Optical Response of Photonic Crystals Requiring High Precision Band Calculation in the Form of<b>k</b>(ω) Including Evanescent Waves

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  • Cho Kikuo
    Graduate School of Engineering Science, Osaka University
  • Ushida Jun
    Fundamental and Environmental Research Laboratories, NEC Corporation
  • Bamba Motoaki
    Graduate School of Engineering Science, Osaka University

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  • Optical Response of Photonic Crystals Requiring High Precision Band Calculation in the Form of k(.OMEGA.) Including Evanescent Waves

抄録

We give a general method to calculate photonic band structure in the form of wave number k as a function of frequency ω, which is required whenever we want to calculate signal intensity related with photonic band structure. This method is based on the fact that the elements of the coefficient matrix for the plane wave expansion of the Maxwell equations contain wave number up to the second order, which allows us to rewrite the original eigenvalue equation for ω2 into that for wave number. This method is much better, especially for complex wave numbers, than the transfer matrix method of Pendry, which gives the eigenvalues in the form of exp[ikd]. The present method leads to a good improvement in the calculation of reflectivity spectrum by eliminating unphysical part due to insufficient precision of numerical results, showing the cross-section dependence of a surface of given Miller index more precisely.

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