Abstract

The advances in fabrication processes in different material platforms employed in integrated optics are opening the path towards the implementation of circuits with increasing degrees of complexity. In addition to the more conventional application specific photonic circuit paradigm, the programmable multifunctional photonics (PMP) approach is a transversal concept inspired by similar approaches, which are already employed in other technology fields. For instance, in electronics, field programmable gate array devices enable a much more flexible universal operation as compared to application specific integrated circuits. In photonics, the PMP concept is enabled by two-dimensional (2D) waveguide meshes for which the number of possible input/outputs ports quickly builds up, and, furthermore, internal signal flow paths make the computation of transfer functions an intractable problem. Here we report a scalable method based on mathematical induction that allows one to obtain the scattering matrix of any 2D integrated photonic waveguide mesh circuit composed of an arbitrary number of cells and that is easily programmable. To our knowledge this is the first report of the kind, and our results open the path to unblocking this important design bottleneck.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (4)

Y. Shen, M. H. N. Hattink, P. Samadi, Q. Cheng, Z. Hu, A. Gazman, and K. Bergman, “Software-defined networking control plane for seamless integration of multiple silicon photonic switches in Datacom networks,” Opt. Express 26, 10914–10929 (2018).
[Crossref]

H. Peng, M. A. Nahmias, T. F. de Lima, A. N. Tait, and B. J. Shastri, “Neuromorphic photonic integrated circuits,” IEEE J. Sel. Top. Quantum Electron. 24, 6101715 (2018).
[Crossref]

G. Harari, M. A. Bandres, Y. Lumer, M. C. Rechtsman, Y. D. Chong, M. Khajavikhan, D. N. Christodoulides, and M. Segev, “Topological insulator laser: theory,” Science 359, eaar4003 (2018).
[Crossref]

M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Topological insulator laser: experiments,” Science 359, eaar4005 (2018).
[Crossref]

2017 (6)

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. Photonics 11, 441–446 (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]

D. Pérez, I. Gasulla, F. J. Fraile, L. Crudgington, D. J. Thomson, A. Z. Khokhar, K. Li, W. Cao, G. Z. Mashanovich, and J. Capmany, “Silicon photonics rectangular universal interferometer,” Laser Photon. Rev. 11, 1700219 (2017).
[Crossref]

R. Burgwal, W. R. Clements, D. H. Smith, J. C. Gates, W. S. Kolthammer, J. J. Renema, and I. A. Walmsley, “Using an imperfect photonic network to implement random unitaries,” Opt. Express 25, 28236–28245 (2017).
[Crossref]

F. Flamini, N. Spagnolo, N. Viggianiello, A. Crespi, R. Osellame, and F. Sciarrino, “Benchmarking integrated linear-optic architectures for quantum information processing,” Sci. Rep. 7, 15133 (2017).
[Crossref]

J. S. Fandiño, D. Domenech, P. Muñoz, and J. Capmany, “A monolithic integrated photonic microwave filter,” Nat. Photonics 11, 124–129 (2017).
[Crossref]

2016 (7)

O. Graydon, “Birth of the programmable optical chip,” Nat. Photonics 10, 1 (2016).
[Crossref]

J. Capmany, I. Gasulla, and D. Perez, “Microwave photonics: the programmable processor,” Nat. Photonics 10, 6–8 (2016).
[Crossref]

D. Pérez, I. Gasulla, J. Capmany, and R. A. Soref, “Reconfigurable lattice mesh designs for programmable photonic processors,” Opt. Express 24, 12093–12106 (2016).
[Crossref]

W. R. Clements, P. C. Humphreys, B. J. Metcalf, W. S. Kolthammer, and I. A. Walmsley, “Optimal design for universal multiport interferometers,” Optica 3, 1460–1465 (2016).
[Crossref]

T. Ozawa, H. M. Price, N. Goldman, O. Zilberberg, and I. Carusotto, “Synthetic dimensions in integrated photonics: from optical isolation to four-dimensional quantum Hall physics,” Phys. Rev. A 93, 043827 (2016).
[Crossref]

