Abstract

Microring weight banks present novel opportunities for reconfigurable, high-performance analog signal processing in photonics. Controlling microring filter response is a challenge due to fabrication variations and thermal sensitivity. Prior work showed continuous weight control of multiple wavelength-division multiplexed signals in a bank of microrings based on calibration and feedforward control. Other prior work has shown resonance locking based on feedback control by monitoring photoabsorption-induced changes in resistance across in-ring photoconductive heaters. In this work, we demonstrate continuous, multi-channel control of a microring weight bank with an effective 5.1 bits of accuracy on 2Gbps signals. Unlike resonance locking, the approach relies on an estimate of filter transmission versus photo-induced resistance changes. We introduce an estimate still capable of providing 4.2 bits of accuracy without any direct transmission measurements. Furthermore, we present a detailed characterization of this response for different values of carrier wavelength offset and power. Feedback weight control renders tractable the weight control problem in reconfigurable analog photonic networks.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (3)

F. D. L. Coarer, M. Sciamanna, A. Katumba, M. Freiberger, J. Dambre, P. Bienstman, and D. Rontani, “All-optical reservoir computing on a photonic chip using silicon-based ring resonators,” IEEE J. Sel. Top. Quantum Electron. 24, 1–8 (2018).
[Crossref]

H. T. Peng, M. A. Nahmias, T. F. de Lima, A. N. Tait, B. J. Shastri, and P. Prucnal, “Neuromorphic photonic integrated circuits,” IEEE J. Sel. Top. Quantum Electron. 24, 1 (2018).

A. N. Tait, A. X. Wu, T. F. de Lima, M. A. Nahmias, B. J. Shastri, and P. R. Prucnal, “Two-pole microring weight banks,” Opt. Lett. 43, 2276–2279 (2018).
[Crossref] [PubMed]

2017 (13)

Y. Liu, A. Choudhary, D. Marpaung, and B. J. Eggleton, “Gigahertz optical tuning of an on-chip radio frequency photonic delay line,” Optica 4, 418–423 (2017).
[Crossref]

Z. Lu, J. Jhoja, J. Klein, X. Wang, A. Liu, J. Flueckiger, J. Pond, and L. Chrostowski, “Performance prediction for silicon photonics integrated circuits with layout-dependent correlated manufacturing variability,” Opt. Express 25, 9712–9733 (2017).
[Crossref] [PubMed]

T. Deng, J. Robertson, and A. Hurtado, “Controlled propagation of spiking dynamics in vertical-cavity surface-emitting lasers: Towards neuromorphic photonic networks,” IEEE J. Sel. Top. Quantum Electron. 23, 1–8 (2017).

S. Buckley, J. Chiles, A. N. McCaughan, G. Moody, K. L. Silverman, M. J. Stevens, R. P. Mirin, S. W. Nam, and J. M. Shainline, “All-silicon light-emitting diodes waveguide-integrated with superconducting single-photon detectors,” Appl. Phys. Lett. 111, 141101 (2017).
[Crossref]

A. Annoni, E. Guglielmi, M. Carminati, G. Ferrari, M. Sampietro, D. A. Miller, A. Melloni, and F. Morichetti, “Unscrambling light—automatically undoing strong mixing between modes,” Light Sci. Appl. 6, e17110 (2017).
[Crossref]

M. Carminati, A. Annoni, F. Morichetti, E. Guglielmi, G. Ferrari, D. O. M. de Aguiar, A. Melloni, and M. Sampietro, “Design guidelines for contactless integrated photonic probes in dense photonic circuits,” J. Lightw. Technol. 35, 3042–3049 (2017).
[Crossref]

V. K. Narayana, S. Sun, A.-H. A. Badawy, V. J. Sorger, and T. El-Ghazawi, “MorphoNoC: Exploring the design space of a configurable hybrid NoC using nanophotonics,” Microprocess. Microsyst. 50, 113 (2017).
[Crossref]

J. Chiles, S. Buckley, N. Nader, S. W. Nam, R. P. Mirin, and J. M. Shainline, “Multi-planar amorphous silicon photonics with compact interplanar couplers, cross talk mitigation, and low crossing loss,” APL Photonics 2, 116101 (2017).
[Crossref]

