Abstract

Ultra compact photonic crystal filters with and without metallic parts operating at telecommunication wavelengths are designed using the multiple multipole program combined with the model-based parameter estimation technique. Material loss is taken into account and measured material properties are employed for practical design considerations. Stochastic and deterministic optimization techniques are applied to obtain optimum filter characteristics.

© 2007 Optical Society of America

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References

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  1. K. Yasumoto, Electromagnetic Theory and Applications for Photonic Crystals (CRC Press, 2005).
    [CrossRef]
  2. Ch. Hafner, "Drude model replacement by symbolic regression," J. Comput. Theor. Nanosci. 2, 88-98 (2005).
  3. Ch. Hafner, Cui Xudong, and R. Vahldiek, "Metallic photonic crystals at optical frequencies," J. Comput. Theor. Nanosci. 2, 240-250 (2005).
    [CrossRef]
  4. Arthur R. McGurn and Alexei A. Maradudin, "Photonic band structures of two and three dimensional metal or semiconductor arrays," Phys. Rev. B 48, 17576-17579 (1993).
    [CrossRef]
  5. R. Zengerle and O. Leminger, "Phase-shifted Bragg grating filters with improved transmission characteristics," J. Lightwave Technol. 13, 2354-2358 (1995).
    [CrossRef]
  6. G. P. Agrawal and S. Radic, "Phase-shifted fiber Bragg gratings and their application for wavelength demultiplexing," IEEE Photon. Technol. Lett. 6, 995-997 (1994).
    [CrossRef]
  7. Ch. Hafner, J. Smajic, and D. Erni, "Simulation and optimization of composite doped metamaterials," in Handbook of Theoretical and Computational Nanotechnology, M.Riedt, W.Schommers, eds. (American Scientific), to be published.
  8. J. Smajic, Ch. Hafner, and D. Erni, "Optimiztion of photonic crystal structures," J. Opt. Soc. Am. A 21, 2223-2232 (2004).
    [CrossRef]
  9. Ch. Hafner, Post-Modern Electromagnetics (Wiley, 1999).
  10. Ch. Hafner, MAX-1, A Visual Electromagnetics Platform for PCs (Wiley, 1999).
  11. E. Miller, "Model-based parameter estimation in electromagnetics," IEEE Antennas Propag. Mag. 40, 42-51 (1998).
    [CrossRef]
  12. K. Tavzarashvili, Ch. Hafner, C. Xudong, R. Vahldieck, D. Karkashadze, and G. Ghvedashvili, "Model-based parameter estimation (MBPE) for metallic photonic crystal filters," Appl. Comput. Electromagn. Soc. J. (to be published).
  13. G. Winter, J. Périaux, M. Galan, and P. Cuesta, Genetic Algorithms in Engineering and Computer Science (Wiley, 1995).
  14. D. Quagliarella, J. Périaux, C. Poloni, and G. Winter, Genetic Algorithms and Evolution Strategies in Engineering and Computer Science (Wiley, 1998).
  15. Cui Xudong, Ch. Hafner, K. Tavzarashvili, and R. Vahldieck, "Design of ultra-compact metallo-dielectric photonic crystal filters," Opt. Express 13, 6175-6180 (2005).
    [CrossRef] [PubMed]
  16. L. Mendioroz, R. Gonzalo, and C. del Roi, "Design of electromagnetic crystal filters for rectangular waveguides," Microwave Opt. Technol. Lett. 30, 81-84 (2001).
    [CrossRef]
  17. R. Costa, A. Melloni, and M. Martinelli, "Bandpass resonant filters in photonic-crystal waveguides," IEEE Photon. Technol. Lett. 15, 401-403 (2003).
    [CrossRef]
  18. A. S. Jugessur, P. Pottier, and R. M. De La Rue, "One dimensional periodic photonic crystal microcavity filters with transition mode matching features, embedded in ridge waveguides," Electron. Lett. 39, 367-368 (2003).
    [CrossRef]

2005 (3)

Ch. Hafner, "Drude model replacement by symbolic regression," J. Comput. Theor. Nanosci. 2, 88-98 (2005).

