Abstract

Filter characteristics of metallo-dielectric photonic crystal slabs are analyzed using the Multiple Multipole Program combined with the Model-Based Parameter Estimation technique. This approach takes losses and material dispersion into account and provides highly accurate results at short computation time. Starting from this analysis, different ultra-compact band pass filters for telecommunication wavelengths are designed. The filters consist of five silver wires embedded in a waveguide structure. By applying stochastic and deterministic techniques the filter structures are optimized to obtain the desired characteristics.

© 2005 Optical Society of America

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References

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  1. Ch. Hafner, Cui Xudong, and R. Vahldiek, “Metallic Photonic Crystals at Optical Frequency,” J. Comp. Theor. Nanoscience 2, No.2, 240–250 (2005).
    [CrossRef]
  2. O. Takayama and M. Cada, “Two-dimensional hexagonal metallic photonic crystals embedded in anodic porous alumina for optical wavelengths,” Appl. Phys. Lett.,  Vol. 85, No. 8, pp.1311–1313 (2004).
    [CrossRef]
  3. Ch. Hafner, “Drude Model Replacement by Symbolic Regression,” J. Comp. Theor. Nanoscience 2, 88–98 (2005).
  4. http://alphard.ethz.ch/hafner/MaX/max1.htm.
  5. P. B. John and R. W. Christie, Phys. Rev. B 6, 4370 (1972).
    [CrossRef]
  6. A. S. Jugessur, P. Pottier, and R. M. De La Rue, “Engineering the filter response of photonic crystal microcavity filters,” Opt. Express 12, 1304–1312 (2004),http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-7-1304.
    [CrossRef] [PubMed]
  7. W. Nakagawa, Pang-Chen Sun, Chyong-Hua Chen, and Y. Fainman, “Wide-field-of -view narrow-band spectral filters based on photonic crystal nanocavities,” Opt. Lett. 27, 191–193 (2002).
    [CrossRef]
  8. C. Ciminelli, F. Peluso, and M. N. Armenise, “Modeling and Design of Two-Dimensional Guided-Wave photonic band-gap devices, ” J. Lightwave. Technol. 23, 886–901 (2005).
    [CrossRef]
  9. R. Costa, A. Melloni, and M. Martinelli, “Bandpass Resonant filters in Photonic-Crystal Waveguides”, IEEE Photo. Tech. Lett. 15, 401–403 (2003).
    [CrossRef]
  10. J. Smajic, Ch. Hafner, and D. Erni, “On the design of photonic crystal multiplexers,” Opt. Express 11, 566–571 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-6-566.
    [CrossRef] [PubMed]
  11. Ch. Hafner, J. Smajic, and D. Erni, “Simulation and Optimization of Composite Doped Metamaterials,” Chapter in M. Riedt and W. Schommers, “Handbook of Theoretical and Computational Nanotechnology,” American Scientific Publishers (2005).
  12. E. Miller, “Model-Based Parameter Estimation in Electromagnetics,” IEEE AP Vol.40, No.1 (1998).
  13. J. Smajic, Ch. Hafner, and D. Erni, “Optimiztion of photonic crystal structures,” J. Opt. Soc. Am. A 21, 2223–2232 (2004).
    [CrossRef]

2005 (3)

Ch. Hafner, Cui Xudong, and R. Vahldiek, “Metallic Photonic Crystals at Optical Frequency,” J. Comp. Theor. Nanoscience 2, No.2, 240–250 (2005).
[CrossRef]

Ch. Hafner, “Drude Model Replacement by Symbolic Regression,” J. Comp. Theor. Nanoscience 2, 88–98 (2005).

C. Ciminelli, F. Peluso, and M. N. Armenise, “Modeling and Design of Two-Dimensional Guided-Wave photonic band-gap devices, ” J. Lightwave. Technol. 23, 886–901 (2005).
[CrossRef]

2004 (3)

2003 (2)

R. Costa, A. Melloni, and M. Martinelli, “Bandpass Resonant filters in Photonic-Crystal Waveguides”, IEEE Photo. Tech. Lett. 15, 401–403 (2003).
[CrossRef]

J. Smajic, Ch. Hafner, and D. Erni, “On the design of photonic crystal multiplexers,” Opt. Express 11, 566–571 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-6-566.
[CrossRef] [PubMed]

2002 (1)

1998 (1)

E. Miller, “Model-Based Parameter Estimation in Electromagnetics,” IEEE AP Vol.40, No.1 (1998).

1972 (1)

P. B. John and R. W. Christie, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Armenise, M. N.

C. Ciminelli, F. Peluso, and M. N. Armenise, “Modeling and Design of Two-Dimensional Guided-Wave photonic band-gap devices, ” J. Lightwave. Technol. 23, 886–901 (2005).
[CrossRef]

Cada, M.

