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applscia/6981/10.1490/369869.4783appscia/Grating design methodology for tailored free-space beam-forming

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Grating design methodology for tailored free-space beam-forming

Gillenhaal J. Beck, Jonathan P. Home, Karan K. Mehta --------- G.J. Beck and J.P. Home are with the Institute of Quantum Electronics, ETH Zurich, Zurich, Switzerland. K.K. Mehta is with the school of Electrical and Computer Engineering, Cornell University, Ithaca, NY, USA. email:
Applied Science Letters

2023 ° 17(06) ° 1685-4783

DOI: 10.1490/369869.4783appscia


We present a design methodology for free-space beam-forming with general profiles from grating couplers which avoids the need for numerical optimization, motivated by applications in ion trap physics. We demonstrate its capabilities through a variety of gratings using different wavelengths and waveguide materials, designed for new ion traps with all optics fully integrated, including UV and visible wavelengths. We demonstrate designs for diffraction-limited focusing without restriction on waveguide taper geometry, emission angle, or focus height, as well as focused higher order Hermite-Gaussian and Laguerre-Gaussian beams. Additional investigations examine the influence of grating length and taper angle on beam-forming, indicating the importance of focal shift in apertured beams. The design methodology presented allows for efficient design of beamforming gratings with the accuracy as well as the flexibility of beam profile and operating wavelength demanded by application in atomic systems.


Waveguide -to-free-space outcoupling has enabled new developments in optical-phased arrays, beamsteering, LiDAR, and quantum information processing [1], [2], [3], [4], with high outcoupling efficiencies and straightforward fabrication making diffractive grating outcouplers ideal for applications requiring small device footprints and precise beam delivery. In trapped-ion systems, integrated beam delivery in surface traps provides a number of benefits over free-space addressing including robustness to external vibrations, tight focusing, and the potential for scalability [4]. Systems for various ion species have been demonstrated [5], [6] as well as high-fidelity entanglement [7], indicating promise for scalable trapped-ion systems with applications from quantum sensing and metrology to large-scale quantum computing [8]. Grating coupler design methodologies are most commonly motivated by efficient coupling to fibers, often for nearinfrared wavelengths [9], [10], [11], [12], [13], [14]. More recently, devices targeting free-space emission have been presented for various applications in atomic systems [15], [16], but current methodologies involve approximations that pose challenges when faced with the stringent demands of these systems, including varied beam waist requirements, operation at multiple wavelengths spanning the UV to IR, and the delivery of nontrivial spatial field profiles. A general approach for grating chirp and apodization was demonstrated in [17], but grating line curvatures for transverse focusing were restricted to back-emitting geometries and determined according to approximations limiting focusing accuracy.

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