Abstract

We show how to design an optical device that can perform any linear function or coupling between inputs and outputs. This design method is progressive, requiring no global optimization. We also show how the device can configure itself progressively, avoiding design calculations and allowing the device to stabilize itself against drifts in component properties and to continually adjust itself to changing conditions. This self-configuration operates by training with the desired pairs of orthogonal input and output functions, using sets of detectors and local feedback loops to set individual optical elements within the device, with no global feedback or multiparameter optimization required. Simple mappings, such as spatial mode conversions and polarization control, can be implemented using standard planar integrated optics. In the spirit of a universal machine, we show that other linear operations, including frequency and time mappings, as well as nonreciprocal operation, are possible in principle, even if very challenging in practice, thus proving there is at least one constructive design for any conceivable linear optical component; such a universal device can also be self-configuring. This approach is general for linear waves, and could be applied to microwaves, acoustics, and quantum mechanical superpositions.

© 2013 Chinese Laser Press

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    [CrossRef]
  34. P. P. Baveja, Y. Xiao, S. Arora, G. P. Agrawal, and D. N. Maywar, “All-optical semiconductor optical amplifier-based wavelength converters with sub-mW pumping,” IEEE Photon. Technol. Lett. 25, 78–80 (2013).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  45. Z. Wang and S. H. Fan, “Optical circulators in two-dimensional magneto-optical photonic crystals,” Opt. Lett. 30, 1989–1991 (2005).
    [CrossRef]
  46. S. Kawanishi, “Ultrahigh-speed optical time-division-multiplexed transmission technology based on optical signal processing,” IEEE J. Quantum Electron. 34, 2064–2079 (1998).
    [CrossRef]
  47. E. Palushani, H. C. Hansen Mulvad, M. Galili, H. Hu, L. K. Oxenløwe, A. T. Clausen, and P. Jeppesen, “OTDM-to-WDM conversion based on time-to-frequency mapping by time-domain optical Fourier transformation,” IEEE J. Sel. Top. Quantum Electron. 18, 681–688 (2012).
    [CrossRef]

2013

D. A. B. Miller, “How complicated must an optical component be?,” J. Opt. Soc. Am. A 30, 238–251 (2013).
[CrossRef]

V. Liu, D. A. B. Miller, and S. H. Fan, “Highly tailored computational electromagnetics methods for nanophotonic design and discovery,” Proc. IEEE 101, 484–493 (2013).
[CrossRef]

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

P. P. Baveja, Y. Xiao, S. Arora, G. P. Agrawal, and D. N. Maywar, “All-optical semiconductor optical amplifier-based wavelength converters with sub-mW pumping,” IEEE Photon. Technol. Lett. 25, 78–80 (2013).
[CrossRef]

2012

R. N. Mahalati, D. Askarov, J. P. Wilde, and J. M. Kahn, “Adaptive control of input field to achieve desired output intensity profile in multimode fiber with random mode coupling,” Opt. Express 20, 14321–14337 (2012).
[CrossRef]

P. Markov, J. G. Valentine, and S. M. Weiss, “Fiber-to-chip coupler designed using an optical transformation,” Opt. Express 20, 14705–14713 (2012).
[CrossRef]

D. Dai, Y. Tang, and J. E. Bowers, “Mode conversion in tapered submicron silicon ridge optical waveguides,” Opt. Express 20, 13425–13439 (2012).
[CrossRef]

S. H. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on ‘Nonreciprocal light propagation in a silicon photonic circuit’,” Science 335, 38 (2012).
[CrossRef]

D. A. B. Miller, “All linear optical devices are mode converters,” Opt. Express 20, 23985–23993 (2012).
[CrossRef]

T. Su, R. P. Scott, S. S. Djordjevic, N. K. Fontaine, D. J. Geisler, X. Cai, and S. J. B. Yoo, “Demonstration of free space coherent optical communication using integrated silicon photonic orbital angular momentum devices,” Opt. Express 20, 9396–9402 (2012).
[CrossRef]

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96 km of few-mode fiber using coherent 6×6 MIMO processing,” J. Lightwave Technol. 30, 521–531 (2012).
[CrossRef]

E. Palushani, H. C. Hansen Mulvad, M. Galili, H. Hu, L. K. Oxenløwe, A. T. Clausen, and P. Jeppesen, “OTDM-to-WDM conversion based on time-to-frequency mapping by time-domain optical Fourier transformation,” IEEE J. Sel. Top. Quantum Electron. 18, 681–688 (2012).
[CrossRef]

