Abstract

Reflectors are an essential component for on-chip integrated photonics. Here, we propose a new method for designing reflectors on the prevalent thin-film-on-insulator platform by using genetic-algorithm optimization. In simulation, the designed reflector with a footprint of only 2.16  μm×2.16  μm can achieve ∼97% reflectivity and 1 dB bandwidth as wide as 220 nm. The structure is composed of randomly distributed pixels and is highly robust against the inevitable corner rounding effect in device fabrication. In experiment, we fabricated on-chip Fabry–Perot (FP) cavities constructed from optimized reflectors. Those FP cavities have intrinsic quality factors of >2000 with the highest value beyond 4000 in a spectral width of 200 nm. The reflectivity fitted from the FP cavity resonances is >85% in the entire wavelength range of 1440–1640 nm and is beyond 95% at some wavelengths. The fabrication processes are CMOS compatible and require only one step of lithography and etch. The devices can be used as a standard module in integrated photonic circuitry for wide applications in on-chip semiconductor laser structures and optical signal processing.

© 2017 Chinese Laser Press

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References

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  1. T. Mukaihara, N. Yamanaka, N. Iwai, M. Funabashi, S. Arakawa, T. Ishikawa, and A. Kasukawa, “Integrated GaInAsP laser diodes with monitoring photodiodes through semiconductor/air Bragg reflector (SABAR),” IEEE J. Sel. Top. Quantum Electron. 5, 469–475 (1999).
    [Crossref]
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    [Crossref]
  3. B. Docter, T. Segawa, T. Kakitsuka, S. Matsuo, T. Ishii, Y. Kawaguchi, Y. Kondo, H. Suzuki, F. Karouta, and M. K. Smit, “Short cavity DBR laser using vertical groove gratings for large-scale photonic integrated circuits,” IEEE Photon. Technol. Lett. 19, 1469–1471 (2007).
    [Crossref]
  4. C. A. Barrios, V. R. Almeida, R. R. Panepucci, B. S. Schmidt, and M. Lipson, “Compact silicon tunable Fabry–Perot resonator with low power consumption,” IEEE Photon. Technol. Lett. 16, 506–508 (2004).
    [Crossref]
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    [Crossref]
  9. S. Zamek, L. Feng, M. Khajavikhan, D. T. H. Tan, M. Ayache, and Y. Fainman, “Micro-resonator with metallic mirrors coupled to a bus waveguide,” Opt. Express 19, 2417–2425 (2011).
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  12. L. H. Frandsen, Y. Elesin, L. F. Frellsen, M. Mitrovic, Y. Ding, O. Sigmund, and K. Yvind, “Topology optimized mode conversion in a photonic crystal waveguide fabricated in silicon-on-insulator material,” Opt. Express 22, 8525–8532 (2014).
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  13. J. S. Jensen and O. Sigmund, “Topology optimization for nano-photonics,” Laser Photon. Rev. 5, 308–321 (2011).
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  15. A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vučković, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9, 374–377 (2015).
    [Crossref]
  16. B. Shen, P. Wang, R. Polson, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4 × 2.4  μm2 footprint,” Nat. Photonics 9, 378–382 (2015).
    [Crossref]
  17. J. C. C. Mak, C. Sideris, J. Jeong, A. Hajimiri, and J. K. S. Poon, “Binary particle swarm optimized 2 × 2 power splitters in a standard foundry silicon photonic platform,” Opt. Lett. 41, 3868–3871 (2016).
    [Crossref]
  18. K. Xu, L. Liu, X. Wen, W. Sun, N. Zhang, N. Yi, S. Sun, S. Xiao, and Q. Song, “Integrated photonic power divider with arbitrary power ratios,” Opt. Lett. 42, 855–858 (2017).
    [Crossref]
  19. L. F. Frellsen, Y. Ding, O. Sigmund, and L. H. Frandsen, “Topology optimized mode multiplexing in silicon-on-insulator photonic wire waveguides,” Opt. Express 24, 16866–16873 (2016).
    [Crossref]
  20. Y. A. Vlasov and S. J. McNab, “Losses in single-mode silicon-on-insulator strip waveguides and bends,” Opt. Express 12, 1622–1631 (2004).
    [Crossref]
  21. J. Wu, T. Moein, X. Xu, G. Ren, A. Mitchell, and D. J. Moss, “Micro-ring resonator quality factor enhancement via an integrated Fabry–Perot cavity,” APL Photon. 2, 056103 (2017).
    [Crossref]
  22. D. G. Rabus, Integrated Ring Resonators (Springer-Verlag, 2007).

