Abstract

We design and fabricate a series of broadband silicon arbitrary power splitters with various split ratios using shortcuts to adiabaticity. In this approach, the system evolution is designed using the decoupled system states, and the desired split ratios are guaranteed by the boundary conditions. Furthermore, the system evolutions are optimized to be as close to the adiabatic states as possible, thus enhancing the robustness to wavelength and fabrication variations. The devices are more compact then the conventional adiabatic designs. Fabricated devices show broadband response for a wide wavelength range from 1.47 to 1.62 µm and also have excellent robustness against fabrication errors across an 8-inch wafer.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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2019 (9)

Z. Lin, L. Rusch, Y Chen, and W. Shi, “Chip-scale, full-stokes polarimeter,” Opt. Express 27(4), 4867–4877 (2019).
[Crossref]

A. Melikyan and P. Dong, “Adiabatic mode converters for silicon photonics: Power and polarization broadband manipulators,” APL Photonics 4(3), 030803 (2019).
[Crossref]

D. Mao, Y. Wang, E. El-Fiky, L. Xu, A. Kumar, M. Jaques, A. Samani, O. Carpentier, S. Bernal, M. S. Alam, J. Zhang, M. Zhu, P. C. Koh, and D. V. Plant, “Adiabatic coupler with design-intended splitting ratio,” J. Lightwave Technol. 37(24), 6147–6155 (2019).
[Crossref]

J. Y. Sie, H. C. Chung, X. Chen, and S. Y. Tseng, “Robust arbitrary ratio power splitter by fast quasi-adiabatic elimination in optical waveguides,” Opt. Express 27(26), 37622–37633 (2019).
[Crossref]

D. Guéry-Odelin, A. Ruschhaupt, A. Kiely, E. Torrontegui, S. Martínez-Garaot, and J. G. Muga, “Shortcuts to adiabaticity: concepts, methods, and applications,” Rev. Mod. Phys. 91(4), 045001 (2019).
[Crossref]

H. C. Chung, Z. Y. Li, F. C. Liang, K. S. Lee, and S. Y. Tseng, “The fast quasiadiabatic approach to optical waveguide design,” Proc. SPIE 11031, 33 (2019).
[Crossref]

H. C. Chung, S. Martínez-Garaot, X. Chen, J. G. Muga, and S.-Y. Tseng, “Shortcuts to adiabaticity in optical waveguides,” EPL 127(3), 34001–34007 (2019).
[Crossref]

Y. J. Hung, Z. Y. Li, H. C. Chung, F. C. Liang, M. Y. Jung, T. H. Yen, and S. Y. Tseng, “Mode-evolution-based silicon-on-insulator 3 dB coupler using fast quasiadiabatic dynamics,” Opt. Lett. 44(4), 815–818 (2019).
[Crossref]

H. C. Chung and S. Y. Tseng, “High fabrication tolerance and broadband silicon polarization beam splitter by point-symmetric cascaded fast quasiadiabatic couplers,” OSA Continuum 2(10), 2795–2808 (2019).
[Crossref]

2018 (7)

H. C. Chung and S.-Y. Tseng, “Ultrashort and broadband silicon polarization splitter-rotator using fast quasiadiabatic dynamics,” Opt. Express 26(8), 9655–9665 (2018).
[Crossref]

H. C. Chung and S. Y. Tseng, “Robust silicon 3-dB coupler using inverse engineering based optimization,” Jpn. J. Appl. Phys. 57(8S2), 08PC01 (2018).
[Crossref]

D. Guo and T. Chu, “Compact broadband silicon 3 dB coupler based on shortcuts to adiabaticity,” Opt. Lett. 43(19), 4795–4798 (2018).
[Crossref]

D. Guo and T. Chu, “Broadband and low-crosstalk polarization splitter-rotator with optimized tapers,” OSA Continuum 1(3), 841–850 (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(12), 2144–2157 (2018).
[Crossref]

P. Cheben, R. Halir, J. H. Schmid, H. A. Atwater, and D. R. Smith, “Subwavelength integrated photonics,” Nature 560(7720), 565–572 (2018).
[Crossref]

H. Xu and Y. Shi, “Flat-top CWDM (de)multiplexer based on MZI with bent directional couplers,” IEEE Photonics Technol. Lett. 30(2), 169–172 (2018).
[Crossref]

2017 (3)

2016 (3)

2015 (2)

2014 (3)

S. Y. Tseng, R. D. Wen, Y. F. Chiu, and X. Chen, “Short and robust directional couplers designed by shortcuts to adiabaticity,” Opt. Express 22(16), 18849–18859 (2014).
[Crossref]

P. Dong, X. Liu, S. Chandrasekhar, L. L. Buhl, R. Aroca, and Y. K. Chen, “Monolithic silicon photonic integrated circuits for compact 100+Gb/s coherent optical receivers and transmitters,” IEEE J. Sel. Top. Quantum Electron. 20(4), 150–157 (2014).
[Crossref]

Q. Deng, L. Liu, X. Li, and Z. Zhou, “Arbitrary-ratio 1×2 power splitter based on asymmetric multimode interference,” Opt. Lett. 39(19), 5590–5593 (2014).
[Crossref]

2013 (5)

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013).
[Crossref]

