Abstract
Using the rigorous multiple-scattering theory, we study the dispersion relation of electromagnetic (EM) waves in two dimensional dielectric photonic crystals (PCs) and metallic photonic crystals (MPCs) in the low-frequency limit. Analytic formula for the effective velocity of EM waves in PCs and MPCs is obtained. Accuracy of our formula is checked by comparing the results with rigorous calculations. For PCs, our result is exactly the same as the coherent potential approximation (CPA), which is accurate even when the filling fraction is high. But for MPCs, our approach demonstrates special advantages, while the CPA theory fails, in predicting the effective velocity of EM waves in MPCs at low frequency.
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References
Datta S, Chan C T, Ho K M, et al. Effective Dielectric Constant of Periodic Composite Structures[J]. Phys Rev B, 1993, 48:14936–14943.
Maxwell-Garnett J C. Colours in Metal Glasses and in Metal Films[J]. Phil Trans R Soc, 1904, 203: 385–420.
Yablonovitch E. Inhibited Spontaneous Emission in Solid-State Physics and Electronics[J]. Phys Rev Letter, 1987, 58: 2059–2062.
Ho K M, Chan C T, Soukoulis C M. Existence of a Photonic Gap in Periodic Dielectric Structures[J]. Phys Rev Letter, 1990, 65:3152–3155.
Cassagne D, Jouanin C, Bertho D. Hexagonal Photonic-Band-Gap Structures [J]. Phys Rev B, 1996, 53: 7134–7142.
Li Z Y, Wang J, Gu B Y. Creation of Partial Band Gaps in Anisotropic Photonic-Band-Gap Structures[J].Phys Rev B, 1998, 58:3721–3729.
Ward A J, Pendry J B. Calculating Photonic Green’s Functions Using a Nonorthogonal Finite-Difference Time-Domain Method[J]. Phys Rev B, 1998, 58: 7252–7259.
Ryu H Y, Notomi M, Lee Y H. Finite-Difference Time-Domain Investigation of Band-Edge Resonant Modes in Finite-Size Two-Dimensional Photonic Crystal Slab[J]. Phys Rev B, 2003, 68:452091–452098.
Fan S H, Villeneuve P R, Joannopoulos J D. Large Omnidirectional Band Gaps in Metallodielectric Photonic Crystals[J]. Phys Rev B,1996,54:11245–11251.
Li Z Y, Lin L L. Photonic Band Structures Solved by a Plane-Wave-Based Transfer-Matrix Method[J]. Phys Rev E, 2003, 67:4660701–4660711.
Stefanou N, Yannopapas V, Modinos A. Heterostructures of Photonic Crystals: Frequency Bands and Transmission Coefficients[ J]. Comput Phys Commun, 1998, 113:49–77.
Yannopapas V, Modinos A, Stefanou N. Waveguides of Defect Chains in Photonic Crystals [J]. Phys Rev B, 2002, 65: 2352011–2352016.
Tao R, Chen Z, Sheng P. First-Principles Fourier Approach for the Calculation of the Effective Dielectric Constant of Periodic Composites[J].Phys Rev B, 1990, 41:2417–2420.
Shen L C, Liu C, Korringa J, et al. Computation of Conductivity and Dielectric Constant of Periodic Porous Media [J]. J Appl Phys, 1990, 67: 7071–7081.
Sheng P. Intruduction to Wave Scattering, Localization, and Mesoscopic Phenomena[M]. New York: Academic Press, 1995.
Liu Z Y, Chen C T, Sheng P. Elastic Wave Scattering by Periodic Structures of Spherical Objects: Theory and Experiment Phys [J]. Phys Rev B, 2000, 62:2446–2457.
Chin S K, Nicorovici N A, Mcphedran R C. Green’s Function and Lattice Sums for Electromagnetic Scattering by a Square Array of Cylinders[J]. Phys Rev E, 1994, 49:4590–4602.
Nicorovici N A, McPhedran R C. Photonic Band Gaps for Arrays of Perfectly Conducting Cylinders[J]. Phys Rev E, 1995, 52:1135–1145.
Kuzmiak V, Maradudin A A, Pincemin F. Photonic Band Structures of Two-Dimensional Systems Containing Metallic Components[J]. Phys Rev B, 1994, 50:16835–16844.
Moreno E, Erni D, Hafner C. Band Structure Computations of Metallic Photonic Crystals with the Multiple Multipole Method[J]. Phys Rev B, 2002, 65: 2352001–2352010.
Ito T, Sakoda K. Photonic Bands of Metallic Systems II Features of Surface Plasmon Polaritons[J]. Phys Rev B, 2001, 64:451171–451178.
Kuzmiak V, Maradudin A A. Photonic Band Structures of One-and Two-Dimensional Periodic Systems with Metallic Components in the Presence of Dissipation[J]. Phys Rev B, 1996, 55: 7427–7444.
Towne D H. Wave Phenomena[M]. New York: Dover Press, 1988.
Sakoda K, Kawai N, Ito T. Photonic Bands of Metallic Systems. I. Principle of Calculation and Accuracy[J]. Phys Rev B, 2001, 64: 451161–451168.
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Foundation item: Supported by the National Natural Science Foundation of China (50425206, 50702038)
Biography: WANG Yun(1984–), female, Ph.D.candidate, research direction: phononic crystals, photonic crystals.
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Wang, Y., Jia, H., Tian, Z. et al. Low frequency dispersion law for two-dimensional metallic photonic crystals. Wuhan Univ. J. Nat. Sci. 13, 50–54 (2008). https://doi.org/10.1007/s11859-008-0110-8
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DOI: https://doi.org/10.1007/s11859-008-0110-8