Abstract

This paper explores the wavelength-dependent reflectivity of alternating high and low refractive index multilayers with a thickness profile defined by a pseudo-random, maximum length sequence (MLS). An MLS contains all possible combinations of a binary sequence save one; thus, a multilayer with an MLS profile contains a superposition of a broad range of periods. The range of periodicities in an MLS multilayer should make these systems more effective broad wavelength reflectors as compared to purely periodic counterparts. We compute the reflection characteristics of MLS and periodic dielectric sequences at visible wavelengths over a range of incident angles using the transfer matrix method (TMM), a recursive multilayer calculation method. The materials SiO2 and TiO2 are chosen as the low and high refractive index materials, respectively, because these materials are commonly used in optical multilayers and because their wavelength-dependent refractive index is well known. Our results show that it is possible to create an MLS structure with high average reflectivity across the entire visible spectrum (400 nm – 700 nm) at all incident angles and polarizations. Finally, we compare the reflection characteristics of dielectric multilayers with metallic reflectors whose refractive index is based on a Brendel-Bormann (BB) model. The comparison shows that a seventh order MLS aperiodic multilayer exhibits slightly higher average reflectivity over the visible spectum than silver or aluminum metallic reflectors.

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

Full Article  |  PDF Article
OSA Recommended Articles
Diffraction and diffuse scattering from dielectric multilayers

J. M. Elson
J. Opt. Soc. Am. 69(1) 48-54 (1979)

Goos–Hänchen shift for Gaussian beams impinging on monolayer-MoS2-coated surfaces

Akash Das and Manik Pradhan
J. Opt. Soc. Am. B 35(8) 1956-1962 (2018)

References

  • View by:
  • |
  • |
  • |

  1. W. M. Robertson, “Experimental measurement of the effect of termination on surface electromagnetic waves in one-dimensional photonic bandgap arrays,” J. Lightwave Technol. 17, 2013–2017 (1999).
    [Crossref]
  2. M. Shinn and W. M. Robertson, “Surface plasmon-like sensor based on surface electromagnetic waves in a photonic band-gap material,” Sens. Actuators B,  105(2), 360–364 (2005).
    [Crossref]
  3. M. Vishanathan, Simulation of Digital Communication Systems Using Matlab (M. Vishanathan, 2013).
  4. M. Cohn and A. Lempe, “On fast M-sequence transforms,” IEEE Trans. Inform. Theory 23, 135–137 (1977).
    [Crossref]
  5. D. V. Sarwate and M. B. Pursley, “Cross correlation properties of pseudo random and related sequences,” Proc. IEEE 68(5), 593–619 (1980).
    [Crossref]
  6. H. Jens, “Impulse response measurements using MLS,” (2003), http://jenshee.dk/signalprocessing/mls.pdf .
  7. Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679 (1998).
    [Crossref] [PubMed]
  8. B. Gallas, S. Fisson, E. Charron, A. B. Bruneau, G. Vuye, and J. Rivory, “Making an omnidirectional reflector,” Appl. Opt. 40, 5056–5063 (2001).
    [Crossref]
  9. A. Rakic, A. Djurisic, J. Elazar, and M. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37, 5271–5283 (1998).
    [Crossref]
  10. V. Koju and W. M. Robertson, “Excitation of Bloch-like surface waves in quasi-crystals and aperiodic dielectric multilayers,” Opt. Lett. 41, 2915–2918 (2016).
    [Crossref] [PubMed]
  11. D. L. Negro and S. V. Boriskina, “Simulation methods for multiperiodic and aperiodic nanostructured dielectric waveguides. Deterministic aperiodic nanostructures for photonics and plasmonics applications,” Laser Photon. Rev. 6(2), 178–218 (2012).
    [Crossref]
  12. Z. V. Vardeny, A. Nahata, and A. Agrawal, “Optics of photonic quasicrystals,” Nat. Photonics 7, 117 (2013).
    [Crossref]
  13. N. H. Liu, “Propagation of light waves in Thue-Morse dielectric multilayers,” Phys. Rev. B 553543–3547 (1997).
    [Crossref]
  14. M. Dulea, M. Johansson, and R. Riklund, “Localization of electrons and electromagnetic waves in a deterministic aperiodic system,” Phys. Rev. B 45, 105–114 (1992).
    [Crossref]
  15. M. Paulsen, L. T. Neustock, S. Jahns, J. Adam, and M. Gerken, “Simulation methods for multiperiodic and aperiodic nanostructured dielectric waveguides,” Opt. Quantum Electron. 49, 107 (2017).
    [Crossref]
  16. M. Kohmoto, L. P. Kadanoff, and C. Tang, “Localization problem in one dimension: mapping and escape,” Phys. Rev. Lett. 50, 1870 (1983).
    [Crossref]
  17. R. Nava, J. T. Martinez, J. A. D. Rio, and G. G. Naumis, “Perfect light transmission in Fibonacci arrays of dielectric multilayers,” J. Phys. Condens. Matter 21, 155901 (2009).
    [Crossref] [PubMed]
  18. M. P. Van Albada and A. Lagendijk, ,“Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
    [Crossref] [PubMed]
  19. Z. Cheng, R. Savit, and R. Merlin, “Structure and electronic properties of Thue-Morse lattices,” Phys. Rev.B 375, 4375–4382 (1988).
    [Crossref]
  20. E. Macia, “Exploiting aperiodic designs in nanophotonic devices,” Rep. Prog. Phys. 75, 036502 (2012).
    [Crossref] [PubMed]
  21. M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: quasiperiodic media,” Phys. Rev. Lett. 58, 2436–2438 (1987).
    [Crossref] [PubMed]
  22. M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72, 633–636 (1994).
    [Crossref] [PubMed]
  23. L. D. Negro, N. Feng, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A. 10, 0640138 (2008).
    [Crossref]
  24. M. Schroeder, “Diffuse sound reflection by maximum-length sequences,” J. Acoust. Soc. Am. 57, 149–150 (1975).
    [Crossref]
  25. J. Xu, H. Fang, and Z. Lin, “Expanding high reflection range in a dielectric multilayer reflector by disorder and inhomogeneity,” J. Phys. D 34, 445–449 (2001).
    [Crossref]
  26. J. Xu, H. Fang, and Z. Lin, “Broadband optical reflector-an application of light localization in one dimension,” Appl. Phy. Lett. 67, 2431–2432 (1995).
    [Crossref]
  27. K. N. Poudel, V. Koju, and W. Robertson, “Maximum length sequence (MLS) multilayer reflector using rigorous coupled wave analysis and FEM,” in IEEE USNC-URSI Radio Science Meeting Joint with AP-S, Boston, Massachusetts, USA, July 7–14 2018 (IEEE, 2018).
  28. W. P. Guidorzi, L. Barbaresi, D. D’Orazio, and M. Garai, “Impulse responses measured with MLS or swept-sine signals applied to architectural acoustics: an in-depth analysis of the two methods and some case studies of measurements inside theaters,” Energy Procedia 78, 1611–1616 (2015).
    [Crossref]
  29. K. N. Poudel and S. Gangaju, “Spectral efficiency, diversity gain and multiplexing capacity analysis for massive MIMO, 5G communications system,” in Int. Conf. Net. Net. Appl. (2017), pp. 133–137.
  30. W. T. Chu, “Impulse-response and reverberation-decay measurements made by using a periodic pseudorandom sequence,” Appl. Acous. 29, 193–205 (1990).
    [Crossref]
  31. S. W. Golomb, “Spread spectrum techniques and applications,” in IEEE Third Intl. Symposium on Spread Spectrum Techniques and Application (1994).
  32. J. R. Devore, “Refractive indices of rutile and sphalerite,” J. Opt. Soc. Am. A 41, 416–419 (1951).
    [Crossref]
  33. I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. A 55, 1205–1209 (1965).
    [Crossref]
  34. T. Siefke, S. Kroker, K. Pfeiffer, O. Puffky, K. Dietrich, D. Franta, I. Ohlídal, A. Szeghalmi, E.-B. Kley, and A. Tünnermann, “Materials pushing the application limits of wire grid polarizers further into the deep ultraviolet spectral range,” Adv. Opt. Mater. 4, 1780 (2016).
    [Crossref]
  35. S. J. Orfanidis, “Electromagnetic waves and antennas, online book,” (2016), chap. 6, pp. 1–1413, http://eceweb1.rutgers.edu/orfanidi/ewa/ .
  36. J. Lekner, “Omnidirectional reflection by multilayer dielectric mirrors,” J. Opt. A 2, 349–352 (2000).
    [Crossref]
  37. L. Li, J. A. Dobrowolski, M. Jacobson, and C. Cooksey, “Broadband transmission filters from the 2013 Optical Interference Coatings manufacturing problem contest,” Appl. Opt. 53A248–A258 (2014).
    [Crossref] [PubMed]