D. Pérez, I. Gasulla, L. Crudgington, D. J. Thomson, A. Z. Khokhar, K. Li, W. Cao, G. Z. Mashanovich, and J. Capmany, “Multipurpose silicon photonics signal processor core,” Nat. Commun. 8, 636 (2017).
[Crossref] [PubMed]

A. N. Tait, T. F. de Lima, E. Zhou, A. X. Wu, M. A. Nahmias, B. J. Shastri, and P. R. Prucnal, “Neuromorphic photonic networks using silicon photonic weight banks,” Sci. Rep. 7, 7430 (2017).
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Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljačić, “Deep learning with coherent nanophotonic circuits,” Nat. Photon. 11, 441–446 (2017).
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J. M. Shainline, S. M. Buckley, R. P. Mirin, and S. W. Nam, “Superconducting optoelectronic circuits for neuromorphic computing,” Phys. Rev. Appl. 7, 034013 (2017).
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T. Ferreira de Lima, B. J. Shastri, A. N. Tait, M. A. Nahmias, and P. R. Prucnal, “Progress in neuromorphic photonics,” Nanophotonics 6, 577–599 (2017).
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2016 (10)

D. Thomson, A. Zilkie, J. E. Bowers, T. Komljenovic, G. T. Reed, L. Vivien, D. Marris-Morini, E. Cassan, L. Virot, J.-M. Fédéli, J.-M. Hartmann, J. H. Schmid, D.-X. Xu, F. Boeuf, P. O’Brien, G. Z. Mashanovich, and M. Nedeljkovic, “Roadmap on silicon photonics,” J. Opt. 18, 073003 (2016).
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W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, “A fully reconfigurable photonic integrated signal processor,” Nat. Photon. 10, 190–195 (2016).
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N. C. Harris, D. Bunandar, M. Pant, G. R. Steinbrecher, J. Mower, M. Prabhu, T. Baehr-Jones, M. Hochberg, and D. Englund, “Large-scale quantum photonic circuits in silicon,” Nanophotonics 5, 456 (2016).
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A. N. Tait, A. X. Wu, T. Ferreira de Lima, E. Zhou, B. J. Shastri, M. A. Nahmias, and P. R. Prucnal, “Microring weight banks,” IEEE J. Sel. Top. Quantum Electron. 22, 312 (2016).
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T. Ferreira de Lima, A. N. Tait, M. A. Nahmias, B. J. Shastri, and P. R. Prucnal, “Scalable wideband principal component analysis via microwave photonics,” IEEE Photon. J. 8, 1–9 (2016).
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A. Tait, T. Ferreira de Lima, M. Nahmias, B. Shastri, and P. Prucnal, “Continuous calibration of microring weights for analog optical networks,” IEEE Photon. Techol. Lett. 28, 887–890 (2016).
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B. J. Shastri, M. A. Nahmias, A. N. Tait, A. W. Rodriguez, B. Wu, and P. R. Prucnal, “Spike processing with a graphene excitable laser,” Sci. Rep. 6, 19126 (2016).
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B. Romeira, R. Avó, J. M. L. Figueiredo, S. Barland, and J. Javaloyes, “Regenerative memory in time-delayed neuromorphic photonic resonators,” Sci. Rep. 6, 19510 (2016).
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A. N. Tait, T. Ferreira de Lima, M. A. Nahmias, B. J. Shastri, and P. R. Prucnal, “Multi-channel control for microring weight banks,” Opt. Express 24, 8895–8906 (2016).
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P. R. Prucnal, B. J. Shastri, T. Ferreira de Lima, M. A. Nahmias, and A. N. Tait, “Recent progress in semiconductor excitable lasers for photonic spike processing,” Adv. Opt. Photon. 8, 228–299 (2016).
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2015 (11)

