Channel-drop filters in three-dimensional woodpile photonic crystalsRong-Juan Liu, Zhi-Yuan Li, Zhi-Fang Feng, Bing-Ying Cheng, and Dao-Zhong Zhang

Citation: Journal of Applied Physics 103, 094514 (2008); doi: 10.1063/1.2909982 View online: http://dx.doi.org/10.1063/1.2909982 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/103/9?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Unidirectional channel-drop filter by one-way gyromagnetic photonic crystal waveguides Appl. Phys. Lett. 98, 211104 (2011); 10.1063/1.3593027 Waveguide bend designs in three-dimensional woodpile photonic crystals J. Appl. Phys. 103, 034502 (2008); 10.1063/1.2833385 Optical filter based on two-dimensional photonic crystal surface-mode cavity in amorphous silicon-on-silicastructure Appl. Phys. Lett. 90, 041108 (2007); 10.1063/1.2432228 Add-drop filters in three-dimensional layer-by-layer photonic crystals using waveguides and resonant cavities Appl. Phys. Lett. 89, 231103 (2006); 10.1063/1.2400398 Design of a channel drop filter in a two-dimensional triangular photonic crystal Appl. Phys. Lett. 83, 1074 (2003); 10.1063/1.1599982

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Channel-drop filters in three-dimensional woodpile photonic crystalsRong-Juan Liu, Zhi-Yuan Li,a� Zhi-Fang Feng, Bing-Ying Cheng, and Dao-Zhong ZhangInstitute of Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100080,People’s Republic of China

�Received 13 September 2007; accepted 23 February 2008; published online 9 May 2008�

Optical waveguides are characterized by high-efficiency transmission of electromagnetic �EM�waves and optical cavities have frequency selective property. The combination of opticalwaveguides and cavities can result in a large amount of devices in optical integrated circuit, amongwhich a channel-drop filter is an important member. A three-dimensional �3D� woodpile photoniccrystal �PC� can possess a complete band gap that allows perfect confinement of EM waves. Wetheoretically and experimentally study the property of the x-type waveguide and acceptor-typedefect cavity that are created in the 3D woodpile PC working in the microwave regime. On the basisof resonant coupling between the x-type wave guide and acceptor-type cavity, a series of three-portin-plane-type channel-drop filters are built: single-cavity, double-cavity, three-cavity, andfour-cavity channel-drop filters. All of them exhibit good frequency responding property bychanging the size of cavity. The multicavity channel-drop filter demonstrates the possibility to buildmultichannel wavelength division multiplexers in the 3D PC platform. © 2008 American Instituteof Physics. �DOI: 10.1063/1.2909982�

I. INTRODUCTION

Photonic crystals �PCs� are expected to become a keyplatform for future large-scale optical integrated circuits. PCsare characterized by photonic bands and band gaps. They canlead to interesting physical effects such as spontaneous emis-sion inhibition1 and localization of light,2 which can beachieved by the introduction of defects. Photons, whose fre-quency locates within the photonic band gap, cannot propa-gate through the crystal and will be confined to the defectregion. Defects can take the form of line defects, in whichcase the PC resembles optical waveguides. Another form ofdefects are point defects, in which case the PC creates acavity that confines a single or multiple closely separatedmodes to the spatial location of the point defect. Amongvarious forms of possible applications of PCs, waveguidesand resonators are most important components since they areconsidered as the main building blocks for PC-based inte-grated optical circuits.

Multichannel wavelength division multiplexers3–5

�MWDMs� and channel-drop filters6–24 are devices that arebuilt on the basis of optical waveguides and cavity resona-tors. Recently, interest has grown in functional channel-dropfilters that are composed of point defects and line defects inthe framework of PCs. Basically two types of channel-dropfilter have been under extensive study: one is the four-portsystem, for instance, a structure composed of two parallelwaveguides and one or two cavities lie between the two par-allel waveguides,6–14 and the other is the three-port system,for example, a structure made from one cavity lying betweentwo perpendicular waveguide.3,15–27 Up until now, most re-search works on these devices have been carried out in thetwo-dimensional �2D� PC slab system, due to their relativeease of fabrication in the infrared and visible wavelength

regimes by means of the state-of-the-art microfabricationtechnologies. Fan and co-workers have theoretically investi-gated a four-port in-plane-type channel-drop filter in 2D PCstructures and shown that 100% signal transfer from the buschannel to output signal channel can be realized if the cavitysystem provides at least a pair of degenerate modes of oppo-site symmetry.6–9 However, up until now, the four-portchannel-drop filter with 100% signal transfer efficiency hasyet been realized in experiment due to the difficulty to matchthe strict resonant condition. In comparison, it is easier tobuilt multichannel-drop filters based on three-port channel-drop filter. As a result, the three-port channel-drop filtershave been widely and deeply investigated. In particular,many experimental results of channel-drop filters that arebuilt in the 2D PC slab platform have been reported.3,15,25–27