2017 (1)

M. Paulsen, L. T. Neustock, S. Jahns, J. Adam, and M. Gerken, “Simulation methods for multiperiodic and aperiodic nanostructured dielectric waveguides,” Opt. Quantum Electron. 49, 107 (2017).
[Crossref]

2016 (2)

V. Koju and W. M. Robertson, “Excitation of Bloch-like surface waves in quasi-crystals and aperiodic dielectric multilayers,” Opt. Lett. 41, 2915–2918 (2016).
[Crossref] [PubMed]

T. Siefke, S. Kroker, K. Pfeiffer, O. Puffky, K. Dietrich, D. Franta, I. Ohlídal, A. Szeghalmi, E.-B. Kley, and A. Tünnermann, “Materials pushing the application limits of wire grid polarizers further into the deep ultraviolet spectral range,” Adv. Opt. Mater. 4, 1780 (2016).
[Crossref]

2015 (1)

W. P. Guidorzi, L. Barbaresi, D. D’Orazio, and M. Garai, “Impulse responses measured with MLS or swept-sine signals applied to architectural acoustics: an in-depth analysis of the two methods and some case studies of measurements inside theaters,” Energy Procedia 78, 1611–1616 (2015).
[Crossref]

2014 (1)

2013 (1)

Z. V. Vardeny, A. Nahata, and A. Agrawal, “Optics of photonic quasicrystals,” Nat. Photonics 7, 117 (2013).
[Crossref]

2012 (2)

D. L. Negro and S. V. Boriskina, “Simulation methods for multiperiodic and aperiodic nanostructured dielectric waveguides. Deterministic aperiodic nanostructures for photonics and plasmonics applications,” Laser Photon. Rev. 6(2), 178–218 (2012).
[Crossref]

E. Macia, “Exploiting aperiodic designs in nanophotonic devices,” Rep. Prog. Phys. 75, 036502 (2012).
[Crossref] [PubMed]

