Abstract

Optical phase shifters are extensively used in integrated optics not only for telecom and datacom applications but also for sensors and quantum computing. While various active solutions have been demonstrated, progress in passive phase shifters is still lacking. Here we present a new type of ultra-broadband 90° phase shifter, which exploits the anisotropy and dispersion engineering in subwavelength metamaterial waveguides. Our Floquet–Bloch calculations predict a phase-shift error below ±1.7° over an unprecedented operation range from 1.35 to 1.75 μm, i.e., 400 nm bandwidth covering the E, S, C, L, and U telecommunication bands. The flat spectral response of our phase shifter is maintained even in the presence of fabrication errors up to ±20  nm, showing greater robustness than conventional structures. Our device was experimentally demonstrated using standard 220 nm thick SOI wafers, showing a fourfold reduction in the phase variation compared to conventional phase shifters within the 145 nm wavelength range of our measurement setup. The proposed subwavelength engineered phase shifter paves the way for novel photonic integrated circuits with an ultra-broadband performance.

© 2020 Chinese Laser Press

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2019 (2)

L. McKay, M. Merklein, A. Casas-Bedoya, A. Choudhary, M. Jenkins, C. Middleton, A. Cramer, J. Devenport, A. Klee, R. DeSalvo, and B. J. Eggleton, “Brillouin-based phase shifter in a silicon waveguide,” Optica 6, 907–913 (2019).
[Crossref]

A. Herrero-Bermello, J. M. Luque-González, A. V. Velasco, A. Ortega-Moñux, P. Cheben, and R. Halir, “Design of a broadband polarization splitter based on anisotropy-engineered tilted subwavelength gratings,” IEEE Photon. J. 11, 6601508 (2019).
[Crossref]

2018 (5)

D. González-Andrade, J. G. Wangüemert-Pérez, A. V. Velasco, A. Ortega-Moñux, A. Herrero-Bermello, I. Molina-Fernández, R. Halir, and P. Cheben, “Ultra-broadband mode converter and multiplexer based on sub-wavelength structures,” IEEE Photon. J. 10, 2201010 (2018).
[Crossref]

P. Cheben, R. Halir, J. H. Schmid, H. A. Atwater, and D. R. Smith, “Subwavelength integrated photonics,” Nature 560, 565–572 (2018).
[Crossref]

R. Halir, A. Ortega-Moñux, D. Benedikovic, G. Z. Mashanovich, J. G. Wangüemert-Pérez, J. H. Schmid, Í. Molina-Fernández, and P. Cheben, “Subwavelength-grating metamaterial structures for silicon photonic devices,” Proc. IEEE 106, 2144–2157 (2018).
[Crossref]

J. M. Luque-González, A. Herrero-Bermello, A. Ortega-Moñux, Í. Molina-Fernández, A. V. Velasco, P. Cheben, J. H. Schmid, S. Wang, and R. Halir, “Tilted subwavelength gratings: controlling anisotropy in metamaterial nanophotonic waveguides,” Opt. Lett. 43, 4691–4694 (2018).
[Crossref]

J. Čtyroký, J. G. Wangüemert-Pérez, P. Kwiecien, I. Richter, J. Litvik, J. H. Schmid, Í. Molina-Fernández, A. Ortega-Moñux, M. Dado, and P. Cheben, “Design of narrowband Bragg spectral filters in subwavelength grating metamaterial waveguides,” Opt. Express 26, 179–194 (2018).
[Crossref]

2017 (3)

2016 (2)

R. Halir, P. Cheben, J. M. Luque-González, J. D. Sarmiento-Merenguel, J. H. Schmid, J. G. Wangüemert-Pérez, D.-X. Xu, S. Wang, A. Ortega-Moñux, and Í. Molina-Fernández, “Ultra-broadband nanophotonic beamsplitter using an anisotropic sub-wavelength metamaterial,” Laser Photon. Rev. 10, 1039–1046 (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 (5)

2014 (6)

2012 (2)

2011 (3)

S. S. Djordjevic, L. W. Luo, S. Ibrahim, N. K. Fontaine, C. B. Poitras, B. Guan, L. Zhou, K. Okamoto, Z. Ding, M. Lipson, and S. J. B. Yoo, “Fully reconfigurable silicon photonic lattice filters with four cascaded unit cells,” IEEE Photon. Technol. Lett. 23, 42–44 (2011).
[Crossref]