2011

M. P. J. Lavery, A. Dudley, A. Forbes, J. Courtial, and M. J. Padgett, “Robust interferometer for the routing of light beams carrying orbital angular momentum,” New J. Phys. 13, 093014 (2011).
[CrossRef]

T. Tanemura, K. C. Balram, D.-S. Ly-Gagnon, P. Wahl, J. S. White, M. L. Brongersma, and D. A. B. Miller, “Multiple-wavelength focusing of surface plasmons with a nonperiodic nanoslit coupler,” Nano Lett. 11, 2693–2698 (2011).
[CrossRef]

V. Liu, Y. Jiao, D. A. B. Miller, and S. Fan, “Design methodology for compact photonic-crystal-based wavelength division multiplexers,” Opt. Lett. 36, 591–593 (2011).
[CrossRef]

L. H. Gabrielli and M. Lipson, “Integrated Luneburg lens via ultra-strong index gradient on silicon,” Opt. Express 19, 20122–20127 (2011).
[CrossRef]

M.-C. Wu, F.-C. Hsiao, and S.-Y. Tseng, “Adiabatic mode conversion in multimode waveguides using chirped computer-generated planar holograms,” IEEE Photon. Technol. Lett. 23, 807–809 (2011).
[CrossRef]

2010

J. B. Khurgin, “Slow light in various media: a tutorial,” Adv. Opt. Photon. 2, 287–318 (2010).
[CrossRef]

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9, 387–396 (2010).
[CrossRef]

2009

2006

C. K. Madsen, “Boundless-range optical phase modulator for high-speed frequency-shift heterodyne applications,” J. Lightwave Technol. 24, 2760–2767 (2006).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[CrossRef]

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
[CrossRef]

D. A. B. Miller, “On perfect cloaking,” Opt. Express 14, 12457–12466 (2006).
[CrossRef]

2005

2004

L. Hesselink, S. S. Orlov, and M. C. Bashaw, “Holographic data storage systems,” Proc. IEEE 92, 1231–1280 (2004).
[CrossRef]

M. Gerken and D. A. B. Miller, “Multilayer thin-film stacks with steplike spatial beam shifting,” J. Lightwave Technol. 22, 612–618 (2004).
[CrossRef]

2003

2000

1999

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, “1.5 μm-band wavelength conversion based on cascaded second-order nonlinearity in LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 11, 653–655 (1999).
[CrossRef]

1998

S. Kawanishi, “Ultrahigh-speed optical time-division-multiplexed transmission technology based on optical signal processing,” IEEE J. Quantum Electron. 34, 2064–2079 (1998).
[CrossRef]

1994

F. Heismann, “Analysis of a reset-free polarization controller for fast automatic polarization stabilization in fiber-optic transmission systems,” J. Lightwave Technol. 12, 690–699 (1994).
[CrossRef]

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]

1992

1991

Y. Fujii, “High-isolation polarization-independent optical circulator coupled with single-mode fibers,” J. Lightwave Technol. 9, 456–460 (1991).
[CrossRef]

1982

P. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 199–299 (1982).
[CrossRef]

R. C. Alferness, “Waveguide electrooptic modulators,” IEEE Trans. Microwave Theory 30, 1121–1137 (1982).
[CrossRef]

1980

1978

A. Yariv, “Phase conjugate optics and real-time holography,” IEEE J. Quantum Electron. QE-14, 650–660 (1978).
[CrossRef]

1962

F. Buhrer, D. Baird, and E. M. Conwell, “Optical frequency shifting by electro-optic effect,” Appl. Phys. Lett. 1, 46–49 (1962).
[CrossRef]

Agrawal, G. P.

P. P. Baveja, Y. Xiao, S. Arora, G. P. Agrawal, and D. N. Maywar, “All-optical semiconductor optical amplifier-based wavelength converters with sub-mW pumping,” IEEE Photon. Technol. Lett. 25, 78–80 (2013).
[CrossRef]

Alferness, R. C.

R. C. Alferness, “Waveguide electrooptic modulators,” IEEE Trans. Microwave Theory 30, 1121–1137 (1982).
[CrossRef]

Arora, S.

