Abstract

Layer chirping can be used to extend the photonic band-gap of dielectrics mirrors to cover a wide spectral bandwidth. However, for structures composed of dielectrics with non-negligible absorption and scattering, linear chirping introduces Gires-Tournois resonances that can enhance optical losses within the stop-band. We show that the use double-chirping, a concept originally developed for dispersion compensation in ultra-fast optics, can be used to substantially reduce unwanted losses and improve the spectral reflectance over the entire stop-band. We demonstrate the concept experimentally by fabricating broad-band mirrors in the visible range using porous silicon.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref] [PubMed]
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2016 (1)

2015 (1)

B. Gupta, K. Mai, S. B. Lowe, D. Wakefield, N. Di Girolamo, K. Gaus, P. J. Reece, and J. J. Gooding, “Ultrasensitive and specific measurement of protease activity using functionalized photonic crystals,” Anal. Chem. 87, 9946–9953 (2015).
[Crossref] [PubMed]

2014 (1)

J. Zheng, R. A. Barton, and D. Englund, “Broadband coherent absorption in chirped-planar-dielectric cavities for 2D-material-based photovoltaics and photodetectors,” ACS Photonics 1, 768–774 (2014).
[Crossref]

2011 (2)

S. Guldin, M. Kolle, M. Stefik, R. Langford, D. Eder, U. Wiesner, and U. Steiner, “Tunable mesoporous bragg reflectors based on block-copolymer self-assembly,” Adv. Mater. 23, 3664–3668 (2011).
[Crossref] [PubMed]

A. Boltasseva, H. A. Atwater, and V. M. Shalaev, “Low-Loss Plasmonic Metamaterials,” Science 331, 290–291 (2011).
[Crossref] [PubMed]

2010 (1)

H. Qiao, B. Guan, T. Böcking, M. Gal, J. J. Gooding, and P. J. Reece, “Optical properties of ii-vi colloidal quantum dot doped porous silicon microcavities,” Appl. Phys. Lett. 96, 161106 (2010).
[Crossref]

2009 (1)

Q. Gan, Y. J. Ding, and F. J. Bartoli, “‘Rainbow’ trapping and releasing at telecommunication wavelengths,” Phys. Rev. Lett. 102, 056801 (2009).
[Crossref]

2008 (1)

2007 (2)

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450, 397–401 (2007).
[Crossref] [PubMed]

N. A. Mortensen and S. Xiao, “Slow-light enhancement of beer-lambert-bouguer absorption,” Appl. Phys. Lett. 90, 141108 (2007).
[Crossref]

2004 (1)

W. H. Zheng, P. Reece, B. Q. Sun, and M. Gal, “Broadband laser mirrors made from porous silicon,” Appl. Phys. Lett. 84, 3519–3521 (2004).
[Crossref]

2003 (2)

1998 (1)

N. Matuschek, F. X. Kärtner, and U. Keller, “Theory of double-chirped mirrors,” IEEE J. on Sel. Top. Quantum Electron. 4, 197–208 (1998).
[Crossref]

1997 (2)

1994 (1)

Agrawal, M.

Amir, A.

Atwater, H. A.

A. Boltasseva, H. A. Atwater, and V. M. Shalaev, “Low-Loss Plasmonic Metamaterials,” Science 331, 290–291 (2011).
[Crossref] [PubMed]

Barret, S.

G. Lérondel, R. Romestain, and S. Barret, “Roughness of the porous silicon dissolution interface,” J. Appl. Phys. 81, 6171–6178 (1997).
[Crossref]

Bartoli, F. J.

Q. Gan, Y. J. Ding, and F. J. Bartoli, “‘Rainbow’ trapping and releasing at telecommunication wavelengths,” Phys. Rev. Lett. 102, 056801 (2009).
[Crossref]

Barton, R. A.

J. Zheng, R. A. Barton, and D. Englund, “Broadband coherent absorption in chirped-planar-dielectric cavities for 2D-material-based photovoltaics and photodetectors,” ACS Photonics 1, 768–774 (2014).
[Crossref]

Boardman, A. D.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450, 397–401 (2007).
[Crossref] [PubMed]

Böcking, T.

