Abstract

In many research areas, the reflective properties of a bulk medium are characterized by its impedance or an impedance-like quantity. Such a quantity is essential for the efficient design of stacked structures such as antireflection coatings and thin-film filters. For 2D photonic crystals and metamaterials, the literature contains multiple definitions of impedance, not all of which are consistent. We review these proposed definitions, evaluate their regions of applicability, and numerically test their accuracy in a variety of salient photonic crystal examples.

© 2013 Optical Society of America

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2013 (1)

K.-H. Kim and Q-Han Park, “Perfect anti-reflection from first principles,” Sci. Rep. 3, 1062 (2013).

2012 (7)

F. J. Lawrence, L. C. Botten, K. B. Dossou, R. C. McPhedran, and C. M. de Sterke, “A flexible Bloch mode method for computing complex band structures and impedances of two-dimensional photonic crystals,” J. Appl. Phys. 111, 013105 (2012).
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P. Blown, C. Fisher, F. J. Lawrence, N. Gutman, and C. M. de Sterke, “Semi-analytic method for slow light photonic crystal waveguide design,” Photon. Nanostr. Fundam. Appl. 10, 478–484 (2012).
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A. Khavasi, M. Rezaei, M. Miri, and K. Mehrany, “Circuit model for efficient analysis and design of photonic crystal devices,” J. Opt. 14, 125502 (2012).
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W. Śmigaj and B. Gralak, “Semianalytical design of antireflection gratings for photonic crystals,” Phys. Rev. B 85, 035114 (2012).
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N. Habibi, A. Khavasi, M. Miri, and K. Mehrany, “Circuit model for mode extraction in lossy/lossless photonic crystal waveguides,” J. Opt. Soc. Am. B 29, 170–177 (2012).
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2011 (4)

S. Ha, M. Spasenovi, A. A. Sukhorukovć, T. P. White, C. M. de Sterke, L. K. Kuipers, T. F. Krauss, and Y. S. Kivshar, “Slow-light and evanescent modes at interfaces in photonic crystal waveguides: optimal extraction from experimental near-field measurements,” J. Opt. Soc. Am. B 28, 955–963 (2011).
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C. R. Simovski, “On electromagnetic characterization and homogenization of nanostructured metamaterials,” J. Opt. 13, 013001 (2011).
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W. Śmigaj, P. Lalanne, J. Yang, T. Paul, C. Rockstuhl, and F. Lederer, “Closed-form expression for the scattering coefficients at an interface between two periodic media,” Appl. Phys. Lett. 98, 111107 (2011).
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T. Paul, C. Menzel, W. Śmigaj, C. Rockstuhl, P. Lalanne, and F. Lederer, “Reflection and transmission of light at periodic layered metamaterial films,” Phys. Rev. B 84, 115142 (2011).
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2010 (9)

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C. Tserkezis and N. Stefanou, “Retrieving local effective constitutive parameters for anisotropic photonic crystals,” Phys. Rev. B 81, 115112 (2010).
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G. Scherrer, M. Hofman, W. Śmigaj, B. Gralak, X. Melique, O. Vanbésien, D. Lippens, C. Dumas, B. Cluzel, and F. Fornel, “Interface engineering for improved light transmittance through photonic crystal flat lenses,” Appl. Phys. Lett. 97, 071119 (2010).
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F. J. Lawrence, L. C. Botten, K. B. Dossou, R. C. McPhedran, and C. M. de Sterke, “Photonic-crystal surface modes found from impedances,” Phys. Rev. A 82, 53840 (2010).
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A. Fallahi and C. Hafner, “Analysis of semi-infinite periodic structures using a domain reduction technique,” J. Opt. Soc. Am. A 27, 40–49 (2010).
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P. Y. Chen, R. C. McPhedran, C. M. de Sterke, C. G. Poulton, A. A. Asatryan, L. C. Botten, and M. J. Steel, “Group velocity in lossy periodic structured media,” Phys. Rev. A 82, 053825 (2010).
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2008 (7)

