Molding the flow of light

diagram of symmetry requirements for waveguide crossing, showing waveguide mode profiles and resonant-cavity mode contours. By symmetry the solid-line modes cannot couple with the dashed-line modes and vice versa. tional to the lifetime of the resonance mode. The required parity of the cavity modes is easy to achieve using the results of Figure 5. The desired resonant cavity is created by introducing a single rod of radius 0.3a at the center of an otherwise perfect photonic crystal waveguide crossing, together with three rods of normal radius along the waveguides in the vicinityof the intersection, as shown in Figure 7. This leads to doubly-degenerate modes of the requisite symmetrywith a frequencyof 0.36 (2πc/a). To determine the performance of this waveguide-crossing configuration, we study the effects of sending a broad-spectrum propagation Gaussian pulse to the input port (left). The fractional power transmission is then evaluated as a function of frequency for the output port (right) and one of the transverse ports (top), yielding the throughput and crosstalk, respectively. We find that both the throughput and the crosstalk for an empty intersection lie in the 20–40% range. This is because the empty intersection does not support resonant states of the correct symmetry. In contrast, the intersection shown in Figure 7 reaches nearly 100% throughput with an unprecedented crosstalk of only 5 10–9! Waveguide Splitters Waveguide branches also playan important role in integrated photonic circuits. Ideally, such a device splits the input power into the two output waveguides without significant reflection or radiation losses. Motivated by the goal of miniaturizing photonic components and circuits, there have been many efforts to construct wide-angle branches.16 Despite such efforts, the splitting angles are still limited to a few degrees for conventional structures, due to the inherent radiation loss at the branching region. Moreover, while such loss can be substantially reduced by increasing the index contrast between the guide and the surrounding media, it cannot be completely suppressed. Photonic crystals offer a way to completely eliminate radiation losses, and therebyopen the possibilityof designing wide-angle branches with high performance. Very recently, estimates of the transmission characteristics of a l20° Y-branch in a photonic crystal with hexagonal symmetry have been presented by Yonekura et al.17 However, direct and accurate numerical characterizations of the transmission and reflection properties through a single waveguide branch have not been previously performed. Moreover, a general criterion for ideal performance of waveguide branches in a photonic crystal has only recently been presented.18 In order to obtain a qualitative understanding of waveguide branches in a photonic crystal, we consider the theoretical model shown in Figure 8. The branching region is treated as a cavity that supports a single symmetric resonant mode that couples to the input and output waveguides. The resonance in the cavity then determines the transport properties of the branch. The transmission and reflection properties of such a model can be calculated using coupled-mode theory15, which relates mit physics annual 2001 joannopoulos ( 39 figure 7 Steady-state electric field distribution for the case of the photonic crystal waveguide intersection discussed in the text. Essentially, all the power is transported through the junction with negligible crosstalk in the transverse waveguides.