Noda et al. has proposed the surface-emitting three-portchannel-drop filter, which consists of a cavity side coupled toa waveguide. The signal dropped from the bus channel to thecavity then emits to free space and can be collected.25,26 Amore realistic three-port channel-drop filter in PC slabs ismade from one cavity placed between two perpendicularwaveguide and the in-plane signal drop can beachieved.3,15–18 Based on this structure, multichannel-dropfilters can be designed with each signal channel correspond-ing to one different cavity configuration.

Compared to the deliberate and systematic theoreticaland experimental investigations on 2D PC slab channel-dropfilters, works on channel-drop filters built in three-dimensional �3D� PCs are much fewer and less extensive.The major reason can be attributed to the great challenge tofabricate 3D PC elements and devices in the optical wave-lengths. Among all the 3D PC structures, the 3D layer-by-layer PC structure �so-called woodpile PC structure� that wasfirst proposed by Ho et al. has attracted most interest28 be-cause the structure has alleviated the problem of microfabri-cation to a great extent. Much work has been theoreticallya�Electronic mail: lizy@aphy.iphy.ac.cn.

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and experimentally carried out on this structure.28–40 Amongthem, creation of various linear waveguides and localizedcavities and their coupling remains a hot topic for extensiveinvestigation. In particular, Li and Ho37 and Sell et al.38

showed that it is possible to build a 3D waveguide networkthat consist of linear waveguides along three orthogonal di-rections of a layer-by-layer PC, namely, the x-type, y-type,and z-type waveguides. They can form by either removing acomplete dielectric rod �x-type waveguide�, by removing onesegment in each rod along the in-plane �y-type waveguide�,or by removing some parts of rods along the stacking direc-tion �z-type waveguide�. Bayindir et al.39 experimentally in-vestigated a surface-emitting channel-drop filter in the mi-crowave regime in 2002 and in 2006 Kohli et al.40

experimentally and theoretically demonstrated a specialchannel-drop filter consisting of input and output waveguidesections coupled through a nearby cavity.

In this paper, we theoretically and experimentally inves-tigate the optical properties of the x-type waveguide andacceptor-type cavity41 in a 3D layer-by-layer PC structurewith a size scale in the microwave frequency regime. On thebasis of such knowledge, we construct a series of three-portin-plane-type channel-drop filter composed of x-typewaveguides and acceptor-type cavities. By measuring thetransmission spectra, the functional properties of thesechannel-drop filters are tested. The experiments are per-formed in the microwave regime. The major aim is to inves-tigate and design useful elements and devices in this PCplatform. The principles and results of device design can bedirectly applicable to optical wavelengths.

II. STRAIGHT X-TYPE WAVEGUIDES

As described in Ref. 37, waveguides in a 3D layer-by-layer PC structure can be generally classified in three kinds:the x-type, y-type, and z-type waveguides. In this paper, wefocus on the x-type waveguide whose schematic is shown inFig. 1. The microwave woodpile PC consists of squareshaped alumina rods with a refractive index of 3.0 and di-mensions of 0.32�0.32�30 cm3. The center-to-center sepa-ration between the rods is a=1.1 cm and the filling ration isabout f =0.29. The band gap along the rod extension direc-

tion extends from 10.9 to 13.5 GHz, and the complete bandgap lies in the range between 11.1 and 13.3 GHz.