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T. Matsumoto, T. Asatsuma, and T. Baba, “Experimental demonstration of a wavelength demultiplexer based on negative-refractive photonic-crystal components,” Appl. Phys. Lett. 91, 091117 (2007).
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2006 (4)

T. Decoopman, G. Tayeb, S. Enoch, D. Maystre, and B. Gralak, “Photonic crystal lens: from negative refraction and negative index to negative permittivity and permeability,” Phys. Rev. Lett. 97, 073905 (2006).
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K. B. Dossou, L. C. Botten, C. M. de Sterke, R. C. McPhedran, A. A. Asatryan, S. Chen, and J. Brnovic, “Efficient couplers for photonic crystal waveguides,” Opt. Commun. 265, 207–219 (2006).
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T. Matsumoto, S. Fujita, and T. Baba, “Wavelength demultiplexer consisting of photonic crystal superprism and superlens,” Opt. Express 13, 10768–10776 (2005).
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B. Momeni and A. Adibi, “Adiabatic matching stage for coupling of light to extended Bloch modes of photonic crystals,” Appl. Phys. Lett. 87, 171104 (2005).
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L. C. Botten, T. P. White, A. A. Asatryan, T. N. Langtry, C. M. de Sterke, and R. C. McPhedran, “Bloch mode scattering matrix methods for modeling extended photonic crystal structures. I. Theory,” Phys. Rev. E 70, 056606 (2004).
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J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Scherer, “Mode matching interface for efficient coupling of light into planar photonic crystals,” Phys. Rev. E 69, 046609 (2004).
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T. Baba, T. Matsumoto, and M. Echizen, “Finite difference time domain study of high efficiency photonic crystal superprisms,” Opt. Express 12, 4608–4613 (2004).
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A. Talneau, M. Mulot, S. Anand, and P. Lalanne, “Compound cavity measurement of transmission and reflection of a tapered single-line photonic-crystal waveguide,” Appl. Phys. Lett. 82, 2577–2579 (2003).
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P. Pottier, I. Ntakis, and R. De La Rue, “Photonic crystal continuous taper for low-loss direct coupling into 2D photonic crystal channel waveguides and further device functionality,” Opt. Commun. 223, 339–347 (2003).
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T. F. Krauss, “Planar photonic crystal waveguide devices for integrated optics,” Phys. Status Solidi A 197, 688–702 (2003).
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D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002).
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S. Boscolo, C. Conti, M. Midrio, and C. G. Someda, “Numerical analysis of propagation and impedance matching in 2-D photonic crystal waveguides with finite length,” J. Lightwave Technol. 20, 304–310 (2002).
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B. Gralak, S. Enoch, and G. Tayeb, “From scattering or impedance matrices to Bloch modes of photonic crystals,” J. Opt. Soc. Am. A 19, 1547–1554 (2002).
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A. Talneau, P. Lalanne, M. Agio, and C. M. Soukoulis, “Low-reflection photonic-crystal taper for efficient coupling between guide sections of arbitrary widths,” Opt. Lett. 27, 1522–1524 (2002).
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A. Modinos, N. Stefanou, and V. Yannopapas, “Applications of the layer-KKR method to photonic crystals,” Opt. Express 8, 197–202 (2001).
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T. D. Happ, M. Kamp, and A. Forchel, “Photonic crystal tapers for ultracompact mode conversion,” Opt. Lett. 26, 1102–1104 (2001).
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M. Palamaru and P. Lalanne, “Photonic crystal waveguides: out-of-plane losses and adiabatic modal conversion,” Appl. Phys. Lett. 78, 1466–1468 (2001).
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T. Baba and D. Ohsaki, “Interfaces of photonic crystals for high efficiency light transmission,” Jpn. J. Appl. Phys. 40, 5920–5924 (2001).
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L. C. Botten, N. P. Nicorovici, R. C. McPhedran, C. M. de Sterke, and A. A. Asatryan, “Photonic band structure calculations using scattering matrices,” Phys. Rev. E 64, 046603 (2001).
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R. C. McPhedran, N. P. Nicorovici, L. C. Botten, and K. A. Grubits, “Lattice sums for gratings and arrays,” J. Math. Phys. Sci. 41, 7808–7816 (2000).
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