Abstract

In this paper, we present the design of a novel waveguide structure capable of multifrequency transmission bands with strongly enhanced electric field states. The concept of the structure is based on aperiodic and quasi-periodic fractal ordering of scattering subunits combined within a traditional channel-waveguide scheme. The resulting 3-D fractal waveguides are characterized by complex transmission spectra and sustain quasi-localized field modes with strong enhancement effects due to the lack of translational symmetry. In this paper, we will describe how it is possible to accurately model these complex waveguide structures within a simple 1-D model. We will explore the formation of photonic band gaps and the character of the quasi-localized states in fractal waveguide structures generated according to different deterministic rules, such as Fibonacci, Thue–Morse, and Rudin–Shapiro sequences. Furthermore, we will qualitatively compare the characteristics of the optical gaps and field states in periodic, fractal, and aperiodic waveguides. The results of our comparative study will show that fractal waveguides based on aperiodic order exhibit the richest transmission spectra with field-enhancement effects occurring at multiple frequencies. The proposed fractal waveguide design can provide an attractive route toward the fabrication of optically active devices for multiwavelength operation.

© 2007 IEEE

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  2. R. Pelster, V. Gasparian, G. Nimtz, "Propagation of plane waves and of waveguide modes in quasiperiodic dielectric heterostructures ," Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 55, 7645-7655 (1997).
  3. L. Dal Negro, "Photon band gap properties and omnidirectional reflectance in $\hbox{Si}/ \hbox{SiO}_{2}$ Thue–Morse quasicrystals," Appl. Phys. Lett. 84, 5186-5188 (2004).
  4. F. Qiu, "Omnidirectional reflection of electromagnetic waves on Thue–Morse dielectric multilayers ," Europhys. Lett. 68, 658-663 (2004).
  5. H. Chen, "Effects of defects and disorder on light propagation in one-dimensional photonic band-gap structures," Proc. SPIE 4905, 635-638 (2002).
  6. M. Ghulinyan, "Light pulse propagation in Fibonacci quasicrystals," Phys. Rev. B, Condens. Matter 71, 094 204-1-094 204-8 (2005).
  7. L. Dal Negro, "Spectrally enhanced light emission from aperiodic photonic structure," Appl. Phys. Lett. 86, 261 905 (2005).
  8. W. Gellerman, M. Kohmoto, B. Sutherland, P. C. Taylor, "Localization of light waves in Fibonacci dielectric multilayer," Phys. Rev. Lett. 72, 633-636 (1994).
  9. N. Liu, "Propagation of light waves in Thue–Morse dielectric multilayers," Phys. Rev. B, Condens. Matter 55, 3543-3547 (1997).
  10. L. Dal Negro, "Light transport through the band-edge states of Fibonacci quasicrystals," Phys. Rev. Lett. 90, 055 501-1-055 501-4 (2003).
  11. X. Jiang, "Photonic band gaps and localization in the Thue–Morse structures," Appl. Phys. Lett. 86, 201 110-1-201 110-3 (2005).
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2006 (1)

2005 (3)

M. Ghulinyan, "Light pulse propagation in Fibonacci quasicrystals," Phys. Rev. B, Condens. Matter 71, 094 204-1-094 204-8 (2005).

L. Dal Negro, "Spectrally enhanced light emission from aperiodic photonic structure," Appl. Phys. Lett. 86, 261 905 (2005).

X. Jiang, "Photonic band gaps and localization in the Thue–Morse structures," Appl. Phys. Lett. 86, 201 110-1-201 110-3 (2005).

2004 (4)

L. Dal Negro, "Photon band gap properties and omnidirectional reflectance in $\hbox{Si}/ \hbox{SiO}_{2}$ Thue–Morse quasicrystals," Appl. Phys. Lett. 84, 5186-5188 (2004).