K. Xu, L. G. Yang, J. Y. Sung, Y. M. Chen, Z. Z. Cheng, C. W. Chow, C. H. Yeh, and H. K. Tsang, “Compatibility of silicon mach-zehnder modulators for advanced modulation formats,” J. Lightwave Technol. 31(15), 2550–2554 (2013).
[Crossref]

K. H. Chien, C. S. Yeih, and S. Y. Tseng, “Mode conversion/splitting in multimode waveguides based on invariant engineering,” J. Lightwave Technol. 31(21), 3387–3394 (2013).
[Crossref]

S. Y. Tseng and Y. W. Jhang, “Fast and robust beam coupling in a three waveguide directional coupler,” IEEE Photonics Technol. Lett. 25(24), 2478–2481 (2013).
[Crossref]

S. Martínez-Garaot, E. Torrontegui, X. Chen, M. Modugno, D. D. Guéry-Odelin, S. Y. Tseng, and J. G. Muga, “Vibrational mode multiplexing of ultracold atoms,” Phys. Rev. Lett. 111(21), 213001 (2013).
[Crossref]

2012 (1)

2009 (1)

S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photonics Rev. 3(3), 243–261 (2009).
[Crossref]

2007 (1)

2005 (1)

H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, “Optical directional coupler based on Si-wire waveguides,” IEEE Photonics Technol. Lett. 17(3), 585–587 (2005).
[Crossref]

2003 (1)

S. Matsuo, Y. Yoshikuni, T. Segawa, Y. Ohiso, and H. Okamoto, “A widely tunable optical filter using ladder-type structure,” IEEE Photonics Technol. Lett. 15(8), 1114–1116 (2003).
[Crossref]

1998 (1)

1969 (1)

H. R. Lewis and W. B. Riesenfeld, “An exact quantum theory of the time-dependent harmonic oscillator and of a charged particle in a time-dependent electromagnetic field,” J. Math. Phys. 10(8), 1458–1473 (1969).
[Crossref]

Alam, M. S.

Al-Bader, S.

Arakawa, Y.

H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, “Optical directional coupler based on Si-wire waveguides,” IEEE Photonics Technol. Lett. 17(3), 585–587 (2005).
[Crossref]

Aroca, R.

P. Dong, X. Liu, S. Chandrasekhar, L. L. Buhl, R. Aroca, and Y. K. Chen, “Monolithic silicon photonic integrated circuits for compact 100+Gb/s coherent optical receivers and transmitters,” IEEE J. Sel. Top. Quantum Electron. 20(4), 150–157 (2014).
[Crossref]

Atwater, H. A.

P. Cheben, R. Halir, J. H. Schmid, H. A. Atwater, and D. R. Smith, “Subwavelength integrated photonics,” Nature 560(7720), 565–572 (2018).
[Crossref]

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(12), 2144–2157 (2018).
[Crossref]

Bernal, S.

Bianchi, A.

Brimont, A.

Buhl, L. L.

P. Dong, X. Liu, S. Chandrasekhar, L. L. Buhl, R. Aroca, and Y. K. Chen, “Monolithic silicon photonic integrated circuits for compact 100+Gb/s coherent optical receivers and transmitters,” IEEE J. Sel. Top. Quantum Electron. 20(4), 150–157 (2014).
[Crossref]

Carpentier, O.

Cassese, T.

Chandrasekhar, S.

P. Dong, X. Liu, S. Chandrasekhar, L. L. Buhl, R. Aroca, and Y. K. Chen, “Monolithic silicon photonic integrated circuits for compact 100+Gb/s coherent optical receivers and transmitters,” IEEE J. Sel. Top. Quantum Electron. 20(4), 150–157 (2014).
[Crossref]

Cheben, P.

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(12), 2144–2157 (2018).
[Crossref]

P. Cheben, R. Halir, J. H. Schmid, H. A. Atwater, and D. R. Smith, “Subwavelength integrated photonics,” Nature 560(7720), 565–572 (2018).
[Crossref]

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(12), 13470–13477 (2012).
[Crossref]

Chen, X.

H. C. Chung, S. Martínez-Garaot, X. Chen, J. G. Muga, and S.-Y. Tseng, “Shortcuts to adiabaticity in optical waveguides,” EPL 127(3), 34001–34007 (2019).
[Crossref]

J. Y. Sie, H. C. Chung, X. Chen, and S. Y. Tseng, “Robust arbitrary ratio power splitter by fast quasi-adiabatic elimination in optical waveguides,” Opt. Express 27(26), 37622–37633 (2019).
[Crossref]

S. Y. Tseng, R. D. Wen, Y. F. Chiu, and X. Chen, “Short and robust directional couplers designed by shortcuts to adiabaticity,” Opt. Express 22(16), 18849–18859 (2014).
[Crossref]

S. Martínez-Garaot, E. Torrontegui, X. Chen, M. Modugno, D. D. Guéry-Odelin, S. Y. Tseng, and J. G. Muga, “Vibrational mode multiplexing of ultracold atoms,” Phys. Rev. Lett. 111(21), 213001 (2013).
[Crossref]

Chen, Y

Chen, Y. K.

P. Dong, X. Liu, S. Chandrasekhar, L. L. Buhl, R. Aroca, and Y. K. Chen, “Monolithic silicon photonic integrated circuits for compact 100+Gb/s coherent optical receivers and transmitters,” IEEE J. Sel. Top. Quantum Electron. 20(4), 150–157 (2014).
[Crossref]

Chen, Y. M.

Chen, Z.

Cheng, Z. Z.

