A compact planar channel four-port drop filter is developed experimentally and theoretically in the three-dimensional woodpile photonic crystal having a complete band gap. This consists of two waveguides separated by a defect in a single layer of the photonic crystal. Frequencies for channel dropping can be tuned throughout the band gap, by changing the size of the defect. Quality factors of ~1000 were measured. Simulations demonstrate directional energy transfer between the input and out put waveguides, through excitation of fields in the defect region. The planar nature of the filter is much more amenable to fabrication at optical length wavelengths.
© 2009 Optical Society of America
The existence of a photonic bandgap is the basis for many new compact photonic devices . Photonic crystals (PCs) have shown an unprecedented ability to control light making them an important building block for photonic integrated circuits. Basic photonic crystal devices are composed of point defects, cavities [2,3], line defects, or waveguides (WGs) [4,5]. These basic components can be used to create many devices such as band-pass filters , channel drop filters [7–9], cavity coupled WGs , multiplexers , and matching networks . Channel drop filters have been studied extensively in two-dimensional (2-D) photonic crystals [7,8]. Two-dimensional channel drop filters are easy to fabricate at optical wavelengths using current semiconductor technology. Total internal reflection is used to guide light in the vertical direction of a 2-D PC creating an intrinsic out-of-plane leakage path for light. This can be overcome by using a three-dimensional (3-D) PC.
Previously two-port add-drop filters were developed  in the three-dimensional woodpile PC that required 4 stacked layers between the waveguides and defects, which is difficult to realize at optical/infrared wavelengths. We develop an efficient 4-port planar channel drop filter where the entire filter resides in a single layer of the 3-D PC, thus simplifying fabrication at optical length scales. Such 4-port channel drop filters have not been developed in 3-D PCs, although other multi-port channel drop filters have been studied in the 3-D woodpile PC [6, 9, 13–15].
2. Experimental setup
The three dimensional woodpile photonic crystal used in this paper was originally discovered at Iowa State University by Ho (Ozbay) et al . It consists of alumina rods, with a measured refractive index of 3.0 ± 0.1, in an air background. The lattice constant (a) is 1.07 cm in the x and y directions and 1.28 cm in the z direction, yielding a filling ratio of 29.9%. The complete photonic bandgap of the experimental PC is from 11.2 to 13.3 GHz. The WGs used to create the channel drop filters were X guides  formed by removing an entire rod, with air cavities made by removing a section of an alumina rod. Data was collected by placing a pair of 1.33 cm monopole antennas made from semi-rigid coaxial cable connected to an HP 8510B network analyzer into the WGs of the channel drop filter. Antennas were fabricated from semi-rigid coaxial cable to reduce reflections due to accidental bending after a thru-reflect-line (TRL) calibration was performed. The semi-rigid cable had enough mechanical stability to connect it to a linear stage allowing for fine position adjustments to be made to optimize coupling to the WG. The TRL calibration was performed using offset standards so that the reference plane for the measurement was placed immediately at the base of the monopole antenna where the shielding was cut away.
For the experiments the PC was 28a by 28a by 22 layers thick with the planar channel drop filter placed in layer 11. A 3a long alumina stub rod was placed in each end of the bus WG and the antenna was place immediately adjacent. The rods were placed in the ends of the bus WG to prevent electromagnetic radiation from leaking out of the end of the bus guide and into the end of the drop guide. Microwave absorbing foam was also placed around the four faces of the photonic crystal that did not have WGs in them. The optimum position for the antenna occurred when its base was centered on a rod in the layer below the WG layer about 1a past the stub rod. One side of the coaxial cable leading to the monopole antenna was touching the side of the stub rod. When measuring the system one antenna remained fixed in the bus guide while the other antenna was placed in another port (Fig. 1). Care was taken to ensure the antenna was in the same position in each port.
