Abstract

Tunability of the optical response of multilayered photonic structures has been compared with sequential (SQ) and superposition (SP) addition of refractive index profile functions. The optical response of the composite multilayered structure, formed after the SP addition of the two Bragg type refractive index profile functions has been studied as a function of percentage overlap and relative shift between the profiles. Apart from the substantial advantage in terms of the reduced physical thickness of the SP composite structures (over the SQ addition), at certain optimum values of relative shift, photonic structures with better quality factor resonant modes or a broader PBG could be designed. Similar analysis has been extended for rugate filters as well. The experimental verification of the optical response, was carried out through multilayered dielectric porous silicon structures fabricated by electrochemical anodization.

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    [CrossRef]

2013

2012

V. V. Medvedev, A. E. Yakshin, R. W. E. van de Kruijs, V. M. Krivtsun, A. M. Yakunin, K. N. Koshelev, and F. Bijkerk, “Infrared antireflective filtering for extreme ultraviolet multilayer Bragg reflectors,” Opt. Lett.37, 1169–1171 (2012).
[CrossRef] [PubMed]

S. Li, D. Hu, J. Huang, and L. Cai, “Optical sensing nanostructures for porous silicon rugate filters,” Nano. Res. Lett.7, 000079 (2012).
[CrossRef]

D. Ariza-Flores, L. M. Gaggero-Sager, and V. Agarwal, “White metal-like omnidirectional mirror from porous silicon dielectric multilayers,” Appl. Phys. Lett.101, 031119 (2012).
[CrossRef]

K. S. Pérez, J. O. Estevez, A. Méndez-Blas, J. Arriaga, G. Palestino, and M. E. Mora-Ramos, “Tunable resonance transmission modes in hybrid heterostructures based on porous silicon,” Nano. Res. Lett.7, 000392 (2012).
[CrossRef]

2011

2009

J. O. Estevez, J. Arriaga, A. Méndez-Blas, and V. Agarwal, “Enlargement of omnidirectional photonic bandgap in porous silicon dielectric mirrors with a Gaussian profile refractive index,” Appl. Phys. Lett.94, 061914 (2009).
[CrossRef]

P. Apiratikul, A. M. Rossi, and T. E. Murphy, “Nonlinearities in porous silicon optical waveguides at 1550 nm,” Opt. Express17, 3396–3406 (2009).
[CrossRef] [PubMed]

T. Jalkanen, V. Torres-Costa, J. Salonen, M. Björkqvist, E. Mäkilä, J. M. Martínez-Duart, and V. P. Lehto, “Optical gas sensing properties of thermally hydrocarbonized porous silicon Bragg reflectors,” Opt. Express17, 5446–5456 (2009).
[CrossRef] [PubMed]

M. Y. Chen, S. O. Meade, and M. J. Sailor, “Preparation and analysis of porous silicon multilayers for spectral encoding applications,” Phys. Stat. Sol. (c)6, 1610–1614 (2009).
[CrossRef]

E. Xifré-Pérez, L. F. Marsal, J. Ferré-Borrull, and J. Pallarés, “Low refractive index contrast porous silicon omnidirectional reflectors,” Appl. Phys. B: Lasers and Opt.95, 169–172 (2009).
[CrossRef]

S. O. Meade, M. Y. Chen, M. J. Sailor, and G. M. Miskelly, “Multiplexed DNA detection using spectrally encoded porous SiO2photonic crystal particles,” Anal. Chem.81, 2618–2625 (2009).

2007

S. Ilyas, T. Bocking, K. Kilian, P.J. Reece, J. Gooding, K. Gaus, and M. Gal, “Porous silicon based narrow line-width rugate filters,” Opt. Mat.29, 619–622 (2007).
[CrossRef]

S. O. Meade and M. J. Sailor, “Microfabrication of freestanding porous silicon particles containing spectral barcodes,” Phys. Stat. Sol. (RRL)1, R71–R73 (2007).
[CrossRef]

2006

S. F. Chichibu, T. Ohmori, N. Shibata, and T. Koyama, “Dielectric SiO2/ZrO2distributed Bragg reflectors for ZnO microcavities prepared by the reactive helicon-wave-excited-plasma sputtering method,” Appl. Phys. Lett.88, 161914 (2006).
[CrossRef]

A. Hosseini and Y. Massoud, “A low-loss metal-insulator-metal plasmonic Bragg reflector,” Opt. Express14, 11318–11323 (2006).
[CrossRef]

2004

S. O. Meade, M. S. Yoon, K. H. Ahn, and M. J. Sailor, “Porous silicon photonic crystals as encoded microcarriers,” Adv. Mat.16, 1811–1814 (2004).
[CrossRef]

2003

Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, “Resonance transmission modes in dual-periodical dielectric multilayer films,” Appl. Phys. Lett.82, 004654 (2003).
[CrossRef]

V. Agarwal and J. A. del Río, “Tailoring the photonic band gap of a porous silicon dielectric mirror,” Appl. Phys. Lett.82, 001512 (2003).
[CrossRef]