Chien, K. H.

Chiu, Y. F.

Chow, C. W.

Chrostowski, L.

Y. Wang, Z. Lu, M. Ma, H. Yun, F. Zhang, N. A. F. Jaeger, and L. Chrostowski, “Compact broadband directional couplers using subwavelength gratings,” IEEE Photonics J. 8(3), 1–8 (2016).
[Crossref]

Z. Lu, H. Yun, Y. Wang, Z. Chen, F. Zhang, N. A. F. Jaeger, and L. Chrostowski, “Broadband silicon photonic directional coupler using asymmetric-waveguide based phase control,” Opt. Express 23(3), 3795–3808 (2015).
[Crossref]

Chu, T.

Chung, H. C.

J. Y. Sie, H. C. Chung, X. Chen, and S. Y. Tseng, “Robust arbitrary ratio power splitter by fast quasi-adiabatic elimination in optical waveguides,” Opt. Express 27(26), 37622–37633 (2019).
[Crossref]

H. C. Chung, S. Martínez-Garaot, X. Chen, J. G. Muga, and S.-Y. Tseng, “Shortcuts to adiabaticity in optical waveguides,” EPL 127(3), 34001–34007 (2019).
[Crossref]

Y. J. Hung, Z. Y. Li, H. C. Chung, F. C. Liang, M. Y. Jung, T. H. Yen, and S. Y. Tseng, “Mode-evolution-based silicon-on-insulator 3 dB coupler using fast quasiadiabatic dynamics,” Opt. Lett. 44(4), 815–818 (2019).
[Crossref]

H. C. Chung and S. Y. Tseng, “High fabrication tolerance and broadband silicon polarization beam splitter by point-symmetric cascaded fast quasiadiabatic couplers,” OSA Continuum 2(10), 2795–2808 (2019).
[Crossref]

H. C. Chung, Z. Y. Li, F. C. Liang, K. S. Lee, and S. Y. Tseng, “The fast quasiadiabatic approach to optical waveguide design,” Proc. SPIE 11031, 33 (2019).
[Crossref]

H. C. Chung and S.-Y. Tseng, “Ultrashort and broadband silicon polarization splitter-rotator using fast quasiadiabatic dynamics,” Opt. Express 26(8), 9655–9665 (2018).
[Crossref]

H. C. Chung and S. Y. Tseng, “Robust silicon 3-dB coupler using inverse engineering based optimization,” Jpn. J. Appl. Phys. 57(8S2), 08PC01 (2018).
[Crossref]

H. C. Chung, K. S. Lee, and S. Y. Tseng, “Short and broadband silicon asymmetric Y-junction two-mode (de)multiplexer using fast quasiadiabatic dynamics,” Opt. Express 25(12), 13626–13634 (2017).
[Crossref]

De Angelis, G.

Deng, Q.

Dong, P.

A. Melikyan and P. Dong, “Adiabatic mode converters for silicon photonics: Power and polarization broadband manipulators,” APL Photonics 4(3), 030803 (2019).
[Crossref]

P. Dong, X. Liu, S. Chandrasekhar, L. L. Buhl, R. Aroca, and Y. K. Chen, “Monolithic silicon photonic integrated circuits for compact 100+Gb/s coherent optical receivers and transmitters,” IEEE J. Sel. Top. Quantum Electron. 20(4), 150–157 (2014).
[Crossref]

El-Fiky, E.

Fuentes-Hernandez, C.

Griol, A.

Guéry-Odelin, D.

D. Guéry-Odelin, A. Ruschhaupt, A. Kiely, E. Torrontegui, S. Martínez-Garaot, and J. G. Muga, “Shortcuts to adiabaticity: concepts, methods, and applications,” Rev. Mod. Phys. 91(4), 045001 (2019).
[Crossref]

Guéry-Odelin, D. D.

S. Martínez-Garaot, E. Torrontegui, X. Chen, M. Modugno, D. D. Guéry-Odelin, S. Y. Tseng, and J. G. Muga, “Vibrational mode multiplexing of ultracold atoms,” Phys. Rev. Lett. 111(21), 213001 (2013).
[Crossref]

Guo, D.

Halir, R.

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(12), 2144–2157 (2018).
[Crossref]

P. Cheben, R. Halir, J. H. Schmid, H. A. Atwater, and D. R. Smith, “Subwavelength integrated photonics,” Nature 560(7720), 565–572 (2018).
[Crossref]

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(12), 13470–13477 (2012).
[Crossref]

Hamming, R. W.

R. W. Hamming, Digital filters (Prentice Hall, 1989).

Ho, C. P.

Hosseini, E. S.

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013).
[Crossref]

Hung, Y. J.

Ishida, S.

H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, “Optical directional coupler based on Si-wire waveguides,” IEEE Photonics Technol. Lett. 17(3), 585–587 (2005).
[Crossref]

Jaeger, N. A. F.

Y. Wang, Z. Lu, M. Ma, H. Yun, F. Zhang, N. A. F. Jaeger, and L. Chrostowski, “Compact broadband directional couplers using subwavelength gratings,” IEEE Photonics J. 8(3), 1–8 (2016).
[Crossref]

Z. Lu, H. Yun, Y. Wang, Z. Chen, F. Zhang, N. A. F. Jaeger, and L. Chrostowski, “Broadband silicon photonic directional coupler using asymmetric-waveguide based phase control,” Opt. Express 23(3), 3795–3808 (2015).
[Crossref]

Janz, S.