Ch. Hafner, Cui Xudong, and R. Vahldiek, "Metallic photonic crystals at optical frequencies," J. Comput. Theor. Nanosci. 2, 240-250 (2005).
[CrossRef]

Cui Xudong, Ch. Hafner, K. Tavzarashvili, and R. Vahldieck, "Design of ultra-compact metallo-dielectric photonic crystal filters," Opt. Express 13, 6175-6180 (2005).
[CrossRef] [PubMed]

2004 (1)

2003 (2)

R. Costa, A. Melloni, and M. Martinelli, "Bandpass resonant filters in photonic-crystal waveguides," IEEE Photon. Technol. Lett. 15, 401-403 (2003).
[CrossRef]

A. S. Jugessur, P. Pottier, and R. M. De La Rue, "One dimensional periodic photonic crystal microcavity filters with transition mode matching features, embedded in ridge waveguides," Electron. Lett. 39, 367-368 (2003).
[CrossRef]

2001 (1)

L. Mendioroz, R. Gonzalo, and C. del Roi, "Design of electromagnetic crystal filters for rectangular waveguides," Microwave Opt. Technol. Lett. 30, 81-84 (2001).
[CrossRef]

1998 (1)

E. Miller, "Model-based parameter estimation in electromagnetics," IEEE Antennas Propag. Mag. 40, 42-51 (1998).
[CrossRef]

1995 (1)

R. Zengerle and O. Leminger, "Phase-shifted Bragg grating filters with improved transmission characteristics," J. Lightwave Technol. 13, 2354-2358 (1995).
[CrossRef]

1994 (1)

G. P. Agrawal and S. Radic, "Phase-shifted fiber Bragg gratings and their application for wavelength demultiplexing," IEEE Photon. Technol. Lett. 6, 995-997 (1994).
[CrossRef]

1993 (1)

Arthur R. McGurn and Alexei A. Maradudin, "Photonic band structures of two and three dimensional metal or semiconductor arrays," Phys. Rev. B 48, 17576-17579 (1993).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal and S. Radic, "Phase-shifted fiber Bragg gratings and their application for wavelength demultiplexing," IEEE Photon. Technol. Lett. 6, 995-997 (1994).
[CrossRef]

Costa, R.

R. Costa, A. Melloni, and M. Martinelli, "Bandpass resonant filters in photonic-crystal waveguides," IEEE Photon. Technol. Lett. 15, 401-403 (2003).
[CrossRef]

Cuesta, P.

G. Winter, J. Périaux, M. Galan, and P. Cuesta, Genetic Algorithms in Engineering and Computer Science (Wiley, 1995).

De La Rue, R. M.

A. S. Jugessur, P. Pottier, and R. M. De La Rue, "One dimensional periodic photonic crystal microcavity filters with transition mode matching features, embedded in ridge waveguides," Electron. Lett. 39, 367-368 (2003).
[CrossRef]

del Roi, C.

L. Mendioroz, R. Gonzalo, and C. del Roi, "Design of electromagnetic crystal filters for rectangular waveguides," Microwave Opt. Technol. Lett. 30, 81-84 (2001).
[CrossRef]

Erni, D.

J. Smajic, Ch. Hafner, and D. Erni, "Optimiztion of photonic crystal structures," J. Opt. Soc. Am. A 21, 2223-2232 (2004).
[CrossRef]

Ch. Hafner, J. Smajic, and D. Erni, "Simulation and optimization of composite doped metamaterials," in Handbook of Theoretical and Computational Nanotechnology, M.Riedt, W.Schommers, eds. (American Scientific), to be published.

Galan, M.

G. Winter, J. Périaux, M. Galan, and P. Cuesta, Genetic Algorithms in Engineering and Computer Science (Wiley, 1995).

Ghvedashvili, G.

K. Tavzarashvili, Ch. Hafner, C. Xudong, R. Vahldieck, D. Karkashadze, and G. Ghvedashvili, "Model-based parameter estimation (MBPE) for metallic photonic crystal filters," Appl. Comput. Electromagn. Soc. J. (to be published).

Gonzalo, R.

L. Mendioroz, R. Gonzalo, and C. del Roi, "Design of electromagnetic crystal filters for rectangular waveguides," Microwave Opt. Technol. Lett. 30, 81-84 (2001).
[CrossRef]

Hafner, Ch.

Ch. Hafner, Cui Xudong, and R. Vahldiek, "Metallic photonic crystals at optical frequencies," J. Comput. Theor. Nanosci. 2, 240-250 (2005).
[CrossRef]

Cui Xudong, Ch. Hafner, K. Tavzarashvili, and R. Vahldieck, "Design of ultra-compact metallo-dielectric photonic crystal filters," Opt. Express 13, 6175-6180 (2005).
[CrossRef] [PubMed]

Ch. Hafner, "Drude model replacement by symbolic regression," J. Comput. Theor. Nanosci. 2, 88-98 (2005).