P. P. Baveja, Y. Xiao, S. Arora, G. P. Agrawal, and D. N. Maywar, “All-optical semiconductor optical amplifier-based wavelength converters with sub-mW pumping,” IEEE Photon. Technol. Lett. 25, 78–80 (2013).
[CrossRef]

Askarov, D.

Baets, R.

S. H. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on ‘Nonreciprocal light propagation in a silicon photonic circuit’,” Science 335, 38 (2012).
[CrossRef]

F. Van Laere, W. Bogaerts, P. Dumon, G. Roelkens, D. Van Thourhout, and R. Baets, “Focusing polarization diversity grating couplers in silicon-on-insulator,” J. Lightwave Technol. 27, 612–618 (2009).
[CrossRef]

Baird, D.

F. Buhrer, D. Baird, and E. M. Conwell, “Optical frequency shifting by electro-optic effect,” Appl. Phys. Lett. 1, 46–49 (1962).
[CrossRef]

Balram, K. C.

T. Tanemura, K. C. Balram, D.-S. Ly-Gagnon, P. Wahl, J. S. White, M. L. Brongersma, and D. A. B. Miller, “Multiple-wavelength focusing of surface plasmons with a nonperiodic nanoslit coupler,” Nano Lett. 11, 2693–2698 (2011).
[CrossRef]

Bashaw, M. C.

L. Hesselink, S. S. Orlov, and M. C. Bashaw, “Holographic data storage systems,” Proc. IEEE 92, 1231–1280 (2004).
[CrossRef]

Baveja, P. P.

P. P. Baveja, Y. Xiao, S. Arora, G. P. Agrawal, and D. N. Maywar, “All-optical semiconductor optical amplifier-based wavelength converters with sub-mW pumping,” IEEE Photon. Technol. Lett. 25, 78–80 (2013).
[CrossRef]

Bernstein, H. J.

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]

Bertani, P.

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]

Bogaerts, W.

Bolle, C.

Bowers, J. E.

Boyd, R. W.

R. W. Boyd and D. J. Gauthier, “Controlling the velocity of light pulses,” Science 326, 1074–1077 (2009).
[CrossRef]

Brener, I.

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, “1.5 μm-band wavelength conversion based on cascaded second-order nonlinearity in LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 11, 653–655 (1999).
[CrossRef]

Brinkmeyer, E.

S. H. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on ‘Nonreciprocal light propagation in a silicon photonic circuit’,” Science 335, 38 (2012).
[CrossRef]

Brongersma, M. L.

T. Tanemura, K. C. Balram, D.-S. Ly-Gagnon, P. Wahl, J. S. White, M. L. Brongersma, and D. A. B. Miller, “Multiple-wavelength focusing of surface plasmons with a nonperiodic nanoslit coupler,” Nano Lett. 11, 2693–2698 (2011).
[CrossRef]

Buhl, L. L.

C. R. Doerr, N. K. Fontaine, M. Hirano, T. Sasaki, L. L. Buhl, and P. J. Winzer, “Silicon photonic integrated circuit for coupling to a ring-core multimode fiber for space-division multiplexing,” in European Conference on Optical Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.A.3.

Buhrer, F.

F. Buhrer, D. Baird, and E. M. Conwell, “Optical frequency shifting by electro-optic effect,” Appl. Phys. Lett. 1, 46–49 (1962).
[CrossRef]

Burrows, E. C.

Cai, X.

Chaban, E. E.

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, “1.5 μm-band wavelength conversion based on cascaded second-order nonlinearity in LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 11, 653–655 (1999).
[CrossRef]

Chan, C. T.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9, 387–396 (2010).
[CrossRef]

Chen, H.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9, 387–396 (2010).
[CrossRef]

Chou, M. H.

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, “1.5 μm-band wavelength conversion based on cascaded second-order nonlinearity in LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 11, 653–655 (1999).
[CrossRef]

Christman, S. B.

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, “1.5 μm-band wavelength conversion based on cascaded second-order nonlinearity in LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 11, 653–655 (1999).
[CrossRef]

Clausen, A. T.

E. Palushani, H. C. Hansen Mulvad, M. Galili, H. Hu, L. K. Oxenløwe, A. T. Clausen, and P. Jeppesen, “OTDM-to-WDM conversion based on time-to-frequency mapping by time-domain optical Fourier transformation,” IEEE J. Sel. Top. Quantum Electron. 18, 681–688 (2012).
[CrossRef]

Conwell, E. M.