H. Qiao, B. Guan, T. Böcking, M. Gal, J. J. Gooding, and P. J. Reece, “Optical properties of ii-vi colloidal quantum dot doped porous silicon microcavities,” Appl. Phys. Lett. 96, 161106 (2010).
[Crossref]

Boltasseva, A.

A. Boltasseva, H. A. Atwater, and V. M. Shalaev, “Low-Loss Plasmonic Metamaterials,” Science 331, 290–291 (2011).
[Crossref] [PubMed]

Cook, C. Q.

Ding, Y. J.

Q. Gan, Y. J. Ding, and F. J. Bartoli, “‘Rainbow’ trapping and releasing at telecommunication wavelengths,” Phys. Rev. Lett. 102, 056801 (2009).
[Crossref]

Eder, D.

S. Guldin, M. Kolle, M. Stefik, R. Langford, D. Eder, U. Wiesner, and U. Steiner, “Tunable mesoporous bragg reflectors based on block-copolymer self-assembly,” Adv. Mater. 23, 3664–3668 (2011).
[Crossref] [PubMed]

Englund, D.

J. Zheng, R. A. Barton, and D. Englund, “Broadband coherent absorption in chirped-planar-dielectric cavities for 2D-material-based photovoltaics and photodetectors,” ACS Photonics 1, 768–774 (2014).
[Crossref]

Ferencz, K.

Gal, M.

H. Qiao, B. Guan, T. Böcking, M. Gal, J. J. Gooding, and P. J. Reece, “Optical properties of ii-vi colloidal quantum dot doped porous silicon microcavities,” Appl. Phys. Lett. 96, 161106 (2010).
[Crossref]

W. H. Zheng, P. Reece, B. Q. Sun, and M. Gal, “Broadband laser mirrors made from porous silicon,” Appl. Phys. Lett. 84, 3519–3521 (2004).
[Crossref]

Gan, Q.

Q. Gan, Y. J. Ding, and F. J. Bartoli, “‘Rainbow’ trapping and releasing at telecommunication wavelengths,” Phys. Rev. Lett. 102, 056801 (2009).
[Crossref]

Gaus, K.

B. Gupta, K. Mai, S. B. Lowe, D. Wakefield, N. Di Girolamo, K. Gaus, P. J. Reece, and J. J. Gooding, “Ultrasensitive and specific measurement of protease activity using functionalized photonic crystals,” Anal. Chem. 87, 9946–9953 (2015).
[Crossref] [PubMed]

Girolamo, N. Di

B. Gupta, K. Mai, S. B. Lowe, D. Wakefield, N. Di Girolamo, K. Gaus, P. J. Reece, and J. J. Gooding, “Ultrasensitive and specific measurement of protease activity using functionalized photonic crystals,” Anal. Chem. 87, 9946–9953 (2015).
[Crossref] [PubMed]

Gooding, J. J.

B. Gupta, K. Mai, S. B. Lowe, D. Wakefield, N. Di Girolamo, K. Gaus, P. J. Reece, and J. J. Gooding, “Ultrasensitive and specific measurement of protease activity using functionalized photonic crystals,” Anal. Chem. 87, 9946–9953 (2015).
[Crossref] [PubMed]

H. Qiao, B. Guan, T. Böcking, M. Gal, J. J. Gooding, and P. J. Reece, “Optical properties of ii-vi colloidal quantum dot doped porous silicon microcavities,” Appl. Phys. Lett. 96, 161106 (2010).
[Crossref]

Guan, B.

H. Qiao, B. Guan, T. Böcking, M. Gal, J. J. Gooding, and P. J. Reece, “Optical properties of ii-vi colloidal quantum dot doped porous silicon microcavities,” Appl. Phys. Lett. 96, 161106 (2010).
[Crossref]

Guldin, S.