H. G. De Chatellus, L. R. Cortés, and J. Azaña, “Optical real-time Fourier transformation with kilohertz resolutions,” Optica 3, 1–8 (2016).
[Crossref]

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, 456–468 (2016).
[Crossref]

2015 (3)

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528, 534–538 (2015).
[Crossref]

L. Zhuang, C. G. H. Roeloffzen, M. Hoekman, K.-J. Boller, and A. J. Lowery, “Programmable photonic signal processor chip for radiofrequency applications,” Optica 2, 854–859 (2015).
[Crossref]

D. A. B. Miller, “Perfect optics with imperfect components,” Optica 2, 747–750 (2015).
[Crossref]

2014 (1)

2013 (5)

D. A. B. Miller, “Self-configuring universal linear optical component,” Photon. Res. 1, 1–15 (2013).
[Crossref]

D. A. B. Miller, “Self-aligning universal beam coupler,” Opt. Express 21, 6360–6370 (2013).
[Crossref]

J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X. M. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339, 798–801 (2013).
[Crossref]

M. A. Broome, A. Fedrizzi, S. Rahimi-Keshari, J. Dove, S. Aaronson, T. C. Ralph, and A. G. White, “Photonic boson sampling in a tunable circuit,” Science 339, 794–798 (2013).
[Crossref]

A. Crespi, R. Osellame, R. Ramponi, D. J. Brod, E. F. Galvão, N. Spagnolo, C. Vitelli, E. Maiorino, P. Mataloni, and F. Sciarrino, “Integrated multimode interferometers with arbitrary designs for photonic boson sampling,” Nat. Photonics 7, 545–549 (2013).
[Crossref]

2012 (3)

Y. Shen, M. H. N. Hattink, P. Samadi, Q. Cheng, Z. Hu, A. Gazman, and K. Bergman, “Novel microwave photonic fractional Hilbert transformer using a ring resonator-based optical all-pass filter,” Opt. Express 20, 26499–26510 (2012).
[Crossref]

M. C. Estevez, M. Alvarez, and L. Lechuga, “Integrated optical devices for lab-on-a-chip biosensing applications,” Laser Photon. Rev. 6, 463–487 (2012).
[Crossref]

R. Heideman, M. Hoekman, and E. Schreuder, “TriPleX-based integrated optical ring resonators for lab-on-a-chip and environmental detection,” IEEE J. Sel. Top. Quantum Electron. 18, 1583–1596 (2012).
[Crossref]

2011 (1)

M. G. Thompson, A. Politi, J. C. Matthews, and J. L. O’Brien, “Integrated waveguide circuits for optical quantum computing,” IET Circuits Devices Syst. 5, 94–102 (2011).
[Crossref]

2010 (3)

K. Kieling, J. L. O’Brien, and J. Eisert, “On photonic controlled phase gates,” New J. Phys. 12, 013003 (2010).
[Crossref]

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1, 29 (2010).
[Crossref]

B. P. Lanyon, J. D. Whitfield, G. G. Gillett, M. E. Goggin, M. P. Almeida, I. Kassal, J. D. Biamonte, M. Mohseni, B. J. Powell, M. Barbieri, A. Aspuru-Guzik, and A. G. White, “Towards quantum chemistry on a quantum computer,” Nat. Chem. 2, 106–111 (2010).
[Crossref]

2009 (2)

J. L. O’Brien, A. Furusawa, and J. Vučković, “Photonic quantum technologies,” Nat. Photonics 3, 687–695 (2009).
[Crossref]

A. Politi, J. Matthews, M. G. Thompson, and J. L. O’Brien, “Integrated quantum photonics,” IEEE J. Sel. Top. Quantum Electron. 15, 1673–1684 (2009).
[Crossref]

2008 (1)

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
[Crossref]

2007 (1)

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[Crossref]

2001 (1)

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[Crossref]

2000 (1)

1996 (1)

K. Jinguji, “Synthesis of coherent two-port optical delay-line circuit with ring waveguides,” J. Lightwave Technol. 14, 1882–1898 (1996).
[Crossref]

1995 (1)

K. Jinguji, “Synthesis of coherent two-port lattice-form optical delay-line circuit,” J. Lightwave Technol. 13, 73–82 (1995).
[Crossref]

1994 (1)

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73, 58–61 (1994).
[Crossref]

Aaronson, S.

