Abstract

This paper contains an analysis of the optical properties of aperiodic multilayer structures constructed using the Morse–Thue, double-period, Fibonacci, and Rudin–Shapiro numerical sequences. A general quantitative law is established that determines how the scaling in their Fourier transforms is related to their spectral characteristics. Some practical aspects of the use of aperiodic systems are considered.

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  1. E. L. Albuquerque and M. G. Cottam, “Theory of elementary excitations in quasi-periodic structures,” Phys. Rep. 376, 225 (2003).
    [CrossRef]
  2. V. A. Bushuev, B. I. Mantsyzov, and A. D. Pryamikov, “Analysis of the second-harmonic-generation efficiency in one-dimensional photonic crystals as a function of the wavelength and the layer thickness,” Perspek. Mat. No. 6, 38 (2001).
  3. L. N. Makarava, M. M. Nazarov, I. A. Ozheredov, A. P. Shkurinov, A. G. Smirnov, and S. V. Zhukovsky, “Fibonacci-like photonic structure for femtosecond pulse compression,” Phys. Rev. E 75, 036609 (2007).
    [CrossRef]
  4. F. Chiadini, V. Fiumara, I. Gallina, and A. Scaglione, “Omnidirectional band gap in Cantor dielectric multilayers,” Opt. Commun. 282, 4009 (2009).
    [CrossRef]
  5. S. Golmohammadi and A. Rostami, “Optical filters using optical multi-layer structures for optical communication systems,” Fiber Integr. Opt. 29, 209 (2010).
    [CrossRef]
  6. W.-G. Feng, W.-Z. He, D.-P. Xue, Y.-B. Xu, and X. Wu, “Reflection of soft x-rays and extreme ultraviolet from a metallic Fibonacci quasi-superlattice,” J. Phys. Condens. Matter 1, 8241 (1989).
    [CrossRef]
  7. E. A. Sakun, A. V. Polyushkevich, P. A. Kharlashin, O. V. Semenova, and A. Ya. Korets, “Development of porous silicon-based structures,” J. Sib. Fed. Univ. Eng. Technol. 3, 430 (2010).
  8. O. V. Angelsky, “New feasibilities for characterizing rough surfaces by optical correlation techniques,” Proc. SPIE 4607, 241 (2002).
    [CrossRef]
  9. S. K. Stafeev and A. A. Zinchik, “Using fractal masks to visualize the optical inhomogeneities of transparent materials,” Opt. Zh. 70, No. 11, 49 (2003). [J. Opt. Technol. 70, 806 (2003)].
  10. F. Axel, J.-P. Allouchet, and Z.-Y. Wen, “On certain properties of high-resolution x-ray diffraction spectra of finite-size generalized Rudin–Shapiro multilayer heterostructures,” J. Phys. Condens. Matter 4, 8713 (1992).
    [CrossRef]
  11. N. V. Grushina, A. M. Zotov, P. V. Korolenko, and A. Yu. Mishin, “Gold. Cross-section and self-similar structures in optics,” Vest. Moskov. Univ. Fiz. Astron. No. 4, 47 (2009).
  12. K. Esaki, M. Sato, and M. Kohmoto, “Wave propagation through Cantor-set media: chaos, scaling, and fractal structures,” Phys. Rev. E 79, 056226 (2009).
    [CrossRef]
  13. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light (Pergamon Press, Oxford, 1965; Nauka, Moscow, 1970).
  14. E. Maciá, “The role of aperiodic order in science and technology,” Rep. Prog. Phys. 69, 397 (2006).
    [CrossRef]
  15. J. Feder, Fractals (Plenum Press, New York, 1988; Mir, Moscow, 1991).

2010 (2)

S. Golmohammadi and A. Rostami, “Optical filters using optical multi-layer structures for optical communication systems,” Fiber Integr. Opt. 29, 209 (2010).
[CrossRef]

E. A. Sakun, A. V. Polyushkevich, P. A. Kharlashin, O. V. Semenova, and A. Ya. Korets, “Development of porous silicon-based structures,” J. Sib. Fed. Univ. Eng. Technol. 3, 430 (2010).

2009 (3)

F. Chiadini, V. Fiumara, I. Gallina, and A. Scaglione, “Omnidirectional band gap in Cantor dielectric multilayers,” Opt. Commun. 282, 4009 (2009).
[CrossRef]

N. V. Grushina, A. M. Zotov, P. V. Korolenko, and A. Yu. Mishin, “Gold. Cross-section and self-similar structures in optics,” Vest. Moskov. Univ. Fiz. Astron. No. 4, 47 (2009).