J. Smajic, Ch. Hafner, and D. Erni, "Optimiztion of photonic crystal structures," J. Opt. Soc. Am. A 21, 2223-2232 (2004).
[CrossRef]

Ch. Hafner, J. Smajic, and D. Erni, "Simulation and optimization of composite doped metamaterials," in Handbook of Theoretical and Computational Nanotechnology, M.Riedt, W.Schommers, eds. (American Scientific), to be published.

K. Tavzarashvili, Ch. Hafner, C. Xudong, R. Vahldieck, D. Karkashadze, and G. Ghvedashvili, "Model-based parameter estimation (MBPE) for metallic photonic crystal filters," Appl. Comput. Electromagn. Soc. J. (to be published).

Ch. Hafner, Post-Modern Electromagnetics (Wiley, 1999).

Ch. Hafner, MAX-1, A Visual Electromagnetics Platform for PCs (Wiley, 1999).

Jugessur, A. S.

A. S. Jugessur, P. Pottier, and R. M. De La Rue, "One dimensional periodic photonic crystal microcavity filters with transition mode matching features, embedded in ridge waveguides," Electron. Lett. 39, 367-368 (2003).
[CrossRef]

Karkashadze, D.

K. Tavzarashvili, Ch. Hafner, C. Xudong, R. Vahldieck, D. Karkashadze, and G. Ghvedashvili, "Model-based parameter estimation (MBPE) for metallic photonic crystal filters," Appl. Comput. Electromagn. Soc. J. (to be published).

Leminger, O.

R. Zengerle and O. Leminger, "Phase-shifted Bragg grating filters with improved transmission characteristics," J. Lightwave Technol. 13, 2354-2358 (1995).
[CrossRef]

Maradudin, Alexei A.

Arthur R. McGurn and Alexei A. Maradudin, "Photonic band structures of two and three dimensional metal or semiconductor arrays," Phys. Rev. B 48, 17576-17579 (1993).
[CrossRef]

Martinelli, M.

R. Costa, A. Melloni, and M. Martinelli, "Bandpass resonant filters in photonic-crystal waveguides," IEEE Photon. Technol. Lett. 15, 401-403 (2003).
[CrossRef]

McGurn, Arthur R.

Arthur R. McGurn and Alexei A. Maradudin, "Photonic band structures of two and three dimensional metal or semiconductor arrays," Phys. Rev. B 48, 17576-17579 (1993).
[CrossRef]

Melloni, A.

R. Costa, A. Melloni, and M. Martinelli, "Bandpass resonant filters in photonic-crystal waveguides," IEEE Photon. Technol. Lett. 15, 401-403 (2003).
[CrossRef]

Mendioroz, L.

L. Mendioroz, R. Gonzalo, and C. del Roi, "Design of electromagnetic crystal filters for rectangular waveguides," Microwave Opt. Technol. Lett. 30, 81-84 (2001).
[CrossRef]

Miller, E.

E. Miller, "Model-based parameter estimation in electromagnetics," IEEE Antennas Propag. Mag. 40, 42-51 (1998).
[CrossRef]

Périaux, J.

D. Quagliarella, J. Périaux, C. Poloni, and G. Winter, Genetic Algorithms and Evolution Strategies in Engineering and Computer Science (Wiley, 1998).

G. Winter, J. Périaux, M. Galan, and P. Cuesta, Genetic Algorithms in Engineering and Computer Science (Wiley, 1995).

Poloni, C.

D. Quagliarella, J. Périaux, C. Poloni, and G. Winter, Genetic Algorithms and Evolution Strategies in Engineering and Computer Science (Wiley, 1998).

Pottier, P.

A. S. Jugessur, P. Pottier, and R. M. De La Rue, "One dimensional periodic photonic crystal microcavity filters with transition mode matching features, embedded in ridge waveguides," Electron. Lett. 39, 367-368 (2003).
[CrossRef]

Quagliarella, D.

D. Quagliarella, J. Périaux, C. Poloni, and G. Winter, Genetic Algorithms and Evolution Strategies in Engineering and Computer Science (Wiley, 1998).

Radic, S.

G. P. Agrawal and S. Radic, "Phase-shifted fiber Bragg gratings and their application for wavelength demultiplexing," IEEE Photon. Technol. Lett. 6, 995-997 (1994).
[CrossRef]

Smajic, J.

J. Smajic, Ch. Hafner, and D. Erni, "Optimiztion of photonic crystal structures," J. Opt. Soc. Am. A 21, 2223-2232 (2004).
[CrossRef]

Ch. Hafner, J. Smajic, and D. Erni, "Simulation and optimization of composite doped metamaterials," in Handbook of Theoretical and Computational Nanotechnology, M.Riedt, W.Schommers, eds. (American Scientific), to be published.