Y. Li and A. W. Poon, “Active resonance wavelength stabilization for silicon microring resonators with an in-resonator defect-state-absorption-based photodetector,” Opt. Express 23, 360–372 (2015).
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A. N. Tait, J. Chang, B. J. Shastri, M. A. Nahmias, and P. R. Prucnal, “Demonstration of WDM weighted addition for principal component analysis,” Opt. Express 23, 12758–12765 (2015).
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D. Brunner and I. Fischer, “Reconfigurable semiconductor laser networks based on diffractive coupling,” Opt. Lett. 40, 3854–3857 (2015).
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D. A. B. Miller, “Perfect optics with imperfect components,” Optica 2, 747–750 (2015).
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H. Jayatilleka, K. Murray, M. Ángel Guillén-Torres, M. Caverley, R. Hu, N. A. F. Jaeger, L. Chrostowski, and S. Shekhar, “Wavelength tuning and stabilization of microring-based filters using silicon in-resonator photoconductive heaters,” Opt. Express 23, 25084–25097 (2015).
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P. Alipour, A. H. Atabaki, M. Askari, A. Adibi, and A. A. Eftekhar, “Robust postfabrication trimming of ultracompact resonators on silicon on insulator with relaxed requirements on resolution and alignment,” Opt. Lett. 40, 4476–4479 (2015).
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J. Carolan, C. Harrold, C. Sparrow, E. Martín-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349, 711 (2015).
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F. Akopyan, J. Sawada, A. Cassidy, R. Alvarez-Icaza, J. Arthur, P. Merolla, N. Imam, Y. Nakamura, P. Datta, G.-J. Nam, B. Taba, M. Beakes, B. Brezzo, J. Kuang, R. Manohar, W. Risk, B. Jackson, and D. Modha, “TrueNorth: Design and tool flow of a 65 mW 1 million neuron programmable neurosynaptic chip,” IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 34, 1537–1557 (2015).
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J. C. C. Mak, W. D. Sacher, T. Xue, J. C. Mikkelsen, Z. Yong, and J. K. S. Poon, “Automatic resonance alignment of high-order microring filters,” IEEE J. Quantum Electron. 51, 1–11 (2015).
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J. Wang, H. Shen, L. Fan, R. Wu, B. Niu, L. T. Varghese, Y. Xuan, D. E. Leaird, X. Wang, F. Gan, A. M. Weiner, and M. Qi, “Reconfigurable radio-frequency arbitrary waveforms synthesized in a silicon photonic chip,” Nat. Commun. 6, 5957 (2015).
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M. P. Chang, N. Wang, B. Wu, and P. R. Prucnal, “A simultaneous variable optical weight and delay in a semiconductor optical amplifier for microwave photonics,” J. Lightw. Technol. 33, 2120–2126 (2015).
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2014 (6)

A.-J. Lim, J. Song, Q. Fang, C. Li, X. Tu, N. Duan, K. K. Chen, R.-C. Tern, and T.-Y. Liow, “Review of silicon photonics foundry efforts,” IEEE J. Sel. Top. Quantum Electron. 20, 405–416 (2014).
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K. Vandoorne, P. Mechet, T. Van Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, and P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 5, 5341 (2014).
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A. N. Tait, M. A. Nahmias, B. J. Shastri, and P. R. Prucnal, “Broadcast and weight: An integrated network for scalable photonic spike processing,” J. Lightw. Technol. 32, 4029–4041 (2014).
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F. Selmi, R. Braive, G. Beaudoin, I. Sagnes, R. Kuszelewicz, and S. Barbay, “Relative refractory period in an excitable semiconductor laser,” Phys. Rev. Lett. 112, 183902 (2014).
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J. A. Cox, A. L. Lentine, D. C. Trotter, and A. L. Starbuck, “Control of integrated micro-resonator wavelength via balanced homodyne locking,” Opt. Express 22, 11279–11289 (2014).
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S. Grillanda, M. Carminati, F. Morichetti, P. Ciccarella, A. Annoni, G. Ferrari, M. Strain, M. Sorel, M. Sampietro, and A. Melloni, “Non-invasive monitoring and control in silicon photonics using cmos integrated electronics,” Optica 1, 129–136 (2014).
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2013 (11)