2017 (4)

2016 (3)

2015 (2)

A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vučković, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9, 374–377 (2015).
[Crossref]

B. Shen, P. Wang, R. Polson, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4 × 2.4  μm2 footprint,” Nat. Photonics 9, 378–382 (2015).
[Crossref]

2014 (1)

2011 (2)

2007 (3)

2004 (2)

C. A. Barrios, V. R. Almeida, R. R. Panepucci, B. S. Schmidt, and M. Lipson, “Compact silicon tunable Fabry–Perot resonator with low power consumption,” IEEE Photon. Technol. Lett. 16, 506–508 (2004).
[Crossref]

Y. A. Vlasov and S. J. McNab, “Losses in single-mode silicon-on-insulator strip waveguides and bends,” Opt. Express 12, 1622–1631 (2004).
[Crossref]

2002 (1)

S. R. Selmic, G. A. Evans, T. M. Chou, J. B. Kirk, J. N. Walpole, J. P. Donnelly, C. T. Harris, and L. J. Missaggia, “Single frequency 1550-nm AlGaInAs-InP tapered high-power laser with a distributed Bragg reflector,” IEEE Photon. Technol. Lett. 14, 890–892 (2002).
[Crossref]

2001 (1)

N. Ulbrich, G. Scarpa, A. Sigl, J. Roßkopf, G. Böhm, G. Abstreiter, and M.-C. Amann, “High-temperature (T ≥ 470  K) pulsed operation of 5.5  μm quantum cascade lasers with high-reflection coating,” Electron. Lett. 37, 1341–1342 (2001).
[Crossref]

1999 (1)

T. Mukaihara, N. Yamanaka, N. Iwai, M. Funabashi, S. Arakawa, T. Ishikawa, and A. Kasukawa, “Integrated GaInAsP laser diodes with monitoring photodiodes through semiconductor/air Bragg reflector (SABAR),” IEEE J. Sel. Top. Quantum Electron. 5, 469–475 (1999).
[Crossref]

Abstreiter, G.

N. Ulbrich, G. Scarpa, A. Sigl, J. Roßkopf, G. Böhm, G. Abstreiter, and M.-C. Amann, “High-temperature (T ≥ 470  K) pulsed operation of 5.5  μm quantum cascade lasers with high-reflection coating,” Electron. Lett. 37, 1341–1342 (2001).
[Crossref]

Almeida, V. R.

C. A. Barrios, V. R. Almeida, R. R. Panepucci, B. S. Schmidt, and M. Lipson, “Compact silicon tunable Fabry–Perot resonator with low power consumption,” IEEE Photon. Technol. Lett. 16, 506–508 (2004).
[Crossref]

Amann, M.-C.

N. Ulbrich, G. Scarpa, A. Sigl, J. Roßkopf, G. Böhm, G. Abstreiter, and M.-C. Amann, “High-temperature (T ≥ 470  K) pulsed operation of 5.5  μm quantum cascade lasers with high-reflection coating,” Electron. Lett. 37, 1341–1342 (2001).
[Crossref]

Arakawa, S.

T. Mukaihara, N. Yamanaka, N. Iwai, M. Funabashi, S. Arakawa, T. Ishikawa, and A. Kasukawa, “Integrated GaInAsP laser diodes with monitoring photodiodes through semiconductor/air Bragg reflector (SABAR),” IEEE J. Sel. Top. Quantum Electron. 5, 469–475 (1999).
[Crossref]

Ayache, M.

Babinec, T. M.

A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vučković, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9, 374–377 (2015).
[Crossref]

Barrios, C. A.

C. A. Barrios, V. R. Almeida, R. R. Panepucci, B. S. Schmidt, and M. Lipson, “Compact silicon tunable Fabry–Perot resonator with low power consumption,” IEEE Photon. Technol. Lett. 16, 506–508 (2004).
[Crossref]

Böhm, G.