3. Finite difference time domain simulation setup
The field profiles of the channel drop filters were calculated using finite difference time domain (FDTD) simulations. The simulations utilized a 20a wide by 16 layer (4a) tall PC similar to the experiment. The rod-to-rod spacing was 10 grid spaces (10Δx). Each rod had a width of 3Δx and height of 3Δz providing a dielectric filling ratio of 0.3. At the boundary of the simulation cell we use the second order Liao absorbing boundary conditions . A requisite region of empty space (~10 grid spaces) separates the PC from the absorbing boundaries. The computational cell consisted of a 210 × 210 × 80 real space grid. The refractive index of the rods was 3.0, similar to the experiments. As in the experiment a sufficient number of unit cells (>6) are kept between the WG and the boundary of the photonic crystal.
Waveguide modes were excited by a small dipole source in the bus WG close to boundary of the PC and far from the defect. The input wave was polarized with the E along the z axis. The output fields were calculated at different points along the forward and backward directions of the exit waveguide. For comparison, the fields in the straight WG were also calculated at different points downstream from the source. The dipole source was excited by a pulse and the output fields (E(r),H(r)) were calculated at each time step at a grid of points in the exit WG . The Fourier transforms of the fields were calculated at each grid point in the exit WG. The Fourier transformed field intensity E 2(r i,f) was averaged over a grid of points (ri) in the exit WG to obtain the frequency (f) dependent transmission in the forward and backward directions of the exit guide.
By identifying frequencies where there are peaks of the intensity in the exit guide we can identify the channel drop frequencies where the entrance guide couples to the exit guide, and compare with measurements. The size of the defect can be easily varied. Once a channel drop frequency has been identified, FDTD simulation can be carried out at that frequency to obtain the modal field pattern of the channel drop modes, and a physical picture of the WG coupling.
4. Channel drop filters
Channel drop filters are devices that transfer electromagnetic energy of a specific frequency from a bus, or input, WG to a drop, or output, WG. In a PC channel drop filter this task is performed completely optically through the use of a standing wave resonator. The channel drop filters consist of a bus WG, a drop WG, and a cavity. The cavity is placed between the two WGs. Photons at the resonant frequency of the cavity will tunnel into the cavity from the bus guide and then tunnel out to the drop guide. We study a planar 4-port channel drop filter (Fig. 1) with air defects used to make the cavity. All of its components are in a single stacking layer, which makes fabrication relatively simple compared to multilayer channel drop filter designs. A detailed explanation on the theory of channel drop filters has been given by Manolatou .
Planar channel drop filters with 1, 2, 3, and 4a of separation between the cavity and the WGs were tested. The straight waveguide dispersion relation has been simulated by the FDTD method  and the plane wave expansion method , and found to have a mono-mode in the lower to middle portion of the band gap and a multi-mode in the upper portion of the band gap. We use the mono-modal region of the waveguide dispersion (around 12.2 GHz) for the channel dropping studies. A cavity-WG separation of 1a was not acceptable due to direct coupling between the WGs. For separations of 2 and 3a, the planar channel drop filter worked well with 10 to 30 dB of separation between the signal level and the noise floor. Increasing the cavity-WG separation to 4a yielded a 15 to 40 dB separation between the signal and noise levels, however no frequencies could be transferred to the drop guide. Measurements (Fig. 2) were made for cavity sizes (L) from 0.25 to 3a. As the cavity size increased the transfer frequency also increased, with multiple channel drop frequencies for larger L (Fig. 2). The overall trend is the same for both the channel drop filter with 2 and 3 uc of cavity-WG separation.
Not all transfer modes were detected in both channel drop filter configurations. There are two possible explanations for this. The first explanation is decreased coupling between the WGs and the cavities, which occurs as cavity-WG separation increases. Increased cavity-WG separation decreases the amount of energy coupled into the cavity, especially for certain modes. This is analogous to the decrease in direct coupling between the WGs as the separation increases. The second reason is less intense peaks may fall below the noise floor created by direct coupling between the bus and drop WGs. This occurs when the cavity-WG separation is small. In each configuration, the most intense frequency points are observed for each of the different cavity-WG separations, however the less intense frequency points are masked.