M. C. Soriano, S. Ortín, D. Brunner, L. Larger, C. R. Mirasso, I. Fischer, and L. Pesquera, “Optoelectronic reservoir computing: tackling noise-induced performance degradation,” Opt. Express 21, 12–20 (2013).
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C. Sima, J. C. Gates, H. L. Rogers, P. L. Mennea, C. Holmes, M. N. Zervas, and P. G. R. Smith, “Phase controlled integrated interferometric single-sideband filter based on planar bragg gratings implementing photonic hilbert transform,” Opt. Lett. 38, 727–729 (2013).
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D. A. B. Miller, “Self-aligning universal beam coupler,” Opt. Express 21, 6360–6370 (2013).
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A. H. Atabaki, A. A. Eftekhar, M. Askari, and A. Adibi, “Accurate post-fabrication trimming of ultra-compact resonators on silicon,” Opt. Express 21, 14139–14145 (2013).
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C. Mesaritakis, V. Papataxiarhis, and D. Syvridis, “Micro ring resonators as building blocks for an all-optical high-speed reservoir-computing bit-pattern-recognition system,” J. Opt. Soc. Am. B 30, 3048–3055 (2013).
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M. A. Nahmias, B. J. Shastri, A. N. Tait, and P. R. Prucnal, “A leaky integrate-and-fire laser neuron for ultrafast cognitive computing,” IEEE J. Sel. Top. Quantum Electron. 19, 1–12 (2013).
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W. A. Zortman, A. L. Lentine, D. C. Trotter, and M. R. Watts, “Bit-error-rate monitoring for active wavelength control of resonant modulators,” IEEE Micro 33, 42–52 (2013).
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D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photonics Rev. 7, 506–538 (2013).
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S. Friedmann, N. Frémaux, J. Schemmel, W. Gerstner, and K. Meier, “Reward-based learning under hardware constraints - using a RISC processor embedded in a neuromorphic substrate,” Front. Neurosci. 7, 160 (2013).
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Y. Wang, J. Flueckiger, C. Lin, and L. Chrostowski, “Universal grating coupler design,” Proc. SPIE 8915, 89150Y (2013).
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M. Hochberg, N. C. Harris, R. Ding, Y. Zhang, A. Novack, Z. Xuan, and T. Baehr-Jones, “Silicon photonics: The next fabless semiconductor industry,” IEEE Solid-State Circ. Mag. 5, 48–58 (2013).
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2012 (2)

T. Pfeil, T. Potjans, S. Schrader, W. Potjans, J. Schemmel, M. Diesmann, and K. Meier, “Is a 4-bit synaptic weight resolution enough? – constraints on enabling spike-timing dependent plasticity in neuromorphic hardware,” Front. Neurosci. 6, 90 (2012).
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J. S. Orcutt, B. Moss, C. Sun, J. Leu, M. Georgas, J. Shainline, E. Zgraggen, H. Li, J. Sun, M. Weaver, S. Urošević, M. Popović, R. J. Ram, and V. Stojanović, “Open foundry platform for high-performance electronic-photonic integration,” Opt. Express 20, 12222–12232 (2012).
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2006 (2)

A. J. Seeds and K. J. Williams, “Microwave photonics,” J. Lightw. Technol. 24, 4628–4641 (2006).
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G. Cowan, R. Melville, and Y. Tsividis, “A VLSI analog computer/digital computer accelerator,” IEEE J. Solid-State Circuits 41, 42–53 (2006).
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R. Genov and G. Cauwenberghs, “Charge-mode parallel architecture for vector-matrix multiplication,” IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process. (1993–2003) 48, 930–936 (2001).
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D. Psaltis and Y. Quio, “Optical neural networks,” Opt. Photon. News 1, 17–21 (1990).
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R. W. Keyes, “Optical logic-in the light of computer technology,” Optica Acta 32, 525–535 (1985).
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Alvarez-Icaza, R.