O. Takayama and M. Cada, “Two-dimensional hexagonal metallic photonic crystals embedded in anodic porous alumina for optical wavelengths,” Appl. Phys. Lett.,  Vol. 85, No. 8, pp.1311–1313 (2004).
[CrossRef]

Chen, Chyong-Hua

Christie, R. W.

P. B. John and R. W. Christie, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Ciminelli, C.

C. Ciminelli, F. Peluso, and M. N. Armenise, “Modeling and Design of Two-Dimensional Guided-Wave photonic band-gap devices, ” J. Lightwave. Technol. 23, 886–901 (2005).
[CrossRef]

Costa, R.

R. Costa, A. Melloni, and M. Martinelli, “Bandpass Resonant filters in Photonic-Crystal Waveguides”, IEEE Photo. Tech. Lett. 15, 401–403 (2003).
[CrossRef]

De La Rue, R. M.

Erni, D.

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

J. Smajic, Ch. Hafner, and D. Erni, “On the design of photonic crystal multiplexers,” Opt. Express 11, 566–571 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-6-566.
[CrossRef] [PubMed]

Ch. Hafner, J. Smajic, and D. Erni, “Simulation and Optimization of Composite Doped Metamaterials,” Chapter in M. Riedt and W. Schommers, “Handbook of Theoretical and Computational Nanotechnology,” American Scientific Publishers (2005).

Fainman, Y.

Hafner, Ch.

Ch. Hafner, “Drude Model Replacement by Symbolic Regression,” J. Comp. Theor. Nanoscience 2, 88–98 (2005).

Ch. Hafner, Cui Xudong, and R. Vahldiek, “Metallic Photonic Crystals at Optical Frequency,” J. Comp. Theor. Nanoscience 2, No.2, 240–250 (2005).
[CrossRef]

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

J. Smajic, Ch. Hafner, and D. Erni, “On the design of photonic crystal multiplexers,” Opt. Express 11, 566–571 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-6-566.
[CrossRef] [PubMed]

Ch. Hafner, J. Smajic, and D. Erni, “Simulation and Optimization of Composite Doped Metamaterials,” Chapter in M. Riedt and W. Schommers, “Handbook of Theoretical and Computational Nanotechnology,” American Scientific Publishers (2005).

John, P. B.

P. B. John and R. W. Christie, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Jugessur, A. S.

Martinelli, M.

R. Costa, A. Melloni, and M. Martinelli, “Bandpass Resonant filters in Photonic-Crystal Waveguides”, IEEE Photo. Tech. Lett. 15, 401–403 (2003).
[CrossRef]

Melloni, A.

R. Costa, A. Melloni, and M. Martinelli, “Bandpass Resonant filters in Photonic-Crystal Waveguides”, IEEE Photo. Tech. Lett. 15, 401–403 (2003).
[CrossRef]

Miller, E.

E. Miller, “Model-Based Parameter Estimation in Electromagnetics,” IEEE AP Vol.40, No.1 (1998).

Nakagawa, W.

Peluso, F.

C. Ciminelli, F. Peluso, and M. N. Armenise, “Modeling and Design of Two-Dimensional Guided-Wave photonic band-gap devices, ” J. Lightwave. Technol. 23, 886–901 (2005).
[CrossRef]

Pottier, P.

Riedt, M.

Ch. Hafner, J. Smajic, and D. Erni, “Simulation and Optimization of Composite Doped Metamaterials,” Chapter in M. Riedt and W. Schommers, “Handbook of Theoretical and Computational Nanotechnology,” American Scientific Publishers (2005).

Schommers, W.

Ch. Hafner, J. Smajic, and D. Erni, “Simulation and Optimization of Composite Doped Metamaterials,” Chapter in M. Riedt and W. Schommers, “Handbook of Theoretical and Computational Nanotechnology,” American Scientific Publishers (2005).

Smajic, J.

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

J. Smajic, Ch. Hafner, and D. Erni, “On the design of photonic crystal multiplexers,” Opt. Express 11, 566–571 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-6-566.
[CrossRef] [PubMed]

Ch. Hafner, J. Smajic, and D. Erni, “Simulation and Optimization of Composite Doped Metamaterials,” Chapter in M. Riedt and W. Schommers, “Handbook of Theoretical and Computational Nanotechnology,” American Scientific Publishers (2005).

Sun, Pang-Chen

Takayama, O.

O. Takayama and M. Cada, “Two-dimensional hexagonal metallic photonic crystals embedded in anodic porous alumina for optical wavelengths,” Appl. Phys. Lett.,  Vol. 85, No. 8, pp.1311–1313 (2004).
[CrossRef]

Vahldiek, R.