Jaques, M.

Jhang, Y. W.

S. Y. Tseng and Y. W. Jhang, “Fast and robust beam coupling in a three waveguide directional coupler,” IEEE Photonics Technol. Lett. 25(24), 2478–2481 (2013).
[Crossref]

Jung, M. Y.

Kiely, A.

D. Guéry-Odelin, A. Ruschhaupt, A. Kiely, E. Torrontegui, S. Martínez-Garaot, and J. G. Muga, “Shortcuts to adiabaticity: concepts, methods, and applications,” Rev. Mod. Phys. 91(4), 045001 (2019).
[Crossref]

Kippelen, B.

Koh, P. C.

Kumar, A.

Lee, K. S.

H. C. Chung, Z. Y. Li, F. C. Liang, K. S. Lee, and S. Y. Tseng, “The fast quasiadiabatic approach to optical waveguide design,” Proc. SPIE 11031, 33 (2019).
[Crossref]

H. C. Chung, K. S. Lee, and S. Y. Tseng, “Short and broadband silicon asymmetric Y-junction two-mode (de)multiplexer using fast quasiadiabatic dynamics,” Opt. Express 25(12), 13626–13634 (2017).
[Crossref]

Lewis, H. R.

H. R. Lewis and W. B. Riesenfeld, “An exact quantum theory of the time-dependent harmonic oscillator and of a charged particle in a time-dependent electromagnetic field,” J. Math. Phys. 10(8), 1458–1473 (1969).
[Crossref]

Li, X.

Li, Z. Y.

H. C. Chung, Z. Y. Li, F. C. Liang, K. S. Lee, and S. Y. Tseng, “The fast quasiadiabatic approach to optical waveguide design,” Proc. SPIE 11031, 33 (2019).
[Crossref]

Y. J. Hung, Z. Y. Li, H. C. Chung, F. C. Liang, M. Y. Jung, T. H. Yen, and S. Y. Tseng, “Mode-evolution-based silicon-on-insulator 3 dB coupler using fast quasiadiabatic dynamics,” Opt. Lett. 44(4), 815–818 (2019).
[Crossref]

Liang, F. C.

Y. J. Hung, Z. Y. Li, H. C. Chung, F. C. Liang, M. Y. Jung, T. H. Yen, and S. Y. Tseng, “Mode-evolution-based silicon-on-insulator 3 dB coupler using fast quasiadiabatic dynamics,” Opt. Lett. 44(4), 815–818 (2019).
[Crossref]

H. C. Chung, Z. Y. Li, F. C. Liang, K. S. Lee, and S. Y. Tseng, “The fast quasiadiabatic approach to optical waveguide design,” Proc. SPIE 11031, 33 (2019).
[Crossref]

Lin, Z.

Liu, L.

Liu, X.

P. Dong, X. Liu, S. Chandrasekhar, L. L. Buhl, R. Aroca, and Y. K. Chen, “Monolithic silicon photonic integrated circuits for compact 100+Gb/s coherent optical receivers and transmitters,” IEEE J. Sel. Top. Quantum Electron. 20(4), 150–157 (2014).
[Crossref]

Longhi, S.

S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photonics Rev. 3(3), 243–261 (2009).
[Crossref]

Lu, Z.

Y. Wang, Z. Lu, M. Ma, H. Yun, F. Zhang, N. A. F. Jaeger, and L. Chrostowski, “Compact broadband directional couplers using subwavelength gratings,” IEEE Photonics J. 8(3), 1–8 (2016).
[Crossref]

Z. Lu, H. Yun, Y. Wang, Z. Chen, F. Zhang, N. A. F. Jaeger, and L. Chrostowski, “Broadband silicon photonic directional coupler using asymmetric-waveguide based phase control,” Opt. Express 23(3), 3795–3808 (2015).
[Crossref]

Ma, M.

Y. Wang, Z. Lu, M. Ma, H. Yun, F. Zhang, N. A. F. Jaeger, and L. Chrostowski, “Compact broadband directional couplers using subwavelength gratings,” IEEE Photonics J. 8(3), 1–8 (2016).
[Crossref]

Maese-Novo, A.

Mao, D.

Marti, J.

Martínez-Garaot, S.

H. C. Chung, S. Martínez-Garaot, X. Chen, J. G. Muga, and S.-Y. Tseng, “Shortcuts to adiabaticity in optical waveguides,” EPL 127(3), 34001–34007 (2019).
[Crossref]

D. Guéry-Odelin, A. Ruschhaupt, A. Kiely, E. Torrontegui, S. Martínez-Garaot, and J. G. Muga, “Shortcuts to adiabaticity: concepts, methods, and applications,” Rev. Mod. Phys. 91(4), 045001 (2019).
[Crossref]

S. Martínez-Garaot, E. Torrontegui, X. Chen, M. Modugno, D. D. Guéry-Odelin, S. Y. Tseng, and J. G. Muga, “Vibrational mode multiplexing of ultracold atoms,” Phys. Rev. Lett. 111(21), 213001 (2013).
[Crossref]

Mashanovich, G. Z.

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(12), 2144–2157 (2018).
[Crossref]

Matsuo, S.

S. Matsuo, Y. Yoshikuni, T. Segawa, Y. Ohiso, and H. Okamoto, “A widely tunable optical filter using ladder-type structure,” IEEE Photonics Technol. Lett. 15(8), 1114–1116 (2003).
[Crossref]

Melikyan, A.