F. Akopyan, J. Sawada, A. Cassidy, R. Alvarez-Icaza, J. Arthur, P. Merolla, N. Imam, Y. Nakamura, P. Datta, G.-J. Nam, B. Taba, M. Beakes, B. Brezzo, J. Kuang, R. Manohar, W. Risk, B. Jackson, and D. Modha, “TrueNorth: Design and tool flow of a 65 mW 1 million neuron programmable neurosynaptic chip,” IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 34, 1537–1557 (2015).
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A. Annoni, E. Guglielmi, M. Carminati, G. Ferrari, M. Sampietro, D. A. Miller, A. Melloni, and F. Morichetti, “Unscrambling light—automatically undoing strong mixing between modes,” Light Sci. Appl. 6, e17110 (2017).
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M. Carminati, A. Annoni, F. Morichetti, E. Guglielmi, G. Ferrari, D. O. M. de Aguiar, A. Melloni, and M. Sampietro, “Design guidelines for contactless integrated photonic probes in dense photonic circuits,” J. Lightw. Technol. 35, 3042–3049 (2017).
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S. Grillanda, M. Carminati, F. Morichetti, P. Ciccarella, A. Annoni, G. Ferrari, M. Strain, M. Sorel, M. Sampietro, and A. Melloni, “Non-invasive monitoring and control in silicon photonics using cmos integrated electronics,” Optica 1, 129–136 (2014).
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F. Akopyan, J. Sawada, A. Cassidy, R. Alvarez-Icaza, J. Arthur, P. Merolla, N. Imam, Y. Nakamura, P. Datta, G.-J. Nam, B. Taba, M. Beakes, B. Brezzo, J. Kuang, R. Manohar, W. Risk, B. Jackson, and D. Modha, “TrueNorth: Design and tool flow of a 65 mW 1 million neuron programmable neurosynaptic chip,” IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 34, 1537–1557 (2015).
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B. Romeira, R. Avó, J. M. L. Figueiredo, S. Barland, and J. Javaloyes, “Regenerative memory in time-delayed neuromorphic photonic resonators,” Sci. Rep. 6, 19510 (2016).
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V. K. Narayana, S. Sun, A.-H. A. Badawy, V. J. Sorger, and T. El-Ghazawi, “MorphoNoC: Exploring the design space of a configurable hybrid NoC using nanophotonics,” Microprocess. Microsyst. 50, 113 (2017).
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Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljačić, “Deep learning with coherent nanophotonic circuits,” Nat. Photon. 11, 441–446 (2017).
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N. C. Harris, D. Bunandar, M. Pant, G. R. Steinbrecher, J. Mower, M. Prabhu, T. Baehr-Jones, M. Hochberg, and D. Englund, “Large-scale quantum photonic circuits in silicon,” Nanophotonics 5, 456 (2016).
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M. Hochberg, N. C. Harris, R. Ding, Y. Zhang, A. Novack, Z. Xuan, and T. Baehr-Jones, “Silicon photonics: The next fabless semiconductor industry,” IEEE Solid-State Circ. Mag. 5, 48–58 (2013).
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F. Selmi, R. Braive, G. Beaudoin, I. Sagnes, R. Kuszelewicz, and S. Barbay, “Relative refractory period in an excitable semiconductor laser,” Phys. Rev. Lett. 112, 183902 (2014).
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B. Romeira, R. Avó, J. M. L. Figueiredo, S. Barland, and J. Javaloyes, “Regenerative memory in time-delayed neuromorphic photonic resonators,” Sci. Rep. 6, 19510 (2016).
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N. C. Harris, D. Bunandar, M. Pant, G. R. Steinbrecher, J. Mower, M. Prabhu, T. Baehr-Jones, M. Hochberg, and D. Englund, “Large-scale quantum photonic circuits in silicon,” Nanophotonics 5, 456 (2016).
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A. Annoni, E. Guglielmi, M. Carminati, G. Ferrari, M. Sampietro, D. A. Miller, A. Melloni, and F. Morichetti, “Unscrambling light—automatically undoing strong mixing between modes,” Light Sci. Appl. 6, e17110 (2017).
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Figures (10)