The straight x-type waveguide is formed by removingone single rod from an otherwise perfect woodpile PC. Wecalculated the dispersion relationship of the guided modes bythe plane-wave expansion method in combination of a super-cell technique42–45 and the transmission spectrum of EMwaves propagating along the waveguide by the finite-difference time-domain method.46 When we calculated thedispersion relationship, a 1�5�5 supercell is employed.When we calculated the transmission spectrum, a plane-wavepulse source with a Gaussian temporal profile is set to liebefore the incidence port of the waveguide. We measured thetransmission spectrum by an Agilent microwave networkanalyzer. The incident coaxial cable is inserted into the inputport of the x-type waveguide and the detection coaxial cableis inserted into the output port. The calculated dispersiondiagram and transmission spectrum and the measured trans-mission spectrum of this waveguide structure are shown inFigs. 2�a�–2�c�, respectively. From the dispersion diagram, itcan be seen that there are two guided-mode bands within theband gap. The calculated and measured transmission spectraare basically consistent with the dispersion diagram. Thetransmission spectra can be divided into two sections withinthe band gap, which happen to correspond to the two guided-mode bands of the dispersion relationship. The calculatedtransmission spectrum �Fig. 2�b�� shows the directional bandgap, while the measured transmission spectrum �Fig. 2�c��exhibits the waveguide band within the complete band gap.The reason is that the source of the calculated spectrum is aplane-wave source while the source of the measured spec-trum is a point source like coaxial cable. In the waveguide,only the waveguide mode can transmit from the input port tothe output port, so when we placed the incident and detectioncoaxial cable into the waveguide, the measured transmissionspectrum can well reveal the waveguide band. Although wecan also use a pair of horns as a plane-wave source in ourexperiment, the signal of the excited waveguide modes isfound to be much weaker than the signal from the coaxial-cable inserted into the waveguide. The reason might be thestrong impedance mismatch at the waveguide exit.

We also calculated the typical Ez-field distribution pat-tern �namely, the z component of the electric field� in thecentral xy plane that crosses the waveguide axis for the twobands within the band gap, which are shown in Fig. 3. Thecalculation showed that Ez is dominant among the three com-ponents of electric field: Ex, Ey, and Ez. Bands 1 and 2 areboth even modes with respect to a vertical plane passing thewaveguide axis. The field is well concentrated inside thewaveguide for both modes. It seems that the higher fre-quency mode in band 2 has a stronger localization around thewaveguide axis than the mode in band 1.

III. CAVITIES

The cavities we design in this work are the acceptor-typedefect cavities, which are created by removing a portion ofone dielectric rod, whose size is �L. The plane-wave expan-sion method in combination with a supercell technique has

FIG. 1. �Color online� Schematic structure of an x-type straight waveguideby removing a single dielectric rod.

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been employed to understand the resonant frequency andmode profile of the cavity modes. It is found that when thecavity size increases, more and more localized cavity statesappear. The calculation result of the resonant frequency ofeach defect mode is shown in Fig. 4 as a function of defectsize �L, which varied from 0.1a to 2.8a. It can be seen thatthe resonant frequency can be tuned well by simply changingthe size of the defect so the cavity has a very good frequencyselection property. Only when the defect size is larger than0.4 cm can the resonant cavity mode be excited. When thedefect size is less than 0.8 cm, it excites a single-mode reso-nance. When the defect size is between 0.8 and 1.6 cm, tworesonant modes are excited; and when between 1.6 and

2.2 cm, three resonant modes are excited. It is clear that thelarger the defect size is, the more resonant modes can beexcited. In Fig. 4, we have designated these three zones ofcavity size by one-mode, two-mode, and three-mode zone,respectively.

We have systematically investigated the modal field dis-tribution for the different cavity modes corresponding to dif-ferent cavity sizes. The calculated Ez field patterns in thecentral xy plane for several typical situations are displayed inFig. 5. Figure 5�a� is for the single-mode cavity state whenthe defect size is equal to 0.6 cm �lying in the one-modezone�, while Figs. 5�b� and 5�c� are for the two cavity modesfor �L=1.2 cm in the two-mode zone, and Figs. 5�d�–5�f�

FIG. 2. �Color online� �a� Calculateddispersion diagram of the x-typewaveguide whose structure is shownin Fig. 1. �b� and �c� are the calculatedand measured transmission spectra forthe waveguide.

FIG. 3. �Color online� Ez field distribution in the central xy plane for atypical guided mode in �a� band 1 with a wave vector of kx=0.355�� /a� anda frequency of f =0.462�c /a�, and �b� band 2 with kx=0.355�� /a� and f=0.429�c /a�.

FIG. 4. �Color online� Calculated resonant frequency of the cavity mode asa function of the defect size. According to the number of cavity modes, threezones are categorized as the one-mode, two-mode, and three-mode zones.