2009 (1)

R. Nava, J. T. Martinez, J. A. D. Rio, and G. G. Naumis, “Perfect light transmission in Fibonacci arrays of dielectric multilayers,” J. Phys. Condens. Matter 21, 155901 (2009).
[Crossref] [PubMed]

2008 (1)

L. D. Negro, N. Feng, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A. 10, 0640138 (2008).
[Crossref]

2005 (1)

M. Shinn and W. M. Robertson, “Surface plasmon-like sensor based on surface electromagnetic waves in a photonic band-gap material,” Sens. Actuators B,  105(2), 360–364 (2005).
[Crossref]

2001 (2)

B. Gallas, S. Fisson, E. Charron, A. B. Bruneau, G. Vuye, and J. Rivory, “Making an omnidirectional reflector,” Appl. Opt. 40, 5056–5063 (2001).
[Crossref]

J. Xu, H. Fang, and Z. Lin, “Expanding high reflection range in a dielectric multilayer reflector by disorder and inhomogeneity,” J. Phys. D 34, 445–449 (2001).
[Crossref]

2000 (1)

J. Lekner, “Omnidirectional reflection by multilayer dielectric mirrors,” J. Opt. A 2, 349–352 (2000).
[Crossref]

1999 (1)

1998 (2)

A. Rakic, A. Djurisic, J. Elazar, and M. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37, 5271–5283 (1998).
[Crossref]

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679 (1998).
[Crossref] [PubMed]

1997 (1)

N. H. Liu, “Propagation of light waves in Thue-Morse dielectric multilayers,” Phys. Rev. B 553543–3547 (1997).
[Crossref]

1995 (1)

J. Xu, H. Fang, and Z. Lin, “Broadband optical reflector-an application of light localization in one dimension,” Appl. Phy. Lett. 67, 2431–2432 (1995).
[Crossref]

1994 (1)

M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72, 633–636 (1994).
[Crossref] [PubMed]

1992 (1)

M. Dulea, M. Johansson, and R. Riklund, “Localization of electrons and electromagnetic waves in a deterministic aperiodic system,” Phys. Rev. B 45, 105–114 (1992).
[Crossref]

1990 (1)

W. T. Chu, “Impulse-response and reverberation-decay measurements made by using a periodic pseudorandom sequence,” Appl. Acous. 29, 193–205 (1990).
[Crossref]

1988 (1)

Z. Cheng, R. Savit, and R. Merlin, “Structure and electronic properties of Thue-Morse lattices,” Phys. Rev.B 375, 4375–4382 (1988).
[Crossref]

1987 (1)

M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: quasiperiodic media,” Phys. Rev. Lett. 58, 2436–2438 (1987).
[Crossref] [PubMed]

1985 (1)

M. P. Van Albada and A. Lagendijk, ,“Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[Crossref] [PubMed]

1983 (1)

M. Kohmoto, L. P. Kadanoff, and C. Tang, “Localization problem in one dimension: mapping and escape,” Phys. Rev. Lett. 50, 1870 (1983).
[Crossref]

1980 (1)

D. V. Sarwate and M. B. Pursley, “Cross correlation properties of pseudo random and related sequences,” Proc. IEEE 68(5), 593–619 (1980).
[Crossref]

1977 (1)

M. Cohn and A. Lempe, “On fast M-sequence transforms,” IEEE Trans. Inform. Theory 23, 135–137 (1977).
[Crossref]

1975 (1)

M. Schroeder, “Diffuse sound reflection by maximum-length sequences,” J. Acoust. Soc. Am. 57, 149–150 (1975).
[Crossref]

1965 (1)

I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. A 55, 1205–1209 (1965).
[Crossref]

1951 (1)

J. R. Devore, “Refractive indices of rutile and sphalerite,” J. Opt. Soc. Am. A 41, 416–419 (1951).
[Crossref]

Adam, J.

M. Paulsen, L. T. Neustock, S. Jahns, J. Adam, and M. Gerken, “Simulation methods for multiperiodic and aperiodic nanostructured dielectric waveguides,” Opt. Quantum Electron. 49, 107 (2017).
[Crossref]

Agrawal, A.

Z. V. Vardeny, A. Nahata, and A. Agrawal, “Optics of photonic quasicrystals,” Nat. Photonics 7, 117 (2013).
[Crossref]

Barbaresi, L.

W. P. Guidorzi, L. Barbaresi, D. D’Orazio, and M. Garai, “Impulse responses measured with MLS or swept-sine signals applied to architectural acoustics: an in-depth analysis of the two methods and some case studies of measurements inside theaters,” Energy Procedia 78, 1611–1616 (2015).
[Crossref]

Boriskina, S. V.

D. L. Negro and S. V. Boriskina, “Simulation methods for multiperiodic and aperiodic nanostructured dielectric waveguides. Deterministic aperiodic nanostructures for photonics and plasmonics applications,” Laser Photon. Rev. 6(2), 178–218 (2012).
[Crossref]

Bruneau, A. B.

Charron, E.

Chen, C.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679 (1998).
[Crossref] [PubMed]

Cheng, Z.

Z. Cheng, R. Savit, and R. Merlin, “Structure and electronic properties of Thue-Morse lattices,” Phys. Rev.B 375, 4375–4382 (1988).
[Crossref]

Chu, W. T.