F. Buhrer, D. Baird, and E. M. Conwell, “Optical frequency shifting by electro-optic effect,” Appl. Phys. Lett. 1, 46–49 (1962).
[CrossRef]

Courtial, J.

M. P. J. Lavery, A. Dudley, A. Forbes, J. Courtial, and M. J. Padgett, “Robust interferometer for the routing of light beams carrying orbital angular momentum,” New J. Phys. 13, 093014 (2011).
[CrossRef]

Dai, D.

Djordjevic, S. S.

Doerr, C. R.

S. H. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on ‘Nonreciprocal light propagation in a silicon photonic circuit’,” Science 335, 38 (2012).
[CrossRef]

C. R. Doerr, N. K. Fontaine, M. Hirano, T. Sasaki, L. L. Buhl, and P. J. Winzer, “Silicon photonic integrated circuit for coupling to a ring-core multimode fiber for space-division multiplexing,” in European Conference on Optical Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.A.3.

Dudley, A.

M. P. J. Lavery, A. Dudley, A. Forbes, J. Courtial, and M. J. Padgett, “Robust interferometer for the routing of light beams carrying orbital angular momentum,” New J. Phys. 13, 093014 (2011).
[CrossRef]

Dumon, P.

Eich, M.

S. H. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on ‘Nonreciprocal light propagation in a silicon photonic circuit’,” Science 335, 38 (2012).
[CrossRef]

Esmaeelpour, M.

Essiambre, R.-J.

Fan, S.

Fan, S. H.

V. Liu, D. A. B. Miller, and S. H. Fan, “Highly tailored computational electromagnetics methods for nanophotonic design and discovery,” Proc. IEEE 101, 484–493 (2013).
[CrossRef]

S. H. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on ‘Nonreciprocal light propagation in a silicon photonic circuit’,” Science 335, 38 (2012).
[CrossRef]

Z. Wang and S. H. Fan, “Optical circulators in two-dimensional magneto-optical photonic crystals,” Opt. Lett. 30, 1989–1991 (2005).
[CrossRef]

Y. Jiao, S. H. Fan, and D. A. B. Miller, “Demonstration of systematic photonic crystal device design and optimization by low rank adjustments: an extremely compact mode separator,” Opt. Lett. 30, 141–143 (2005).
[CrossRef]

Fejer, M. M.

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, “1.5 μm-band wavelength conversion based on cascaded second-order nonlinearity in LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 11, 653–655 (1999).
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Forbes, A.

M. P. J. Lavery, A. Dudley, A. Forbes, J. Courtial, and M. J. Padgett, “Robust interferometer for the routing of light beams carrying orbital angular momentum,” New J. Phys. 13, 093014 (2011).
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S. H. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on ‘Nonreciprocal light propagation in a silicon photonic circuit’,” Science 335, 38 (2012).
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R. W. Boyd and D. J. Gauthier, “Controlling the velocity of light pulses,” Science 326, 1074–1077 (2009).
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J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts, 2005).

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P. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 199–299 (1982).
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L. Hesselink, S. S. Orlov, and M. C. Bashaw, “Holographic data storage systems,” Proc. IEEE 92, 1231–1280 (2004).
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C. R. Doerr, N. K. Fontaine, M. Hirano, T. Sasaki, L. L. Buhl, and P. J. Winzer, “Silicon photonic integrated circuit for coupling to a ring-core multimode fiber for space-division multiplexing,” in European Conference on Optical Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.A.3.

Hsiao, F.-C.