Fig. 1
Fig. 1 a) An isolated microring weight bank. Input signals, xi, are power modulated onto WDM carriers and multiplexed. Each is weighted by one tunable MRR weight, µi, whose value is the difference of complementary thru and drop port transmissions. A balanced photodetector produces their weighted sum. b) A recurrent silicon photonic broadcast-and-weight network. WDM pumps are multiplexed off-chip and modulated by MRR modulator-class photonic neurons. Connections between neurons are controlled by MRR weights in a square matrix. Balanced photodetectors drive the neurons, which are biased by Vbias and Rrec.
Fig. 2
Fig. 2 a) Picture of one N-doped microring. b) Cross section of microring showing etch geometry and dopant pattern. c) Picture of photonic weight bank with two N-doped microring weights. The weight MRRs are tuned by current sources with voltage sense, and other MRRs for sensing are unused. The common voltage is across the parasitic resistance of the common ground connection. d) Experimental setup for generating 1Gbps independently modulated WDM inputs [62]. Weights are measured by a balanced photodiode connected to an oscilloscope.
Fig. 3
Fig. 3 (a–d) Electrical response to bias current (a, c) and nominal power (b, d) with the DFB laser on (red) and off (blue). Resistance is dependent on temperature changes due to ohmic heating and on the presence of circulating optical power. The meanings of several device and control variables are illustrated. (e–g) Optical properties of the resonator vs. bias. To first order, wavelength shifts (e) are a quadratic function of current. Above a bias of 0.6mA, extinction ratio (f) and Q factor (g) begin to degrade due to additional loss in the heater.
Fig. 4
Fig. 4 Concept of feedback control and control evaluation. In feedforward control, there is no sensor path from the device back to the controller.
Fig. 5
Fig. 5 a) Simplified control model. Feedback control occurs in the domain of δ D ^, which are invertible functions of current and voltage. b) Illustration of the feedback control rule. First, an estimated transmission is requested. Then, the controller performs a binary search for the commanded value over the δ domain. The converged value of δ becomes the commanded value for the thermoelectric control step. Blue, dotted curve: Example measurement of D ^ vs. δ. This curve is not measured during calibration because it can shift horizontally with environmental fluctuations.
Fig. 6
Fig. 6 1D command-control evaluations of accuracy (accu., center-red lines) and precision (prec., high/low-blue lines) at 24°C and 26°C. The actual measured weight, µ, is plotted against desired command weights, μ ^, and compared to the ideal target (black dashed lines). In (a)–(b), the optical weight edge is not directly measured during calibration (Step 3.5: edge calibration), while, in (c)–(d) the weight edge calibration is performed.
Fig. 7
Fig. 7 Evaluation of two-channel command and control, following the format of [52], Fig. 4. Black grid crossings: desired weight vectors. Red arrows: offset between desired and the mean of actual weights over 3 repetitions. Blue ellipses: variance of actual weight values over the repetitions. a) Without the weight edge calibration (Step 3.5) the accuracy is 4.2 bits. b) With edge calibration, the accuracy is 5.1 bits. Accuracy is worse at negative weights because this corresponds to the more sensitive on-resonance point.
Fig. 8
Fig. 8 Saturation characteristic of a N-doped weight. (a–b) A sweep through relative tuning, normalized to HWHM, over a range of input laser powers (input laser colors in legend). a) Change in voltage away from the nominal value expected in absence of a laser; b) Transmission of the drop port measured directly by a power meter. c) Peak photoresponse on-resonance as a function of the laser power, where the black line represents proportionality. d) Actual transmission, from (b), plotted against estimated transmission, a function of (a), where the solid black line represents an ideal estimate.
Fig. 9
Fig. 9 Transmission and photoresponse for a range of initial laser wavelength detunings. a) Change in measured voltage away from baseline. b) Actual transmission measured by a power meter. c) Actual transmission, D, from (b) plotted against estimated transmission, where the solid black line represents an ideal estimate.
Fig. 10
Fig. 10 Physical model of the N-doped heater embedded in a MRR with an incident laser. Red: fluctuating source of variability, Blue: fixed sources of variability. Feedforward control would require high-fidelity modeling of this system, but the feedback control model, shown in Fig. 5, can use a vastly simplified. The effects of varying laser wavelength and power parameters are examined in Sec. 5.

Tables (3)

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Table 1 Control variables

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Table 2 Calibrated parameters used during control

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Table 3 Accuracy and precision of weight control strategies

Equations (24)

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X = [ x 1 , [ t = 1 ] x 2 , [ t = 1 ] x N , [ t = 1 ] x 1 , [ t = 2 ] x 2 , [ t = 2 ] x N , [ t = 2 ]       ]
= [ x 1 , x 2 , , x N ]
μ ^ = X + y
μ D D ^ δ feedback control rule P _ I
I i = I s e t 0 ; I j i = 0
R c o m m , j i = V j , m e a s / I s e t j
δ P _ P _ r e s P h w h m
P = I V = I 2 R ( Ohm s law , Joule s low )
R = R 0 ( 1 + β Δ T ) ( Temperature-dependent resistance )
Δ T = z P + Δ T e n v i r o n m e n t a l ( Temperature )
R _ R 0 ( 1 + α P )
P _ I 2 R 0 1 α I 2 R 0
D = ( λ r λ c a r r i e r H W H M [ λ ] ) ( Resonator transmission )
λ r = λ 0 + k Δ T ( Thermo-optic resonance shift )
a = u D p c a r r i e r ( Photo absorption )
a max = u p c a r r i e r
D D max = D = a a max
V = V _ f ( a ) (Photovoltage)
D ^ = ( Δ V Δ V max ) 2
D = g ( D ^ )
μ = 1 2 D
V G N D 0 V i , c o m m
V i , m e a s = V i , h e a t e r + V i , c o m m
V i , c o m m = Σ j R c o m m , i j I j

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