F. Qiu, "Omnidirectional reflection of electromagnetic waves on Thue–Morse dielectric multilayers ," Europhys. Lett. 68, 658-663 (2004).

L. Kroon, R. Riklund, "Absence of localization in a model with correlation measure as a random lattice," Phys. Rev. B, Condens. Matter 69, 094 204-1-094 204-5 (2004).

N. N. Feng, W. P. Huang, "Time domain reflective beam propagation method," IEEE J. Quantum Electron. 40, 778-783 (2004).

2003 (2)

L. Dal Negro, "Light transport through the band-edge states of Fibonacci quasicrystals," Phys. Rev. Lett. 90, 055 501-1-055 501-4 (2003).

F. Qiu, "Resonant transmission and frequency trifurcation of light waves in Thue–Morse dielectric multilayers," Europhys. Lett. 63, 853-859 (2003).

2002 (3)

L. Kroon, E. Lennholm, R. Riklund, "Localization-delocalization in aperiodic systems," Phys. Rev. B, Condens. Matter 66, 094 204-1-094 204-9 (2002).

H. Chen, "Effects of defects and disorder on light propagation in one-dimensional photonic band-gap structures," Proc. SPIE 4905, 635-638 (2002).

C. C. Katsidis, D. I. Siapkas, "General transfer-matrix method for optical multilayer systems with coherent, partially coherent and incoherent interference," Appl. Opt. 41, 3978-3987 (2002).

1997 (3)

T. F. Krauss, B. Vögele, C. R. Stanley, R. M. De La Rue, "Waveguide microcavity based photonic microstructures," IEEE Photon. Technol. Lett. 9, 176-178 (1997).

R. Pelster, V. Gasparian, G. Nimtz, "Propagation of plane waves and of waveguide modes in quasiperiodic dielectric heterostructures ," Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 55, 7645-7655 (1997).

N. Liu, "Propagation of light waves in Thue–Morse dielectric multilayers," Phys. Rev. B, Condens. Matter 55, 3543-3547 (1997).

1996 (1)

T. F. Krauss, R. M. De La Rue, "Optical characterization of waveguide based photonics microstructures," Appl. Phys. Lett. 68, 1613-1615 (1996).

1994 (2)

J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).

W. Gellerman, M. Kohmoto, B. Sutherland, P. C. Taylor, "Localization of light waves in Fibonacci dielectric multilayer," Phys. Rev. Lett. 72, 633-636 (1994).

1993 (1)

A. Sudbo, "Film mode matching: A versatile numerical method for vector mode field calculations in dielectric waveguides," Pure Appl. Opt. 2, 211-233 (1993).

1992 (1)

M. Dulea, M. Johansson, R. Riklund, "Localization of electrons and electromagnetic waves in a deterministic aperiodic system ," Phys. Rev. B, Condens. Matter 45, 105-114 (1992).

1991 (1)

W. P. Huang, S. T. Chu, A. Goss, S. K. Chaudhuri, "A scalar finite difference time domain approach to guided wave optics," IEEE Photon. Technol. Lett. 3, 524-526 (1991).

1988 (1)

Z. Cheng, R. Savit, R. Merlin, "Structure and electronic properties of Thue–Morse lattices," Phys. Rev. B, Condens. Matter 37, 4375-4382 (1988).

Appl. Opt. (1)

Appl. Phys. Lett. (4)

T. F. Krauss, R. M. De La Rue, "Optical characterization of waveguide based photonics microstructures," Appl. Phys. Lett. 68, 1613-1615 (1996).

L. Dal Negro, "Photon band gap properties and omnidirectional reflectance in $\hbox{Si}/ \hbox{SiO}_{2}$ Thue–Morse quasicrystals," Appl. Phys. Lett. 84, 5186-5188 (2004).

L. Dal Negro, "Spectrally enhanced light emission from aperiodic photonic structure," Appl. Phys. Lett. 86, 261 905 (2005).