S. Guldin, M. Kolle, M. Stefik, R. Langford, D. Eder, U. Wiesner, and U. Steiner, “Tunable mesoporous bragg reflectors based on block-copolymer self-assembly,” Adv. Mater. 23, 3664–3668 (2011).
[Crossref] [PubMed]

Gupta, B.

B. Gupta, K. Mai, S. B. Lowe, D. Wakefield, N. Di Girolamo, K. Gaus, P. J. Reece, and J. J. Gooding, “Ultrasensitive and specific measurement of protease activity using functionalized photonic crystals,” Anal. Chem. 87, 9946–9953 (2015).
[Crossref] [PubMed]

Han, P.

Haus, H. A.

Heine, C.

Hess, O.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450, 397–401 (2007).
[Crossref] [PubMed]

Kärtner, F. X.

Keller, U.

Kolle, M.

S. Guldin, M. Kolle, M. Stefik, R. Langford, D. Eder, U. Wiesner, and U. Steiner, “Tunable mesoporous bragg reflectors based on block-copolymer self-assembly,” Adv. Mater. 23, 3664–3668 (2011).
[Crossref] [PubMed]

Krausz, F.

Langford, R.

S. Guldin, M. Kolle, M. Stefik, R. Langford, D. Eder, U. Wiesner, and U. Steiner, “Tunable mesoporous bragg reflectors based on block-copolymer self-assembly,” Adv. Mater. 23, 3664–3668 (2011).
[Crossref] [PubMed]

Lérondel, G.

G. Lérondel, R. Romestain, and S. Barret, “Roughness of the porous silicon dissolution interface,” J. Appl. Phys. 81, 6171–6178 (1997).
[Crossref]

Lowe, S. B.

B. Gupta, K. Mai, S. B. Lowe, D. Wakefield, N. Di Girolamo, K. Gaus, P. J. Reece, and J. J. Gooding, “Ultrasensitive and specific measurement of protease activity using functionalized photonic crystals,” Anal. Chem. 87, 9946–9953 (2015).
[Crossref] [PubMed]

MacLeod, H.

H. MacLeod, Thin-Film Optical Filters, Third Edition, Series in Optics and Optoelectronics (CRC Press, 2001).
[Crossref]

Mai, K.

B. Gupta, K. Mai, S. B. Lowe, D. Wakefield, N. Di Girolamo, K. Gaus, P. J. Reece, and J. J. Gooding, “Ultrasensitive and specific measurement of protease activity using functionalized photonic crystals,” Anal. Chem. 87, 9946–9953 (2015).
[Crossref] [PubMed]

Matuschek, N.

Morf, R.

Mortensen, N. A.

N. A. Mortensen and S. Xiao, “Slow-light enhancement of beer-lambert-bouguer absorption,” Appl. Phys. Lett. 90, 141108 (2007).
[Crossref]

Peumans, P.

Qiao, H.

H. Qiao, B. Guan, T. Böcking, M. Gal, J. J. Gooding, and P. J. Reece, “Optical properties of ii-vi colloidal quantum dot doped porous silicon microcavities,” Appl. Phys. Lett. 96, 161106 (2010).
[Crossref]

Reece, P.

W. H. Zheng, P. Reece, B. Q. Sun, and M. Gal, “Broadband laser mirrors made from porous silicon,” Appl. Phys. Lett. 84, 3519–3521 (2004).
[Crossref]

Reece, P. J.

B. Gupta, K. Mai, S. B. Lowe, D. Wakefield, N. Di Girolamo, K. Gaus, P. J. Reece, and J. J. Gooding, “Ultrasensitive and specific measurement of protease activity using functionalized photonic crystals,” Anal. Chem. 87, 9946–9953 (2015).
[Crossref] [PubMed]

H. Qiao, B. Guan, T. Böcking, M. Gal, J. J. Gooding, and P. J. Reece, “Optical properties of ii-vi colloidal quantum dot doped porous silicon microcavities,” Appl. Phys. Lett. 96, 161106 (2010).
[Crossref]

Romestain, R.