A. Melikyan and P. Dong, “Adiabatic mode converters for silicon photonics: Power and polarization broadband manipulators,” APL Photonics 4(3), 030803 (2019).
[Crossref]

Modugno, M.

S. Martínez-Garaot, E. Torrontegui, X. Chen, M. Modugno, D. D. Guéry-Odelin, S. Y. Tseng, and J. G. Muga, “Vibrational mode multiplexing of ultracold atoms,” Phys. Rev. Lett. 111(21), 213001 (2013).
[Crossref]

Molina-Fernández, I.

Molina-fernández, Í.

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(12), 2144–2157 (2018).
[Crossref]

Muga, J. G.

D. Guéry-Odelin, A. Ruschhaupt, A. Kiely, E. Torrontegui, S. Martínez-Garaot, and J. G. Muga, “Shortcuts to adiabaticity: concepts, methods, and applications,” Rev. Mod. Phys. 91(4), 045001 (2019).
[Crossref]

H. C. Chung, S. Martínez-Garaot, X. Chen, J. G. Muga, and S.-Y. Tseng, “Shortcuts to adiabaticity in optical waveguides,” EPL 127(3), 34001–34007 (2019).
[Crossref]

S. Martínez-Garaot, E. Torrontegui, X. Chen, M. Modugno, D. D. Guéry-Odelin, S. Y. Tseng, and J. G. Muga, “Vibrational mode multiplexing of ultracold atoms,” Phys. Rev. Lett. 111(21), 213001 (2013).
[Crossref]

Ohiso, Y.

S. Matsuo, Y. Yoshikuni, T. Segawa, Y. Ohiso, and H. Okamoto, “A widely tunable optical filter using ladder-type structure,” IEEE Photonics Technol. Lett. 15(8), 1114–1116 (2003).
[Crossref]

Okamoto, H.

S. Matsuo, Y. Yoshikuni, T. Segawa, Y. Ohiso, and H. Okamoto, “A widely tunable optical filter using ladder-type structure,” IEEE Photonics Technol. Lett. 15(8), 1114–1116 (2003).
[Crossref]

Okamoto, K.

K. Okamoto, Fundamentals of optical waveguides (Academic University, 2006).

Ortega-moñux, A.

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(12), 2144–2157 (2018).
[Crossref]

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(12), 13470–13477 (2012).
[Crossref]

Owens, D.

Plant, D. V.

Preite, M. V.

Riesenfeld, W. B.

H. R. Lewis and W. B. Riesenfeld, “An exact quantum theory of the time-dependent harmonic oscillator and of a charged particle in a time-dependent electromagnetic field,” J. Math. Phys. 10(8), 1458–1473 (1969).
[Crossref]

Romagnoli, M.

Rusch, L.

Ruschhaupt, A.

D. Guéry-Odelin, A. Ruschhaupt, A. Kiely, E. Torrontegui, S. Martínez-Garaot, and J. G. Muga, “Shortcuts to adiabaticity: concepts, methods, and applications,” Rev. Mod. Phys. 91(4), 045001 (2019).
[Crossref]

Samani, A.

Sanchis, P.

Schmid, J. H.

P. Cheben, R. Halir, J. H. Schmid, H. A. Atwater, and D. R. Smith, “Subwavelength integrated photonics,” Nature 560(7720), 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(12), 2144–2157 (2018).
[Crossref]

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(12), 13470–13477 (2012).
[Crossref]

Schneider, V. M.

Segawa, T.

S. Matsuo, Y. Yoshikuni, T. Segawa, Y. Ohiso, and H. Okamoto, “A widely tunable optical filter using ladder-type structure,” IEEE Photonics Technol. Lett. 15(8), 1114–1116 (2003).
[Crossref]

Shi, W.

Shi, Y.

H. Xu and Y. Shi, “Flat-top CWDM (de)multiplexer based on MZI with bent directional couplers,” IEEE Photonics Technol. Lett. 30(2), 169–172 (2018).
[Crossref]

Sie, J. Y.

Smith, D. R.

P. Cheben, R. Halir, J. H. Schmid, H. A. Atwater, and D. R. Smith, “Subwavelength integrated photonics,” Nature 560(7720), 565–572 (2018).
[Crossref]

Song, Q.

Sorianello, V.

Sun, J.

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013).
[Crossref]

Sun, S.

Sun, W.

Sung, J. Y.

Syahriar, A.

Testa, F.

Timurdogan, E.

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013).
[Crossref]

Torrontegui, E.

D. Guéry-Odelin, A. Ruschhaupt, A. Kiely, E. Torrontegui, S. Martínez-Garaot, and J. G. Muga, “Shortcuts to adiabaticity: concepts, methods, and applications,” Rev. Mod. Phys. 91(4), 045001 (2019).
[Crossref]

S. Martínez-Garaot, E. Torrontegui, X. Chen, M. Modugno, D. D. Guéry-Odelin, S. Y. Tseng, and J. G. Muga, “Vibrational mode multiplexing of ultracold atoms,” Phys. Rev. Lett. 111(21), 213001 (2013).
[Crossref]

Tsang, H. K.

Tseng, S. Y.