M.-C. Wu, F.-C. Hsiao, and S.-Y. Tseng, “Adiabatic mode conversion in multimode waveguides using chirped computer-generated planar holograms,” IEEE Photon. Technol. Lett. 23, 807–809 (2011).
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E. Palushani, H. C. Hansen Mulvad, M. Galili, H. Hu, L. K. Oxenløwe, A. T. Clausen, and P. Jeppesen, “OTDM-to-WDM conversion based on time-to-frequency mapping by time-domain optical Fourier transformation,” IEEE J. Sel. Top. Quantum Electron. 18, 681–688 (2012).
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S. H. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on ‘Nonreciprocal light propagation in a silicon photonic circuit’,” Science 335, 38 (2012).
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E. Palushani, H. C. Hansen Mulvad, M. Galili, H. Hu, L. K. Oxenløwe, A. T. Clausen, and P. Jeppesen, “OTDM-to-WDM conversion based on time-to-frequency mapping by time-domain optical Fourier transformation,” IEEE J. Sel. Top. Quantum Electron. 18, 681–688 (2012).
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S. H. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on ‘Nonreciprocal light propagation in a silicon photonic circuit’,” Science 335, 38 (2012).
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S. H. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on ‘Nonreciprocal light propagation in a silicon photonic circuit’,” Science 335, 38 (2012).
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M. P. J. Lavery, A. Dudley, A. Forbes, J. Courtial, and M. J. Padgett, “Robust interferometer for the routing of light beams carrying orbital angular momentum,” New J. Phys. 13, 093014 (2011).
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V. Liu, D. A. B. Miller, and S. H. Fan, “Highly tailored computational electromagnetics methods for nanophotonic design and discovery,” Proc. IEEE 101, 484–493 (2013).
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R. Loudon, The Quantum Theory of Light, 3rd ed. (Oxford, 2000), pp. 88–91.

Ly-Gagnon, D.-S.

T. Tanemura, K. C. Balram, D.-S. Ly-Gagnon, P. Wahl, J. S. White, M. L. Brongersma, and D. A. B. Miller, “Multiple-wavelength focusing of surface plasmons with a nonperiodic nanoslit coupler,” Nano Lett. 11, 2693–2698 (2011).
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Madsen, C. K.

Mahalati, R. N.

Markov, P.

Maywar, D. N.

P. P. Baveja, Y. Xiao, S. Arora, G. P. Agrawal, and D. N. Maywar, “All-optical semiconductor optical amplifier-based wavelength converters with sub-mW pumping,” IEEE Photon. Technol. Lett. 25, 78–80 (2013).
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McCurdy, A. H.

Melloni, A.

S. H. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on ‘Nonreciprocal light propagation in a silicon photonic circuit’,” Science 335, 38 (2012).
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Miller, D. A. B.

V. Liu, D. A. B. Miller, and S. H. Fan, “Highly tailored computational electromagnetics methods for nanophotonic design and discovery,” Proc. IEEE 101, 484–493 (2013).
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D. A. B. Miller, “Self-aligning universal beam coupler,” Opt. Express 21, 6360–6370 (2013).
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D. A. B. Miller, “How complicated must an optical component be?,” J. Opt. Soc. Am. A 30, 238–251 (2013).
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D. A. B. Miller, “All linear optical devices are mode converters,” Opt. Express 20, 23985–23993 (2012).
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V. Liu, Y. Jiao, D. A. B. Miller, and S. Fan, “Design methodology for compact photonic-crystal-based wavelength division multiplexers,” Opt. Lett. 36, 591–593 (2011).
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T. Tanemura, K. C. Balram, D.-S. Ly-Gagnon, P. Wahl, J. S. White, M. L. Brongersma, and D. A. B. Miller, “Multiple-wavelength focusing of surface plasmons with a nonperiodic nanoslit coupler,” Nano Lett. 11, 2693–2698 (2011).
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D. A. B. Miller, “On perfect cloaking,” Opt. Express 14, 12457–12466 (2006).
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Y. Jiao, S. H. Fan, and D. A. B. Miller, “Demonstration of systematic photonic crystal device design and optimization by low rank adjustments: an extremely compact mode separator,” Opt. Lett. 30, 141–143 (2005).
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M. Gerken and D. A. B. Miller, “Multilayer thin-film stacks with steplike spatial beam shifting,” J. Lightwave Technol. 22, 612–618 (2004).
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M. Gerken and D. A. B. Miller, “Multilayer thin-film structures with high spatial dispersion,” Appl. Opt. 42, 1330–1345 (2003).
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D. A. B. Miller, “Communicating with waves between volumes—evaluating orthogonal spatial channels and limits on coupling strengths,” Appl. Opt. 39, 1681–1699 (2000).
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D. A. B. Miller, Quantum Mechanics for Scientists and Engineers (Cambridge, 2008).

Mulvad, H. C. Hansen

E. Palushani, H. C. Hansen Mulvad, M. Galili, H. Hu, L. K. Oxenløwe, A. T. Clausen, and P. Jeppesen, “OTDM-to-WDM conversion based on time-to-frequency mapping by time-domain optical Fourier transformation,” IEEE J. Sel. Top. Quantum Electron. 18, 681–688 (2012).
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Mumtaz, S.

Murnaghan, F. D.