W. T. Chu, “Impulse-response and reverberation-decay measurements made by using a periodic pseudorandom sequence,” Appl. Acous. 29, 193–205 (1990).
[Crossref]

Cohn, M.

M. Cohn and A. Lempe, “On fast M-sequence transforms,” IEEE Trans. Inform. Theory 23, 135–137 (1977).
[Crossref]

Cooksey, C.

D’Orazio, D.

W. P. Guidorzi, L. Barbaresi, D. D’Orazio, and M. Garai, “Impulse responses measured with MLS or swept-sine signals applied to architectural acoustics: an in-depth analysis of the two methods and some case studies of measurements inside theaters,” Energy Procedia 78, 1611–1616 (2015).
[Crossref]

Devore, J. R.

J. R. Devore, “Refractive indices of rutile and sphalerite,” J. Opt. Soc. Am. A 41, 416–419 (1951).
[Crossref]

Dietrich, K.

T. Siefke, S. Kroker, K. Pfeiffer, O. Puffky, K. Dietrich, D. Franta, I. Ohlídal, A. Szeghalmi, E.-B. Kley, and A. Tünnermann, “Materials pushing the application limits of wire grid polarizers further into the deep ultraviolet spectral range,” Adv. Opt. Mater. 4, 1780 (2016).
[Crossref]

Djurisic, A.

Dobrowolski, J. A.

Dulea, M.

M. Dulea, M. Johansson, and R. Riklund, “Localization of electrons and electromagnetic waves in a deterministic aperiodic system,” Phys. Rev. B 45, 105–114 (1992).
[Crossref]

Elazar, J.

Fan, S.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679 (1998).
[Crossref] [PubMed]

Fang, H.

J. Xu, H. Fang, and Z. Lin, “Expanding high reflection range in a dielectric multilayer reflector by disorder and inhomogeneity,” J. Phys. D 34, 445–449 (2001).
[Crossref]

J. Xu, H. Fang, and Z. Lin, “Broadband optical reflector-an application of light localization in one dimension,” Appl. Phy. Lett. 67, 2431–2432 (1995).
[Crossref]

Feng, N.

L. D. Negro, N. Feng, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A. 10, 0640138 (2008).
[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,” Science 282, 1679 (1998).
[Crossref] [PubMed]

Fisson, S.

Franta, D.

T. Siefke, S. Kroker, K. Pfeiffer, O. Puffky, K. Dietrich, D. Franta, I. Ohlídal, A. Szeghalmi, E.-B. Kley, and A. Tünnermann, “Materials pushing the application limits of wire grid polarizers further into the deep ultraviolet spectral range,” Adv. Opt. Mater. 4, 1780 (2016).
[Crossref]

Gallas, B.

Gangaju, S.

K. N. Poudel and S. Gangaju, “Spectral efficiency, diversity gain and multiplexing capacity analysis for massive MIMO, 5G communications system,” in Int. Conf. Net. Net. Appl. (2017), pp. 133–137.

Garai, M.

W. P. Guidorzi, L. Barbaresi, D. D’Orazio, and M. Garai, “Impulse responses measured with MLS or swept-sine signals applied to architectural acoustics: an in-depth analysis of the two methods and some case studies of measurements inside theaters,” Energy Procedia 78, 1611–1616 (2015).
[Crossref]

Gerken, M.

M. Paulsen, L. T. Neustock, S. Jahns, J. Adam, and M. Gerken, “Simulation methods for multiperiodic and aperiodic nanostructured dielectric waveguides,” Opt. Quantum Electron. 49, 107 (2017).
[Crossref]

Golomb, S. W.

S. W. Golomb, “Spread spectrum techniques and applications,” in IEEE Third Intl. Symposium on Spread Spectrum Techniques and Application (1994).

Gopinath, A.

L. D. Negro, N. Feng, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A. 10, 0640138 (2008).
[Crossref]

Guidorzi, W. P.

W. P. Guidorzi, L. Barbaresi, D. D’Orazio, and M. Garai, “Impulse responses measured with MLS or swept-sine signals applied to architectural acoustics: an in-depth analysis of the two methods and some case studies of measurements inside theaters,” Energy Procedia 78, 1611–1616 (2015).
[Crossref]

Iguchi, K.

M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72, 633–636 (1994).
[Crossref] [PubMed]

M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: quasiperiodic media,” Phys. Rev. Lett. 58, 2436–2438 (1987).
[Crossref] [PubMed]

Jacobson, M.

Jahns, S.

M. Paulsen, L. T. Neustock, S. Jahns, J. Adam, and M. Gerken, “Simulation methods for multiperiodic and aperiodic nanostructured dielectric waveguides,” Opt. Quantum Electron. 49, 107 (2017).
[Crossref]

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,” Science 282, 1679 (1998).
[Crossref] [PubMed]

Johansson, M.

M. Dulea, M. Johansson, and R. Riklund, “Localization of electrons and electromagnetic waves in a deterministic aperiodic system,” Phys. Rev. B 45, 105–114 (1992).
[Crossref]

Kadanoff, L. P.

M. Kohmoto, L. P. Kadanoff, and C. Tang, “Localization problem in one dimension: mapping and escape,” Phys. Rev. Lett. 50, 1870 (1983).
[Crossref]

Kley, E.-B.