2002

P. J. Reece, G. Lérondel, W. H. Zheng, and M. Gal, “Optical microcavities with subnanometer linewidths based on porous silicon,” Appl. Phys. Lett.81, 004895 (2002).
[CrossRef]

D. Bria, B. Djafari-Rouhani, E. H. El Boudouti, A. Mir, A. Akjouj, and A. Nougaoui, “Omnidirectional optical mirror in a cladded-superlattice structure,” J. Appl. Phys.91, 2569–2572 (2002).
[CrossRef]

1999

P. A. Snow, E. K. Squire, P. St. J. Russell, and L. T. Canham, “Vapor sensing using the optical properties of porous silicon Bragg mirrors,” J. Appl. Phys.86, 1781–1784 (1999).
[CrossRef]

1998

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science282, 1679–1682 (1998).
[CrossRef] [PubMed]

1996

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett.77, 3787–3790 (1996).
[CrossRef] [PubMed]

1995

C. Mazzoleni and L. Pavesi, “Application to optical components of dielectric porous silicon multilayers,” Appl. Phys. Lett.67, 002983 (1995).
[CrossRef]

1987

K. Kojima, S. Noda, K. Mitsunaga, K. Kyuma, and K. Hamanaka, “Continuous wave operation of a surface emitting AlGaAs/GaAs multiquantum well distributed Bragg reflector laser,” Appl. Phys. Lett.50, 001705 (1987).
[CrossRef]

Agarwal, V.

D. Ariza-Flores, L. M. Gaggero-Sager, and V. Agarwal, “White metal-like omnidirectional mirror from porous silicon dielectric multilayers,” Appl. Phys. Lett.101, 031119 (2012).
[CrossRef]

J. O. Estevez, J. Arriaga, A. Méndez-Blas, and V. Agarwal, “Enlargement of omnidirectional photonic bandgap in porous silicon dielectric mirrors with a Gaussian profile refractive index,” Appl. Phys. Lett.94, 061914 (2009).
[CrossRef]

V. Agarwal and J. A. del Río, “Tailoring the photonic band gap of a porous silicon dielectric mirror,” Appl. Phys. Lett.82, 001512 (2003).
[CrossRef]

Ahn, K. H.

S. O. Meade, M. S. Yoon, K. H. Ahn, and M. J. Sailor, “Porous silicon photonic crystals as encoded microcarriers,” Adv. Mat.16, 1811–1814 (2004).
[CrossRef]

Akjouj, A.

D. Bria, B. Djafari-Rouhani, E. H. El Boudouti, A. Mir, A. Akjouj, and A. Nougaoui, “Omnidirectional optical mirror in a cladded-superlattice structure,” J. Appl. Phys.91, 2569–2572 (2002).
[CrossRef]

Apiratikul, P.

Ariza-Flores, D.

D. Ariza-Flores, L. M. Gaggero-Sager, and V. Agarwal, “White metal-like omnidirectional mirror from porous silicon dielectric multilayers,” Appl. Phys. Lett.101, 031119 (2012).
[CrossRef]

Arriaga, J.

K. S. Pérez, J. O. Estevez, A. Méndez-Blas, J. Arriaga, G. Palestino, and M. E. Mora-Ramos, “Tunable resonance transmission modes in hybrid heterostructures based on porous silicon,” Nano. Res. Lett.7, 000392 (2012).
[CrossRef]

J. O. Estevez, J. Arriaga, A. Méndez-Blas, and V. Agarwal, “Enlargement of omnidirectional photonic bandgap in porous silicon dielectric mirrors with a Gaussian profile refractive index,” Appl. Phys. Lett.94, 061914 (2009).
[CrossRef]

Bijkerk, F.

Björkqvist, M.

Bocking, T.

S. Ilyas, T. Bocking, K. Kilian, P.J. Reece, J. Gooding, K. Gaus, and M. Gal, “Porous silicon based narrow line-width rugate filters,” Opt. Mat.29, 619–622 (2007).
[CrossRef]

Bourouina, T.

Bria, D.

D. Bria, B. Djafari-Rouhani, E. H. El Boudouti, A. Mir, A. Akjouj, and A. Nougaoui, “Omnidirectional optical mirror in a cladded-superlattice structure,” J. Appl. Phys.91, 2569–2572 (2002).
[CrossRef]

Cai, L.

S. Li, D. Hu, J. Huang, and L. Cai, “Optical sensing nanostructures for porous silicon rugate filters,” Nano. Res. Lett.7, 000079 (2012).
[CrossRef]

Canham, L. T.

P. A. Snow, E. K. Squire, P. St. J. Russell, and L. T. Canham, “Vapor sensing using the optical properties of porous silicon Bragg mirrors,” J. Appl. Phys.86, 1781–1784 (1999).
[CrossRef]

Chen, C.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science282, 1679–1682 (1998).
[CrossRef] [PubMed]

Chen, J. C.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett.77, 3787–3790 (1996).
[CrossRef] [PubMed]

Chen, M. Y.