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are for the three cavity modes at �L=1.9 cm in the three-mode zone. In Fig. 5, we assume that the removed segmentof rod takes place in the x-axis rod so its axis is along the xaxis. From Fig. 5, we can find that all the cavity modes areeven modes with respect to the y-axis mirror-reflection sym-metry. Mode 1 in all the three zones are all odd modes withrespect to the x-axis mirror-reflection symmetry. Mode 2 inthe two-mode and three-mode zones are both even modes,while mode 3 in the three-mode zone is an odd mode. Look-ing into the field profile feature of all the cavity modes, it canbe seen that the field energy of all the modes are well con-centrated around the cavity center. However, different modesin different size zones have different degrees of localization.For instance, mode 1 in Fig. 5�a� is more dispersed into thewalls of the cavity than other modes. The analysis of the fieldprofile of both the waveguide modes and cavity modes canoffer useful information of how a light signal tunnels fromthe input wavguide channel to the output waveguide channelthrough excitation of the cavity modes.

IV. CHANNEL-DROP FILTERS BUILT FROM X-TYPEWAVEGUIDES AND CAVITIES

A. Single-cavity channel-drop filters

In the above sections, it has been shown through exami-nation of the dispersion relationship, transmission spectra,and modal field distribution of the x-type waveguide andacceptor-type defect cavity that the cavity has good fre-quency selection property and there is a high coupling pos-sibility between waveguide and cavity. By utilizing theseproperties of the x-type waveguide and cavity, we can con-

struct a useful integrated optical device, a three-port in-planechannel-drop filter, whose schematic configuration is shownin Fig. 6 for single-cavity one. This channel-drop filter iscomposed of an x-type input bus waveguide �port 0� and anx-type output signal waveguide �port 1� coupled through anacceptor-type cavity between them. The input waveguide andcavity are in the same layer, and the output waveguide is onelayer above and perpendicular to the input waveguide. Thedistances between the cavity and the bus waveguide and theoutput waveguide are 2a. Figure 7 shows the measured trans-mission spectra at ports 0 and 1 for a cavity of size �L=0.7 cm. In order to clearly show the frequency selectionproperty of the cavity, the measured transmission spectrum atthe absence of the cavity ��L=0� is also shown in Fig. 7 as

FIG. 5. �Color online� Modal Ez-field distributions of several typical cavitymodes in the central xy plane: �a� mode 1 at �L=0.6 cm in the one-modezone; �b� and �c� are for modes 1 and 2 at �L=1.2 cm in the two-modezone; �d�–�f� are for modes 1–3 at �L=1.9 cm in the three-mode zone.

FIG. 6. �Color online� Schematic structure of a single-cavity channel-dropfilter composed of an input x-type bus waveguide �port 0� and an outputx-type signal waveguide �port 1� coupled through an acceptor-type cavityformed by removing a segment of rod.

FIG. 7. �Color online� Measured transmission spectra at ports 0 and 1 witha cavity size of �L=0.7 cm, as well as the transmission spectrum at theabsence of the cavity ��L=0 cm�.

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a reference. We can see that there is a sharp dip with aquality factor �Q factor� about 1160 in the transmission spec-trum of port 0. The resonance takes place at the frequency of12.2 GHz. At the same frequency of 12.2 GHz, there appearsa peak with a Q factor about 217 in the transmission spec-trum of port 1. The difference of the two measured Q factorscan be attributed to the remarkable noise of the measureddropped signal at port 1 when the device is off-resonance andthe signal is at low level. The calculated resonant frequencyin Fig. 4 for a cavity of size 0.7 cm is 12.36 GHz. The smalldiscrepancy between theory and experiment in regard to theresonant frequency of the cavity �about 0.16 GHz� might beattributed to the inaccuracy of the measured geometric andphysical parameters of the woodpile PC and also to the in-accuracy of the numerical calculations.

Beyond the resonance region, the transmission spectrumis almost the same as for a straight waveguide, which meansa negligible influence of the cavity and the output waveguideon the bus channel when the system is off-resonant. Thesetransfer features clearly indicate that the structure has an ex-cellent demultiplexing and channel-drop filtering functional-ity. The physical mechanism for the channel-drop has beenwell understood. Due to coupling between the guided modesand the localized cavity mode, EM waves at the resonancefrequency of a cavity are dropped from the input bus wave-guide mode to the cavity. Then, a single mode of EM fieldoscillation is excited inside the cavity. Finally, the cavitymode further couples into the output signal waveguidethrough an evanescent field.