Ch. Hafner, Cui Xudong, and R. Vahldiek, “Metallic Photonic Crystals at Optical Frequency,” J. Comp. Theor. Nanoscience 2, No.2, 240–250 (2005).
[CrossRef]

Xudong, Cui

Ch. Hafner, Cui Xudong, and R. Vahldiek, “Metallic Photonic Crystals at Optical Frequency,” J. Comp. Theor. Nanoscience 2, No.2, 240–250 (2005).
[CrossRef]

Appl. Phys. Lett. (1)

O. Takayama and M. Cada, “Two-dimensional hexagonal metallic photonic crystals embedded in anodic porous alumina for optical wavelengths,” Appl. Phys. Lett.,  Vol. 85, No. 8, pp.1311–1313 (2004).
[CrossRef]

IEEE AP (1)

E. Miller, “Model-Based Parameter Estimation in Electromagnetics,” IEEE AP Vol.40, No.1 (1998).

IEEE Photo. Tech. Lett. (1)

R. Costa, A. Melloni, and M. Martinelli, “Bandpass Resonant filters in Photonic-Crystal Waveguides”, IEEE Photo. Tech. Lett. 15, 401–403 (2003).
[CrossRef]

J. Comp. Theor. Nanoscience (2)

Ch. Hafner, “Drude Model Replacement by Symbolic Regression,” J. Comp. Theor. Nanoscience 2, 88–98 (2005).

Ch. Hafner, Cui Xudong, and R. Vahldiek, “Metallic Photonic Crystals at Optical Frequency,” J. Comp. Theor. Nanoscience 2, No.2, 240–250 (2005).
[CrossRef]

J. Lightwave. Technol. (1)

C. Ciminelli, F. Peluso, and M. N. Armenise, “Modeling and Design of Two-Dimensional Guided-Wave photonic band-gap devices, ” J. Lightwave. Technol. 23, 886–901 (2005).
[CrossRef]

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

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. B (1)

P. B. John and R. W. Christie, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Other (2)

http://alphard.ethz.ch/hafner/MaX/max1.htm.

Ch. Hafner, J. Smajic, and D. Erni, “Simulation and Optimization of Composite Doped Metamaterials,” Chapter in M. Riedt and W. Schommers, “Handbook of Theoretical and Computational Nanotechnology,” American Scientific Publishers (2005).

Supplementary Material (4)

» Media 1: GIF (49 KB)     
» Media 2: GIF (42 KB)     
» Media 3: GIF (36 KB)     
» Media 4: GIF (30 KB)     

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Figures (4)

Fig. 1.
Fig. 1.

(a) Band diagram for silver photonic crystals consisting of circular rods with radius r on a square lattice with lattice constant a=820nm, Ez-polarization (electric field parallel to the silver rods); black: r/a=0.2683; red: r/a=0.1114; blue: r/a=0.089. Green line: Wavelength 1.55μm. (b) Part of the band diagram of an infinite MPhC (left) and frequency dependence of the transmission coefficient of a 9 layer MPhC slab (right) for silver wires on a square lattice with a=820nm, r/a=0.0894, Ez-polarization. Green line: Wavelength 1.55μm.

Fig. 2.
Fig. 2.

Transmission characteristics for MPhC band pass filters, operating at 1.55μm; 5 layers of silver rods; lattice constant a=820nm. (a): version optimized for maximum transmission at 1.55μm; radii of the wires: r1 =r5 =91nm, r2 =r4 =73nm, r3 =220nm. The colored curves show the transmission response when all radii are simultaneously decreased by 1, 2, 3, 4nm, respectively. Inset: calculation unit in MMP. (b): Radii r1 =r5 =89.8nm, r3 =207.44nm, r2 =r4 tuned from 20nm (dark color) to 200nm (bright color).

Fig. 3.
Fig. 3.

Transmission coefficient versus frequency for various MPhC structures with 5 layers of silver rods. (a): (50kB movie) random search; (b): (42kB movie) deterministic search, starting at a reasonable initial guess. The desired filter characteristic is indicated by the red and green lines: For the frequency ranges marked red/green line, maximum/minimum transmission is desired. Radii for the optimal solution: r1 =r5 =89.8nm, r3 =207.4nm, r2 =r4 =87.9nm.

Fig. 4.
Fig. 4.

Transmission coefficient versus frequency. Optimization of two MDPhC structures with 5 layers of silver rods, lattice constant a=500nm. Left hand side: (37kB movie) relative permittivity of the background material ϵB =2.0; right hand side: (31kB movie) ϵB =2.5. Radii for the optimal solution with different background material: (1) ϵB =2.0: r1 =r5 =49.70nm, r3 =87.70nm, r2 =r4 =20.00nm; (2) ϵB =2.5: r1 =r5 =42.80nm, r3 =123.70nm, r2 =r4 =64.00nm.

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