M. Y. Chen, S. O. Meade, and M. J. Sailor, “Preparation and analysis of porous silicon multilayers for spectral encoding applications,” Phys. Stat. Sol. (c)6, 1610–1614 (2009).
[CrossRef]

S. O. Meade, M. Y. Chen, M. J. Sailor, and G. M. Miskelly, “Multiplexed DNA detection using spectrally encoded porous SiO2photonic crystal particles,” Anal. Chem.81, 2618–2625 (2009).

Chichibu, S. F.

S. F. Chichibu, T. Ohmori, N. Shibata, and T. Koyama, “Dielectric SiO2/ZrO2distributed Bragg reflectors for ZnO microcavities prepared by the reactive helicon-wave-excited-plasma sputtering method,” Appl. Phys. Lett.88, 161914 (2006).
[CrossRef]

del Río, J. A.

V. Agarwal and J. A. del Río, “Tailoring the photonic band gap of a porous silicon dielectric mirror,” Appl. Phys. Lett.82, 001512 (2003).
[CrossRef]

Djafari-Rouhani, B.

D. Bria, B. Djafari-Rouhani, E. H. El Boudouti, A. Mir, A. Akjouj, and A. Nougaoui, “Omnidirectional optical mirror in a cladded-superlattice structure,” J. Appl. Phys.91, 2569–2572 (2002).
[CrossRef]

El Boudouti, E. H.

D. Bria, B. Djafari-Rouhani, E. H. El Boudouti, A. Mir, A. Akjouj, and A. Nougaoui, “Omnidirectional optical mirror in a cladded-superlattice structure,” J. Appl. Phys.91, 2569–2572 (2002).
[CrossRef]

Estevez, J. O.

K. S. Pérez, J. O. Estevez, A. Méndez-Blas, J. Arriaga, G. Palestino, and M. E. Mora-Ramos, “Tunable resonance transmission modes in hybrid heterostructures based on porous silicon,” Nano. Res. Lett.7, 000392 (2012).
[CrossRef]

J. O. Estevez, J. Arriaga, A. Méndez-Blas, and V. Agarwal, “Enlargement of omnidirectional photonic bandgap in porous silicon dielectric mirrors with a Gaussian profile refractive index,” Appl. Phys. Lett.94, 061914 (2009).
[CrossRef]

Fan, S.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science282, 1679–1682 (1998).
[CrossRef] [PubMed]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett.77, 3787–3790 (1996).
[CrossRef] [PubMed]

Ferré-Borrull, J.

E. Xifré-Pérez, L. F. Marsal, J. Ferré-Borrull, and J. Pallarés, “Low refractive index contrast porous silicon omnidirectional reflectors,” Appl. Phys. B: Lasers and Opt.95, 169–172 (2009).
[CrossRef]

Fink, Y.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science282, 1679–1682 (1998).
[CrossRef] [PubMed]

Fukami, K.

Gaber, N.

Gaggero-Sager, L. M.

D. Ariza-Flores, L. M. Gaggero-Sager, and V. Agarwal, “White metal-like omnidirectional mirror from porous silicon dielectric multilayers,” Appl. Phys. Lett.101, 031119 (2012).
[CrossRef]

Gal, M.

S. Ilyas, T. Bocking, K. Kilian, P.J. Reece, J. Gooding, K. Gaus, and M. Gal, “Porous silicon based narrow line-width rugate filters,” Opt. Mat.29, 619–622 (2007).
[CrossRef]

P. J. Reece, G. Lérondel, W. H. Zheng, and M. Gal, “Optical microcavities with subnanometer linewidths based on porous silicon,” Appl. Phys. Lett.81, 004895 (2002).
[CrossRef]

Gaus, K.

S. Ilyas, T. Bocking, K. Kilian, P.J. Reece, J. Gooding, K. Gaus, and M. Gal, “Porous silicon based narrow line-width rugate filters,” Opt. Mat.29, 619–622 (2007).
[CrossRef]

Gooding, J.

S. Ilyas, T. Bocking, K. Kilian, P.J. Reece, J. Gooding, K. Gaus, and M. Gal, “Porous silicon based narrow line-width rugate filters,” Opt. Mat.29, 619–622 (2007).
[CrossRef]

Gray, D. E.

D. E. Gray, American Institute of Physics Handbook (AIP, 1972).

Hamanaka, K.

K. Kojima, S. Noda, K. Mitsunaga, K. Kyuma, and K. Hamanaka, “Continuous wave operation of a surface emitting AlGaAs/GaAs multiquantum well distributed Bragg reflector laser,” Appl. Phys. Lett.50, 001705 (1987).
[CrossRef]

Hecht, E.

E. Hecht, Optics (Addison-Wesley, 1998).

Hosseini, A.

Hu, D.

S. Li, D. Hu, J. Huang, and L. Cai, “Optical sensing nanostructures for porous silicon rugate filters,” Nano. Res. Lett.7, 000079 (2012).
[CrossRef]

Huang, J.