It has been clear from Fig. 4 that the resonant frequencyof the cavity sensitively depends on the cavity size. Thisfeature can be readily explored to build a MWDM, whereeach signal channel corresponds to a particular cavity. Todemonstrate this, we have continuously changed the cavitysize and measured the transmission spectra at port 1. Theexperimental results are shown in Fig. 8. Figure 8�a� showsthe case of small cavity size in the one-mode zone, where asingle peak in the transmission spectrum for port 1 can beclearly seen. When the sizes are 0.4, 0.5, 0.55, and 0.7 cm,the corresponding resonant frequencies are 12.08, 12.15,12.18, and 12.23 GHz, respectively. The peaks are located inthe first section of the waveguide transmission spectrum,which corresponds to the guided-mode band 1 for the x-typewaveguide as depicted in Fig. 2. When the cavity size �L islarger than 0.8 cm and less than 1.5 cm, two peaks are foundfrom the transmission spectra that are measured at port 1.The results are displayed in Fig. 8�b�. The high-frequencyresonant peak is located in the frequency range of the secondsection in the waveguide transmission spectrum �guided-mode band 2�. The low-frequency resonant peak is located inthe guided-mode band 1. When the cavity size is 0.95 cm,the two resonant peaks are located at 12.01 and 12.27 GHz,respectively. The measured resonant frequencies are 12.05and 12.3 GHz for the cavity of size 1.0 cm, 12.15 and12.36 GHz for the cavity of size 1.1 cm, and 12.24 and12.4 GHz for the cavity of size 1.25 cm.

Figure 8�c� shows the measured transmission spectra atport 1 for even larger cavity size corresponding to the three-mode zone and multiple-mode zone. Three or more reso-

nance peaks can be identified from the spectra. The spectrafor these large cavity size situations exhibit much compli-cated features than for smaller size cavity situations. Themeasurement results of the frequency ranges for the one-peak, two-peak, and three-peak situations agree well with thecalculation results of the one-mode zone, two-mode zone,and three-mode zones, as displayed in Fig. 4. The theoreticaland experimental results both confirm that by tuning the sizeof cavity, the designed channel-drop filter has a very goodfrequency selective property. We can further tailor this char-acteristic to build a more complicated multiple-channelwavelength division multiplexer.

FIG. 8. �Color online� The measured transmission spectra from port 1. �a�Cavity size ranges from 0 to 0.75 cm; �b� cavity size ranges from0.95 to 1.25 cm; �c� cavity size ranges from 1.55 to 2.55 cm.

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B. Double-cavity channel-drop filters

Now that we have obtained some basic concepts aboutsingle-cavity channel-drop filters, we proceed to experimen-tally realize double-cavity channel-drop filters. The two-channel structure is schematically shown in Fig. 9. The firstcavity �cavity 1� has a size of 0.9 cm and the second cavity�cavity 2� has a size of 0.4 cm. The transmission spectrameasured from ports 1 and 2 are shown in Fig. 10. In orderto clearly show the resonant peak selected by the two cavi-ties, the transmission spectrum when the cavity size is zero isalso shown in Fig. 10 as a reference. It can be seen that port1 can select two resonant frequencies of 11.76 and12.26 GHz, and, at the same time, port 2 can select a single

resonant frequency of 12.18 GHz. This proves the feasibilityof constructing multifrequency channel-drop filter and mul-tichannel wavelength division multiplexer.