K. Esaki, M. Sato, and M. Kohmoto, “Wave propagation through Cantor-set media: chaos, scaling, and fractal structures,” Phys. Rev. E 79, 056226 (2009).
[CrossRef]

2007 (1)

L. N. Makarava, M. M. Nazarov, I. A. Ozheredov, A. P. Shkurinov, A. G. Smirnov, and S. V. Zhukovsky, “Fibonacci-like photonic structure for femtosecond pulse compression,” Phys. Rev. E 75, 036609 (2007).
[CrossRef]

2006 (1)

E. Maciá, “The role of aperiodic order in science and technology,” Rep. Prog. Phys. 69, 397 (2006).
[CrossRef]

2003 (2)

S. K. Stafeev and A. A. Zinchik, “Using fractal masks to visualize the optical inhomogeneities of transparent materials,” Opt. Zh. 70, No. 11, 49 (2003). [J. Opt. Technol. 70, 806 (2003)].

E. L. Albuquerque and M. G. Cottam, “Theory of elementary excitations in quasi-periodic structures,” Phys. Rep. 376, 225 (2003).
[CrossRef]

2002 (1)

O. V. Angelsky, “New feasibilities for characterizing rough surfaces by optical correlation techniques,” Proc. SPIE 4607, 241 (2002).
[CrossRef]

2001 (1)

V. A. Bushuev, B. I. Mantsyzov, and A. D. Pryamikov, “Analysis of the second-harmonic-generation efficiency in one-dimensional photonic crystals as a function of the wavelength and the layer thickness,” Perspek. Mat. No. 6, 38 (2001).

1992 (1)

F. Axel, J.-P. Allouchet, and Z.-Y. Wen, “On certain properties of high-resolution x-ray diffraction spectra of finite-size generalized Rudin–Shapiro multilayer heterostructures,” J. Phys. Condens. Matter 4, 8713 (1992).
[CrossRef]

1989 (1)

W.-G. Feng, W.-Z. He, D.-P. Xue, Y.-B. Xu, and X. Wu, “Reflection of soft x-rays and extreme ultraviolet from a metallic Fibonacci quasi-superlattice,” J. Phys. Condens. Matter 1, 8241 (1989).
[CrossRef]

Albuquerque, E. L.

E. L. Albuquerque and M. G. Cottam, “Theory of elementary excitations in quasi-periodic structures,” Phys. Rep. 376, 225 (2003).
[CrossRef]

Allouchet, J.-P.

F. Axel, J.-P. Allouchet, and Z.-Y. Wen, “On certain properties of high-resolution x-ray diffraction spectra of finite-size generalized Rudin–Shapiro multilayer heterostructures,” J. Phys. Condens. Matter 4, 8713 (1992).
[CrossRef]

Angelsky, O. V.

O. V. Angelsky, “New feasibilities for characterizing rough surfaces by optical correlation techniques,” Proc. SPIE 4607, 241 (2002).
[CrossRef]

Axel, F.

F. Axel, J.-P. Allouchet, and Z.-Y. Wen, “On certain properties of high-resolution x-ray diffraction spectra of finite-size generalized Rudin–Shapiro multilayer heterostructures,” J. Phys. Condens. Matter 4, 8713 (1992).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light (Pergamon Press, Oxford, 1965; Nauka, Moscow, 1970).

Bushuev, V. A.

V. A. Bushuev, B. I. Mantsyzov, and A. D. Pryamikov, “Analysis of the second-harmonic-generation efficiency in one-dimensional photonic crystals as a function of the wavelength and the layer thickness,” Perspek. Mat. No. 6, 38 (2001).

Chiadini, F.

F. Chiadini, V. Fiumara, I. Gallina, and A. Scaglione, “Omnidirectional band gap in Cantor dielectric multilayers,” Opt. Commun. 282, 4009 (2009).
[CrossRef]

Cottam, M. G.

E. L. Albuquerque and M. G. Cottam, “Theory of elementary excitations in quasi-periodic structures,” Phys. Rep. 376, 225 (2003).
[CrossRef]

Esaki, K.

K. Esaki, M. Sato, and M. Kohmoto, “Wave propagation through Cantor-set media: chaos, scaling, and fractal structures,” Phys. Rev. E 79, 056226 (2009).
[CrossRef]

Feder, J.