H. C. Chung and S. Y. Tseng, “High fabrication tolerance and broadband silicon polarization beam splitter by point-symmetric cascaded fast quasiadiabatic couplers,” OSA Continuum 2(10), 2795–2808 (2019).
[Crossref]

Y. J. Hung, Z. Y. Li, H. C. Chung, F. C. Liang, M. Y. Jung, T. H. Yen, and S. Y. Tseng, “Mode-evolution-based silicon-on-insulator 3 dB coupler using fast quasiadiabatic dynamics,” Opt. Lett. 44(4), 815–818 (2019).
[Crossref]

H. C. Chung, Z. Y. Li, F. C. Liang, K. S. Lee, and S. Y. Tseng, “The fast quasiadiabatic approach to optical waveguide design,” Proc. SPIE 11031, 33 (2019).
[Crossref]

J. Y. Sie, H. C. Chung, X. Chen, and S. Y. Tseng, “Robust arbitrary ratio power splitter by fast quasi-adiabatic elimination in optical waveguides,” Opt. Express 27(26), 37622–37633 (2019).
[Crossref]

H. C. Chung and S. Y. Tseng, “Robust silicon 3-dB coupler using inverse engineering based optimization,” Jpn. J. Appl. Phys. 57(8S2), 08PC01 (2018).
[Crossref]

H. C. Chung, K. S. Lee, and S. Y. Tseng, “Short and broadband silicon asymmetric Y-junction two-mode (de)multiplexer using fast quasiadiabatic dynamics,” Opt. Express 25(12), 13626–13634 (2017).
[Crossref]

C. P. Ho and S. Y. Tseng, “Optimization of adiabaticity in coupled-waveguide devices using shortcuts to adiabaticity,” Opt. Lett. 40(21), 4831–4834 (2015).
[Crossref]

S. Y. Tseng, R. D. Wen, Y. F. Chiu, and X. Chen, “Short and robust directional couplers designed by shortcuts to adiabaticity,” Opt. Express 22(16), 18849–18859 (2014).
[Crossref]

S. Y. Tseng and Y. W. Jhang, “Fast and robust beam coupling in a three waveguide directional coupler,” IEEE Photonics Technol. Lett. 25(24), 2478–2481 (2013).
[Crossref]

K. H. Chien, C. S. Yeih, and S. Y. Tseng, “Mode conversion/splitting in multimode waveguides based on invariant engineering,” J. Lightwave Technol. 31(21), 3387–3394 (2013).
[Crossref]

S. Martínez-Garaot, E. Torrontegui, X. Chen, M. Modugno, D. D. Guéry-Odelin, S. Y. Tseng, and J. G. Muga, “Vibrational mode multiplexing of ultracold atoms,” Phys. Rev. Lett. 111(21), 213001 (2013).
[Crossref]

S. Y. Tseng, C. Fuentes-Hernandez, D. Owens, and B. Kippelen, “Variable splitting ratio 2×2 MMI couplers using multimode waveguide holograms,” Opt. Express 15(14), 9015–9021 (2007).
[Crossref]

Tseng, S.-Y.

H. C. Chung, S. Martínez-Garaot, X. Chen, J. G. Muga, and S.-Y. Tseng, “Shortcuts to adiabaticity in optical waveguides,” EPL 127(3), 34001–34007 (2019).
[Crossref]

H. C. Chung and S.-Y. Tseng, “Ultrashort and broadband silicon polarization splitter-rotator using fast quasiadiabatic dynamics,” Opt. Express 26(8), 9655–9665 (2018).
[Crossref]

Velha, P.

Wang, Y.

Wangüemert-pérez, J. G.

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(12), 2144–2157 (2018).
[Crossref]

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(12), 13470–13477 (2012).
[Crossref]

Watts, M. R.

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013).
[Crossref]

Wen, R. D.

Wen, X.

Xiao, S.

Xu, D. X.

Xu, H.

H. Xu and Y. Shi, “Flat-top CWDM (de)multiplexer based on MZI with bent directional couplers,” IEEE Photonics Technol. Lett. 30(2), 169–172 (2018).
[Crossref]

Xu, K.

Xu, L.

Yaacobi, A.

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013).
[Crossref]

Yamada, H.

H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, “Optical directional coupler based on Si-wire waveguides,” IEEE Photonics Technol. Lett. 17(3), 585–587 (2005).
[Crossref]

Yang, L. G.

Yeh, C. H.

Yeih, C. S.

Yen, T. H.

Yi, N.

Yoshikuni, Y.

S. Matsuo, Y. Yoshikuni, T. Segawa, Y. Ohiso, and H. Okamoto, “A widely tunable optical filter using ladder-type structure,” IEEE Photonics Technol. Lett. 15(8), 1114–1116 (2003).
[Crossref]

Yun, H.

Y. Wang, Z. Lu, M. Ma, H. Yun, F. Zhang, N. A. F. Jaeger, and L. Chrostowski, “Compact broadband directional couplers using subwavelength gratings,” IEEE Photonics J. 8(3), 1–8 (2016).
[Crossref]

Z. Lu, H. Yun, Y. Wang, Z. Chen, F. Zhang, N. A. F. Jaeger, and L. Chrostowski, “Broadband silicon photonic directional coupler using asymmetric-waveguide based phase control,” Opt. Express 23(3), 3795–3808 (2015).
[Crossref]

Zanzi, A.

Zhang, F.