C. Three-cavity channel-drop filters

The three-channel structure is schematically shown inFig. 11. Cavities 1 and 3 lie at one side of the bus waveguideand cavity 2 lies at the other side. The distances between thethree cavities and the bus and output waveguide are all 2a.The sizes of cavities 1, 2, and 3 are 0.3, 0.9, and 0.8 cm,respectively. The transmission spectra measured from Ports0, 1, 2, and 3 are shown in Figs. 12�a�–12�d�. In order toclearly show the resonant peak selected by the three cavities,the transmission spectra when the cavity size is zero �namely,the cavity is closed� is also shown in each figure of Fig. 12 asa reference. In Figs. 12�b�–12�d�, the measured spectra atport 0 are also presented so that the position of dips andpeaks can be compared apparently. It can be seen that thethree cavities with different sizes can select signal of differ-ent frequencies from the bus waveguide, which causes dipsin the transmission spectrum at port 0 and produces peaks onthe transmission spectrum at ports 1, 2, and 3, respectively.The frequency positions of the peak and dip for a certain sizeof cavity accord with each other quite well. To estimate thedrop efficiency of each channel, we have adopted the calcu-lation method of drop efficiency proposed in the supportingonline material of Ref. 26. Taking the first cavity as an ex-ample, we calculate its drop efficiency according to the trans-mission spectra at port 0 in Fig. 12�a� with cavity 1 open orclosed. When the cavity is closed, the transmittance at about11.84 GHz is viewed as 100. Then the transmittance is 62.2at the corresponding frequency of the dip in the spectrumwhen the cavity is open. By this method, the drop efficiencyof �100–62.2� /100=37.8% can be obtained. The resonantfrequencies for the three channels are 11.84, 12.33, and

FIG. 9. �Color online� Schematic configuration of a double-cavity channel-drop filter built from an input bus channel waveguide coupled with twooutput waveguide �port 1 and 2� through two cavities.

FIG. 10. �Color online� Measured transmission spectra at ports 1 and 2 fordouble-cavity channel-drop filter. The sizes of cavities 1 and 2 are 0.9 and0.4 cm, respectively. The black line is the transmission spectrum when thecavity size is zero and is displayed here for reference.

FIG. 11. �Color online� Schematic configuration of a three-cavity channel-drop filter built from an input bus channel waveguide coupled with threeoutput waveguides �Ports 1, 2, and 3� through three cavities.

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12.25 GHz, respectively. The drop efficiencies of the threecavities are 37.8%, 36.7%, and 64.4%, respectively. Thedrop efficiency is related to the size of cavity and the dis-tance between the cavity and the bus waveguide. To achievehigh drop efficiencies, it needs elaborated design like theachievement of high drop efficiency in the 2DPC.6,17,18,27,37,38

D. Four-cavity channel-drop filters

The four-channel structure is schematically shown inFig. 13�a�. Cavities 1, 2, 3, and 4 are symmetrically locatedat the two sides of the bus waveguide. The distances betweenthe cavities and the bus and output waveguide are all 2a.Cavity 1 has a size of 0.85 cm, cavity 2 has a size of0.95 cm, cavity 3 has a size of 0.35 cm, and cavity 4 has asize of 0.7 cm. The transmission spectra measured fromports 0, 1, 2, 3, and 4 are shown in Figs. 13�b�–13�f�. Inorder to clearly show the resonant peaks and dropped dipsselected by the four cavities, the transmission spectra whenthe cavity sizes are all zero are also shown in each figure ofFig. 13 as a reference. In Figs. 13�c�–13�f�, the measuredspectra at port 0 are also presented so that the position of

dips and peaks can be compared. It can be seen that the fourcavities with different sizes can select different frequenciesfrom the bus waveguide, which causes dips in the transmis-sion spectrum at port 0 and produces peaks in the transmis-sion spectrum at ports 1, 2, 3, and 4. The frequency positionsof the peak and dip for a certain size of cavity accord witheach other. The resonant frequencies for the four channelsare 12.28, 12.42, 11.86, and 12.17 GHz, respectively. Thedrop efficiencies of the four cavities are about 25%, 49%,22%, and 19%, respectively. From the transmission spectrameasured at ports 1 and 2, we can see that there are smallpeaks at low frequency about 11.9 and 11.96 GHz for cavi-ties 1 and 2, respectively, which accords with the simulatedresult that there are double modes when the cavity size ismore than 0.8 cm. However, there is no obvious dip in thespectrum measured at port 0 at the corresponding frequencypositions. The reason might be that the signal is too weak tobe shown out in the transmission spectrum, which exhibits acertain degree of fluctuation around a high level of transmis-sion signals.

