TY - JOUR

T1 - Analysis of multimode point-defect cavities in three-dimensional photonic crystals using group theory in frequency and time domains

AU - Okano, Makoto

AU - Noda, Susumu

N1 - Funding Information:
This work was supported in part by CREST, JST, by a Grand-in-Aid for Scientific Research from JSPS, by 21COE of Kyoto Univ. and an IT Program from MEXT.

PY - 2004/9

Y1 - 2004/9

N2 - We present analysis of a multimode point-defect cavity in a three-dimensional (3D) photonic crystal belonging to the point group, utilizing group-theoretical classifications in both the plane-wave expansion (PWE) and 3D finite-difference time-domain (FDTD) methods. In the PWE method, application of the projection operator to the electromagnetic fields is proposed to classify the point-defect modes into a basis of the irreducible representation of the point group. This is a simple computational process. A group-theory formulation is developed for Maxwell's equations in the time domain, involving the electric and magnetic current densities. It is demonstrated that a temporal analysis can be made independently about each basis vector of the irreducible representation of the symmetry group and this fact establishes Bloch's theorem in the time domain. In the FDTD method, the number of the point-defect modes dealt with in each calculation becomes small so that analysis of the multimode point-defect cavity is much simplified. In practice, we investigate various properties of multimode point-defect cavities belonging to the point group C2h, including resonant frequency, field distribution, quality factor, light-extraction efficiency, radiation pattern, and polarization.

AB - We present analysis of a multimode point-defect cavity in a three-dimensional (3D) photonic crystal belonging to the point group, utilizing group-theoretical classifications in both the plane-wave expansion (PWE) and 3D finite-difference time-domain (FDTD) methods. In the PWE method, application of the projection operator to the electromagnetic fields is proposed to classify the point-defect modes into a basis of the irreducible representation of the point group. This is a simple computational process. A group-theory formulation is developed for Maxwell's equations in the time domain, involving the electric and magnetic current densities. It is demonstrated that a temporal analysis can be made independently about each basis vector of the irreducible representation of the symmetry group and this fact establishes Bloch's theorem in the time domain. In the FDTD method, the number of the point-defect modes dealt with in each calculation becomes small so that analysis of the multimode point-defect cavity is much simplified. In practice, we investigate various properties of multimode point-defect cavities belonging to the point group C2h, including resonant frequency, field distribution, quality factor, light-extraction efficiency, radiation pattern, and polarization.

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U2 - 10.1103/PhysRevB.70.125105

DO - 10.1103/PhysRevB.70.125105

M3 - Article

AN - SCOPUS:19744381596

SN - 0163-1829

VL - 70

SP - 125105-1-125105-15

JO - Physical Review B - Condensed Matter and Materials Physics

JF - Physical Review B - Condensed Matter and Materials Physics

IS - 12

M1 - 125105

ER -