S. Li, D. Hu, J. Huang, and L. Cai, “Optical sensing nanostructures for porous silicon rugate filters,” Nano. Res. Lett.7, 000079 (2012).
[CrossRef]

Ilyas, S.

S. Ilyas, T. Bocking, K. Kilian, P.J. Reece, J. Gooding, K. Gaus, and M. Gal, “Porous silicon based narrow line-width rugate filters,” Opt. Mat.29, 619–622 (2007).
[CrossRef]

Jalkanen, T.

Joannopoulos, J. D.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science282, 1679–1682 (1998).
[CrossRef] [PubMed]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett.77, 3787–3790 (1996).
[CrossRef] [PubMed]

Kilian, K.

S. Ilyas, T. Bocking, K. Kilian, P.J. Reece, J. Gooding, K. Gaus, and M. Gal, “Porous silicon based narrow line-width rugate filters,” Opt. Mat.29, 619–622 (2007).
[CrossRef]

Kojima, K.

K. Kojima, S. Noda, K. Mitsunaga, K. Kyuma, and K. Hamanaka, “Continuous wave operation of a surface emitting AlGaAs/GaAs multiquantum well distributed Bragg reflector laser,” Appl. Phys. Lett.50, 001705 (1987).
[CrossRef]

Koshelev, K. N.

Koyama, T.

S. F. Chichibu, T. Ohmori, N. Shibata, and T. Koyama, “Dielectric SiO2/ZrO2distributed Bragg reflectors for ZnO microcavities prepared by the reactive helicon-wave-excited-plasma sputtering method,” Appl. Phys. Lett.88, 161914 (2006).
[CrossRef]

Krivtsun, V. M.

Kurland, I.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett.77, 3787–3790 (1996).
[CrossRef] [PubMed]

Kyuma, K.

K. Kojima, S. Noda, K. Mitsunaga, K. Kyuma, and K. Hamanaka, “Continuous wave operation of a surface emitting AlGaAs/GaAs multiquantum well distributed Bragg reflector laser,” Appl. Phys. Lett.50, 001705 (1987).
[CrossRef]

Lehto, V. P.

Lérondel, G.

P. J. Reece, G. Lérondel, W. H. Zheng, and M. Gal, “Optical microcavities with subnanometer linewidths based on porous silicon,” Appl. Phys. Lett.81, 004895 (2002).
[CrossRef]

Li, S.

S. Li, D. Hu, J. Huang, and L. Cai, “Optical sensing nanostructures for porous silicon rugate filters,” Nano. Res. Lett.7, 000079 (2012).
[CrossRef]

Lu, H.

Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, “Resonance transmission modes in dual-periodical dielectric multilayer films,” Appl. Phys. Lett.82, 004654 (2003).
[CrossRef]

Mäkilä, E.

Malak, M.

Marsal, L. F.

E. Xifré-Pérez, L. F. Marsal, J. Ferré-Borrull, and J. Pallarés, “Low refractive index contrast porous silicon omnidirectional reflectors,” Appl. Phys. B: Lasers and Opt.95, 169–172 (2009).
[CrossRef]

Martínez-Duart, J. M.

Marty, F.

Massoud, Y.

Mazzoleni, C.

C. Mazzoleni and L. Pavesi, “Application to optical components of dielectric porous silicon multilayers,” Appl. Phys. Lett.67, 002983 (1995).
[CrossRef]

Meade, S. O.

M. Y. Chen, S. O. Meade, and M. J. Sailor, “Preparation and analysis of porous silicon multilayers for spectral encoding applications,” Phys. Stat. Sol. (c)6, 1610–1614 (2009).
[CrossRef]

S. O. Meade, M. Y. Chen, M. J. Sailor, and G. M. Miskelly, “Multiplexed DNA detection using spectrally encoded porous SiO2photonic crystal particles,” Anal. Chem.81, 2618–2625 (2009).

S. O. Meade and M. J. Sailor, “Microfabrication of freestanding porous silicon particles containing spectral barcodes,” Phys. Stat. Sol. (RRL)1, R71–R73 (2007).
[CrossRef]

S. O. Meade, M. S. Yoon, K. H. Ahn, and M. J. Sailor, “Porous silicon photonic crystals as encoded microcarriers,” Adv. Mat.16, 1811–1814 (2004).
[CrossRef]

M. J. Sailor and S. O. Meade, Method for forming optically encoded thin films and particles with grey scale spectra. U.S. Patent #8,308, 066, (2012).

Medvedev, V. V.

Mekis, A.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett.77, 3787–3790 (1996).
[CrossRef] [PubMed]

Méndez-Blas, A.

K. S. Pérez, J. O. Estevez, A. Méndez-Blas, J. Arriaga, G. Palestino, and M. E. Mora-Ramos, “Tunable resonance transmission modes in hybrid heterostructures based on porous silicon,” Nano. Res. Lett.7, 000392 (2012).
[CrossRef]

J. O. Estevez, J. Arriaga, A. Méndez-Blas, and V. Agarwal, “Enlargement of omnidirectional photonic bandgap in porous silicon dielectric mirrors with a Gaussian profile refractive index,” Appl. Phys. Lett.94, 061914 (2009).
[CrossRef]

Michel, J.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science282, 1679–1682 (1998).
[CrossRef] [PubMed]

Ming, N. B.

Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, “Resonance transmission modes in dual-periodical dielectric multilayer films,” Appl. Phys. Lett.82, 004654 (2003).
[CrossRef]

Mir, A.

D. Bria, B. Djafari-Rouhani, E. H. El Boudouti, A. Mir, A. Akjouj, and A. Nougaoui, “Omnidirectional optical mirror in a cladded-superlattice structure,” J. Appl. Phys.91, 2569–2572 (2002).
[CrossRef]

Miskelly, G. M.

S. O. Meade, M. Y. Chen, M. J. Sailor, and G. M. Miskelly, “Multiplexed DNA detection using spectrally encoded porous SiO2photonic crystal particles,” Anal. Chem.81, 2618–2625 (2009).

Mitsunaga, K.

K. Kojima, S. Noda, K. Mitsunaga, K. Kyuma, and K. Hamanaka, “Continuous wave operation of a surface emitting AlGaAs/GaAs multiquantum well distributed Bragg reflector laser,” Appl. Phys. Lett.50, 001705 (1987).
[CrossRef]

Mora-Ramos, M. E.

K. S. Pérez, J. O. Estevez, A. Méndez-Blas, J. Arriaga, G. Palestino, and M. E. Mora-Ramos, “Tunable resonance transmission modes in hybrid heterostructures based on porous silicon,” Nano. Res. Lett.7, 000392 (2012).
[CrossRef]

Murphy, T. E.

Noda, S.

K. Kojima, S. Noda, K. Mitsunaga, K. Kyuma, and K. Hamanaka, “Continuous wave operation of a surface emitting AlGaAs/GaAs multiquantum well distributed Bragg reflector laser,” Appl. Phys. Lett.50, 001705 (1987).
[CrossRef]

Nougaoui, A.

D. Bria, B. Djafari-Rouhani, E. H. El Boudouti, A. Mir, A. Akjouj, and A. Nougaoui, “Omnidirectional optical mirror in a cladded-superlattice structure,” J. Appl. Phys.91, 2569–2572 (2002).
[CrossRef]

Ogata, Y. H.

Ohmori, T.

S. F. Chichibu, T. Ohmori, N. Shibata, and T. Koyama, “Dielectric SiO2/ZrO2distributed Bragg reflectors for ZnO microcavities prepared by the reactive helicon-wave-excited-plasma sputtering method,” Appl. Phys. Lett.88, 161914 (2006).
[CrossRef]

Palestino, G.

K. S. Pérez, J. O. Estevez, A. Méndez-Blas, J. Arriaga, G. Palestino, and M. E. Mora-Ramos, “Tunable resonance transmission modes in hybrid heterostructures based on porous silicon,” Nano. Res. Lett.7, 000392 (2012).
[CrossRef]

Pallarés, J.

E. Xifré-Pérez, L. F. Marsal, J. Ferré-Borrull, and J. Pallarés, “Low refractive index contrast porous silicon omnidirectional reflectors,” Appl. Phys. B: Lasers and Opt.95, 169–172 (2009).
[CrossRef]

Pavesi, L.

C. Mazzoleni and L. Pavesi, “Application to optical components of dielectric porous silicon multilayers,” Appl. Phys. Lett.67, 002983 (1995).
[CrossRef]

L. Pavesi and R. Turan, Silicon Nanocrystals (WILEY-VCH, 2010).

Pavy, N.

Pérez, K. S.

K. S. Pérez, J. O. Estevez, A. Méndez-Blas, J. Arriaga, G. Palestino, and M. E. Mora-Ramos, “Tunable resonance transmission modes in hybrid heterostructures based on porous silicon,” Nano. Res. Lett.7, 000392 (2012).
[CrossRef]

Qin, Q.

Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, “Resonance transmission modes in dual-periodical dielectric multilayer films,” Appl. Phys. Lett.82, 004654 (2003).
[CrossRef]

Reece, P. J.

P. J. Reece, G. Lérondel, W. H. Zheng, and M. Gal, “Optical microcavities with subnanometer linewidths based on porous silicon,” Appl. Phys. Lett.81, 004895 (2002).
[CrossRef]

Reece, P.J.

S. Ilyas, T. Bocking, K. Kilian, P.J. Reece, J. Gooding, K. Gaus, and M. Gal, “Porous silicon based narrow line-width rugate filters,” Opt. Mat.29, 619–622 (2007).
[CrossRef]

Richalo, E.

Rossi, A. M.

Russell, P. St. J.

P. A. Snow, E. K. Squire, P. St. J. Russell, and L. T. Canham, “Vapor sensing using the optical properties of porous silicon Bragg mirrors,” J. Appl. Phys.86, 1781–1784 (1999).
[CrossRef]

Sailor, M. J.