Tavzarashvili, K.

Cui Xudong, Ch. Hafner, K. Tavzarashvili, and R. Vahldieck, "Design of ultra-compact metallo-dielectric photonic crystal filters," Opt. Express 13, 6175-6180 (2005).
[CrossRef] [PubMed]

K. Tavzarashvili, Ch. Hafner, C. Xudong, R. Vahldieck, D. Karkashadze, and G. Ghvedashvili, "Model-based parameter estimation (MBPE) for metallic photonic crystal filters," Appl. Comput. Electromagn. Soc. J. (to be published).

Vahldieck, R.

Cui Xudong, Ch. Hafner, K. Tavzarashvili, and R. Vahldieck, "Design of ultra-compact metallo-dielectric photonic crystal filters," Opt. Express 13, 6175-6180 (2005).
[CrossRef] [PubMed]

K. Tavzarashvili, Ch. Hafner, C. Xudong, R. Vahldieck, D. Karkashadze, and G. Ghvedashvili, "Model-based parameter estimation (MBPE) for metallic photonic crystal filters," Appl. Comput. Electromagn. Soc. J. (to be published).

Vahldiek, R.

Ch. Hafner, Cui Xudong, and R. Vahldiek, "Metallic photonic crystals at optical frequencies," J. Comput. Theor. Nanosci. 2, 240-250 (2005).
[CrossRef]

Winter, G.

D. Quagliarella, J. Périaux, C. Poloni, and G. Winter, Genetic Algorithms and Evolution Strategies in Engineering and Computer Science (Wiley, 1998).

G. Winter, J. Périaux, M. Galan, and P. Cuesta, Genetic Algorithms in Engineering and Computer Science (Wiley, 1995).

Xudong, C.

K. Tavzarashvili, Ch. Hafner, C. Xudong, R. Vahldieck, D. Karkashadze, and G. Ghvedashvili, "Model-based parameter estimation (MBPE) for metallic photonic crystal filters," Appl. Comput. Electromagn. Soc. J. (to be published).

Xudong, Cui

Ch. Hafner, Cui Xudong, and R. Vahldiek, "Metallic photonic crystals at optical frequencies," J. Comput. Theor. Nanosci. 2, 240-250 (2005).
[CrossRef]

Cui Xudong, Ch. Hafner, K. Tavzarashvili, and R. Vahldieck, "Design of ultra-compact metallo-dielectric photonic crystal filters," Opt. Express 13, 6175-6180 (2005).
[CrossRef] [PubMed]

Yasumoto, K.

K. Yasumoto, Electromagnetic Theory and Applications for Photonic Crystals (CRC Press, 2005).
[CrossRef]

Zengerle, R.

R. Zengerle and O. Leminger, "Phase-shifted Bragg grating filters with improved transmission characteristics," J. Lightwave Technol. 13, 2354-2358 (1995).
[CrossRef]

Electron. Lett. (1)

A. S. Jugessur, P. Pottier, and R. M. De La Rue, "One dimensional periodic photonic crystal microcavity filters with transition mode matching features, embedded in ridge waveguides," Electron. Lett. 39, 367-368 (2003).
[CrossRef]

IEEE Antennas Propag. Mag. (1)

E. Miller, "Model-based parameter estimation in electromagnetics," IEEE Antennas Propag. Mag. 40, 42-51 (1998).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

R. Costa, A. Melloni, and M. Martinelli, "Bandpass resonant filters in photonic-crystal waveguides," IEEE Photon. Technol. Lett. 15, 401-403 (2003).
[CrossRef]

G. P. Agrawal and S. Radic, "Phase-shifted fiber Bragg gratings and their application for wavelength demultiplexing," IEEE Photon. Technol. Lett. 6, 995-997 (1994).
[CrossRef]

J. Comput. Theor. Nanosci. (2)

Ch. Hafner, "Drude model replacement by symbolic regression," J. Comput. Theor. Nanosci. 2, 88-98 (2005).