T. Siefke, S. Kroker, K. Pfeiffer, O. Puffky, K. Dietrich, D. Franta, I. Ohlídal, A. Szeghalmi, E.-B. Kley, and A. Tünnermann, “Materials pushing the application limits of wire grid polarizers further into the deep ultraviolet spectral range,” Adv. Opt. Mater. 4, 1780 (2016).
[Crossref]

Kohmoto, M.

M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72, 633–636 (1994).
[Crossref] [PubMed]

M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: quasiperiodic media,” Phys. Rev. Lett. 58, 2436–2438 (1987).
[Crossref] [PubMed]

M. Kohmoto, L. P. Kadanoff, and C. Tang, “Localization problem in one dimension: mapping and escape,” Phys. Rev. Lett. 50, 1870 (1983).
[Crossref]

Koju, V.

V. Koju and W. M. Robertson, “Excitation of Bloch-like surface waves in quasi-crystals and aperiodic dielectric multilayers,” Opt. Lett. 41, 2915–2918 (2016).
[Crossref] [PubMed]

K. N. Poudel, V. Koju, and W. Robertson, “Maximum length sequence (MLS) multilayer reflector using rigorous coupled wave analysis and FEM,” in IEEE USNC-URSI Radio Science Meeting Joint with AP-S, Boston, Massachusetts, USA, July 7–14 2018 (IEEE, 2018).

Kroker, S.

T. Siefke, S. Kroker, K. Pfeiffer, O. Puffky, K. Dietrich, D. Franta, I. Ohlídal, A. Szeghalmi, E.-B. Kley, and A. Tünnermann, “Materials pushing the application limits of wire grid polarizers further into the deep ultraviolet spectral range,” Adv. Opt. Mater. 4, 1780 (2016).
[Crossref]

Lagendijk, A.

M. P. Van Albada and A. Lagendijk, ,“Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[Crossref] [PubMed]

Lekner, J.

J. Lekner, “Omnidirectional reflection by multilayer dielectric mirrors,” J. Opt. A 2, 349–352 (2000).
[Crossref]

Lempe, A.

M. Cohn and A. Lempe, “On fast M-sequence transforms,” IEEE Trans. Inform. Theory 23, 135–137 (1977).
[Crossref]

Li, L.

Lin, Z.

J. Xu, H. Fang, and Z. Lin, “Expanding high reflection range in a dielectric multilayer reflector by disorder and inhomogeneity,” J. Phys. D 34, 445–449 (2001).
[Crossref]

J. Xu, H. Fang, and Z. Lin, “Broadband optical reflector-an application of light localization in one dimension,” Appl. Phy. Lett. 67, 2431–2432 (1995).
[Crossref]

Liu, N. H.

N. H. Liu, “Propagation of light waves in Thue-Morse dielectric multilayers,” Phys. Rev. B 553543–3547 (1997).
[Crossref]

Macia, E.

E. Macia, “Exploiting aperiodic designs in nanophotonic devices,” Rep. Prog. Phys. 75, 036502 (2012).
[Crossref] [PubMed]

Majewski, M.

Malitson, I. H.

I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. A 55, 1205–1209 (1965).
[Crossref]

Martinez, J. T.

R. Nava, J. T. Martinez, J. A. D. Rio, and G. G. Naumis, “Perfect light transmission in Fibonacci arrays of dielectric multilayers,” J. Phys. Condens. Matter 21, 155901 (2009).
[Crossref] [PubMed]

Merlin, R.

Z. Cheng, R. Savit, and R. Merlin, “Structure and electronic properties of Thue-Morse lattices,” Phys. Rev.B 375, 4375–4382 (1988).
[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,” Science 282, 1679 (1998).
[Crossref] [PubMed]

Nahata, A.

Z. V. Vardeny, A. Nahata, and A. Agrawal, “Optics of photonic quasicrystals,” Nat. Photonics 7, 117 (2013).
[Crossref]

Naumis, G. G.

R. Nava, J. T. Martinez, J. A. D. Rio, and G. G. Naumis, “Perfect light transmission in Fibonacci arrays of dielectric multilayers,” J. Phys. Condens. Matter 21, 155901 (2009).
[Crossref] [PubMed]

Nava, R.

R. Nava, J. T. Martinez, J. A. D. Rio, and G. G. Naumis, “Perfect light transmission in Fibonacci arrays of dielectric multilayers,” J. Phys. Condens. Matter 21, 155901 (2009).
[Crossref] [PubMed]

Negro, D. L.

D. L. Negro and S. V. Boriskina, “Simulation methods for multiperiodic and aperiodic nanostructured dielectric waveguides. Deterministic aperiodic nanostructures for photonics and plasmonics applications,” Laser Photon. Rev. 6(2), 178–218 (2012).
[Crossref]

Negro, L. D.

L. D. Negro, N. Feng, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A. 10, 0640138 (2008).
[Crossref]

Neustock, L. T.

M. Paulsen, L. T. Neustock, S. Jahns, J. Adam, and M. Gerken, “Simulation methods for multiperiodic and aperiodic nanostructured dielectric waveguides,” Opt. Quantum Electron. 49, 107 (2017).
[Crossref]

Ohlídal, I.

T. Siefke, S. Kroker, K. Pfeiffer, O. Puffky, K. Dietrich, D. Franta, I. Ohlídal, A. Szeghalmi, E.-B. Kley, and A. Tünnermann, “Materials pushing the application limits of wire grid polarizers further into the deep ultraviolet spectral range,” Adv. Opt. Mater. 4, 1780 (2016).
[Crossref]

Paulsen, M.