The factors affecting the quality factor of a transferred mode are the separation between cavities and WGs, the amount of cladding around the cavities and WGs, and absorption in the PC’s materials. In this experiment the material absorption is low and the amount of cladding surrounding the cavities and WGs is large making loss out of the sides of the PC low [4, 6, 21]. So, the quality factor of the transferred modes is primarily due to coupling between the cavity and the WGs of the channel drop filter. The quality factors were about 1000.
Manolatou et al  have established the theory of resonant channel drop filters, where a bus and a drop waveguide are coupled to a resonant cavity defect. It is necessary for the cavity to have degenerate symmetric and anti-symmetric modes to achieve directional channel dropping (into forward or backward directions) when special phase relationships between the cavity modes and the waveguide modes, are satisfied. In the absence of a special phase relationship, it is predicted  that such a filter exhibits channel dropping into both forward and backward directions of the drop guide, which is what we observe in the proposed experiment and simulation. At a frequency of 12.19 GHz with a 2 uc cavity, FDTD simulations and experimental measurements identified a transfer mode. The experimental spectra (Fig. 3) shows that the intensity of the drop mode is comparable to the input (bus) guide. There is also a weaker mode at 12.4 GHz. This mode is a secondary weaker mode. The mode is not weaker because the channel drop filter is less sensitive to this frequency range. Experimental results have shown that a strong transfer mode can be excited at 12.4 GHz using a 1.7 uc cavity.
Figure 3 shows losses of about 20 dB to the top of the guided band for the waveguides. These losses are primarily due to poor coupling between the WGs and the monopole antennas . This coupling problem could be potentially solved at optical wavelengths by routing a dielectric waveguide into and through the PC in the space where the air waveguide is used in this paper. Defects could be placed in the ends of the PC to help with mode matching and reduce reflection at the dielectric WG - PC interface as has been done in 2-D PCs .
A FDTD simulation was performed using a constant frequency source to obtain the field pattern in the channel drop filter. The field intensity builds up in the input guide initially (~1 ns, 1000 ΔT). At longer time (Fig. 4) there are appreciable fields excited in the defect region coupled with an intensity buildup in the exit guide in both the forward and backward direction after ~3ns (3000 Δt). There is a weak field intensity buildup in the photonic crystal between the WGs and the defects. Strong fields are excited in the PC in line with the cavity defect. The field profiles (Fig. 4) show the periodic structure of the PC. Larger WG-defect separations cause longer times for the excitation of the channel drop modes in the exit guide. FDTD simulations of the frequency dependent transmission and channel dropping are shown (Fig. 4b) using a pulse technique. The calculated waveguide bands are shifted downward in frequency by ~0.5 GHz compared to experimental results (Fig. 3). The frequency resolution in simulation is ~0.16 GHz- significantly larger than experiment, owing to the finite time of the FDTD simulation. Hence, channel drop peaks in the simulation are much broader. As in experiment, the forward drop is higher in intensity than the reverse drop, and both drop intensities are lower than the forward bus straight waveguide. As in the measurements there are channel drop modes near midgap where the transmitted intensity is only somewhat lower than the forward bus. The comparison between simulation and measurement can be improved with longer simulation time and finer spatial grids.
A planar channel drop filter design has been examined experimentally and using FDTD simulations. This channel drop filter design is fabricated in a single layer making it easier to fabricate at optical and infrared wavelengths than multilayer designs. It has been shown that the transfer frequency can be tuned to any frequency within the band gap by changing the size of the air cavity. The quality factor of the transferred modes was ~1000. Simulations showed that directional energy transfer may be possible using this system if reflections within this system can be reduced or eliminated.
Research at the Ames Laboratory was supported by the Department of Energy, Division of Basic Energy Sciences, under Contract No. DE-AC02-07CH11358.
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