Y. Wang, Z. Lu, M. Ma, H. Yun, F. Zhang, N. A. F. Jaeger, and L. Chrostowski, “Compact broadband directional couplers using subwavelength gratings,” IEEE Photonics J. 8(3), 1–8 (2016).
[Crossref]

Z. Lu, H. Yun, Y. Wang, Z. Chen, F. Zhang, N. A. F. Jaeger, and L. Chrostowski, “Broadband silicon photonic directional coupler using asymmetric-waveguide based phase control,” Opt. Express 23(3), 3795–3808 (2015).
[Crossref]

Zhang, J.

Zhang, N.

Zhou, Z.

Zhu, M.

APL Photonics (1)

A. Melikyan and P. Dong, “Adiabatic mode converters for silicon photonics: Power and polarization broadband manipulators,” APL Photonics 4(3), 030803 (2019).
[Crossref]

EPL (1)

H. C. Chung, S. Martínez-Garaot, X. Chen, J. G. Muga, and S.-Y. Tseng, “Shortcuts to adiabaticity in optical waveguides,” EPL 127(3), 34001–34007 (2019).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

P. Dong, X. Liu, S. Chandrasekhar, L. L. Buhl, R. Aroca, and Y. K. Chen, “Monolithic silicon photonic integrated circuits for compact 100+Gb/s coherent optical receivers and transmitters,” IEEE J. Sel. Top. Quantum Electron. 20(4), 150–157 (2014).
[Crossref]

IEEE Photonics J. (1)

Y. Wang, Z. Lu, M. Ma, H. Yun, F. Zhang, N. A. F. Jaeger, and L. Chrostowski, “Compact broadband directional couplers using subwavelength gratings,” IEEE Photonics J. 8(3), 1–8 (2016).
[Crossref]

IEEE Photonics Technol. Lett. (4)

H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, “Optical directional coupler based on Si-wire waveguides,” IEEE Photonics Technol. Lett. 17(3), 585–587 (2005).
[Crossref]

S. Matsuo, Y. Yoshikuni, T. Segawa, Y. Ohiso, and H. Okamoto, “A widely tunable optical filter using ladder-type structure,” IEEE Photonics Technol. Lett. 15(8), 1114–1116 (2003).
[Crossref]

H. Xu and Y. Shi, “Flat-top CWDM (de)multiplexer based on MZI with bent directional couplers,” IEEE Photonics Technol. Lett. 30(2), 169–172 (2018).
[Crossref]

S. Y. Tseng and Y. W. Jhang, “Fast and robust beam coupling in a three waveguide directional coupler,” IEEE Photonics Technol. Lett. 25(24), 2478–2481 (2013).
[Crossref]

J. Lightwave Technol. (4)

J. Math. Phys. (1)

H. R. Lewis and W. B. Riesenfeld, “An exact quantum theory of the time-dependent harmonic oscillator and of a charged particle in a time-dependent electromagnetic field,” J. Math. Phys. 10(8), 1458–1473 (1969).
[Crossref]

Jpn. J. Appl. Phys. (1)

H. C. Chung and S. Y. Tseng, “Robust silicon 3-dB coupler using inverse engineering based optimization,” Jpn. J. Appl. Phys. 57(8S2), 08PC01 (2018).
[Crossref]

Laser Photonics Rev. (1)

S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photonics Rev. 3(3), 243–261 (2009).
[Crossref]

Nature (2)

P. Cheben, R. Halir, J. H. Schmid, H. A. Atwater, and D. R. Smith, “Subwavelength integrated photonics,” Nature 560(7720), 565–572 (2018).
[Crossref]

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013).
[Crossref]

Opt. Express (9)

S. Y. Tseng, R. D. Wen, Y. F. Chiu, and X. Chen, “Short and robust directional couplers designed by shortcuts to adiabaticity,” Opt. Express 22(16), 18849–18859 (2014).
[Crossref]

S. Y. Tseng, C. Fuentes-Hernandez, D. Owens, and B. Kippelen, “Variable splitting ratio 2×2 MMI couplers using multimode waveguide holograms,” Opt. Express 15(14), 9015–9021 (2007).
[Crossref]

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(12), 13470–13477 (2012).
[Crossref]

Z. Lu, H. Yun, Y. Wang, Z. Chen, F. Zhang, N. A. F. Jaeger, and L. Chrostowski, “Broadband silicon photonic directional coupler using asymmetric-waveguide based phase control,” Opt. Express 23(3), 3795–3808 (2015).
[Crossref]

D. Guo and T. Chu, “Silicon mode (de)multiplexers with parameters optimized using shortcuts to adiabaticity,” Opt. Express 25(8), 9160–9170 (2017).
[Crossref]

H. C. Chung, K. S. Lee, and S. Y. Tseng, “Short and broadband silicon asymmetric Y-junction two-mode (de)multiplexer using fast quasiadiabatic dynamics,” Opt. Express 25(12), 13626–13634 (2017).
[Crossref]

H. C. Chung and S.-Y. Tseng, “Ultrashort and broadband silicon polarization splitter-rotator using fast quasiadiabatic dynamics,” Opt. Express 26(8), 9655–9665 (2018).
[Crossref]

Z. Lin, L. Rusch, Y Chen, and W. Shi, “Chip-scale, full-stokes polarimeter,” Opt. Express 27(4), 4867–4877 (2019).
[Crossref]

J. Y. Sie, H. C. Chung, X. Chen, and S. Y. Tseng, “Robust arbitrary ratio power splitter by fast quasi-adiabatic elimination in optical waveguides,” Opt. Express 27(26), 37622–37633 (2019).
[Crossref]