M. Paulsen, L. T. Neustock, S. Jahns, J. Adam, and M. Gerken, “Simulation methods for multiperiodic and aperiodic nanostructured dielectric waveguides,” Opt. Quantum Electron. 49, 107 (2017).
[Crossref]

Pfeiffer, K.

T. Siefke, S. Kroker, K. Pfeiffer, O. Puffky, K. Dietrich, D. Franta, I. Ohlídal, A. Szeghalmi, E.-B. Kley, and A. Tünnermann, “Materials pushing the application limits of wire grid polarizers further into the deep ultraviolet spectral range,” Adv. Opt. Mater. 4, 1780 (2016).
[Crossref]

Poudel, K. N.

K. N. Poudel and S. Gangaju, “Spectral efficiency, diversity gain and multiplexing capacity analysis for massive MIMO, 5G communications system,” in Int. Conf. Net. Net. Appl. (2017), pp. 133–137.

K. N. Poudel, V. Koju, and W. Robertson, “Maximum length sequence (MLS) multilayer reflector using rigorous coupled wave analysis and FEM,” in IEEE USNC-URSI Radio Science Meeting Joint with AP-S, Boston, Massachusetts, USA, July 7–14 2018 (IEEE, 2018).

Puffky, O.

T. Siefke, S. Kroker, K. Pfeiffer, O. Puffky, K. Dietrich, D. Franta, I. Ohlídal, A. Szeghalmi, E.-B. Kley, and A. Tünnermann, “Materials pushing the application limits of wire grid polarizers further into the deep ultraviolet spectral range,” Adv. Opt. Mater. 4, 1780 (2016).
[Crossref]

Pursley, M. B.

D. V. Sarwate and M. B. Pursley, “Cross correlation properties of pseudo random and related sequences,” Proc. IEEE 68(5), 593–619 (1980).
[Crossref]

Rakic, A.

Riklund, R.

M. Dulea, M. Johansson, and R. Riklund, “Localization of electrons and electromagnetic waves in a deterministic aperiodic system,” Phys. Rev. B 45, 105–114 (1992).
[Crossref]

Rio, J. A. D.

R. Nava, J. T. Martinez, J. A. D. Rio, and G. G. Naumis, “Perfect light transmission in Fibonacci arrays of dielectric multilayers,” J. Phys. Condens. Matter 21, 155901 (2009).
[Crossref] [PubMed]

Rivory, J.

Robertson, W.

K. N. Poudel, V. Koju, and W. Robertson, “Maximum length sequence (MLS) multilayer reflector using rigorous coupled wave analysis and FEM,” in IEEE USNC-URSI Radio Science Meeting Joint with AP-S, Boston, Massachusetts, USA, July 7–14 2018 (IEEE, 2018).

Robertson, W. M.

Sarwate, D. V.

D. V. Sarwate and M. B. Pursley, “Cross correlation properties of pseudo random and related sequences,” Proc. IEEE 68(5), 593–619 (1980).
[Crossref]

Savit, R.

Z. Cheng, R. Savit, and R. Merlin, “Structure and electronic properties of Thue-Morse lattices,” Phys. Rev.B 375, 4375–4382 (1988).
[Crossref]

Schroeder, M.

M. Schroeder, “Diffuse sound reflection by maximum-length sequences,” J. Acoust. Soc. Am. 57, 149–150 (1975).
[Crossref]

Shinn, M.

M. Shinn and W. M. Robertson, “Surface plasmon-like sensor based on surface electromagnetic waves in a photonic band-gap material,” Sens. Actuators B,  105(2), 360–364 (2005).
[Crossref]

Siefke, T.

T. Siefke, S. Kroker, K. Pfeiffer, O. Puffky, K. Dietrich, D. Franta, I. Ohlídal, A. Szeghalmi, E.-B. Kley, and A. Tünnermann, “Materials pushing the application limits of wire grid polarizers further into the deep ultraviolet spectral range,” Adv. Opt. Mater. 4, 1780 (2016).
[Crossref]

Sutherland, B.

M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72, 633–636 (1994).
[Crossref] [PubMed]

M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: quasiperiodic media,” Phys. Rev. Lett. 58, 2436–2438 (1987).
[Crossref] [PubMed]

Szeghalmi, A.

T. Siefke, S. Kroker, K. Pfeiffer, O. Puffky, K. Dietrich, D. Franta, I. Ohlídal, A. Szeghalmi, E.-B. Kley, and A. Tünnermann, “Materials pushing the application limits of wire grid polarizers further into the deep ultraviolet spectral range,” Adv. Opt. Mater. 4, 1780 (2016).
[Crossref]

Tang, C.

M. Kohmoto, L. P. Kadanoff, and C. Tang, “Localization problem in one dimension: mapping and escape,” Phys. Rev. Lett. 50, 1870 (1983).
[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,” Science 282, 1679 (1998).
[Crossref] [PubMed]

Tünnermann, A.

T. Siefke, S. Kroker, K. Pfeiffer, O. Puffky, K. Dietrich, D. Franta, I. Ohlídal, A. Szeghalmi, E.-B. Kley, and A. Tünnermann, “Materials pushing the application limits of wire grid polarizers further into the deep ultraviolet spectral range,” Adv. Opt. Mater. 4, 1780 (2016).
[Crossref]

Van Albada, M. P.