J. H. Schmid, M. Ibrahim, P. Cheben, J. Lapointe, S. Janz, P. J. Bock, A. Densmore, B. Lamontagne, R. Ma, W. N. Ye, and D.-X. Xu, “Temperature-independent silicon subwavelength grating waveguides,” Opt. Lett. 36, 2110–2112 (2011).
[Crossref]

W. Bogaerts and S. K. Selvaraja, “Compact single-mode silicon hybrid rib/strip waveguide with adiabatic bends,” IEEE Photon. J. 3, 422–432 (2011).
[Crossref]

2010 (6)

2009 (1)

2008 (1)

Q. Chang, Q. Li, Z. Zhang, M. Qiu, T. Ye, and Y. Su, “A tunable broadband photonic RF phase shifter based on a silicon microring resonator,” IEEE Photon. Technol. Lett. 21, 60–62 (2008).
[Crossref]

2006 (1)

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]

1999 (1)

T. Saida, A. Himeno, M. Okuno, A. Sugita, and K. Okamoto, “Silica-based 2×2 multimode interference coupler with arbitrary power splitting ratio,” Electron. Lett. 35, 2031–2033 (1999).
[Crossref]

1998 (1)

1997 (1)

S. Yegnanarayanan, P. D. Trinh, F. Coppinger, and B. Jalali, “Compact silicon-based integrated optic time delays,” IEEE Photon. Technol. Lett. 9, 634–635 (1997).
[Crossref]

1995 (2)

C. K. Tang and G. T. Reed, “Highly efficient optical phase modulator in SOI waveguides,” Electron. Lett. 31, 451–452 (1995).
[Crossref]

L. B. Soldano and E. C. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13, 615–627 (1995).
[Crossref]

1993 (1)

R. A. Soref, “Silicon-based optoelectronics,” Proc. IEEE 81, 1687–1706 (1993).
[Crossref]

1987 (1)

R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23, 123–129 (1987).
[Crossref]

1965 (1)

1957 (1)

Aalto, T.

Alonso-Ramos, C.

R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photon. Rev. 9, 25–49 (2015).
[Crossref]

J. G. Wangüemert-Pérez, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, D. Pérez-Galacho, R. Halir, I. Molina-Fernández, D.-X. Xu, and J. H. Schmid, “Evanescent field waveguide sensing with subwavelength grating structures in silicon-on-insulator,” Opt. Lett. 39, 4442–4445 (2014).
[Crossref]

Ang, K.-W.

Assefa, S.

Atwater, H. A.

P. Cheben, R. Halir, J. H. Schmid, H. A. Atwater, and D. R. Smith, “Subwavelength integrated photonics,” Nature 560, 565–572 (2018).
[Crossref]

Azaña, J.

Baehr-Jones, T.

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]

N. C. Harris, Y. Ma, J. Mower, T. Baehr-Jones, D. Englund, M. Hochberg, and C. Galland, “Efficient, compact and low loss thermo-optic phase shifter in silicon,” Opt. Express 22, 10487–10493 (2014).
[Crossref]

Bassi, P.

Ben Ezra, S.

Benedikovic, D.

R. Halir, A. Ortega-Moñux, D. Benedikovic, G. Z. Mashanovich, J. G. Wangüemert-Pérez, J. H. Schmid, Í. Molina-Fernández, and P. Cheben, “Subwavelength-grating metamaterial structures for silicon photonic devices,” Proc. IEEE 106, 2144–2157 (2018).
[Crossref]

D. Benedikovic, P. Cheben, J. H. Schmid, D.-X. Xu, B. Lamontagne, S. Wang, J. Lapointe, R. Halir, A. Ortega-Moñux, S. Janz, and M. Dado, “Subwavelength index engineered surface grating coupler with sub-decibel efficiency for 220-nm silicon-on-insulator waveguides,” Opt. Express 23, 22628–22635 (2015).
[Crossref]

Bennett, B. R.

R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23, 123–129 (1987).
[Crossref]

Besse, P. A.

Bock, P. J.

Bogaerts, W.

W. Bogaerts and S. K. Selvaraja, “Compact single-mode silicon hybrid rib/strip waveguide with adiabatic bends,” IEEE Photon. J. 3, 422–432 (2011).
[Crossref]

Bunandar, D.