S. O. Meade, M. Y. Chen, M. J. Sailor, and G. M. Miskelly, “Multiplexed DNA detection using spectrally encoded porous SiO2photonic crystal particles,” Anal. Chem.81, 2618–2625 (2009).

M. Y. Chen, S. O. Meade, and M. J. Sailor, “Preparation and analysis of porous silicon multilayers for spectral encoding applications,” Phys. Stat. Sol. (c)6, 1610–1614 (2009).
[CrossRef]

S. O. Meade and M. J. Sailor, “Microfabrication of freestanding porous silicon particles containing spectral barcodes,” Phys. Stat. Sol. (RRL)1, R71–R73 (2007).
[CrossRef]

S. O. Meade, M. S. Yoon, K. H. Ahn, and M. J. Sailor, “Porous silicon photonic crystals as encoded microcarriers,” Adv. Mat.16, 1811–1814 (2004).
[CrossRef]

M. J. Sailor and S. O. Meade, Method for forming optically encoded thin films and particles with grey scale spectra. U.S. Patent #8,308, 066, (2012).

Sakka, T.

Salonen, J.

Shibata, N.

S. F. Chichibu, T. Ohmori, N. Shibata, and T. Koyama, “Dielectric SiO2/ZrO2distributed Bragg reflectors for ZnO microcavities prepared by the reactive helicon-wave-excited-plasma sputtering method,” Appl. Phys. Lett.88, 161914 (2006).
[CrossRef]

Snow, P. A.

P. A. Snow, E. K. Squire, P. St. J. Russell, and L. T. Canham, “Vapor sensing using the optical properties of porous silicon Bragg mirrors,” J. Appl. Phys.86, 1781–1784 (1999).
[CrossRef]

Squire, E. K.

P. A. Snow, E. K. Squire, P. St. J. Russell, and L. T. Canham, “Vapor sensing using the optical properties of porous silicon Bragg mirrors,” J. Appl. Phys.86, 1781–1784 (1999).
[CrossRef]

Thomas, E. L.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science282, 1679–1682 (1998).
[CrossRef] [PubMed]

Torres-Costa, V.

Turan, R.

L. Pavesi and R. Turan, Silicon Nanocrystals (WILEY-VCH, 2010).

van de Kruijs, R. W. E.

Villeneuve, P. R.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett.77, 3787–3790 (1996).
[CrossRef] [PubMed]

Winn, J. N.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science282, 1679–1682 (1998).
[CrossRef] [PubMed]

Xifré-Pérez, E.

E. Xifré-Pérez, L. F. Marsal, J. Ferré-Borrull, and J. Pallarés, “Low refractive index contrast porous silicon omnidirectional reflectors,” Appl. Phys. B: Lasers and Opt.95, 169–172 (2009).
[CrossRef]

Yakshin, A. E.

Yakunin, A. M.

Yoon, M. S.

S. O. Meade, M. S. Yoon, K. H. Ahn, and M. J. Sailor, “Porous silicon photonic crystals as encoded microcarriers,” Adv. Mat.16, 1811–1814 (2004).
[CrossRef]

Yuan, C. S.

Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, “Resonance transmission modes in dual-periodical dielectric multilayer films,” Appl. Phys. Lett.82, 004654 (2003).
[CrossRef]

Zheng, W. H.

P. J. Reece, G. Lérondel, W. H. Zheng, and M. Gal, “Optical microcavities with subnanometer linewidths based on porous silicon,” Appl. Phys. Lett.81, 004895 (2002).
[CrossRef]

Zhu, S. N.

Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, “Resonance transmission modes in dual-periodical dielectric multilayer films,” Appl. Phys. Lett.82, 004654 (2003).
[CrossRef]

Zhu, Y. Y.

Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, “Resonance transmission modes in dual-periodical dielectric multilayer films,” Appl. Phys. Lett.82, 004654 (2003).
[CrossRef]

Adv. Mat.

S. O. Meade, M. S. Yoon, K. H. Ahn, and M. J. Sailor, “Porous silicon photonic crystals as encoded microcarriers,” Adv. Mat.16, 1811–1814 (2004).
[CrossRef]

Anal. Chem.

S. O. Meade, M. Y. Chen, M. J. Sailor, and G. M. Miskelly, “Multiplexed DNA detection using spectrally encoded porous SiO2photonic crystal particles,” Anal. Chem.81, 2618–2625 (2009).

Appl. Phys. B: Lasers and Opt.

E. Xifré-Pérez, L. F. Marsal, J. Ferré-Borrull, and J. Pallarés, “Low refractive index contrast porous silicon omnidirectional reflectors,” Appl. Phys. B: Lasers and Opt.95, 169–172 (2009).
[CrossRef]

Appl. Phys. Lett.