The above experimental results on a series of three-portchannel-drop filters built in the 3D woodpile PC structure,

FIG. 12. �Color online� Measured transmission spectra for a three-cavity three-port channel-drop filter. �a� Measured transmission spectrum �red curve� at port0 when the sizes of the three cavities are �L=0.3, 0.9, and 0.8 cm, respectively, and reference spectrum �thin black curve� when the three-cavity sizes are allclosed, namely, with sizes of 0 cm. Three dips are clearly seen and correspond to the resonant signal dropped by the cavities to the output ports. �b� Measuredtransmission spectrum at port 1 of the three-port channel-drop filter when cavity 1 is open �green curve� or is closed �thick black curve�. The spectra shownin �a� are also presented in this panel and the following two panels to clearly visualize the position of the corresponding peaks and dips caused by cavities.A very strong transmission peak appears in the green curve and corresponds to the signal dropped from cavity 1 to port 1, and this peak coincides with thedip measured in port 0. Signal dropped to port 1 is blocked when cavity 1 is closed and as a result the transmission peak disappears. �c� Measured transmissionspectra at port 2 when cavity 2 is open �cyan curve� or is closed �thick black curve�. �d� Measured transmission spectra at port 3 when cavity 3 is open �bluecurve� or is closed �thick black curve�.

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such as one-cavity, two-cavity, three-cavity, and four-cavityfilters show that each cavity can independently act to realizethe filtering functionality. The cross-talk between differentchannels does not occur. This feature makes it possible toadd more signal channels into the system and build a densewave divisional multiplexer/demultiplexer in this 3D PCframework. A major problem for better practical use of thecurrent device is the relatively low coupling efficiency �drop-ping efficiency� of each signal channel. Unlike the ideal 2DPC design of channel-drop filters by Fan et al., where the100% efficiency can be achieved, the current filters have alarge space to improve the efficiency, although the efficiency�20%–40%� has been comparable to most three-port

channel-drop filters designed in 2D PC slabs. It is thus de-sirable to optimize the local geometry around the cavity andthe input and output waveguides.

V. CONCLUSION

In summary, we have systematically investigated the dis-persion relationship, transmission property, and mode fielddistribution of x-type waveguides and acceptor-type cavitiesthat are created in a 3D woodpile PC working in the micro-wave regime. We have found that the cavity has a good fre-quency selective property by simply changing its size, and itis easy to realize mode match coupling between thewaveguides and cavities. By utilizing these properties, a se-ries of three-port system in-plane channel-drop filter are con-

FIG. 13. �Color online� �a� Schematicconfiguration of a four-cavity channel-drop filter built from an input buschannel waveguide coupled with fouroutput waveguides �ports 1, 2, 3, and4� through four acceptor-type cavities.��b�–�f�� Measured transmission spec-tra for the four-port channel-drop fil-ter. �b� Measured transmission spec-trum �red curve� at port 0 when thesizes of the three cavities are �L=0.85, 0.95, 0.35, and 0.7 cm, respec-tively, and reference spectrum �thinblack curve� when the three cavitysizes are all closed, namely, with sizesof 0 cm. Four dips are clearly seen andcorrespond to the resonant signaldropped by the cavities to the outputports. �c� Measured transmission spec-trum at port 1 when cavity 1 is open�green curve� or is closed �thick blackcurve�. �d� Measured transmissionspectra at port 2 when cavity 2 is open�cyan curve� or is closed �thick blackcurve�. �e� Measured transmissionspectra at port 3 when cavity 3 is open�blue curve� or is closed �thick blackcurve�. �f� Measured transmissionspectra at port 4 when cavity 4 is open�magenta curve� or is closed �thickblack curve�. The spectra shown inpanel �b� are also presented in panels�c�–�f�, which show that the positionof the peaks and dips caused by reso-nant cavities accords with each otherquite well.

094514-8 Liu et al. J. Appl. Phys. 103, 094514 �2008�

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structed. We have evaluated the optical functionality by mea-suring the transmission spectra at the output ports, and foundthat all the designed channel-drop filters can drop signalsfrom the bus waveguide channel efficiently at different reso-nant frequencies by changing the cavity size. The double-cavity, three-cavity, and four-cavity channel-drop filtersprove the feasibility of constructing multichannel wave-length division multiplexer. Our theoretical and experimentalstudies for the current microwave PC devices can offer auseful reference for designing and realizing optical inte-grated optical devices in 3D PCs with a submicrometer scale.

ACKNOWLEDGMENTS

The authors would like to acknowledge the financialsupport from the National Natural Science Foundation ofChina under Grant Nos. 10525419 and 10404036, the Na-tional Key Basic Research Special Foundation of China un-der Grant No. 2006CB921702.

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