Using three-dimensional photonic crystals as add-drop filters

The Internet is the driver for modern communication, transporting an increasing density of data. Much of this is being carried over optical fibers using wavelength division multiplexing (WDM), in which multiple wavelengths are transported along the same optical fiber. At different points on the fiber it is necessary to pull off (drop) individual wavelength channels for end-users. Simultaneously it is necessary to add data streams into empty wavelength channels. Waveguides in two-dimensional photonic crystals (PCs) and ring resonators have been extensively investigated as all-optical add-drop filters. We show that three-dimensional photonic band gap crystals with complete band gaps can be novel add-drop filters.

We used a microwave-scale layer-by-layer PC that has been extensively developed at Ames Laboratory and Iowa State University with a complete band gap from 11GHz to 12.9GHz, for all directions of wave propagation. The add-drop filter has an entrance waveguide and exit waveguide created by removing rod segments. These waveguides were separated by a dielectric rod of length d (see Figure 1). We created a cavity of length L one unit cell above the waveguide layer. The cavity-waveguide interaction and the crosstalk between the waveguides is controlled by the separation d.¹

Since all modes carried by the waveguide are within the photonic band gap, there is no leakage of modes to the outside—an inherent problem with both two-dimensional PCs and add-drop filters using ring resonators.

Figure 1. The PC add-drop filter, with the input and output waveguides separated by a distance d and coupled through a cavity of length L.

Figure 2. Measured transmission for the straight waveguide (solid) compared to transmission for waveguides separated by 9a, with (dotted) and without (dashed) a cavity of L=0.75a. The cavity-induced resonance (arrow) is ∼1dB below the straight guide.

Figure 2 shows the results of transmission measurements for a straight waveguide, two waveguides separated by d=8a without a cavity, and two waveguides with separation d=8a and a cavity with L=0.75a, where a is the rod spacing for the PC. The straight waveguide has a strong transmission band from 11.8 to 12.8GHz. By separating entrance and exit waveguides, the transmission is reduced by >20dB over all frequencies. With the cavity, a narrow transmission peak appears at 12.22GHz (see Figure 2). The peak transmission of this mode is nearly that of the straight waveguide, suggesting excellent coupling. The 12.22GHz mode is the resonant frequency of a single mode cavity of length L =0.75a. We studied the coupling for different cavity sizes (L) and waveguide separations (d). Each cavity has a different resonant frequency. Larger cavities support more than one mode. The larger multimode cavity (shown in Figure 3) of size L=5.5a (and separation d=9a) exhibits three cavity modes with three strong transmission peaks.

Finite difference time domain (FDTD) simulations provide an appealing physical picture. Simulations used a 20-layer PC similar to the one shown in Figure 1, with two waveguide sections coupled by a cavity of length L. Computational constraints necessitated using smaller L and d (d=6a; L=3a) than in the experiments. The frequency response was obtained by exciting the input guide with a pulsed dipole source and simulating the transmitted E fields in the exit guide. Three simulated transmission peaks were obtained similar to those measured,¹ indicating resonant cavity modes that couple the input and output streams.

After identifying resonant modes, we obtained a visual understanding by exciting the input guide with a constant frequency source tuned to a resonance (12.5GHz) and simulating the temporal evolution of the fields. Initially (1000Δt, where the time step Δt=2.06ps), large fields exist only in the input waveguide (as shown in Figure 4). As time progresses (3000Δt), the fields grow within the cavity, indicating input waveguide-cavity coupling. At a later time (5000Δt), the intensity gradually builds in the exit guide. Still later (9000Δt), a large excitation of the output guide is accompanied by the excitation of the cavity (see Figure 4). The slow coupling requires >5000 time steps to excite the cavity and then couple to the exit guide.

Figure 3. Measured transmission for a cavity of length L=5.5a (dashed) displaying three resonant frequencies, compared to the straight waveguide and no cavity (d=9a).

Figure 4. E-field intensities from FDTD simulation in the plane containing the input waveguide, the exit waveguide, and the cavity. Simulations are for the resonant frequency of 12.5GHz at 1000, 3000, 5000, and 9000 time steps. The intensity scale is logarithmic.

Waveguides in three-dimensional PCs can couple through defect cavities. The resonant frequency of the cavity can be selected from the input guide and dropped to the output guide. These designs can be scaled down to telecommunications wavelengths (1.5μ). Controlling the geometry of defect cavities can lead to realistic novel add-drop filters for telecommunications applications.