top of page
Locked
applscia/6981/10.1490/369869.4783appscia/Grating design methodology for tailored free-space beam-forming
.png)
Research
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
https://www.wikipt.org/applscilettersa
DOI: 10.1490/369869.4783appscia
Abstract
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.
Introduction
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.
Unlock Only
Read-only this publication
This option will drive you towards only the selected publication. If you want to save money then choose the full access plan from the right side.
Conclusion
This work presents a grating outcoupler design process for waveguide-to-free-space beam-forming, capable of the precision and flexibility required for applications in trappedion addressing and beyond. Ideas from previous works— namely longitudinal focusing from [17] and holographic phase Fig. 12. Focused Laguerre-Gaussian emission at 732 nm. The beam was designed for emission at 32◦, focusing to a waist of 1.5 μm, with a minimum feature size of 75 nm, truncation at χ1 = 0.75 and χ2 = 1.52, and no silicon substrate. (a) Intensity distribution along the xz-plane, with insets showing the intensity and phase at a beam-orthogonal slice at z = 70 μm (color scale same as Fig. 11). Inset at bottom left displays the corresponding intensity along the y axis. (b) Grating and intensity distribution at z = 7 μm. matching (e.g. as presented in [18])—were unified and built upon with a number of explicit improvements. Firstly, rigorous analytical treatment of the desired freespace beam provides the flexibility for astigmatic, elliptical focusing while also accommodating refraction at the oxide cladding. Secondly, explicit integration of the simulationextracted effective index to account for the grating’s influence on the propagating waveguide field enables applicability across materials and fabrication methods/grating structures. Lastly, we utilize focal shift theory to determine the beam offset and taper angle adjustments required to ensure the desired position of the true focus. Collectively, these improvements allow design at not only general emission angles and focal heights, but also waveguide taper geometries—such flexibility is critical in systems involv-
ACKNOWLEDGMENT
We thank LioniX International for fabrication of designs described here, and Tanja Mehlstaubler for discussions on ¨ application of Hermite-Gauss modes to precision metrology with single ions. We acknowledge funding from ETH Zurich, the ETH/PSI Quantum Computing Hub, the Swiss National Science Foundation (Grant No. 200020 207334), the EU Horizon 2020 FET Open project PIEDMONS (Grant No. 801285), and Cornell University.
bottom of page