N. Ulbrich, G. Scarpa, A. Sigl, J. Roßkopf, G. Böhm, G. Abstreiter, and M.-C. Amann, “High-temperature (T ≥ 470  K) pulsed operation of 5.5  μm quantum cascade lasers with high-reflection coating,” Electron. Lett. 37, 1341–1342 (2001).
[Crossref]

Canning, J.

Chen, S.

S. Chen, Y. Shi, S. He, and D. Dai, “Variable optical attenuator based on a reflective Mach–Zehnder interferometer,” Opt. Commun. 361, 55–58 (2016).
[Crossref]

Chou, T. M.

S. R. Selmic, G. A. Evans, T. M. Chou, J. B. Kirk, J. N. Walpole, J. P. Donnelly, C. T. Harris, and L. J. Missaggia, “Single frequency 1550-nm AlGaInAs-InP tapered high-power laser with a distributed Bragg reflector,” IEEE Photon. Technol. Lett. 14, 890–892 (2002).
[Crossref]

Cui, H.

Dai, D.

S. Chen, Y. Shi, S. He, and D. Dai, “Variable optical attenuator based on a reflective Mach–Zehnder interferometer,” Opt. Commun. 361, 55–58 (2016).
[Crossref]

Ding, Y.

Docter, B.

B. Docter, T. Segawa, T. Kakitsuka, S. Matsuo, T. Ishii, Y. Kawaguchi, Y. Kondo, H. Suzuki, F. Karouta, and M. K. Smit, “Short cavity DBR laser using vertical groove gratings for large-scale photonic integrated circuits,” IEEE Photon. Technol. Lett. 19, 1469–1471 (2007).
[Crossref]

Donnelly, J. P.

S. R. Selmic, G. A. Evans, T. M. Chou, J. B. Kirk, J. N. Walpole, J. P. Donnelly, C. T. Harris, and L. J. Missaggia, “Single frequency 1550-nm AlGaInAs-InP tapered high-power laser with a distributed Bragg reflector,” IEEE Photon. Technol. Lett. 14, 890–892 (2002).
[Crossref]

Elesin, Y.

L. H. Frandsen, Y. Elesin, L. F. Frellsen, M. Mitrovic, Y. Ding, O. Sigmund, and K. Yvind, “Topology optimized mode conversion in a photonic crystal waveguide fabricated in silicon-on-insulator material,” Opt. Express 22, 8525–8532 (2014).
[Crossref]

L. H. Frandsen, Y. Elesin, O. Sigmund, and K. Yvind, “Topology optimization of coupled photonic crystal cavities for flat-top drop filter functionality,” in European Conference on Lasers and Electro-Optics-European Quantum Electronics Conference, Munich, Germany (Optical Society of America, 2015), paper CK_9_1.

Evans, G. A.

S. R. Selmic, G. A. Evans, T. M. Chou, J. B. Kirk, J. N. Walpole, J. P. Donnelly, C. T. Harris, and L. J. Missaggia, “Single frequency 1550-nm AlGaInAs-InP tapered high-power laser with a distributed Bragg reflector,” IEEE Photon. Technol. Lett. 14, 890–892 (2002).
[Crossref]

Fainman, Y.

Feng, L.

Frandsen, L. H.

Frellsen, L. F.

Funabashi, M.

T. Mukaihara, N. Yamanaka, N. Iwai, M. Funabashi, S. Arakawa, T. Ishikawa, and A. Kasukawa, “Integrated GaInAsP laser diodes with monitoring photodiodes through semiconductor/air Bragg reflector (SABAR),” IEEE J. Sel. Top. Quantum Electron. 5, 469–475 (1999).
[Crossref]

Gao, S.

Hajimiri, A.

Harris, C. T.

S. R. Selmic, G. A. Evans, T. M. Chou, J. B. Kirk, J. N. Walpole, J. P. Donnelly, C. T. Harris, and L. J. Missaggia, “Single frequency 1550-nm AlGaInAs-InP tapered high-power laser with a distributed Bragg reflector,” IEEE Photon. Technol. Lett. 14, 890–892 (2002).
[Crossref]

He, S.

S. Chen, Y. Shi, S. He, and D. Dai, “Variable optical attenuator based on a reflective Mach–Zehnder interferometer,” Opt. Commun. 361, 55–58 (2016).
[Crossref]

Ishii, T.

