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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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]

Handbook of Theor. and Comput. Nano. (1)

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

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

Other (1)

<a href="http://alphard.ethz.ch/hafner/MaX/max1.htm">http://alphard.ethz.ch/hafner/MaX/max1.htm</a>.

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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