M. P. Van Albada and A. Lagendijk, ,“Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[Crossref] [PubMed]

Vardeny, Z. V.

Z. V. Vardeny, A. Nahata, and A. Agrawal, “Optics of photonic quasicrystals,” Nat. Photonics 7, 117 (2013).
[Crossref]

Vishanathan, M.

M. Vishanathan, Simulation of Digital Communication Systems Using Matlab (M. Vishanathan, 2013).

Vuye, G.

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,” Science 282, 1679 (1998).
[Crossref] [PubMed]

Xu, J.

J. Xu, H. Fang, and Z. Lin, “Expanding high reflection range in a dielectric multilayer reflector by disorder and inhomogeneity,” J. Phys. D 34, 445–449 (2001).
[Crossref]

J. Xu, H. Fang, and Z. Lin, “Broadband optical reflector-an application of light localization in one dimension,” Appl. Phy. Lett. 67, 2431–2432 (1995).
[Crossref]

Adv. Opt. Mater. (1)

T. Siefke, S. Kroker, K. Pfeiffer, O. Puffky, K. Dietrich, D. Franta, I. Ohlídal, A. Szeghalmi, E.-B. Kley, and A. Tünnermann, “Materials pushing the application limits of wire grid polarizers further into the deep ultraviolet spectral range,” Adv. Opt. Mater. 4, 1780 (2016).
[Crossref]

Appl. Acous. (1)

W. T. Chu, “Impulse-response and reverberation-decay measurements made by using a periodic pseudorandom sequence,” Appl. Acous. 29, 193–205 (1990).
[Crossref]

Appl. Opt. (3)

Appl. Phy. Lett. (1)

J. Xu, H. Fang, and Z. Lin, “Broadband optical reflector-an application of light localization in one dimension,” Appl. Phy. Lett. 67, 2431–2432 (1995).
[Crossref]

Energy Procedia (1)

W. P. Guidorzi, L. Barbaresi, D. D’Orazio, and M. Garai, “Impulse responses measured with MLS or swept-sine signals applied to architectural acoustics: an in-depth analysis of the two methods and some case studies of measurements inside theaters,” Energy Procedia 78, 1611–1616 (2015).
[Crossref]

IEEE Trans. Inform. Theory (1)

M. Cohn and A. Lempe, “On fast M-sequence transforms,” IEEE Trans. Inform. Theory 23, 135–137 (1977).
[Crossref]

J. Acoust. Soc. Am. (1)

M. Schroeder, “Diffuse sound reflection by maximum-length sequences,” J. Acoust. Soc. Am. 57, 149–150 (1975).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. A (1)

J. Lekner, “Omnidirectional reflection by multilayer dielectric mirrors,” J. Opt. A 2, 349–352 (2000).
[Crossref]

J. Opt. A. (1)

L. D. Negro, N. Feng, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A. 10, 0640138 (2008).
[Crossref]

J. Opt. Soc. Am. A (2)

J. R. Devore, “Refractive indices of rutile and sphalerite,” J. Opt. Soc. Am. A 41, 416–419 (1951).
[Crossref]

I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. A 55, 1205–1209 (1965).
[Crossref]

J. Phys. Condens. Matter (1)

R. Nava, J. T. Martinez, J. A. D. Rio, and G. G. Naumis, “Perfect light transmission in Fibonacci arrays of dielectric multilayers,” J. Phys. Condens. Matter 21, 155901 (2009).
[Crossref] [PubMed]

J. Phys. D (1)

J. Xu, H. Fang, and Z. Lin, “Expanding high reflection range in a dielectric multilayer reflector by disorder and inhomogeneity,” J. Phys. D 34, 445–449 (2001).
[Crossref]

Laser Photon. Rev. (1)

D. L. Negro and S. V. Boriskina, “Simulation methods for multiperiodic and aperiodic nanostructured dielectric waveguides. Deterministic aperiodic nanostructures for photonics and plasmonics applications,” Laser Photon. Rev. 6(2), 178–218 (2012).
[Crossref]

Nat. Photonics (1)

Z. V. Vardeny, A. Nahata, and A. Agrawal, “Optics of photonic quasicrystals,” Nat. Photonics 7, 117 (2013).
[Crossref]

Opt. Lett. (1)

Opt. Quantum Electron. (1)

M. Paulsen, L. T. Neustock, S. Jahns, J. Adam, and M. Gerken, “Simulation methods for multiperiodic and aperiodic nanostructured dielectric waveguides,” Opt. Quantum Electron. 49, 107 (2017).
[Crossref]

Phys. Rev. B (2)

N. H. Liu, “Propagation of light waves in Thue-Morse dielectric multilayers,” Phys. Rev. B 553543–3547 (1997).
[Crossref]

M. Dulea, M. Johansson, and R. Riklund, “Localization of electrons and electromagnetic waves in a deterministic aperiodic system,” Phys. Rev. B 45, 105–114 (1992).
[Crossref]

Phys. Rev. Lett. (4)

M. Kohmoto, L. P. Kadanoff, and C. Tang, “Localization problem in one dimension: mapping and escape,” Phys. Rev. Lett. 50, 1870 (1983).
[Crossref]

M. P. Van Albada and A. Lagendijk, ,“Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[Crossref] [PubMed]

M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: quasiperiodic media,” Phys. Rev. Lett. 58, 2436–2438 (1987).
[Crossref] [PubMed]