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]

Burla, M.

Calvo, M. L.

Canciamilla, A.

Casas-Bedoya, A.

Chandrasekhar, S.

Chang, Q.

Q. Chang, Q. Li, Z. Zhang, M. Qiu, T. Ye, and Y. Su, “A tunable broadband photonic RF phase shifter based on a silicon microring resonator,” IEEE Photon. Technol. Lett. 21, 60–62 (2008).
[Crossref]

Cheben, P.

A. Herrero-Bermello, J. M. Luque-González, A. V. Velasco, A. Ortega-Moñux, P. Cheben, and R. Halir, “Design of a broadband polarization splitter based on anisotropy-engineered tilted subwavelength gratings,” IEEE Photon. J. 11, 6601508 (2019).
[Crossref]

J. M. Luque-González, A. Herrero-Bermello, A. Ortega-Moñux, Í. Molina-Fernández, A. V. Velasco, P. Cheben, J. H. Schmid, S. Wang, and R. Halir, “Tilted subwavelength gratings: controlling anisotropy in metamaterial nanophotonic waveguides,” Opt. Lett. 43, 4691–4694 (2018).
[Crossref]

R. Halir, A. Ortega-Moñux, D. Benedikovic, G. Z. Mashanovich, J. G. Wangüemert-Pérez, J. H. Schmid, Í. Molina-Fernández, and P. Cheben, “Subwavelength-grating metamaterial structures for silicon photonic devices,” Proc. IEEE 106, 2144–2157 (2018).
[Crossref]

D. González-Andrade, J. G. Wangüemert-Pérez, A. V. Velasco, A. Ortega-Moñux, A. Herrero-Bermello, I. Molina-Fernández, R. Halir, and P. Cheben, “Ultra-broadband mode converter and multiplexer based on sub-wavelength structures,” IEEE Photon. J. 10, 2201010 (2018).
[Crossref]

P. Cheben, R. Halir, J. H. Schmid, H. A. Atwater, and D. R. Smith, “Subwavelength integrated photonics,” Nature 560, 565–572 (2018).
[Crossref]

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R. Halir, A. Ortega-Moñux, D. Benedikovic, G. Z. Mashanovich, J. G. Wangüemert-Pérez, J. H. Schmid, Í. Molina-Fernández, and P. Cheben, “Subwavelength-grating metamaterial structures for silicon photonic devices,” Proc. IEEE 106, 2144–2157 (2018).
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R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photon. Rev. 9, 25–49 (2015).
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R. Halir, A. Maese-Novo, A. Ortega-Moñux, I. Molina-Fernández, J. G. Wangüemert-Pérez, P. Cheben, D.-X. Xu, J. H. Schmid, and S. Janz, “Colorless directional coupler with dispersion engineered sub-wavelength structure,” Opt. Express 20, 13470–13477 (2012).
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M. Poot and H. X. Tang, “Broadband nanoelectromechanical phase shifting of light on a chip,” Appl. Phys. Lett. 104, 061101 (2014).
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C. K. Tang and G. T. Reed, “Highly efficient optical phase modulator in SOI waveguides,” Electron. Lett. 31, 451–452 (1995).
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Romero-Cortés, L.