J. Feder, Fractals (Plenum Press, New York, 1988; Mir, Moscow, 1991).

Feng, W.-G.

W.-G. Feng, W.-Z. He, D.-P. Xue, Y.-B. Xu, and X. Wu, “Reflection of soft x-rays and extreme ultraviolet from a metallic Fibonacci quasi-superlattice,” J. Phys. Condens. Matter 1, 8241 (1989).
[CrossRef]

Fiumara, V.

F. Chiadini, V. Fiumara, I. Gallina, and A. Scaglione, “Omnidirectional band gap in Cantor dielectric multilayers,” Opt. Commun. 282, 4009 (2009).
[CrossRef]

Gallina, I.

F. Chiadini, V. Fiumara, I. Gallina, and A. Scaglione, “Omnidirectional band gap in Cantor dielectric multilayers,” Opt. Commun. 282, 4009 (2009).
[CrossRef]

Golmohammadi, S.

S. Golmohammadi and A. Rostami, “Optical filters using optical multi-layer structures for optical communication systems,” Fiber Integr. Opt. 29, 209 (2010).
[CrossRef]

Grushina, N. V.

N. V. Grushina, A. M. Zotov, P. V. Korolenko, and A. Yu. Mishin, “Gold. Cross-section and self-similar structures in optics,” Vest. Moskov. Univ. Fiz. Astron. No. 4, 47 (2009).

He, W.-Z.

W.-G. Feng, W.-Z. He, D.-P. Xue, Y.-B. Xu, and X. Wu, “Reflection of soft x-rays and extreme ultraviolet from a metallic Fibonacci quasi-superlattice,” J. Phys. Condens. Matter 1, 8241 (1989).
[CrossRef]

Kharlashin, P. A.

E. A. Sakun, A. V. Polyushkevich, P. A. Kharlashin, O. V. Semenova, and A. Ya. Korets, “Development of porous silicon-based structures,” J. Sib. Fed. Univ. Eng. Technol. 3, 430 (2010).

Kohmoto, M.

K. Esaki, M. Sato, and M. Kohmoto, “Wave propagation through Cantor-set media: chaos, scaling, and fractal structures,” Phys. Rev. E 79, 056226 (2009).
[CrossRef]

Korets, A. Ya.

E. A. Sakun, A. V. Polyushkevich, P. A. Kharlashin, O. V. Semenova, and A. Ya. Korets, “Development of porous silicon-based structures,” J. Sib. Fed. Univ. Eng. Technol. 3, 430 (2010).

Korolenko, P. V.

N. V. Grushina, A. M. Zotov, P. V. Korolenko, and A. Yu. Mishin, “Gold. Cross-section and self-similar structures in optics,” Vest. Moskov. Univ. Fiz. Astron. No. 4, 47 (2009).

Maciá, E.

E. Maciá, “The role of aperiodic order in science and technology,” Rep. Prog. Phys. 69, 397 (2006).
[CrossRef]

Makarava, L. N.

L. N. Makarava, M. M. Nazarov, I. A. Ozheredov, A. P. Shkurinov, A. G. Smirnov, and S. V. Zhukovsky, “Fibonacci-like photonic structure for femtosecond pulse compression,” Phys. Rev. E 75, 036609 (2007).
[CrossRef]

Mantsyzov, B. I.

V. A. Bushuev, B. I. Mantsyzov, and A. D. Pryamikov, “Analysis of the second-harmonic-generation efficiency in one-dimensional photonic crystals as a function of the wavelength and the layer thickness,” Perspek. Mat. No. 6, 38 (2001).

Mishin, A. Yu.

N. V. Grushina, A. M. Zotov, P. V. Korolenko, and A. Yu. Mishin, “Gold. Cross-section and self-similar structures in optics,” Vest. Moskov. Univ. Fiz. Astron. No. 4, 47 (2009).

Nazarov, M. M.

L. N. Makarava, M. M. Nazarov, I. A. Ozheredov, A. P. Shkurinov, A. G. Smirnov, and S. V. Zhukovsky, “Fibonacci-like photonic structure for femtosecond pulse compression,” Phys. Rev. E 75, 036609 (2007).
[CrossRef]

Ozheredov, I. A.