B. Docter, T. Segawa, T. Kakitsuka, S. Matsuo, T. Ishii, Y. Kawaguchi, Y. Kondo, H. Suzuki, F. Karouta, and M. K. Smit, “Short cavity DBR laser using vertical groove gratings for large-scale photonic integrated circuits,” IEEE Photon. Technol. Lett. 19, 1469–1471 (2007).
[Crossref]

Ishikawa, T.

T. Mukaihara, N. Yamanaka, N. Iwai, M. Funabashi, S. Arakawa, T. Ishikawa, and A. Kasukawa, “Integrated GaInAsP laser diodes with monitoring photodiodes through semiconductor/air Bragg reflector (SABAR),” IEEE J. Sel. Top. Quantum Electron. 5, 469–475 (1999).
[Crossref]

Iwai, N.

T. Mukaihara, N. Yamanaka, N. Iwai, M. Funabashi, S. Arakawa, T. Ishikawa, and A. Kasukawa, “Integrated GaInAsP laser diodes with monitoring photodiodes through semiconductor/air Bragg reflector (SABAR),” IEEE J. Sel. Top. Quantum Electron. 5, 469–475 (1999).
[Crossref]

Jensen, J. S.

J. S. Jensen and O. Sigmund, “Topology optimization for nano-photonics,” Laser Photon. Rev. 5, 308–321 (2011).
[Crossref]

Jeong, J.

Kakitsuka, T.

B. Docter, T. Segawa, T. Kakitsuka, S. Matsuo, T. Ishii, Y. Kawaguchi, Y. Kondo, H. Suzuki, F. Karouta, and M. K. Smit, “Short cavity DBR laser using vertical groove gratings for large-scale photonic integrated circuits,” IEEE Photon. Technol. Lett. 19, 1469–1471 (2007).
[Crossref]

Karouta, F.

B. Docter, T. Segawa, T. Kakitsuka, S. Matsuo, T. Ishii, Y. Kawaguchi, Y. Kondo, H. Suzuki, F. Karouta, and M. K. Smit, “Short cavity DBR laser using vertical groove gratings for large-scale photonic integrated circuits,” IEEE Photon. Technol. Lett. 19, 1469–1471 (2007).
[Crossref]

Kasukawa, A.

T. Mukaihara, N. Yamanaka, N. Iwai, M. Funabashi, S. Arakawa, T. Ishikawa, and A. Kasukawa, “Integrated GaInAsP laser diodes with monitoring photodiodes through semiconductor/air Bragg reflector (SABAR),” IEEE J. Sel. Top. Quantum Electron. 5, 469–475 (1999).
[Crossref]

Kawaguchi, Y.

B. Docter, T. Segawa, T. Kakitsuka, S. Matsuo, T. Ishii, Y. Kawaguchi, Y. Kondo, H. Suzuki, F. Karouta, and M. K. Smit, “Short cavity DBR laser using vertical groove gratings for large-scale photonic integrated circuits,” IEEE Photon. Technol. Lett. 19, 1469–1471 (2007).
[Crossref]

Khajavikhan, M.

Kirk, J. B.

S. R. Selmic, G. A. Evans, T. M. Chou, J. B. Kirk, J. N. Walpole, J. P. Donnelly, C. T. Harris, and L. J. Missaggia, “Single frequency 1550-nm AlGaInAs-InP tapered high-power laser with a distributed Bragg reflector,” IEEE Photon. Technol. Lett. 14, 890–892 (2002).
[Crossref]

Kondo, Y.

B. Docter, T. Segawa, T. Kakitsuka, S. Matsuo, T. Ishii, Y. Kawaguchi, Y. Kondo, H. Suzuki, F. Karouta, and M. K. Smit, “Short cavity DBR laser using vertical groove gratings for large-scale photonic integrated circuits,” IEEE Photon. Technol. Lett. 19, 1469–1471 (2007).
[Crossref]

Kristensen, M.

Lagoudakis, K. G.

A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vučković, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9, 374–377 (2015).
[Crossref]

Lavrinenko, A.

Li, H.

Lipson, M.