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J. M. Luque-González, A. Herrero-Bermello, A. Ortega-Moñux, Í. Molina-Fernández, A. V. Velasco, P. Cheben, J. H. Schmid, S. Wang, and R. Halir, “Tilted subwavelength gratings: controlling anisotropy in metamaterial nanophotonic waveguides,” Opt. Lett. 43, 4691–4694 (2018).
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P. Cheben, R. Halir, J. H. Schmid, H. A. Atwater, and D. R. Smith, “Subwavelength integrated photonics,” Nature 560, 565–572 (2018).
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R. Halir, A. Ortega-Moñux, D. Benedikovic, G. Z. Mashanovich, J. G. Wangüemert-Pérez, J. H. Schmid, Í. Molina-Fernández, and P. Cheben, “Subwavelength-grating metamaterial structures for silicon photonic devices,” Proc. IEEE 106, 2144–2157 (2018).
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A. Ortega-Moñux, J. Čtyroký, P. Cheben, J. H. Schmid, S. Wang, Í. Molina-Fernández, and R. Halir, “Disorder effects in subwavelength grating metamaterial waveguides,” Opt. Express 25, 12222–12236 (2017).
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A. Herrero-Bermello, A. V. Velasco, H. Podmore, P. Cheben, J. H. Schmid, S. Janz, M. L. Calvo, D.-X. Xu, A. Scott, and P. Corredera, “Temperature dependence mitigation in stationary Fourier-transform on-chip spectrometers,” Opt. Lett. 42, 2239–2242 (2017).
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R. Halir, P. Cheben, J. M. Luque-González, J. D. Sarmiento-Merenguel, J. H. Schmid, J. G. Wangüemert-Pérez, D.-X. Xu, S. Wang, A. Ortega-Moñux, and Í. Molina-Fernández, “Ultra-broadband nanophotonic beamsplitter using an anisotropic sub-wavelength metamaterial,” Laser Photon. Rev. 10, 1039–1046 (2016).
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R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photon. Rev. 9, 25–49 (2015).
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D. Benedikovic, P. Cheben, J. H. Schmid, D.-X. Xu, B. Lamontagne, S. Wang, J. Lapointe, R. Halir, A. Ortega-Moñux, S. Janz, and M. Dado, “Subwavelength index engineered surface grating coupler with sub-decibel efficiency for 220-nm silicon-on-insulator waveguides,” Opt. Express 23, 22628–22635 (2015).
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P. Cheben, J. H. Schmid, S. Wang, D.-X. Xu, M. Vachon, S. Janz, J. Lapointe, Y. Painchaud, and M.-J. Picard, “Broadband polarization independent nanophotonic coupler for silicon waveguides with ultra-high efficiency,” Opt. Express 23, 22553–22563 (2015).
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Y. Xiong, J. G. Wangüemert-Pérez, D.-X. Xu, J. H. Schmid, P. Cheben, and N. Y. Winnie, “Polarization splitter and rotator with subwavelength grating for enhanced fabrication tolerance,” Opt. Lett. 39, 6931–6934 (2014).
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J. G. Wangüemert-Pérez, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, D. Pérez-Galacho, R. Halir, I. Molina-Fernández, D.-X. Xu, and J. H. Schmid, “Evanescent field waveguide sensing with subwavelength grating structures in silicon-on-insulator,” Opt. Lett. 39, 4442–4445 (2014).
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R. Halir, A. Maese-Novo, A. Ortega-Moñux, I. Molina-Fernández, J. G. Wangüemert-Pérez, P. Cheben, D.-X. Xu, J. H. Schmid, and S. Janz, “Colorless directional coupler with dispersion engineered sub-wavelength structure,” Opt. Express 20, 13470–13477 (2012).
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J. H. Schmid, M. Ibrahim, P. Cheben, J. Lapointe, S. Janz, P. J. Bock, A. Densmore, B. Lamontagne, R. Ma, W. N. Ye, and D.-X. Xu, “Temperature-independent silicon subwavelength grating waveguides,” Opt. Lett. 36, 2110–2112 (2011).
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P. Cheben, P. J. Bock, J. H. Schmid, J. Lapointe, S. Janz, D.-X. Xu, A. Densmore, A. Delâge, B. Lamontagne, and T. J. Hall, “Refractive index engineering with subwavelength gratings for efficient microphotonic couplers and planar waveguide multiplexers,” Opt. Lett. 35, 2526–2528 (2010).
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Smith, D. R.

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L. B. Soldano and E. C. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13, 615–627 (1995).
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R. A. Soref, “Silicon-based optoelectronics,” Proc. IEEE 81, 1687–1706 (1993).
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R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23, 123–129 (1987).
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Steinbrecher, G. R.

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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Su, Y.

Q. Chang, Q. Li, Z. Zhang, M. Qiu, T. Ye, and Y. Su, “A tunable broadband photonic RF phase shifter based on a silicon microring resonator,” IEEE Photon. Technol. Lett. 21, 60–62 (2008).
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T. Saida, A. Himeno, M. Okuno, A. Sugita, and K. Okamoto, “Silica-based 2×2 multimode interference coupler with arbitrary power splitting ratio,” Electron. Lett. 35, 2031–2033 (1999).
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Tang, C. K.

