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A full degree-of-freedom spatiotemporal light modulator

Nature Photonics volume 16, pages 834–842 (2022)Cite this article

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A Publisher Correction to this article was published on 03 January 2023

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Abstract

Harnessing the full complexity of optical fields requires the complete control of all degrees of freedom within a region of space and time—an open goal for present-day spatial light modulators, active metasurfaces and optical phased arrays. Here, we resolve this challenge with a programmable photonic crystal cavity array enabled by four key advances: (1) near-unity vertical coupling to high-finesse microcavities through inverse design; (2) scalable fabrication by optimized 300 mm full-wafer processing; (3) picometre-precision resonance alignment using automated, closed-loop ‘holographic trimming’; and (4) out-of-plane cavity control via a high-speed μLED array. Combining each, we demonstrate the near-complete spatiotemporal control of a 64 resonator, two-dimensional spatial light modulator with nanosecond- and femtojoule-order switching. Simultaneously operating wavelength-scale modes near the space–bandwidth and time–bandwidth limits, this work opens a new regime of programmability at the fundamental limits of multimode optical control.

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Fig. 1: Full DoF spatiotemporal optical programming.
Fig. 2: The PhC-SLM.
Fig. 3: Conventional versus inverse-designed PhC cavities.
Fig. 4: Full-wafer photonic crystal fabrication in an optimized 300 mm foundry process.
Fig. 5: Parallel, fully automated and low-loss microcavity trimming via structured laser oxidation.
Fig. 6: Nanosecond switching and spatial light modulation.

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Data availability

The main data supporting the findings of this study are available within the Article and its Supplementary Information. Additional data are available from the corresponding authors upon reasonable request.

Code availability

The SLM control and holography software developed for this study is available online via GitHub at https://github.com/QPG-MIT/slmsuite. A sample finite-difference time-domain simulation is available at https://www.flexcompute.com/userprojects/a-full-degree-of-freedom-spatiotemporal-light-modulator. All the other algorithms are documented within the Article and its Supplementary Information.

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Acknowledgements

We thank the MITRE Quantum Moonshot Program for program oversight, Flexcompute for supporting finite-difference time-domain simulations, the MIT.nano staff for fabrication assistance, and M. ElKabbash (MIT) for useful discussions. C.L.P. was supported by the Hertz Foundation Elizabeth and Stephen Fantone Family Fellowship. I.C. was supported by the National Defense Science and Engineering Graduate Fellowship Program and the National Science Foundation (NSF) award DMR-1747426. S.T.-M. is funded by the Schmidt Postdoctoral Award and the Israeli Vatat Scholarship. Experiments were supported in part by Army Research Office grant W911NF-20-1-0084 (D.R.E.), supervised by M. Gerhold; the Air Force Research Laboratory under agreements FA8650-21-2-1000 and FA8750-21-2-0004; the Engineering and Physical Sciences Research Council grants EP/M01326X/1 and EP/T00097X/1 (M.D.D. and M.J.S.); and the Royal Academy of Engineering Research Chairs and Senior Research Fellowships (M.J.S.). This material is based on the research sponsored by the Air Force Research Laboratory under agreement no. FA8650-21-2-1000. The US Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the United States Air Force, the Air Force Research Laboratory or the US Government.

Author information

Authors and Affiliations

  1. Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Christopher L. Panuski, Ian Christen, Cole J. Brabec, Sivan Trajtenberg-Mills & Dirk R. Englund

  2. Flexcompute, Belmont, MA, USA

    Momchil Minkov

  3. Institute of Photonics, Department of Physics, University of Strathclyde, Technology and Innovation Centre, Glasgow, UK

    Alexander D. Griffiths, Jonathan J. D. McKendry, Martin D. Dawson & Michael J. Strain