C. A. Barrios, V. R. Almeida, R. R. Panepucci, B. S. Schmidt, and M. Lipson, “Compact silicon tunable Fabry–Perot resonator with low power consumption,” IEEE Photon. Technol. Lett. 16, 506–508 (2004).
[Crossref]

Liu, L.

Lu, J.

A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vučković, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9, 374–377 (2015).
[Crossref]

Mak, J. C. C.

Martelli, C.

Matsuo, S.

B. Docter, T. Segawa, T. Kakitsuka, S. Matsuo, T. Ishii, Y. Kawaguchi, Y. Kondo, H. Suzuki, F. Karouta, and M. K. Smit, “Short cavity DBR laser using vertical groove gratings for large-scale photonic integrated circuits,” IEEE Photon. Technol. Lett. 19, 1469–1471 (2007).
[Crossref]

McNab, S. J.

Menon, R.

B. Shen, P. Wang, R. Polson, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4 × 2.4  μm2 footprint,” Nat. Photonics 9, 378–382 (2015).
[Crossref]

Missaggia, L. J.

S. R. Selmic, G. A. Evans, T. M. Chou, J. B. Kirk, J. N. Walpole, J. P. Donnelly, C. T. Harris, and L. J. Missaggia, “Single frequency 1550-nm AlGaInAs-InP tapered high-power laser with a distributed Bragg reflector,” IEEE Photon. Technol. Lett. 14, 890–892 (2002).
[Crossref]

Mitchell, A.

J. Wu, T. Moein, X. Xu, G. Ren, A. Mitchell, and D. J. Moss, “Micro-ring resonator quality factor enhancement via an integrated Fabry–Perot cavity,” APL Photon. 2, 056103 (2017).
[Crossref]

Mitrovic, M.

Moein, T.

J. Wu, T. Moein, X. Xu, G. Ren, A. Mitchell, and D. J. Moss, “Micro-ring resonator quality factor enhancement via an integrated Fabry–Perot cavity,” APL Photon. 2, 056103 (2017).
[Crossref]

Moss, D. J.

J. Wu, T. Moein, X. Xu, G. Ren, A. Mitchell, and D. J. Moss, “Micro-ring resonator quality factor enhancement via an integrated Fabry–Perot cavity,” APL Photon. 2, 056103 (2017).
[Crossref]

Mukaihara, T.

T. Mukaihara, N. Yamanaka, N. Iwai, M. Funabashi, S. Arakawa, T. Ishikawa, and A. Kasukawa, “Integrated GaInAsP laser diodes with monitoring photodiodes through semiconductor/air Bragg reflector (SABAR),” IEEE J. Sel. Top. Quantum Electron. 5, 469–475 (1999).
[Crossref]

Panepucci, R. R.

C. A. Barrios, V. R. Almeida, R. R. Panepucci, B. S. Schmidt, and M. Lipson, “Compact silicon tunable Fabry–Perot resonator with low power consumption,” IEEE Photon. Technol. Lett. 16, 506–508 (2004).
[Crossref]

Petykiewicz, J.

A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vučković, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9, 374–377 (2015).
[Crossref]

Piggott, A. Y.

A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vučković, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9, 374–377 (2015).
[Crossref]

Polson, R.

B. Shen, P. Wang, R. Polson, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4 × 2.4  μm2 footprint,” Nat. Photonics 9, 378–382 (2015).
[Crossref]

Poon, J. K. S.

Pruessner, M. W.

Rabinovich, W. S.

Rabus, D. G.

D. G. Rabus, Integrated Ring Resonators (Springer-Verlag, 2007).

Ren, G.

J. Wu, T. Moein, X. Xu, G. Ren, A. Mitchell, and D. J. Moss, “Micro-ring resonator quality factor enhancement via an integrated Fabry–Perot cavity,” APL Photon. 2, 056103 (2017).
[Crossref]

Roßkopf, J.

N. Ulbrich, G. Scarpa, A. Sigl, J. Roßkopf, G. Böhm, G. Abstreiter, and M.-C. Amann, “High-temperature (T ≥ 470  K) pulsed operation of 5.5  μm quantum cascade lasers with high-reflection coating,” Electron. Lett. 37, 1341–1342 (2001).
[Crossref]

Scarpa, G.