G. Lérondel, R. Romestain, and S. Barret, “Roughness of the porous silicon dissolution interface,” J. Appl. Phys. 81, 6171–6178 (1997).
[Crossref]

Sambles, J. R.

P. Vukusic and J. R. Sambles, “Photonic structures in biology,” Nature 424, 852–855 (2003).
[Crossref] [PubMed]

Scheuer, V.

Schibli, T.

Shalaev, V. M.

A. Boltasseva, H. A. Atwater, and V. M. Shalaev, “Low-Loss Plasmonic Metamaterials,” Science 331, 290–291 (2011).
[Crossref] [PubMed]

Spielmann, C.

Stefik, M.

S. Guldin, M. Kolle, M. Stefik, R. Langford, D. Eder, U. Wiesner, and U. Steiner, “Tunable mesoporous bragg reflectors based on block-copolymer self-assembly,” Adv. Mater. 23, 3664–3668 (2011).
[Crossref] [PubMed]

Steiner, U.

S. Guldin, M. Kolle, M. Stefik, R. Langford, D. Eder, U. Wiesner, and U. Steiner, “Tunable mesoporous bragg reflectors based on block-copolymer self-assembly,” Adv. Mater. 23, 3664–3668 (2011).
[Crossref] [PubMed]

Sun, B. Q.

W. H. Zheng, P. Reece, B. Q. Sun, and M. Gal, “Broadband laser mirrors made from porous silicon,” Appl. Phys. Lett. 84, 3519–3521 (2004).
[Crossref]

Szipöcs, R.

Tilsch, M.

Tsakmakidis, K. L.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450, 397–401 (2007).
[Crossref] [PubMed]

Tschudi, T.

Vukusic, P.

P. Vukusic and J. R. Sambles, “Photonic structures in biology,” Nature 424, 852–855 (2003).
[Crossref] [PubMed]

Wakefield, D.

B. Gupta, K. Mai, S. B. Lowe, D. Wakefield, N. Di Girolamo, K. Gaus, P. J. Reece, and J. J. Gooding, “Ultrasensitive and specific measurement of protease activity using functionalized photonic crystals,” Anal. Chem. 87, 9946–9953 (2015).
[Crossref] [PubMed]

Wang, H.

Weber, M.

M. Weber, Handbook of Optical Materials, Laser & Optical Science & Technology (Taylor & Francis, 2002).
[Crossref]

Wiesner, U.

S. Guldin, M. Kolle, M. Stefik, R. Langford, D. Eder, U. Wiesner, and U. Steiner, “Tunable mesoporous bragg reflectors based on block-copolymer self-assembly,” Adv. Mater. 23, 3664–3668 (2011).
[Crossref] [PubMed]

Xiao, S.

N. A. Mortensen and S. Xiao, “Slow-light enhancement of beer-lambert-bouguer absorption,” Appl. Phys. Lett. 90, 141108 (2007).
[Crossref]

Zheng, J.

J. Zheng, R. A. Barton, and D. Englund, “Broadband coherent absorption in chirped-planar-dielectric cavities for 2D-material-based photovoltaics and photodetectors,” ACS Photonics 1, 768–774 (2014).
[Crossref]

Zheng, W. H.

W. H. Zheng, P. Reece, B. Q. Sun, and M. Gal, “Broadband laser mirrors made from porous silicon,” Appl. Phys. Lett. 84, 3519–3521 (2004).
[Crossref]

ACS Photonics (1)

J. Zheng, R. A. Barton, and D. Englund, “Broadband coherent absorption in chirped-planar-dielectric cavities for 2D-material-based photovoltaics and photodetectors,” ACS Photonics 1, 768–774 (2014).
[Crossref]

Adv. Mater. (1)

S. Guldin, M. Kolle, M. Stefik, R. Langford, D. Eder, U. Wiesner, and U. Steiner, “Tunable mesoporous bragg reflectors based on block-copolymer self-assembly,” Adv. Mater. 23, 3664–3668 (2011).
[Crossref] [PubMed]

Anal. Chem. (1)