C. K. Tang and G. T. Reed, “Highly efficient optical phase modulator in SOI waveguides,” Electron. Lett. 31, 451–452 (1995).
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M. Poot and H. X. Tang, “Broadband nanoelectromechanical phase shifting of light on a chip,” Appl. Phys. Lett. 104, 061101 (2014).
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G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4, 518–526 (2010).
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J. M. Luque-González, A. Herrero-Bermello, A. Ortega-Moñux, Í. Molina-Fernández, A. V. Velasco, P. Cheben, J. H. Schmid, S. Wang, and R. Halir, “Tilted subwavelength gratings: controlling anisotropy in metamaterial nanophotonic waveguides,” Opt. Lett. 43, 4691–4694 (2018).
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D. González-Andrade, J. G. Wangüemert-Pérez, A. V. Velasco, A. Ortega-Moñux, A. Herrero-Bermello, I. Molina-Fernández, R. Halir, and P. Cheben, “Ultra-broadband mode converter and multiplexer based on sub-wavelength structures,” IEEE Photon. J. 10, 2201010 (2018).
[Crossref]

A. Herrero-Bermello, A. V. Velasco, H. Podmore, P. Cheben, J. H. Schmid, S. Janz, M. L. Calvo, D.-X. Xu, A. Scott, and P. Corredera, “Temperature dependence mitigation in stationary Fourier-transform on-chip spectrometers,” Opt. Lett. 42, 2239–2242 (2017).
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D. González-Andrade, J. G. Wangüemert-Pérez, A. V. Velasco, A. Ortega-Moñux, A. Herrero-Bermello, I. Molina-Fernández, R. Halir, and P. Cheben, “Ultra-broadband mode converter and multiplexer based on sub-wavelength structures,” IEEE Photon. J. 10, 2201010 (2018).
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R. Halir, A. Ortega-Moñux, D. Benedikovic, G. Z. Mashanovich, J. G. Wangüemert-Pérez, J. H. Schmid, Í. Molina-Fernández, and P. Cheben, “Subwavelength-grating metamaterial structures for silicon photonic devices,” Proc. IEEE 106, 2144–2157 (2018).
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R. Halir, P. Cheben, J. M. Luque-González, J. D. Sarmiento-Merenguel, J. H. Schmid, J. G. Wangüemert-Pérez, D.-X. Xu, S. Wang, A. Ortega-Moñux, and Í. Molina-Fernández, “Ultra-broadband nanophotonic beamsplitter using an anisotropic sub-wavelength metamaterial,” Laser Photon. Rev. 10, 1039–1046 (2016).
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R. Halir, A. Maese-Novo, A. Ortega-Moñux, I. Molina-Fernández, J. G. Wangüemert-Pérez, P. Cheben, D.-X. Xu, J. H. Schmid, and S. Janz, “Colorless directional coupler with dispersion engineered sub-wavelength structure,” Opt. Express 20, 13470–13477 (2012).
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Winter, M.

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Xu, D.-X.

A. Herrero-Bermello, A. V. Velasco, H. Podmore, P. Cheben, J. H. Schmid, S. Janz, M. L. Calvo, D.-X. Xu, A. Scott, and P. Corredera, “Temperature dependence mitigation in stationary Fourier-transform on-chip spectrometers,” Opt. Lett. 42, 2239–2242 (2017).
[Crossref]

R. Halir, P. Cheben, J. M. Luque-González, J. D. Sarmiento-Merenguel, J. H. Schmid, J. G. Wangüemert-Pérez, D.-X. Xu, S. Wang, A. Ortega-Moñux, and Í. Molina-Fernández, “Ultra-broadband nanophotonic beamsplitter using an anisotropic sub-wavelength metamaterial,” Laser Photon. Rev. 10, 1039–1046 (2016).
[Crossref]

R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photon. Rev. 9, 25–49 (2015).
[Crossref]

D. Benedikovic, P. Cheben, J. H. Schmid, D.-X. Xu, B. Lamontagne, S. Wang, J. Lapointe, R. Halir, A. Ortega-Moñux, S. Janz, and M. Dado, “Subwavelength index engineered surface grating coupler with sub-decibel efficiency for 220-nm silicon-on-insulator waveguides,” Opt. Express 23, 22628–22635 (2015).
[Crossref]