M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72, 633–636 (1994).
[Crossref] [PubMed]

Phys. Rev.B (1)

Z. Cheng, R. Savit, and R. Merlin, “Structure and electronic properties of Thue-Morse lattices,” Phys. Rev.B 375, 4375–4382 (1988).
[Crossref]

Proc. IEEE (1)

D. V. Sarwate and M. B. Pursley, “Cross correlation properties of pseudo random and related sequences,” Proc. IEEE 68(5), 593–619 (1980).
[Crossref]

Rep. Prog. Phys. (1)

E. Macia, “Exploiting aperiodic designs in nanophotonic devices,” Rep. Prog. Phys. 75, 036502 (2012).
[Crossref] [PubMed]

Science (1)

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679 (1998).
[Crossref] [PubMed]

Sens. Actuators B (1)

M. Shinn and W. M. Robertson, “Surface plasmon-like sensor based on surface electromagnetic waves in a photonic band-gap material,” Sens. Actuators B,  105(2), 360–364 (2005).
[Crossref]

Other (6)

M. Vishanathan, Simulation of Digital Communication Systems Using Matlab (M. Vishanathan, 2013).

H. Jens, “Impulse response measurements using MLS,” (2003), http://jenshee.dk/signalprocessing/mls.pdf .

K. N. Poudel, V. Koju, and W. Robertson, “Maximum length sequence (MLS) multilayer reflector using rigorous coupled wave analysis and FEM,” in IEEE USNC-URSI Radio Science Meeting Joint with AP-S, Boston, Massachusetts, USA, July 7–14 2018 (IEEE, 2018).

S. J. Orfanidis, “Electromagnetic waves and antennas, online book,” (2016), chap. 6, pp. 1–1413, http://eceweb1.rutgers.edu/orfanidi/ewa/ .

K. N. Poudel and S. Gangaju, “Spectral efficiency, diversity gain and multiplexing capacity analysis for massive MIMO, 5G communications system,” in Int. Conf. Net. Net. Appl. (2017), pp. 133–137.

S. W. Golomb, “Spread spectrum techniques and applications,” in IEEE Third Intl. Symposium on Spread Spectrum Techniques and Application (1994).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1 (a) The MLS generation using shift register and XOR gate. (b) Flat Fourier spectra for 6th order MLS multilayer structure.
Fig. 2
Fig. 2 Illustration of the generation process for the N=3 maximal length sequence.
Fig. 3
Fig. 3 (a) The dielectric alternate high and low refractive index multilayer structure. (b) The 6th order MLS multilayer structure model.
Fig. 4
Fig. 4 Reflection characteristics for 6th order MLS multilayer structure for both s- and p-polarized light incident with 0°, 30°, and 60° respectively.
Fig. 5
Fig. 5 Reflection characteristics for 32 layer alternate high and low index multilayer structure for both s- and p-polarized light incident with 0°, 30°, and 60° respectively.
Fig. 6
Fig. 6 Average reflection as function of incident angle in the visible frequency range for 6th order (N = 6) MLS and 32 layer alternate high and low index multilayer structure for both sand p-polarized light.
Fig. 7
Fig. 7 Reflection characteristics for 7th order MLS multilayer structure for both s- and p-polarized light incident with 0°, 30°, and 60° respectively.
Fig. 8
Fig. 8 Reflection characteristics for metallic reflectors in visible frequency range for both sand p-polarized light incident at an angle of 0°, 30°, and 60°.
Fig. 9
Fig. 9 Average reflection as function of incident angle in visible frequency region for 7th order (N = 7) MLS and metallic reflectors for both s- and p-polarized light.

Tables (7)

Tables Icon

Table 1 Orders of MLS sequence Generation

Tables Icon

Table 2 Average Reflection Coefficient for Different 6th Order MLS for both s- and p-Polarized Light

Tables Icon

Table 3 Average Reflection Coefficient for 32 Layer Alternate High and Low Index Multilayer for both s- and p-Polarized Light

Tables Icon

Table 4 Average Reflection Coefficient for Different 7th Order MLS for both s- and p-Polarized Light

Tables Icon

Table 5 Average Reflection Coefficient for Metallic Reflectors for both s- and p-Polarized Light

Tables Icon

Table 6 Average Reflection Coefficient for Different Random Order Multilayer Structures

Tables Icon

Table 7 Average Reflection Coefficient in Visible Frequency Range for 6th Order MLS Designed Using Different Materials

Equations (7)

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

n SiO 2 = ( 1 + 0.6962 λ 2 λ 2 0.0684 2 + 0.4080 λ 2 λ 2 0.1162 2 + 0.8975 λ 2 λ 2 9.8962 2 ) 1 2
n TiO 2 = ( 5.913 + 0.2441 λ 2 0.0803 ) 1 2
ρ = η H η L η H + η L , ρ 1 = η a η H η a + η H , ρ M + 1 = η H η b η H + η b
Z 2 = η L 2 Z 3 = η L 2 η H 2 Z 4 = ( η H η L ) 4 Z 6 = ( η H η L ) 30 η b
Z 2 = ( η H η L ) 2 N η b
Γ 1 = Z L η a Z L + η a = 1 ( η H η L ) 2 N η H 2 η a η b 1 + ( η H η L ) 2 N η H 2 η a η b
Γ λ λ = π 2 [ 1 a c o s ( ρ ) 1 a c o s ( ρ ) ]