N. Ulbrich, G. Scarpa, A. Sigl, J. Roßkopf, G. Böhm, G. Abstreiter, and M.-C. Amann, “High-temperature (T ≥ 470  K) pulsed operation of 5.5  μm quantum cascade lasers with high-reflection coating,” Electron. Lett. 37, 1341–1342 (2001).
[Crossref]

Schmidt, B. S.

C. A. Barrios, V. R. Almeida, R. R. Panepucci, B. S. Schmidt, and M. Lipson, “Compact silicon tunable Fabry–Perot resonator with low power consumption,” IEEE Photon. Technol. Lett. 16, 506–508 (2004).
[Crossref]

Segawa, T.

B. Docter, T. Segawa, T. Kakitsuka, S. Matsuo, T. Ishii, Y. Kawaguchi, Y. Kondo, H. Suzuki, F. Karouta, and M. K. Smit, “Short cavity DBR laser using vertical groove gratings for large-scale photonic integrated circuits,” IEEE Photon. Technol. Lett. 19, 1469–1471 (2007).
[Crossref]

Selmic, S. R.

S. R. Selmic, G. A. Evans, T. M. Chou, J. B. Kirk, J. N. Walpole, J. P. Donnelly, C. T. Harris, and L. J. Missaggia, “Single frequency 1550-nm AlGaInAs-InP tapered high-power laser with a distributed Bragg reflector,” IEEE Photon. Technol. Lett. 14, 890–892 (2002).
[Crossref]

Shen, B.

B. Shen, P. Wang, R. Polson, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4 × 2.4  μm2 footprint,” Nat. Photonics 9, 378–382 (2015).
[Crossref]

Shi, Y.

S. Chen, Y. Shi, S. He, and D. Dai, “Variable optical attenuator based on a reflective Mach–Zehnder interferometer,” Opt. Commun. 361, 55–58 (2016).
[Crossref]

Sideris, C.

Sigl, A.

N. Ulbrich, G. Scarpa, A. Sigl, J. Roßkopf, G. Böhm, G. Abstreiter, and M.-C. Amann, “High-temperature (T ≥ 470  K) pulsed operation of 5.5  μm quantum cascade lasers with high-reflection coating,” Electron. Lett. 37, 1341–1342 (2001).
[Crossref]

Sigmund, O.

L. F. Frellsen, Y. Ding, O. Sigmund, and L. H. Frandsen, “Topology optimized mode multiplexing in silicon-on-insulator photonic wire waveguides,” Opt. Express 24, 16866–16873 (2016).
[Crossref]

L. H. Frandsen, Y. Elesin, L. F. Frellsen, M. Mitrovic, Y. Ding, O. Sigmund, and K. Yvind, “Topology optimized mode conversion in a photonic crystal waveguide fabricated in silicon-on-insulator material,” Opt. Express 22, 8525–8532 (2014).
[Crossref]

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[Crossref]

L. H. Frandsen, Y. Elesin, O. Sigmund, and K. Yvind, “Topology optimization of coupled photonic crystal cavities for flat-top drop filter functionality,” in European Conference on Lasers and Electro-Optics-European Quantum Electronics Conference, Munich, Germany (Optical Society of America, 2015), paper CK_9_1.

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B. Docter, T. Segawa, T. Kakitsuka, S. Matsuo, T. Ishii, Y. Kawaguchi, Y. Kondo, H. Suzuki, F. Karouta, and M. K. Smit, “Short cavity DBR laser using vertical groove gratings for large-scale photonic integrated circuits,” IEEE Photon. Technol. Lett. 19, 1469–1471 (2007).
[Crossref]

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[Crossref]

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[Crossref]

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APL Photon. (1)

J. Wu, T. Moein, X. Xu, G. Ren, A. Mitchell, and D. J. Moss, “Micro-ring resonator quality factor enhancement via an integrated Fabry–Perot cavity,” APL Photon. 2, 056103 (2017).
[Crossref]

Electron. Lett. (1)

N. Ulbrich, G. Scarpa, A. Sigl, J. Roßkopf, G. Böhm, G. Abstreiter, and M.-C. Amann, “High-temperature (T ≥ 470  K) pulsed operation of 5.5  μm quantum cascade lasers with high-reflection coating,” Electron. Lett. 37, 1341–1342 (2001).
[Crossref]