F. D. Murnaghan, The Unitary and Rotation Groups (Spartan, 1962).

Orlov, S. S.

L. Hesselink, S. S. Orlov, and M. C. Bashaw, “Holographic data storage systems,” Proc. IEEE 92, 1231–1280 (2004).
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Oxenløwe, L. K.

E. Palushani, H. C. Hansen Mulvad, M. Galili, H. Hu, L. K. Oxenløwe, A. T. Clausen, and P. Jeppesen, “OTDM-to-WDM conversion based on time-to-frequency mapping by time-domain optical Fourier transformation,” IEEE J. Sel. Top. Quantum Electron. 18, 681–688 (2012).
[CrossRef]

Padgett, M. J.

M. P. J. Lavery, A. Dudley, A. Forbes, J. Courtial, and M. J. Padgett, “Robust interferometer for the routing of light beams carrying orbital angular momentum,” New J. Phys. 13, 093014 (2011).
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Palushani, E.

E. Palushani, H. C. Hansen Mulvad, M. Galili, H. Hu, L. K. Oxenløwe, A. T. Clausen, and P. Jeppesen, “OTDM-to-WDM conversion based on time-to-frequency mapping by time-domain optical Fourier transformation,” IEEE J. Sel. Top. Quantum Electron. 18, 681–688 (2012).
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J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
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S. H. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on ‘Nonreciprocal light propagation in a silicon photonic circuit’,” Science 335, 38 (2012).
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S. H. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on ‘Nonreciprocal light propagation in a silicon photonic circuit’,” Science 335, 38 (2012).
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Rakuljic, G. A.

Randel, S.

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M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73, 58–61 (1994).
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S. H. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on ‘Nonreciprocal light propagation in a silicon photonic circuit’,” Science 335, 38 (2012).
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Roelkens, G.

Ryf, R.

Sasaki, T.

C. R. Doerr, N. K. Fontaine, M. Hirano, T. Sasaki, L. L. Buhl, and P. J. Winzer, “Silicon photonic integrated circuit for coupling to a ring-core multimode fiber for space-division multiplexing,” in European Conference on Optical Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.A.3.

Schurig, D.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[CrossRef]

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Sheng, P.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9, 387–396 (2010).
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Smith, D. R.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
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T. Tanemura, K. C. Balram, D.-S. Ly-Gagnon, P. Wahl, J. S. White, M. L. Brongersma, and D. A. B. Miller, “Multiple-wavelength focusing of surface plasmons with a nonperiodic nanoslit coupler,” Nano Lett. 11, 2693–2698 (2011).
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Tang, Y.

Tseng, S.-Y.

M.-C. Wu, F.-C. Hsiao, and S.-Y. Tseng, “Adiabatic mode conversion in multimode waveguides using chirped computer-generated planar holograms,” IEEE Photon. Technol. Lett. 23, 807–809 (2011).
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Van Laere, F.

Van Thourhout, D.

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S. H. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on ‘Nonreciprocal light propagation in a silicon photonic circuit’,” Science 335, 38 (2012).
[CrossRef]

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T. Tanemura, K. C. Balram, D.-S. Ly-Gagnon, P. Wahl, J. S. White, M. L. Brongersma, and D. A. B. Miller, “Multiple-wavelength focusing of surface plasmons with a nonperiodic nanoslit coupler,” Nano Lett. 11, 2693–2698 (2011).
[CrossRef]

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White, J. S.

T. Tanemura, K. C. Balram, D.-S. Ly-Gagnon, P. Wahl, J. S. White, M. L. Brongersma, and D. A. B. Miller, “Multiple-wavelength focusing of surface plasmons with a nonperiodic nanoslit coupler,” Nano Lett. 11, 2693–2698 (2011).
[CrossRef]

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Winzer, P. J.

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96 km of few-mode fiber using coherent 6×6 MIMO processing,” J. Lightwave Technol. 30, 521–531 (2012).
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C. R. Doerr, N. K. Fontaine, M. Hirano, T. Sasaki, L. L. Buhl, and P. J. Winzer, “Silicon photonic integrated circuit for coupling to a ring-core multimode fiber for space-division multiplexing,” in European Conference on Optical Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.A.3.

Wu, M.-C.

M.-C. Wu, F.-C. Hsiao, and S.-Y. Tseng, “Adiabatic mode conversion in multimode waveguides using chirped computer-generated planar holograms,” IEEE Photon. Technol. Lett. 23, 807–809 (2011).
[CrossRef]

Xiao, Y.