L. N. Makarava, M. M. Nazarov, I. A. Ozheredov, A. P. Shkurinov, A. G. Smirnov, and S. V. Zhukovsky, “Fibonacci-like photonic structure for femtosecond pulse compression,” Phys. Rev. E 75, 036609 (2007).
[CrossRef]

Polyushkevich, A. V.

E. A. Sakun, A. V. Polyushkevich, P. A. Kharlashin, O. V. Semenova, and A. Ya. Korets, “Development of porous silicon-based structures,” J. Sib. Fed. Univ. Eng. Technol. 3, 430 (2010).

Pryamikov, A. D.

V. A. Bushuev, B. I. Mantsyzov, and A. D. Pryamikov, “Analysis of the second-harmonic-generation efficiency in one-dimensional photonic crystals as a function of the wavelength and the layer thickness,” Perspek. Mat. No. 6, 38 (2001).

Rostami, A.

S. Golmohammadi and A. Rostami, “Optical filters using optical multi-layer structures for optical communication systems,” Fiber Integr. Opt. 29, 209 (2010).
[CrossRef]

Sakun, E. A.

E. A. Sakun, A. V. Polyushkevich, P. A. Kharlashin, O. V. Semenova, and A. Ya. Korets, “Development of porous silicon-based structures,” J. Sib. Fed. Univ. Eng. Technol. 3, 430 (2010).

Sato, M.

K. Esaki, M. Sato, and M. Kohmoto, “Wave propagation through Cantor-set media: chaos, scaling, and fractal structures,” Phys. Rev. E 79, 056226 (2009).
[CrossRef]

Scaglione, A.

F. Chiadini, V. Fiumara, I. Gallina, and A. Scaglione, “Omnidirectional band gap in Cantor dielectric multilayers,” Opt. Commun. 282, 4009 (2009).
[CrossRef]

Semenova, O. V.

E. A. Sakun, A. V. Polyushkevich, P. A. Kharlashin, O. V. Semenova, and A. Ya. Korets, “Development of porous silicon-based structures,” J. Sib. Fed. Univ. Eng. Technol. 3, 430 (2010).

Shkurinov, A. P.

L. N. Makarava, M. M. Nazarov, I. A. Ozheredov, A. P. Shkurinov, A. G. Smirnov, and S. V. Zhukovsky, “Fibonacci-like photonic structure for femtosecond pulse compression,” Phys. Rev. E 75, 036609 (2007).
[CrossRef]

Smirnov, A. G.

L. N. Makarava, M. M. Nazarov, I. A. Ozheredov, A. P. Shkurinov, A. G. Smirnov, and S. V. Zhukovsky, “Fibonacci-like photonic structure for femtosecond pulse compression,” Phys. Rev. E 75, 036609 (2007).
[CrossRef]

Stafeev, S. K.

S. K. Stafeev and A. A. Zinchik, “Using fractal masks to visualize the optical inhomogeneities of transparent materials,” Opt. Zh. 70, No. 11, 49 (2003). [J. Opt. Technol. 70, 806 (2003)].

Wen, Z.-Y.

F. Axel, J.-P. Allouchet, and Z.-Y. Wen, “On certain properties of high-resolution x-ray diffraction spectra of finite-size generalized Rudin–Shapiro multilayer heterostructures,” J. Phys. Condens. Matter 4, 8713 (1992).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light (Pergamon Press, Oxford, 1965; Nauka, Moscow, 1970).

Wu, X.

W.-G. Feng, W.-Z. He, D.-P. Xue, Y.-B. Xu, and X. Wu, “Reflection of soft x-rays and extreme ultraviolet from a metallic Fibonacci quasi-superlattice,” J. Phys. Condens. Matter 1, 8241 (1989).
[CrossRef]

Xu, Y.-B.

W.-G. Feng, W.-Z. He, D.-P. Xue, Y.-B. Xu, and X. Wu, “Reflection of soft x-rays and extreme ultraviolet from a metallic Fibonacci quasi-superlattice,” J. Phys. Condens. Matter 1, 8241 (1989).
[CrossRef]

Xue, D.-P.

W.-G. Feng, W.-Z. He, D.-P. Xue, Y.-B. Xu, and X. Wu, “Reflection of soft x-rays and extreme ultraviolet from a metallic Fibonacci quasi-superlattice,” J. Phys. Condens. Matter 1, 8241 (1989).
[CrossRef]

Zhukovsky, S. V.