M. A. Broome, A. Fedrizzi, S. Rahimi-Keshari, J. Dove, S. Aaronson, T. C. Ralph, and A. G. White, “Photonic boson sampling in a tunable circuit,” Science 339, 794–798 (2013).
[Crossref]

Alloatti, L.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528, 534–538 (2015).
[Crossref]

Almeida, M. P.

B. P. Lanyon, J. D. Whitfield, G. G. Gillett, M. E. Goggin, M. P. Almeida, I. Kassal, J. D. Biamonte, M. Mohseni, B. J. Powell, M. Barbieri, A. Aspuru-Guzik, and A. G. White, “Towards quantum chemistry on a quantum computer,” Nat. Chem. 2, 106–111 (2010).
[Crossref]

Alvarez, M.

M. C. Estevez, M. Alvarez, and L. Lechuga, “Integrated optical devices for lab-on-a-chip biosensing applications,” Laser Photon. Rev. 6, 463–487 (2012).
[Crossref]

Annoni, A.

Asanovic, K.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528, 534–538 (2015).
[Crossref]

Aspuru-Guzik, A.

B. P. Lanyon, J. D. Whitfield, G. G. Gillett, M. E. Goggin, M. P. Almeida, I. Kassal, J. D. Biamonte, M. Mohseni, B. J. Powell, M. Barbieri, A. Aspuru-Guzik, and A. G. White, “Towards quantum chemistry on a quantum computer,” Nat. Chem. 2, 106–111 (2010).
[Crossref]

Atabaki, A. H.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528, 534–538 (2015).
[Crossref]

Avizienis, R. R.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528, 534–538 (2015).
[Crossref]

Azaña, J.

H. G. De Chatellus, L. R. Cortés, and J. Azaña, “Optical real-time Fourier transformation with kilohertz resolutions,” Optica 3, 1–8 (2016).
[Crossref]

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1, 29 (2010).
[Crossref]

Baehr-Jones, T.

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. Photonics 11, 441–446 (2017).
[Crossref]

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, 456–468 (2016).
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C. Taddei, N. T. H. Yen, L. Zhuang, M. Hoekman, A. Leinse, R. Heideman, P. Van Dijk, and C. H. G. Roeloffzen, “Waveguide filter-based on-chip differentiator for microwave photonic signal processing,” in IEEE International Topical Meeting on Microwave Photonics, Alexandria, Virginia, USA (2013), pp. 28–31.

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach, 1st ed. (Wiley, 1999).

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Supplementary Material (1)

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Figures (7)