Ch. Hafner, Cui Xudong, and R. Vahldiek, "Metallic photonic crystals at optical frequencies," J. Comput. Theor. Nanosci. 2, 240-250 (2005).
[CrossRef]

J. Lightwave Technol. (1)

R. Zengerle and O. Leminger, "Phase-shifted Bragg grating filters with improved transmission characteristics," J. Lightwave Technol. 13, 2354-2358 (1995).
[CrossRef]

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

Microwave Opt. Technol. Lett. (1)

L. Mendioroz, R. Gonzalo, and C. del Roi, "Design of electromagnetic crystal filters for rectangular waveguides," Microwave Opt. Technol. Lett. 30, 81-84 (2001).
[CrossRef]

Opt. Express (1)

Phys. Rev. B (1)

Arthur R. McGurn and Alexei A. Maradudin, "Photonic band structures of two and three dimensional metal or semiconductor arrays," Phys. Rev. B 48, 17576-17579 (1993).
[CrossRef]

Other (7)

K. Yasumoto, Electromagnetic Theory and Applications for Photonic Crystals (CRC Press, 2005).
[CrossRef]

Ch. Hafner, J. Smajic, and D. Erni, "Simulation and optimization of composite doped metamaterials," in Handbook of Theoretical and Computational Nanotechnology, M.Riedt, W.Schommers, eds. (American Scientific), to be published.

Ch. Hafner, Post-Modern Electromagnetics (Wiley, 1999).

Ch. Hafner, MAX-1, A Visual Electromagnetics Platform for PCs (Wiley, 1999).

K. Tavzarashvili, Ch. Hafner, C. Xudong, R. Vahldieck, D. Karkashadze, and G. Ghvedashvili, "Model-based parameter estimation (MBPE) for metallic photonic crystal filters," Appl. Comput. Electromagn. Soc. J. (to be published).

G. Winter, J. Périaux, M. Galan, and P. Cuesta, Genetic Algorithms in Engineering and Computer Science (Wiley, 1995).

D. Quagliarella, J. Périaux, C. Poloni, and G. Winter, Genetic Algorithms and Evolution Strategies in Engineering and Computer Science (Wiley, 1998).

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Figures (8)

Fig. 1
Fig. 1

Typical configurations for PhC filters design described in this paper; a rectangular lattice is assumed. (a) PhC slab filter. The structure has periodicity along one direction while the other direction is finite; the dashed rectangular area is the unit cell that is used in calculation. (b) PhCs are embedded inside a waveguide with PEC walls. (c) PhCs are embedded in a dielectric waveguide. (d) PhCs are embedded in a dielectric waveguide and partially coated with metallic material.

Fig. 2
Fig. 2

Fitness function definition for a bandpass filter. The transmission curve is obtained from a five-layer silver photonic crystal slab on a square lattice with lattice constant a = 1 μ m . In the diagram of the frequency dependence of the transmission coefficient T ( f ) , three barriers are defined. T is required to be below barrier 1 and 3 but above barrier 2. Between the barrier areas one has two “don’t care” areas where arbitrary values of T are accepted. The gray areas E1, E2, E3 indicate the error integrals in the three barrier areas.

Fig. 3
Fig. 3

Transmission characteristics of a metallic PhC slab consisting of five layers of silver rods, with optimized rod radii obtained from two different fitness definitions. The lattice constant is 820 nm . Solid curve, fitness defined in such a way that minimum bandwidth is obtained (short barrier 2). Curve with marker, fitness defined for wider bandwidth and small passband ripple (longer barrier 2).

Fig. 4
Fig. 4

Core of a deeply etched optical trench waveguide with two short PhC sections, each consisting of three holes of equal radii. The PhC sections act as “Bragg mirrors” of a cavity resonator.

Fig. 5
Fig. 5

Bandpass filter at optical frequency. The filter is formed by embedding PhC structure into the trench waveguide as shown in Fig. 4. The lattice constant a = 406 nm , hole radii r = 127 nm , cavity length L = 565 nm , width of waveguide w = 400 nm .

Fig. 6
Fig. 6

Transmission characteristics of the PhC filter shown in Fig. 4 without any coating (same as Fig. 5), with a short silver coating section, with a short (hypothetical) PEC coating section, and with an infinite PEC coating (which is the same as a periodic PhC slab). The length of coating L 1 = 8 a , thickness of coating t = 100 nm .

Fig. 7
Fig. 7

PhC filter within a slab waveguide with partial PEC coating. Solid curve, transmission coefficient for the optimized structure with a PEC coating of finite length. Dashed curve, transmission coefficient when the PEC coating is removed.

Fig. 8
Fig. 8

Ultrashort PhC filter within a slab waveguide with partial silver coating obtained from a very rough optimization. Solid curve, reflection coefficient; dotted curve, transmission coefficient.

Equations (3)

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F ( ω ) = k = 0 K n a k ω k k = 0 K d b k ω k ,
Fit ( p 1 , p 2 , , p M ) = 1 n = 1 N b E n ,
Fit ( p 1 , p 2 , , p M ) = 1 n = 1 N b { w n barrier n F [ e n ( f ) ] d f } ,

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