L. N. Makarava, M. M. Nazarov, I. A. Ozheredov, A. P. Shkurinov, A. G. Smirnov, and S. V. Zhukovsky, “Fibonacci-like photonic structure for femtosecond pulse compression,” Phys. Rev. E 75, 036609 (2007).
[CrossRef]

Zinchik, A. A.

S. K. Stafeev and A. A. Zinchik, “Using fractal masks to visualize the optical inhomogeneities of transparent materials,” Opt. Zh. 70, No. 11, 49 (2003). [J. Opt. Technol. 70, 806 (2003)].

Zotov, A. M.

N. V. Grushina, A. M. Zotov, P. V. Korolenko, and A. Yu. Mishin, “Gold. Cross-section and self-similar structures in optics,” Vest. Moskov. Univ. Fiz. Astron. No. 4, 47 (2009).

Fiber Integr. Opt. (1)

S. Golmohammadi and A. Rostami, “Optical filters using optical multi-layer structures for optical communication systems,” Fiber Integr. Opt. 29, 209 (2010).
[CrossRef]

J. Phys. Condens. Matter (2)

W.-G. Feng, W.-Z. He, D.-P. Xue, Y.-B. Xu, and X. Wu, “Reflection of soft x-rays and extreme ultraviolet from a metallic Fibonacci quasi-superlattice,” J. Phys. Condens. Matter 1, 8241 (1989).
[CrossRef]

F. Axel, J.-P. Allouchet, and Z.-Y. Wen, “On certain properties of high-resolution x-ray diffraction spectra of finite-size generalized Rudin–Shapiro multilayer heterostructures,” J. Phys. Condens. Matter 4, 8713 (1992).
[CrossRef]

J. Sib. Fed. Univ. Eng. Technol. (1)

E. A. Sakun, A. V. Polyushkevich, P. A. Kharlashin, O. V. Semenova, and A. Ya. Korets, “Development of porous silicon-based structures,” J. Sib. Fed. Univ. Eng. Technol. 3, 430 (2010).

Opt. Commun. (1)

F. Chiadini, V. Fiumara, I. Gallina, and A. Scaglione, “Omnidirectional band gap in Cantor dielectric multilayers,” Opt. Commun. 282, 4009 (2009).
[CrossRef]

Opt. Zh. (1)

S. K. Stafeev and A. A. Zinchik, “Using fractal masks to visualize the optical inhomogeneities of transparent materials,” Opt. Zh. 70, No. 11, 49 (2003). [J. Opt. Technol. 70, 806 (2003)].

Perspek. Mat. (1)

V. A. Bushuev, B. I. Mantsyzov, and A. D. Pryamikov, “Analysis of the second-harmonic-generation efficiency in one-dimensional photonic crystals as a function of the wavelength and the layer thickness,” Perspek. Mat. No. 6, 38 (2001).

Phys. Rep. (1)

E. L. Albuquerque and M. G. Cottam, “Theory of elementary excitations in quasi-periodic structures,” Phys. Rep. 376, 225 (2003).
[CrossRef]

Phys. Rev. E (2)

L. N. Makarava, M. M. Nazarov, I. A. Ozheredov, A. P. Shkurinov, A. G. Smirnov, and S. V. Zhukovsky, “Fibonacci-like photonic structure for femtosecond pulse compression,” Phys. Rev. E 75, 036609 (2007).
[CrossRef]

K. Esaki, M. Sato, and M. Kohmoto, “Wave propagation through Cantor-set media: chaos, scaling, and fractal structures,” Phys. Rev. E 79, 056226 (2009).
[CrossRef]

Proc. SPIE (1)

O. V. Angelsky, “New feasibilities for characterizing rough surfaces by optical correlation techniques,” Proc. SPIE 4607, 241 (2002).
[CrossRef]

Rep. Prog. Phys. (1)

E. Maciá, “The role of aperiodic order in science and technology,” Rep. Prog. Phys. 69, 397 (2006).
[CrossRef]

Vest. Moskov. Univ. Fiz. Astron. (1)

N. V. Grushina, A. M. Zotov, P. V. Korolenko, and A. Yu. Mishin, “Gold. Cross-section and self-similar structures in optics,” Vest. Moskov. Univ. Fiz. Astron. No. 4, 47 (2009).

Other (2)

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light (Pergamon Press, Oxford, 1965; Nauka, Moscow, 1970).

J. Feder, Fractals (Plenum Press, New York, 1988; Mir, Moscow, 1991).

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