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

T. Mukaihara, N. Yamanaka, N. Iwai, M. Funabashi, S. Arakawa, T. Ishikawa, and A. Kasukawa, “Integrated GaInAsP laser diodes with monitoring photodiodes through semiconductor/air Bragg reflector (SABAR),” IEEE J. Sel. Top. Quantum Electron. 5, 469–475 (1999).
[Crossref]

IEEE Photon. Technol. Lett. (3)

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[Crossref]

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C. A. Barrios, V. R. Almeida, R. R. Panepucci, B. S. Schmidt, and M. Lipson, “Compact silicon tunable Fabry–Perot resonator with low power consumption,” IEEE Photon. Technol. Lett. 16, 506–508 (2004).
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Laser Photon. Rev. (1)

J. S. Jensen and O. Sigmund, “Topology optimization for nano-photonics,” Laser Photon. Rev. 5, 308–321 (2011).
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A. Y. Piggott, J. Lu, K. G. Lagoudakis, J. Petykiewicz, T. M. Babinec, and J. Vučković, “Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer,” Nat. Photonics 9, 374–377 (2015).
[Crossref]

B. Shen, P. Wang, R. Polson, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4 × 2.4  μm2 footprint,” Nat. Photonics 9, 378–382 (2015).
[Crossref]

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S. Chen, Y. Shi, S. He, and D. Dai, “Variable optical attenuator based on a reflective Mach–Zehnder interferometer,” Opt. Commun. 361, 55–58 (2016).
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Opt. Express (6)

Opt. Lett. (4)

Other (2)

D. G. Rabus, Integrated Ring Resonators (Springer-Verlag, 2007).

L. H. Frandsen, Y. Elesin, O. Sigmund, and K. Yvind, “Topology optimization of coupled photonic crystal cavities for flat-top drop filter functionality,” in European Conference on Lasers and Electro-Optics-European Quantum Electronics Conference, Munich, Germany (Optical Society of America, 2015), paper CK_9_1.

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Figures (6)

Fig. 1.
Fig. 1. (a) Initial silicon slab before design optimization. (b) Final optimized structure of the on-chip reflector. Field profiles (Ey component) as the input TE0 mode at a wavelength of 1550 nm reflects (c) from the initial silicon slab and (d) from the optimized structure. Field profiles (Ey component) (e) of the reflected light and (f) of the source at the wavelength of 1550 nm. The scale bars represent 1 μm in (a)–(d) and represent 0.5 μm in (e) and (f). (g) Color code for the vertical structures in (a) and (b). Gray/red pixels denotes the etched/unetched area where no/220-nm silicon layer remains on top of the oxide.

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Fig. 2.
Fig. 2. (a) Flow chart for the genetic optimization process. (b) Illustration showing the crossover process. (c) Reflectivity spectra of the optimized reflector structure (red solid) and of the initial silicon slab (blue dashed). (d) Illustration showing the corner rounding effect. (e) Reflectivity spectra of the optimized reflector considering the corner rounding effect with different rounding radii.

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Fig. 3.
Fig. 3. (a) Layout of an FP cavity constructed from the optimized reflectors. (b) Calculated normalized transmission spectrum of the FP cavity. (c) Normalized transmission spectrum zoomed in at an optical resonance at ∼1551  nm.

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Fig. 4.
Fig. 4. (a) Optical microscope image of an FP cavity device. (b) Zoomed-in SEM image of the left grating coupler. (c) Zoomed-in SEM image of the right reflector.

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Fig. 5.
Fig. 5. (a) Normalized transmission spectrum of an FP cavity device. The wide-range spectrum is composed of spectra measured from four devices with identical FP cavities but different grating couplers to cover different wavelength bands. The red dashed lines denote the stitching points of the spectra. Zoomed-in spectra showing optical resonances at (b) 1443 and (c) 1620 nm, each fitted with a Lorentzian resonance line shape (red).

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Fig. 6.
Fig. 6. Reflectivity spectra of the optimized reflectors simulated for the ideal structure (blue solid line), simulated for the fabricated structure (black dashed line), and derived from the experimentally measured FP cavity quality factors (red dots).

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Equations (1)

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T=|t−κ2tR exp(i4πneffL/λ)1−t2R exp(i4πneffL/λ)|2,

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