P. Cheben, J. H. Schmid, S. Wang, D.-X. Xu, M. Vachon, S. Janz, J. Lapointe, Y. Painchaud, and M.-J. Picard, “Broadband polarization independent nanophotonic coupler for silicon waveguides with ultra-high efficiency,” Opt. Express 23, 22553–22563 (2015).
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Y. Xiong, J. G. Wangüemert-Pérez, D.-X. Xu, J. H. Schmid, P. Cheben, and N. Y. Winnie, “Polarization splitter and rotator with subwavelength grating for enhanced fabrication tolerance,” Opt. Lett. 39, 6931–6934 (2014).
[Crossref]

J. G. Wangüemert-Pérez, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, D. Pérez-Galacho, R. Halir, I. Molina-Fernández, D.-X. Xu, and J. H. Schmid, “Evanescent field waveguide sensing with subwavelength grating structures in silicon-on-insulator,” Opt. Lett. 39, 4442–4445 (2014).
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R. Halir, A. Maese-Novo, A. Ortega-Moñux, I. Molina-Fernández, J. G. Wangüemert-Pérez, P. Cheben, D.-X. Xu, J. H. Schmid, and S. Janz, “Colorless directional coupler with dispersion engineered sub-wavelength structure,” Opt. Express 20, 13470–13477 (2012).
[Crossref]

J. H. Schmid, M. Ibrahim, P. Cheben, J. Lapointe, S. Janz, P. J. Bock, A. Densmore, B. Lamontagne, R. Ma, W. N. Ye, and D.-X. Xu, “Temperature-independent silicon subwavelength grating waveguides,” Opt. Lett. 36, 2110–2112 (2011).
[Crossref]

P. Cheben, P. J. Bock, J. H. Schmid, J. Lapointe, S. Janz, D.-X. Xu, A. Densmore, A. Delâge, B. Lamontagne, and T. J. Hall, “Refractive index engineering with subwavelength gratings for efficient microphotonic couplers and planar waveguide multiplexers,” Opt. Lett. 35, 2526–2528 (2010).
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P. Cheben, D.-X. Xu, S. Janz, and A. Densmore, “Subwavelength waveguide grating for mode conversion and light coupling in integrated optics,” Opt. Express 14, 4695–4702 (2006).
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Xu, J.

Ye, T.

Q. Chang, Q. Li, Z. Zhang, M. Qiu, T. Ye, and Y. Su, “A tunable broadband photonic RF phase shifter based on a silicon microring resonator,” IEEE Photon. Technol. Lett. 21, 60–62 (2008).
[Crossref]

Ye, W. N.

Yegnanarayanan, S.

S. Yegnanarayanan, P. D. Trinh, F. Coppinger, and B. Jalali, “Compact silicon-based integrated optic time delays,” IEEE Photon. Technol. Lett. 9, 634–635 (1997).
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Ylinen, S.

Yoo, S. J. B.

S. S. Djordjevic, L. W. Luo, S. Ibrahim, N. K. Fontaine, C. B. Poitras, B. Guan, L. Zhou, K. Okamoto, Z. Ding, M. Lipson, and S. J. B. Yoo, “Fully reconfigurable silicon photonic lattice filters with four cascaded unit cells,” IEEE Photon. Technol. Lett. 23, 42–44 (2011).
[Crossref]

Zhang, Z.

Q. Chang, Q. Li, Z. Zhang, M. Qiu, T. Ye, and Y. Su, “A tunable broadband photonic RF phase shifter based on a silicon microring resonator,” IEEE Photon. Technol. Lett. 21, 60–62 (2008).
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Zhou, L.

S. S. Djordjevic, L. W. Luo, S. Ibrahim, N. K. Fontaine, C. B. Poitras, B. Guan, L. Zhou, K. Okamoto, Z. Ding, M. Lipson, and S. J. B. Yoo, “Fully reconfigurable silicon photonic lattice filters with four cascaded unit cells,” IEEE Photon. Technol. Lett. 23, 42–44 (2011).
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Zhu, H.