J. O. Estevez, J. Arriaga, A. Méndez-Blas, and V. Agarwal, “Enlargement of omnidirectional photonic bandgap in porous silicon dielectric mirrors with a Gaussian profile refractive index,” Appl. Phys. Lett.94, 061914 (2009).
[CrossRef]

D. Ariza-Flores, L. M. Gaggero-Sager, and V. Agarwal, “White metal-like omnidirectional mirror from porous silicon dielectric multilayers,” Appl. Phys. Lett.101, 031119 (2012).
[CrossRef]

V. Agarwal and J. A. del Río, “Tailoring the photonic band gap of a porous silicon dielectric mirror,” Appl. Phys. Lett.82, 001512 (2003).
[CrossRef]

P. J. Reece, G. Lérondel, W. H. Zheng, and M. Gal, “Optical microcavities with subnanometer linewidths based on porous silicon,” Appl. Phys. Lett.81, 004895 (2002).
[CrossRef]

C. Mazzoleni and L. Pavesi, “Application to optical components of dielectric porous silicon multilayers,” Appl. Phys. Lett.67, 002983 (1995).
[CrossRef]

S. F. Chichibu, T. Ohmori, N. Shibata, and T. Koyama, “Dielectric SiO2/ZrO2distributed Bragg reflectors for ZnO microcavities prepared by the reactive helicon-wave-excited-plasma sputtering method,” Appl. Phys. Lett.88, 161914 (2006).
[CrossRef]

Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, “Resonance transmission modes in dual-periodical dielectric multilayer films,” Appl. Phys. Lett.82, 004654 (2003).
[CrossRef]

K. Kojima, S. Noda, K. Mitsunaga, K. Kyuma, and K. Hamanaka, “Continuous wave operation of a surface emitting AlGaAs/GaAs multiquantum well distributed Bragg reflector laser,” Appl. Phys. Lett.50, 001705 (1987).
[CrossRef]

J. Appl. Phys.

P. A. Snow, E. K. Squire, P. St. J. Russell, and L. T. Canham, “Vapor sensing using the optical properties of porous silicon Bragg mirrors,” J. Appl. Phys.86, 1781–1784 (1999).
[CrossRef]

D. Bria, B. Djafari-Rouhani, E. H. El Boudouti, A. Mir, A. Akjouj, and A. Nougaoui, “Omnidirectional optical mirror in a cladded-superlattice structure,” J. Appl. Phys.91, 2569–2572 (2002).
[CrossRef]

Nano. Res. Lett.

K. S. Pérez, J. O. Estevez, A. Méndez-Blas, J. Arriaga, G. Palestino, and M. E. Mora-Ramos, “Tunable resonance transmission modes in hybrid heterostructures based on porous silicon,” Nano. Res. Lett.7, 000392 (2012).
[CrossRef]

S. Li, D. Hu, J. Huang, and L. Cai, “Optical sensing nanostructures for porous silicon rugate filters,” Nano. Res. Lett.7, 000079 (2012).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Mat.

S. Ilyas, T. Bocking, K. Kilian, P.J. Reece, J. Gooding, K. Gaus, and M. Gal, “Porous silicon based narrow line-width rugate filters,” Opt. Mat.29, 619–622 (2007).
[CrossRef]

Phys. Rev. Lett.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett.77, 3787–3790 (1996).
[CrossRef] [PubMed]

Phys. Stat. Sol. (c)

M. Y. Chen, S. O. Meade, and M. J. Sailor, “Preparation and analysis of porous silicon multilayers for spectral encoding applications,” Phys. Stat. Sol. (c)6, 1610–1614 (2009).
[CrossRef]

Phys. Stat. Sol. (RRL)

S. O. Meade and M. J. Sailor, “Microfabrication of freestanding porous silicon particles containing spectral barcodes,” Phys. Stat. Sol. (RRL)1, R71–R73 (2007).
[CrossRef]

Science

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science282, 1679–1682 (1998).
[CrossRef] [PubMed]

Other

E. Hecht, Optics (Addison-Wesley, 1998).

L. Pavesi and R. Turan, Silicon Nanocrystals (WILEY-VCH, 2010).

M. J. Sailor and S. O. Meade, Method for forming optically encoded thin films and particles with grey scale spectra. U.S. Patent #8,308, 066, (2012).

D. E. Gray, American Institute of Physics Handbook (AIP, 1972).

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Figures (9)

Fig. 1
Fig. 1

Schematics of the refractive index profile of two Bragg mirrors designed for λ0 = 1.0 μm (i) (dotted line) and λ0 = 1.5 μm (ii) (dashed line) along with the resultant structure (iii) (solid line) for (a) superposition and (c) sequential addition, respectively. Figure (b) and (d) show the corresponding reflectivity spectra of the resultant addition in (a) and (c), respectively.

Fig. 2
Fig. 2

Schematics of the refractive index (dotted/dashed line) and the resultant SP addition profile (solid line) of (a) rugate filters and (c) microcavity structures. The corresponding reflectivity spectra are shown in panels (b) and (d).

