference θ between the incident waves on the beam 6 splitter by ϕ = θ + π.
Here we report proof-of-principle experiments demonstrating pattern recognition and image analysis using a metamaterial-based system exploiting the coherent interaction of light with light on a metasurface, see  there is no coherent interaction and therefore the detected intensity I sgl is constant. In contrast, across areas of pattern agreement, coherent interaction between beams A and B on the planar metamaterial causes the detected intensity to oscillate between 4I sgl (row 2, ϕ = 0) and 0 (row 3, ϕ = π) as a function of the phase difference between beams A and B on the metasurface. As a result, areas of agreement are highlighted in row 2, while they are deleted from row 3, thus revealing areas of agreement (similarities) and disagreement (differences), respectively. Direct quantitative comparison of the images is most easily achieved by detecting the total power of the output beam with a photodetector. Here, we use the CCD as an effective photodetector by integrating the total power in each image. We measure (i) the output power when the metamaterial is illuminated by the reference image only P A,sgl , as well as (ii) the maximum P max and (iii) minimum P min output power for simultaneous metasurface illumination by reference and test images. The latter are normalized by 4P A,sgl 8 which yieldsP max andP min as described above, see Fig. 2(b). Theory predicts that the phase-dependent power fluctuation ∆P =P max −P min should correspond to the fraction of the reference pattern that overlaps with the test pattern, and indeed we find that ∆P increases with pattern agreement. We measure ∆P = 0 for 0% pattern agreement increasing to ∆P = 0.8 for 100% pattern agreement, which is slightly less than the theoretical value of 1.0 due to experimental imperfections including about 1% residual transmission through nominally opaque mask areas, pattern misalignment, noise and background signals. 4P min should correspond to the area where the reference and test patterns do not overlap and for 0% pattern agreement our experiments correctly predict that the area of disagreement is twice as large as the illuminated area of the reference pattern.P min decreases monotonously with increasing pattern overlap reaching 0.1 -slightly more than the theoretical value of zero -for complete pattern agreement. Thus, our power measurements are consistent with theory and provide quantitative measurements of the level of image agreement and disagreement with about 80% of the theoretically predicted contrast (double arrows in Fig. 2b).
The experimental imperfections may be most easily taken into account by introducing an instrumental contrast correction factor f , e.g.P corr = f (P exp − 0.5) + 0.5. The ideal case corresponds to f = 1.0 and the contrast correction factor for our setup takes a value of about 1.2 here and about 1.1 with higher contrast masks in the case discussed below.
In order to illustrate the image analysis capabilities of our method, we use it to analyze the ice coverage evolution in the Arctic and Greenland region. We fabricated binary masks based on satellite images available from the National Snow and Ice Data Center (USA). 24 The images were taken one decade apart around the annual ice cover minimum which occurs (a) A target pattern is compared to a set of test patterns. The first row shows images of all patterns as captured by the CCD for single beam illumination. All test patterns are compared with the target pattern by projection onto opposite sides of the planar metamaterial using coherent light, revealing similarities (row 2) and differences (row 3) for phase differences between transmitted reference light and reflected test light of ϕ = 0 and π, respectively. (b) Maxima and minima of the measured (triangles) and expected (lines) total detected power normalized by 4× the total target image power,P . The agreement between test and target patterns corresponds to the normalized power fluctuation, ∆P (double arrows). Comparison to the initial 1982 ice cover by projection of the test and reference masks onto opposite sides of the metasurface using coherent light, revealing similarities (row 2) and differences (row 3) for phase differences between transmitted reference light and reflected test light of ϕ = 0 and π, respectively. (b) Measured normalized powerP max (green, ϕ = 0) andP min (red, ϕ = π), where ∆P =P max −P min (arrows) corresponds to the fraction of ice cover that remained unchanged and 4P min corresponds to the fraction of ice cover change (growth or melting). The power has been determined by integrating the intensity across the corresponding image. (c) Exact theoretical and experimentally determined areas of molten 1 − ∆P , grown 4P avg − 1 − ∆P and remaining ∆P ice cover relative to the original ice cover without (f = 1.0) and with (f = 1.1) contrast correction. 16