Appl. Phys. Lett. (1)

M. Poot and H. X. Tang, “Broadband nanoelectromechanical phase shifting of light on a chip,” Appl. Phys. Lett. 104, 061101 (2014).
[Crossref]

Electron. Lett. (2)

C. K. Tang and G. T. Reed, “Highly efficient optical phase modulator in SOI waveguides,” Electron. Lett. 31, 451–452 (1995).
[Crossref]

T. Saida, A. Himeno, M. Okuno, A. Sugita, and K. Okamoto, “Silica-based 2×2 multimode interference coupler with arbitrary power splitting ratio,” Electron. Lett. 35, 2031–2033 (1999).
[Crossref]

IEEE J. Quantum Electron. (1)

R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23, 123–129 (1987).
[Crossref]

IEEE Photon. J. (3)

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Other (1)

“FullWAVE and FemSIM, available from RSoft,” https://www.synopsys.com/optical-solutions/rsoft/component-design.html .

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Figures (7)

Fig. 1.
Fig. 1. Schematics of three types of passive phase shifters: (a) our proposed ultra-broadband PS comprising two SWG waveguides with the same period (Λ) and duty cycle (DC) but with dissimilar widths WU and WL; (b) state-of-the-art tapered PS consisting of a straight waveguide and two trapezoidal tapers in back-to-back configuration; and (c) state-of-the-art asymmetric PS based on two non-periodic waveguides with different widths WU and WL.
Fig. 2.
Fig. 2. Comparison of the PSE as a function of wavelength for the three designed PSs: tapered PS (blue curve), asymmetric PS (green curve), and asymmetric SWG PS (red curve).
Fig. 3.
Fig. 3. (a) PSE as a function of wavelength for two parallel SWG waveguides with DC=50%, WL=1.6  μm, and WU=1.8  μm obtained via Floquet–Bloch analysis. An almost flat response is achieved for Λ=200  nm. (b) PSE response of the entire SWG PS with a period Λ=200  nm, including the effect of SWG tapers.
Fig. 4.
Fig. 4. Simulated maximum PSE in the wavelength range 1.35–1.75 μm. For each wavelength, the highest error between PSE(Δδ=+20  nm) and PSE(Δδ=20  nm) is represented. Inset: longitudinal and transversal variations for each SWG segment were considered.
Fig. 5.
Fig. 5. Schematic of the test structures used to experimentally characterize (a) the tapered PS and (b) the asymmetric SWG PS. Each structure is composed of two ultra-broadband SWG MMIs and 14 PSs connected in series, forming an MZI. SEM images of the fabricated (c) tapered PS and (d) asymmetric SWG PS as indicated by the blue box in the schematic.
Fig. 6.
Fig. 6. Measured spectra of the MZIs (a) with 14 tapered PSs and (b) with 14 SWG PSs. The light was injected through port 1, and both outputs of the test structure (ports 3 and 4) were measured. (c) Measured PSE for a single tapered PS (solid blue line) and a single asymmetric SWG PS (solid red line). Dotted lines correspond to the simulation results obtained via 3D-FDTD.
Fig. 7.
Fig. 7. Fitting of the circuit model to the measured spectra of the MZIs with (a) 14 tapered PSs and (b) 14 SWG PSs.

Tables (1)

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Table 1. Comparison Between Active and Passive Phase Shiftersa

Equations (14)

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ΔΦ(λ)=[βU(λ)βL(λ)]LPS=2πλΔneff(λ)LPS,
dΔΦ(λ)dλ|λ=λ0=ΔΦ0λ0[1λ0dΔneff(λ)/dλ|λ=λ0Δneff(λ0)].
ΔΦSWG(λ)[πλ4nxxnzz2(1We,L21We,U2)]LPS,
PSE(λ)=ΔΦ(λ)90°.
β(λ)k0ncoreπλ4ncoreWe2,
neff(λ)=β(λ)λ2πncoreλ28ncoreWe2.
Δneff(λ)=neff,U(λ)neff,L(λ)=λ28ncore(1We,L21We,U2).
dneff(λ)dλ=2λ8ncore(1We,L21We,U2).
dΔΦ(λ)dλ|λ=λ0=ΔΦ0λ0[12]=ΔΦ0λ0.
neff(λ)nxxλ28We2nxxnzz2.
Δneff(λ)=λ28nxxnzz2(1We,L21We,U2).
Δneff(λ)λ8(1We,L21We,U2)·c,
dΔΦ(λ)dλ|λ=λ0ΔΦ0λ0[1λ08(1We,L21We,U2)·cλ08(1We,L21We,U2)·c]0.
T¯¯=M¯¯[100ej[sim(λ)+error]]14M¯¯.

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