X. Jiang, "Photonic band gaps and localization in the Thue–Morse structures," Appl. Phys. Lett. 86, 201 110-1-201 110-3 (2005).

Europhys. Lett. (2)

F. Qiu, "Resonant transmission and frequency trifurcation of light waves in Thue–Morse dielectric multilayers," Europhys. Lett. 63, 853-859 (2003).

F. Qiu, "Omnidirectional reflection of electromagnetic waves on Thue–Morse dielectric multilayers ," Europhys. Lett. 68, 658-663 (2004).

IEEE J. Quantum Electron. (1)

N. N. Feng, W. P. Huang, "Time domain reflective beam propagation method," IEEE J. Quantum Electron. 40, 778-783 (2004).

IEEE Photon. Technol. Lett. (2)

W. P. Huang, S. T. Chu, A. Goss, S. K. Chaudhuri, "A scalar finite difference time domain approach to guided wave optics," IEEE Photon. Technol. Lett. 3, 524-526 (1991).

T. F. Krauss, B. Vögele, C. R. Stanley, R. M. De La Rue, "Waveguide microcavity based photonic microstructures," IEEE Photon. Technol. Lett. 9, 176-178 (1997).

J. Comput. Phys. (1)

J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).

Opt. Lett. (1)

Phys. Rev. B, Condens. Matter (6)

M. Ghulinyan, "Light pulse propagation in Fibonacci quasicrystals," Phys. Rev. B, Condens. Matter 71, 094 204-1-094 204-8 (2005).

L. Kroon, E. Lennholm, R. Riklund, "Localization-delocalization in aperiodic systems," Phys. Rev. B, Condens. Matter 66, 094 204-1-094 204-9 (2002).

Z. Cheng, R. Savit, R. Merlin, "Structure and electronic properties of Thue–Morse lattices," Phys. Rev. B, Condens. Matter 37, 4375-4382 (1988).

M. Dulea, M. Johansson, R. Riklund, "Localization of electrons and electromagnetic waves in a deterministic aperiodic system ," Phys. Rev. B, Condens. Matter 45, 105-114 (1992).

L. Kroon, R. Riklund, "Absence of localization in a model with correlation measure as a random lattice," Phys. Rev. B, Condens. Matter 69, 094 204-1-094 204-5 (2004).

N. Liu, "Propagation of light waves in Thue–Morse dielectric multilayers," Phys. Rev. B, Condens. Matter 55, 3543-3547 (1997).

Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. (1)

R. Pelster, V. Gasparian, G. Nimtz, "Propagation of plane waves and of waveguide modes in quasiperiodic dielectric heterostructures ," Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 55, 7645-7655 (1997).

Phys. Rev. Lett. (2)

L. Dal Negro, "Light transport through the band-edge states of Fibonacci quasicrystals," Phys. Rev. Lett. 90, 055 501-1-055 501-4 (2003).

W. Gellerman, M. Kohmoto, B. Sutherland, P. C. Taylor, "Localization of light waves in Fibonacci dielectric multilayer," Phys. Rev. Lett. 72, 633-636 (1994).

Proc. SPIE (1)

H. Chen, "Effects of defects and disorder on light propagation in one-dimensional photonic band-gap structures," Proc. SPIE 4905, 635-638 (2002).

Pure Appl. Opt. (1)

A. Sudbo, "Film mode matching: A versatile numerical method for vector mode field calculations in dielectric waveguides," Pure Appl. Opt. 2, 211-233 (1993).

Other (3)

D. F. G. Gallagher, T. P. Felici, "Eigenmode expansion methods for simulation of optical propagation in photonics—Pros and cons ," Proc. Integr. Opt.: Devices, Mater. Technol. VII, SPIE (2003) pp. 69-82.

C. Janot, Quasicrystals: A Primer (Oxford Univ. Press, 1997).

M. Queffélec, Lecture Notes in Mathematics (Springer-Verlag, 1984).

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