Coupled-Cavity Structures in Photonic Crystals
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Coupled-Cavity Structures in Photonic Crystals Mehmet Bayindir and E. Ozbay Department of Physics, Bilkent University, Bilkent, 06533 Ankara, Turkey ABSTRACT We investigate the localized coupled-cavity modes in two-dimensional dielectric photonic crystals. The transmission, phase, and delay time characteristics of the various coupledcavity structures are measured and calculated. We observed waveguiding through the coupled cavities, splitting of electromagnetic waves in waveguide ports, and switching effect in such structures. The corresponding field patterns and the transmission spectra are obtained from the finite-difference-time-domain (FDTD) simulations. We also develop a theory based on the classical wave analog of the tight-binding (TB) approximation in solid state physics. Experimental results are in good agreement with the FDTD simulations and predictions of the TB approximation. INTRODUCTION
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HOTONIC band gap structures provide a promising tool to control of the flow EM waves in the integrated optical devices. Therefore, there is a growing interest in developing photonic crystal-based waveguide components which can guide and bend EM waves either along a line defect (a row of missing rods) [1, 2], which is called planar waveguide (PW) [See Fig. 1(a)] , or through coupled cavities [3], which is known as coupled-cavity waveguide (CCW) [See Fig. 1(b)]. In the former case, while the EM waves are confined in one direction which is perpendicular to axis of missing rods, and photons can propagate in other direction parallel to the axis of the missing rods [Fig. 1(c)]. On the other hand, in the latter case, which we called coupled-cavity waveguides (CCW) [4], the EM waves were tightly confined at each defect site, and photons can propagate via hopping due to interaction between the neighboring evanescent cavity modes [Fig. 1(d)]. By removing from or adding to materials a perfect photonic crystal, it is possible to create localized EM modes inside the photonic band gap which are reminiscent of the acceptor and donor impurity states in a semiconductor [5, 6]. Therefore, photons with certain wavelengths can locally be trapped inside the defect volume. This important property can be used in various photonic applications. In fact, most of the aforementioned applications are based on cavity structures built around photonic crystals. Since most of the photonic crystal based applications have been demonstrated in twodimensional (2D) photonic structures, especially at optical wavelengths, it is very important to study 2D CCWs in details. In the present chapter, we will present a comprehensive experimental and theoretical study on 2D coupled-cavity structures. PROPAGATION OF PHOTONS BY HOPPING Tight-Binding Picture in Photonic Structures Analogy between the Schr¨odinger equation and Maxwell’s equations allows us to use many
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