  4. State University of New York Polytechnic Institute, Albany, NY, USA

    Gerald L. Leake, Daniel J. Coleman, Cung Tran, Jeffrey St Louis & John Mucci

  5. Applied Nanotools, Edmonton, Alberta, Canada

    Cameron Horvath & Jocelyn N. Westwood-Bachman

  6. Electrical and Microelectronic Engineering, Rochester Institute of Technology, Rochester, NY, USA

    Stefan F. Preble

  7. Air Force Research Laboratory, Information Directorate, Rome, NY, USA

    Michael L. Fanto

Authors
  1. Christopher L. Panuski
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  2. Ian Christen
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  3. Momchil Minkov
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  4. Cole J. Brabec
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  5. Sivan Trajtenberg-Mills
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  6. Alexander D. Griffiths
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  7. Jonathan J. D. McKendry
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  8. Gerald L. Leake
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  9. Daniel J. Coleman
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  10. Cung Tran
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  11. Jeffrey St Louis
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  12. John Mucci
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  13. Cameron Horvath
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  14. Jocelyn N. Westwood-Bachman
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  15. Stefan F. Preble
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  16. Martin D. Dawson
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  17. Michael J. Strain
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  18. Michael L. Fanto
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  19. Dirk R. Englund
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Contributions

C.L.P. and D.R.E. conceived the idea, developed the theory and led the research. M.M. and C.L.P. developed the far-field optimization technique and designs. C.J.B. developed the optimized the resonator detuning theory. C.L.P. conducted the experiments with assistance from I.C. (trimming experiments), S.T.-M. (holography software) and A.D.G. (μLED measurements). J.J.D.M., M.D.D. and M.J.S. contributed the μLED arrays and guided the incoherent switching experiments. C.H. and J.N.W.-B. fabricated the initial samples for evaluation before foundry process development by C.T., J.S.L., J.M. and G.L.L. S.F.P. assisted with the wafer post-processing. M.L.F. coordinated and led the foundry fabrication with assistance from G.L.L. and D.J.C. C.L.P. wrote the manuscript with input from all the authors.

Corresponding authors

Correspondence to Christopher L. Panuski or Dirk R. Englund.

Ethics declarations

Competing interests

C.L.P. and D.R.E. are authors of US patent 11,022,826 (all-optical spatial light modulators) and US patent App. 16/876,477 (high-speed wavelength-scale spatial light modulators with two-dimensional tunable microcavity arrays) that outline the all-optical control scheme and resonant architecture of the PhC-SLM developed here. The other authors declare no competing interests.

Peer review

Peer review information

Nature Photonics thanks Subhojit Dutta, Volkan Gurses and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Table 1 Performance comparison of our PhC-SLM (bold) to selected active 2D spatial light modulators from Fig. 1b. Estimated fill factors ζ are marked by a *. Wavelength-steered devices 100 are excluded to focus on active, individually-addressable arrays
Full size table
Extended Data Table 2 Comparison of previous microcavity array trimming techniques to our parallel laser assisted thermal oxidation (bold). Estimated values are marked with a *. Δλp-p = peak-to-peak wavelength error; Q = mean quality factor
Full size table

Extended Data Fig. 1 Optimized holography with inverse-designed, vertically-coupled microcavity arrays.

(a) Silicon L3 slab defect cavity design (hexagonal lattice constant a = 0.4μm; hole radius r/a = 0.25; slab thickness t = 220 nm) with overlaid midplane magnetic field profile Hz after Q optimization by displacing (δxi, δyi) and resizing (δri) the shaded holes in the \(16a\times 16(\sqrt{3}/2)a\) periodic unit cell. Hole shifts are magnified by 3 × for visualization. The confined cavity mode radiates into the broad far-field profile in (b, background), violating (C1) and yielding a zero-order diffraction efficiency η0 ≪ 1. As a result, simulated trial holograms (c) from a 64 × 64 cavity array with optimized detunings (Supplement Section D) have minimal overall diffraction efficiency η. Inverse design (b) solves these problems. Guided mode expansion (GME) approximates the mode’s Q and far-field profile by sampling the losses {c} at the array’s diffraction orders (white × s) displaced by Bloch boundary conditions \({\overrightarrow{k}}_{i}\) (that is at the coloured dots). An objective function f that maximizes Q, confines \(\overrightarrow{H}\), and minimizes {c} at any non-zero diffraction order can then be efficiently optimized with respect to all hole parameters using reverse-mode automatic differentiation (b). The resulting devices with high-Q, efficient coupling, and directional emission enable high-performance (η ~ 1) resonant holography (d).

Extended Data Fig. 2 Overview of experimental setups for measuring and controlling the photonic crystal SLM (PhC-SLM).