P. P. Baveja, Y. Xiao, S. Arora, G. P. Agrawal, and D. N. Maywar, “All-optical semiconductor optical amplifier-based wavelength converters with sub-mW pumping,” IEEE Photon. Technol. Lett. 25, 78–80 (2013).
[CrossRef]

Yariv, A.

Yoo, S. J. B.

Yu, Z.

S. H. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on ‘Nonreciprocal light propagation in a silicon photonic circuit’,” Science 335, 38 (2012).
[CrossRef]

Zeilinger, A.

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

Appl. Opt.

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S. Kawanishi, “Ultrahigh-speed optical time-division-multiplexed transmission technology based on optical signal processing,” IEEE J. Quantum Electron. 34, 2064–2079 (1998).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

E. Palushani, H. C. Hansen Mulvad, M. Galili, H. Hu, L. K. Oxenløwe, A. T. Clausen, and P. Jeppesen, “OTDM-to-WDM conversion based on time-to-frequency mapping by time-domain optical Fourier transformation,” IEEE J. Sel. Top. Quantum Electron. 18, 681–688 (2012).
[CrossRef]

IEEE Photon. Technol. Lett.

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, “1.5 μm-band wavelength conversion based on cascaded second-order nonlinearity in LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 11, 653–655 (1999).
[CrossRef]

P. P. Baveja, Y. Xiao, S. Arora, G. P. Agrawal, and D. N. Maywar, “All-optical semiconductor optical amplifier-based wavelength converters with sub-mW pumping,” IEEE Photon. Technol. Lett. 25, 78–80 (2013).
[CrossRef]

M.-C. Wu, F.-C. Hsiao, and S.-Y. Tseng, “Adiabatic mode conversion in multimode waveguides using chirped computer-generated planar holograms,” IEEE Photon. Technol. Lett. 23, 807–809 (2011).
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T. Tanemura, K. C. Balram, D.-S. Ly-Gagnon, P. Wahl, J. S. White, M. L. Brongersma, and D. A. B. Miller, “Multiple-wavelength focusing of surface plasmons with a nonperiodic nanoslit coupler,” Nano Lett. 11, 2693–2698 (2011).
[CrossRef]

Nat. Mater.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9, 387–396 (2010).
[CrossRef]

New J. Phys.

M. P. J. Lavery, A. Dudley, A. Forbes, J. Courtial, and M. J. Padgett, “Robust interferometer for the routing of light beams carrying orbital angular momentum,” New J. Phys. 13, 093014 (2011).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rep.

P. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 199–299 (1982).
[CrossRef]

Phys. Rev. Lett.

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]

Proc. IEEE

V. Liu, D. A. B. Miller, and S. H. Fan, “Highly tailored computational electromagnetics methods for nanophotonic design and discovery,” Proc. IEEE 101, 484–493 (2013).
[CrossRef]

L. Hesselink, S. S. Orlov, and M. C. Bashaw, “Holographic data storage systems,” Proc. IEEE 92, 1231–1280 (2004).
[CrossRef]

Science

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[CrossRef]

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
[CrossRef]

R. W. Boyd and D. J. Gauthier, “Controlling the velocity of light pulses,” Science 326, 1074–1077 (2009).
[CrossRef]

S. H. Fan, R. Baets, A. Petrov, Z. Yu, J. D. Joannopoulos, W. Freude, A. Melloni, M. Popović, M. Vanwolleghem, D. Jalas, M. Eich, M. Krause, H. Renner, E. Brinkmeyer, and C. R. Doerr, “Comment on ‘Nonreciprocal light propagation in a silicon photonic circuit’,” Science 335, 38 (2012).
[CrossRef]

Other

R. Loudon, The Quantum Theory of Light, 3rd ed. (Oxford, 2000), pp. 88–91.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts, 2005).

D. A. B. Miller, Quantum Mechanics for Scientists and Engineers (Cambridge, 2008).

F. D. Murnaghan, The Unitary and Rotation Groups (Spartan, 1962).

C. R. Doerr, N. K. Fontaine, M. Hirano, T. Sasaki, L. L. Buhl, and P. J. Winzer, “Silicon photonic integrated circuit for coupling to a ring-core multimode fiber for space-division multiplexing,” in European Conference on Optical Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper Th.13.A.3.

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