Electromagnetic properties of photonic crystals with diamond structure containing defects
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Kazuaki Sakoda National Institute for Materials Science, Tsukuba, Ibaraki 305-0003, Japan
Mitsuo Wada Takeda Department of Physics, Faculty of Science, Shinshu University, Matsumoto 390-8621, Japan (Received 1 April 2003; accepted 25 June 2003)
Three-dimensional photonic crystals with a diamond structure, which are composed of the TiO2-based ceramic particles dispersed in an epoxy lattice, were fabricated by stereolithography. The diamond structure showed a photonic band gap in the 14.3–17.0 GHz range along the ⌫-K 〈110〉 direction, which is close to the band calculation using the plain wave expansion method. Two types of lattice defects—air cavity and dielectric cavity—were introduced into the diamond structure by removing a unit cell of diamond structure or inserting a block of the lattice medium into the air cavity. The transmission of millimeter waves affected by multiple reflections at the defects was measured in the photonic band gap. Resonant frequencies in the defects were calculated and compared with the measurement results.
I. INTRODUCTION
II. DESIGN AND EXPERIMENTAL METHODS
Photonic crystals have a periodic structure of dielectric medium, which forms the photonic band gap and reflects electromagnetic waves with wavelengths similar to the periodicity. When the periodicity corresponds to the wavelength of light, such crystals have potential in various applications including zero-threshold semiconductor lasers, light wave guides, and photonic integrated circuits.1–5 In the case of millimeter waves or microwaves, applications include various cavities, barriers, and directional antennas.6–10 However, for these applications to become reality, techniques are needed to modify the crystal structure, size, and volume fraction of the dielectric lattice medium. To control the propagation of electromagnetic waves, the design of various lattice defects becomes very important. We have succeeded in fabricating the perfect diamond structure, composed of millimeter-order epoxy lattices incorporating TiO2-based ceramic particles by stereolithography.7,8 The photonic band gap is in the gigahertz range. In this study, different types of cavity defects were introduced into the diamond structure and characterized with respect to the defect modes.
The diamond structure was designed on a computer using a computer-aided design (CAD) program (Toyota Caelum Co. Ltd, thinkdesign ver. 8.0, Nagoya, Japan). The lattice is composed of dielectric rods 4.33 × 6.50 mm in dimension. The unit cell dimension is 15 mm. The sample size of the diamond structure is 75 × 75 × 75 mm3, which is composed of 125 unit cells. The volume fraction of the dielectric lattice medium is 34%. The lattice defects were also modeled on a CAD program. Figure 1 shows a schematic illustration of the defect sample and lattice images. The defect is introduced at the center of a sample. We defined two types of defects: air cavity and dielectric cavity. Each defect was formed by removing one unit cell, or by inserting a block of the lattice medium into the air cav
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