Meta-Material Enhanced Spatial Mode Decomposition


 Acquiring precise information about the mode content of a laser is critical for multiplexed optical communications, optical imaging with active wave-front control, and quantum-limited interferometric measurements. Hologram-based mode decomposition devices allow a fast, direct measurement of the mode content, but they have limited precision due to cross-coupling between modes. Here we report the first proof-of-principle demonstration of mode decomposition with a meta-surface, resulting in significantly enhanced precision. A mode-weight fluctuation of 0.6ppm (-62 dB) can be measured with 1 second of averaging at a Fourier frequency of 80 Hz, an improvement on the state-of-the-art by more than three orders of magnitude. The improvement is attributable to the reduction in cross-coupling enabled by the exceptional phase accuracy of the meta-surface. We show a systematic study of the limiting sources of noise, and we show that there is a promising path towards complete mode decomposition with similar precision.

based on Fourier optics 8,9 . A particular mode pattern is encoded onto a diffractive optical element 36 and a Fourier imaging system convolves this pattern with an incoming beam. In the far field, 37 the mode weight is proportional to the on-axis intensity. For an orthogonal mode basis, several 38 patterns can be spatially multiplexed by adding a blazed grating to the spatial carrier, allowing the 39 simultaneous interrogation of multiple modes. In practice, the sensors that read the modal powers 40 must have a finite aperture, inducing cross-coupling by measuring some off-axis intensity. The-41 state-of-the-art accuracy of measuring the mode weighting is around 1% 9, 10 . These measurements 42 are likely limited by this cross-coupling, once this effect is eliminated, mode weights of 0.2 % can 43 be demonstrated 11 . 44 The cross coupling effect has been analysed and is limited by the beam-size at the sensor 11, 12 . 45 More precisely, it scales as square of the ratio of the sensor aperture to beam diameter 12 . Hence-46 forth, to ultimately suppress the cross coupling, larger beams on the sensor are preferred. As a fact 47 of a Fourier imaging systems 12 , this implies a small incoming beam interrogating at the diffractive 48 optical element, which exhibits a challenging requirement. For example, spatial light modulators 49 have fundamental limit of the pixel resolution.

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Furthermore, both of the spatial light modulators we tested exhibited noise at half integer 51 multiples of the display frequency, rendering the device useless for modal measurements be-52 tween 25-250 Hz-essential frequencies in audio band applications such as laser interferometric 53 gravitational-wave detection.

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Recent developments in the field of optical metasurfaces have led to a novel platform for 55 controlling the multiple degrees of freedom of light at subwavelength scale 13 . In our work, we 56 propose a new meta-surface approach to address the cross-coupling and noise issues. As a proof 57 of principle demonstration, we encode three correlation filters for HG00, HG01, and HG10 on one 58 meta-surface chip, which allows for a simple calibration procedure and can be extended to include 59 more spatial modes. With the exceptionally high resolution of the meta-surface, we are able to 60 measure the first-order mode content with a sensitivities in excess of 1 ppm above of 25 Hz.

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The metasurface, shown in Figure 1a, is an ultrathin structured medium composed of spa-  of beam A corresponds to the power in the HG00 mode, while B and C correspond to HG01 and 72 HG10 respectively. A lens focuses these beams to a large waist where the on-axis power is then 73 measured using small aperture photo-diodes. The entire meta-surface is 500 µm×500 µm with 74 10 3 × 10 3 pixels for 1064 nm laser beam.

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To achieve the required phase distributions, the meta-atom is designed based on the concept  Material. We found the coherence between the two devices was superb, as shown in Figure 2b.

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Due to exceptional meta-surface resolution in nano-scale size, cross coupling between all but 91 the largest modes may be safely ignored. Pushing our experimental setup to its limit, we allowed 92 the HG00 to become 10 6 times larger than the HG10. Even at this level, fluctuations in the HG00 93 could be ignored and we only needed to take account of the DC effect, which was subtracted away 94 during online signal processing.

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To date, the state-of-the-art mode weighting method is spatially and spectrally resolved (S 2 ) imag-112 ing, which offers a ∼ 40 dB mode discrimination 27 (and references therein) . However, S 2 imaging requires 113 an incoherent source and is therefore not suitable for in-situ diagnostics in many experiments. We

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show the meta-material enhancement allows correlation filter based imaging to surpass the S 2 tech-115 nique, permitting the investigation of small mode weights among a larger carrier mode, in this case 116 TEM00. This is particularly useful in precision metrology, where high levels of mode matching are 117 required. Furthermore, sub-micron pixels enable a reduction in unused diffraction orders, improv-118 ing power efficiency, thus reducing shot noise and increasing the available spatial multiplexing.

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Thus, increasing the signal to dark-noise ratio.

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Applications requiring high-frequency mode-decomposition, such as mode-division-multiplexing 121 and characterization of single-mode fibers, may reduce cross-talk using the meta-material enhance-122 ment. These systems are likely to be limited by electronic noises in the photo-diode. An improved 123 electronic readout system may permit shot noise limited sensitivity.

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Applications requiring low frequency mode analysis, such as correction of thermally in-125 duced mode mismatches in high power systems, will need to carefully consider the low frequency 126 the stability of the phase-plate, lens, photo-diode and electronics to achieve the very highest dy-