B. Gupta, K. Mai, S. B. Lowe, D. Wakefield, N. Di Girolamo, K. Gaus, P. J. Reece, and J. J. Gooding, “Ultrasensitive and specific measurement of protease activity using functionalized photonic crystals,” Anal. Chem. 87, 9946–9953 (2015).
[Crossref] [PubMed]

Appl. Phys. Lett. (3)

H. Qiao, B. Guan, T. Böcking, M. Gal, J. J. Gooding, and P. J. Reece, “Optical properties of ii-vi colloidal quantum dot doped porous silicon microcavities,” Appl. Phys. Lett. 96, 161106 (2010).
[Crossref]

N. A. Mortensen and S. Xiao, “Slow-light enhancement of beer-lambert-bouguer absorption,” Appl. Phys. Lett. 90, 141108 (2007).
[Crossref]

W. H. Zheng, P. Reece, B. Q. Sun, and M. Gal, “Broadband laser mirrors made from porous silicon,” Appl. Phys. Lett. 84, 3519–3521 (2004).
[Crossref]

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

N. Matuschek, F. X. Kärtner, and U. Keller, “Theory of double-chirped mirrors,” IEEE J. on Sel. Top. Quantum Electron. 4, 197–208 (1998).
[Crossref]

J. Appl. Phys. (1)

G. Lérondel, R. Romestain, and S. Barret, “Roughness of the porous silicon dissolution interface,” J. Appl. Phys. 81, 6171–6178 (1997).
[Crossref]

J. Opt. Soc. Am. B (1)

Nature (2)

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450, 397–401 (2007).
[Crossref] [PubMed]

P. Vukusic and J. R. Sambles, “Photonic structures in biology,” Nature 424, 852–855 (2003).
[Crossref] [PubMed]

Opt. Express (1)

Opt. Lett. (2)

Optica (1)

Phys. Rev. Lett. (1)

Q. Gan, Y. J. Ding, and F. J. Bartoli, “‘Rainbow’ trapping and releasing at telecommunication wavelengths,” Phys. Rev. Lett. 102, 056801 (2009).
[Crossref]

Science (1)

A. Boltasseva, H. A. Atwater, and V. M. Shalaev, “Low-Loss Plasmonic Metamaterials,” Science 331, 290–291 (2011).
[Crossref] [PubMed]

Other (2)

M. Weber, Handbook of Optical Materials, Laser & Optical Science & Technology (Taylor & Francis, 2002).
[Crossref]

H. MacLeod, Thin-Film Optical Filters, Third Edition, Series in Optics and Optoelectronics (CRC Press, 2001).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1 Layer thicknesses versus number for three different Bragg structures. (a) Quarter wave Bragg stack with a λB = 700nm is used as a reference for understanding the impact of intrinsic losses present in porous silicon, (b) a linearly chirped structure where the Bragg wavenumber is chirped from 9.89 µm −1 to 8.25 µm −1. The chirping range is chosen to match the width of the stop band achieved in the double chirped mirror. (c) A double chirped structure consisting of a double chirped impedance matching region (1–24), a linearly chirped region (25–45) and an un-chirped region (45–55). (d) Absorption coefficient of the different porous regions used for the simulations.
Fig. 2
Fig. 2 Cross-sectional SEM of the double-chirped porous silicon structure. Impedance matching is achieved by varying the low porosity layer over the front 12 periods of the structure. The scale bar is equal to 2 µm.
Fig. 3
Fig. 3 (a) Reflectivity versus wavelength for Bragg reflector with no chirp. (b) Reflectivity versus wavelength for linearly chirped structure.(c) Reflectivity versus wavelength for double chirped structure. Dark grey lines, simulated reflectivity with extinction coefficient turned off; blue lines, simulated reflectivity with extinction coefficient turned on; red lines, measured reflectivity.
Fig. 4
Fig. 4 Group delay (GD) versus wavelength for a Bragg reflector, a linearly chirped structure, a double chirped with an air incidence, and double chirped with glass incidence. Oscillations in the GD correspond to Gires-Tournois resonances which leads to enhanced absorption.

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