Opt. Lett. (7)

OSA Continuum (2)

Phys. Rev. Lett. (1)

S. Martínez-Garaot, E. Torrontegui, X. Chen, M. Modugno, D. D. Guéry-Odelin, S. Y. Tseng, and J. G. Muga, “Vibrational mode multiplexing of ultracold atoms,” Phys. Rev. Lett. 111(21), 213001 (2013).
[Crossref]

Proc. IEEE (1)

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(12), 2144–2157 (2018).
[Crossref]

Proc. SPIE (1)

H. C. Chung, Z. Y. Li, F. C. Liang, K. S. Lee, and S. Y. Tseng, “The fast quasiadiabatic approach to optical waveguide design,” Proc. SPIE 11031, 33 (2019).
[Crossref]

Rev. Mod. Phys. (1)

D. Guéry-Odelin, A. Ruschhaupt, A. Kiely, E. Torrontegui, S. Martínez-Garaot, and J. G. Muga, “Shortcuts to adiabaticity: concepts, methods, and applications,” Rev. Mod. Phys. 91(4), 045001 (2019).
[Crossref]

Other (2)

R. W. Hamming, Digital filters (Prentice Hall, 1989).

K. Okamoto, Fundamentals of optical waveguides (Academic University, 2006).

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Figures (11)

Fig. 1.
Fig. 1. Schematic of the coupled silicon waveguides.
Fig. 2.
Fig. 2. (a) θ(z)’s for power splitters with split ratios 50%/50%, 60%/40%, 70%/30%, 80%/20%, and 90%/10%. (b) ϕ(z) obtained using the third order Fourier series with σ-approximation.
Fig. 3.
Fig. 3. (a) Coupling coefficients Ω(z)’s and (b) Mismatches Δ(z)’s for various split ratios obtained using inverse engineering based optimization.
Fig. 4.
Fig. 4. Trajectories of the designed system evolutions for power splitters with split ratios of 50%/50%, 60%/40%, 70%/30%, 80%/20% and 90%/10% on the surface of the Bloch sphere. The black curve is the ideal adiabatic trajectory.
Fig. 5.
Fig. 5. (a) The relation between the coupling coefficient Ω and the waveguide spacing D (b) The relation between the mismatch Δ and the waveguide width difference δW.
Fig. 6.
Fig. 6. Waveguide spacing D(z) for power splitters with split ratio (a) 50%/50%, (b) 60%/40%, (c) 70%/30%, (d) 80%/20%, and (e) 90%/10%.
Fig. 7.
Fig. 7. Waveguide widths W1 and W2 for power splitters with split ratios (a) 50%/50%, (b) 60%/40%, (c) 70%/30%, (d) 80%/20%, and (e) 90%/10%.
Fig. 8.
Fig. 8. Light distribution in the power splitters using inverse engineering based optimization STA with split ratios of (a) 50%/50%, (b) 60%/40%, (c) 70%/30%, (d) 80%/20%, and (e) 90%/10% when TE0 mode is launched into the top waveguide.
Fig. 9.
Fig. 9. SEM images of the fabricated power splitters using inverse engineering based optimization STA with split ratios (a) 50%/50%, (b) 60%/40%, (c) 70%/30%, (d) 80%/20%, (e) 90%/10%.
Fig. 10.
Fig. 10. Measured spectra of power splitters using inverse engineering based optimization with split ratios (a)(f) 50%/50%, (b)(g) 60%/40%, (c)(h) 70%/30%, (d)(i) 80%/20%, (e)(j) 90%/10%. Left column (a-e): light is launched into the top waveguide (waveguide 1). Right column (f-h): light is launched into the bottom waveguide (waveguide 2).
Fig. 11.
Fig. 11. Measured spectra of eight 50%/50% power splitters on different locations of an 8-inch SOI wafer.

Tables (3)

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Table 1. Parameters corresponding to different split ratios.

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Table 2. Split ratios of eight 50%/50% power splitters at 1550 nm.

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Table 3. Comparison of the state-of-the-art arbitrary ratio power splitters.

Equations (8)

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d d z [ A 1 A 2 ] = i [ Δ ( z ) Ω ( z ) Ω ( z ) Δ ( z ) ] [ A 1 A 2 ] ,
| Ψ z +  =  [ cos ( θ / 2 ) exp ( i ϕ / 2 ) sin ( θ / 2 ) exp ( i ϕ / 2 ) ] | Ψ z  =  [ sin ( θ / 2 ) exp ( i ϕ / 2 ) cos ( θ / 2 ) exp ( i ϕ / 2 ) ] .
θ = Ω sin ϕ ϕ = Δ + Ω cos ϕ cot θ
θ = P × π 2 [ 1 - cos ( z π L ) ] ,
ϕ ( 0 ) = π 2 ,   ϕ ( z ) = c  ( c  is a constant) .
ϕ ( z ) = π 2 + ( π 2 c ) k = 1 3 sin ( π k z 2 L ) sinc ( π k z 2 L )  ( n  is odd) .
ϕ ( z ) = π 2 + b 1 sin ( π z 2 L ) + b 3 sin ( 3 π z 2 L ) ,
Ω ( z ) = Ω 0 exp [ γ ( D ( z ) D 0 ) ] Δ ( z ) = m δ W ( z ) + c ,