A cross-polarized microscope (a) featuring balanced homodyne measurement (b) enables near- and far-field characterization of cavity arrays controlled by SLM-distributed coherent light (c) or high-speed incoherent μLED arrays (d). TL: tunable infrared laser (Santec TSL-710), EOM: electro-optic amplitude modulator; λ/2: half-wave plate, PBS: polarizing beamsplitter; L1: 250 mm back-focal-plane lens; DM: long-pass dichroic mirror; OL: objective lens (Nikon Plan Fluor 40 × /0.60 NA or Nikon LU Plan 100 × /0.95 NA), L2: 250 mm back-focal-plane lens; SF: spatial filter; L3: 200 mm tube lens; v-SWIR: visible-short wave infrared camera (Xenics Cheetah 640); DAQ: data acquisition unit (NI USB-6343); Δt: trigger delay generator (SRS DG645); LO: local oscillator; PM: piezo mirror; BD: balanced detector (Thorlabs PDB480C-AC); Phase Lock: TEM LaseLock; LPF: low-pass filter; CWTL: continuous-wave trimming laser (Coherent Verdi V18); MLD: modulated laser diode (Hubner Cobolt or PicoLAS LDP); BE: 5 × visible beam expander; LCOS: high-power liquid crystal SLM (Santec SLM-300); L4: 300 mm; L5: 250 mm; PD: photo-detector; CL: collection lens (Zeiss Fluar 5 × /0.25 NA); VBE: 0.5 × − 2 × variable beam expander; DP: dove prism.

Extended Data Fig. 3 Cross-polarized back-focal-plane (BFP) imaging techniques for a grating-coupled L3 cavity.

Two orthogonally polarized far-field profiles are imaged by orienting the input polarization Ein at a + 45∘ (a) or − 45∘ (b) angle from the dominant cavity polarization axis (dashed line in inset). The complete cavity emission profile \(S(\overrightarrow{k})\) can be reconstructed by summing both images (c) or approximated from a single polarized image (d), yielding near-identical images with quantitative agreement between the extracted η0.

Extended Data Fig. 4 Imaged far-field profiles \(S(\overrightarrow{k})\) (over a 0.9 numerical aperture) for each device in an 8 × 8 array of inverse designed (top) and grating-coupled (bottom) L3 PhC cavities.

The extracted zero-order efficiencies η0 and standard deviations are also provided.

Extended Data Fig. 5 Flowchart of the holographic trimming algorithm.

Trimming holograms are formed with weighted Gerchberg-Saxton (GS) algorithms and projected onto desired cavities for duration Δt with power \({P}_{{{{\rm{trim}}}}}\). Alternating trimming and resonance readout periods continue until the instantaneous wavelength λi of any targeted cavity blueshifts past the target wavelength λt. Thereafter, a new set of target cavities is selected and trimmed. This selection and trimming sub-loop continues until all resonant wavelengths {λ0} are below the ‘rest’ wavelength λrest, at which point trimming is halted and the resonances are continuously monitored at readout interval Δtrest. When the resonances are sufficiently stable (redshifting from moisture adsorption to the silicon membrane is arrested), the total ‘rehydration’ redshift Δλ0 of each cavity is updated to better estimate the true resonant wavelength λ0 ≈ λi + Δλ0 from the instantaneous wavelengths {λi} during trimming. The entire process terminates when the peak-to-peak static resonant wavelength uniformity \(\Delta {\lambda }_{0}^{{{{\rm{p-p}}}}}\) drops below the desired tolerance Δλtol.

Extended Data Fig. 6 Overlaid images of 10×10 cavity (grey) and trimming spot (colour) arrays demonstrating the ≪ μm placement accuracy and percent-order power uniformity of weighted Gerchberg-Saxton phase retrieval with experimental camera feedback.

In general, our holography software (Supplement Section F) creates high-uniformity optical foci to arbitrary image plane locations specified by the user.

Supplementary information

Supplementary Information

Supplementary Sections A–G, Figs. 1–8 and Table 1.

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Panuski, C.L., Christen, I., Minkov, M. et al. A full degree-of-freedom spatiotemporal light modulator. Nat. Photon. 16, 834–842 (2022). https://doi.org/10.1038/s41566-022-01086-9

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