Fig. 1.
Fig. 1. Trilattice building block for 2D hexagonal waveguide meshes and increased complexity in the required number of input/output and internal nodes. (a) Trilattice composed of three TBUs and associated symbol, (b) two trilattices interconnected by the optical node P1, (c) three trilattices creating a closed hexagonal cell, and (d) eight trilattices interconnected to obtain a four-cell count waveguide mesh. (e) The number of optical nodes (ON) and optical ports versus the number of closed cells (C) in a waveguide mesh photonic integrated circuit (IC) in the equation stands for the number of closed cells surrounded by closed cells.
Fig. 2.
Fig. 2. Inductive method description for obtaining the scattering matrix H(n) of a hexagonal 2D waveguide mesh composed of n basic trilattice units by addition of one trilattice unit H(1) to a hexagonal 2D waveguide mesh composed of n1 basic trilattice units H(n1) and general signal flowgraph for its implementation. (a) Interconnection scenario 0. (b) Interconnection scenario 1. (c) Interconnection scenario 2. (d) Interconnection scenario 3.
Fig. 3.
Fig. 3. Scalable analysis method application to single wavelength operation of waveguide mesh configuration for universal linear interferometers. (a) Mesh architecture and configuration for simultaneously implementing 3×3 and 4×4 linear transformations. (b) Equivalent circuit layouts with indication of the input and output ports in red ink. (c) Moduli and phases of all the 40×40 matrix coefficients when the 3×3 and 4×4 transformations are programmed to implement a DFT and a 2×4 optical hybrid, respectively. (d) Moduli and phases of all the 40×40 matrix coefficients when the 3×3 and 4×4 transformations are programmed to implement a three-way beamsplitter and a 4×4 Hadamard matrix, respectively.
Fig. 4.
Fig. 4. Scalable analysis method application to full spectral analysis of a waveguide mesh implementing a feedforward/feedbackward SCISSOR filter composed of five cascaded ring resonators with the same cavity length (six BULs). (a) Mesh architecture and configuration for implementing the SCISSOR filter. (b) Equivalent circuit layouts with indication of the input and output ports in red ink (upper). Moduli of the 40 transfer functions obtained after multiplying the 40×40 matrix of spectral transfer functions by the input vector I=(i1,i2,i40), where ik=0, k16 and i16=1 for the case in which K=0.2 and ϕ1=ϕ2=ϕ3=ϕ4=ϕ5=0 (upper trace). Phase response of h34,16 (intermediate trace) and spectral response h34,16 (lower trace) for two different cases in which the SCISSOR parameters are changed. Case 1: K=0.2 in all the rings and ring resonances are slightly detuned, ϕ1=0.12, ϕ2=0.06, ϕ3=0, ϕ4=0.06, and ϕ5=0.12, to reduce the filter bandpass and main to secondary sidelobes. Second case: coupling constants are apodized, K1=0.39, K2=0.47, K3=0.55, K4=0.63, and K5=0.71, and the ring resonances are strongly detuned, ϕ1=0.4, ϕ2=0.2, ϕ3=0, ϕ4=0.2, and ϕ5=0.4.
Fig. 5.
Fig. 5. Scalable analysis method application to multiparameter error analysis of a waveguide mesh implementing a feedforward/feedbackward double ring loaded MZI with cavity lengths (six BULs). (a) Mesh architecture and configuration for implementing the double ring loaded MZI. (b) Equivalent circuit layout with indication of the input and output ports in red ink. (c)–(f) Results of the Monte Carlo analysis of the spectral transfer function h35,16 after 1000 realizations, where each TBU coupling constant is modeled by means of a Gaussian random variable centered at a mean value corresponding to its ideal setting and featuring a standard deviation σK=0.1 accounting for random fluctuations around the mean. (c) Spectral transfer function realizations, (d) filter extinction ratio statistics, (e) filter passband ripple statistics, and (f) filter insertion loss statistics.
Fig. 6.
Fig. 6. Scalable analysis method application to circuit parameter optimization of a waveguide mesh implementing simultaneously a three-stage CROW with cavity lengths (six BULs) and a MZI. (a) Mesh architecture and configuration for implementing the two circuits. (b) Equivalent circuit layouts with indication of the input and output ports in red ink. (c) Monte Carlo results (1000 runs with σK=0.01) for the spectral transfer functions of the two circuits before optimization. (d) Monte Carlo results for the spectral transfer functions of the two circuits after optimization. (e) Statistical results for crosstalk levels corresponding to transfer functions h30,2, h23,2, h38,17, and h39,17 before optimization and (f) after optimization. (g) Crosstalk levels for different values of standard deviation values of the coupling coefficients σK.
Fig. 7.
Fig. 7. Experimental validation of the model. (a) Programmed waveguide mesh and targeted circuit: optical ring resonator of cavity length equal to six BULs. (b) Experimental (solid) and modeled (dashed) response for different circuit conditions of coupling and phase. (c) Programmed waveguide mesh and targeted circuit: CROW with two ring resonators slightly decoupled. (d) Experimental and modeled response for different phase detuning conditions. (e) Photograph of the fabricated device reported in [8].

Equations (2)

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HDFT3=13(1111ei2π/3ei2π/31ei2π/3ei2π/3),HHybrid=12(111111ii).
HTritter=13(1111ei2π/3ei4π/31ei4π/3ei8π/3),HHad=122(1111111111111111).