Fig. 3
Fig. 3

Reflectivity spectrum of a composite structure obtained by (a) SP and (b) SQ addition of two Bragg mirrors. The dotted/dashed line correspond to typical Bragg mirrors designed for λ0 = 1.362/1.5 μm. Figure (c) shows a contour plot for the reflectivity response as a function of the relative SP (Δλ/λ1) and the wavelength (λ). The first mirror is fixed at (λ2). The color scale indicates the reflectance from 0 (black) to 1 (yellow). Figure (d) shows the reflectance spectra of two SP mirrors, one is localized at 1.362 μm and the other is centered at 1.4 μm (—), 1.5 μm (- - -), 1.6 μm (···), and 1.7 μm (· – ·). Figure (e) shows the comparison of two resonant microcavity modes obtained by superposition (—) and typical half wave microcavity (· – ·) structure designed for λ0 = 1.45 μm.

Fig. 4
Fig. 4

Schematics of the refractive index profile of two Bragg mirrors (i+ii) with maximum/minimum refractive index of 1.81/1.33, and the resultant composite structure (iii) with maximum/minimum refractive index of 1.09/2.05 for (a) 0 %, (c) 0.5 %, (e) 3.3 %, and (g) 9.5 % of shift. Figure (b), (d), (f) and (h) show the reflectivity spectra of the structures with the composite refractive index profile shown in (a), (c), (e) and (g), respectively.

Fig. 5
Fig. 5

(a) Contour plot of the reflectivity spectrum, as a function of wavelength and the percentage of relative shift for two Bragg mirrors under SP addition. The color scale indicates the reflectance from 0 (black) to 1 (yellow). (b) Comparison of the PBG obtained by SP addition for three different values of shift: 4.6 % or 344 nm (· – ·), 33 % or 2474 nm (—) and 100 % shift or SQ addition (- - -), revealing an increase of PBG for SP added structures. Inset shows the PBG as a function of % shift revealing an optimum value of shift for obtaining a maximum PBG

Fig. 6
Fig. 6

(a) Contour plot of the reflectivity spectrum (R), as a function of the wavelength (λ) and the percentage of relative overlapping (Δλ) for two rugate mirrors under superposition addition. The color scale indicates the reflectance from 0 (black) to 0.9 (yellow). (b) Contour plot of the reflectivity spectrum (R), as a function of the wavelength (λ) and the percentage of relative shift for two rugate mirrors under superposition addition. The color scale indicates the reflectance from 0 (black) to 0.7 (yellow).

Fig. 7
Fig. 7

The experimental verification of “shifting” of two overlapping Bragg mirrors (λ1 = 1.5 μm and λ2 = 1.36 μm) under SP addition. The solid line and the dotted line in the reflectivity spectra plot correspond to the experimentally measured and theoretically simulated data lines respectively. The composite structure obtained with (a) 0%, (b) 0.5% (37 nm of optical thickness), (c) 3.3% (247 nm of optical thickness) and (d) 9.5% (712 nm of optical thickness), of shift and maximum/minimum refractive index of 1.09/2.05. The refractive index profiles corresponding to the panels (a), (b), (c), (d) are shown in Fig. 4 (a), (c), (e), (g)

Fig. 8
Fig. 8

Comparison of resonant microcavity (MC) modes obtained by superposition (—), and half-wave microcavity structures with Δn = 0.45 (- - -) and 0.96 (· – ·). The quality factor of SP-microcavity is 149±17 while the quality factor of half-wave microcavities are 86±18 (for Δn = 0.45) and 67±10 (for Δn = 0.96). All the microcavities are designed for λ0 = 1.47 μm.

Fig. 9
Fig. 9

HRSEM cross section of (a) Halfwave microcavity (physical thickness of 5.2 μm ± 0.1 %). SP addition of two Bragg mirrors designed at λ1 = 1500 nm and λ2 = 1362 nm with (b) 0 % shift (physical thickness of 5.4 μm ± 5 %) (c) 3.3% shift (physical thickness of 5.6 μm ± 5 %) (d) 9.5% shift (physical thickness of 5.0 μm ± 5 %). The dark and clear zones correspond to the high (low) and low (high) porosity (refractive index) layers, respectively. Left hand side of the each image shows the corresponding schematic of the refractive index profile along the depth.

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

( E I H I ) = ( cos ( k 0 h ) i sin ( k 0 h ) / Γ I i Γ I sin ( k 0 h ) cos ( k 0 h ) ) ( E I I H I I ) ,
Γ I = ε 0 μ 0 n I .
( E I H I ) = M I ( E I I H I I ) .
( E I I H I I ) = M I I ( E I I I H I I I ) .
( E I H I ) = M I M I I ( E I I I H I I I ) .
( E I H I ) = M I M I I M P ( E P + 1 H P + 1 ) .
M = M I M I I M P = ( m 11 m 12 m 21 m 22 ) .
R = | r | 2
r = Γ 0 m 11 + Γ 0 Γ s m 12 m 21 Γ s m 22 Γ 0 m 11 + Γ 0 Γ s m 12 + m 21 + Γ s m 22
Γ j = ε 0 μ 0 n j ,
n sum = Σ i = 1 N n i ( x ) ( N 1 ) c ,
c = n L n H n i p ( n i ) d n i ,

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