A waveguide coupler is designed and realized in a three-dimensional woodpile photonic crystal at microwave regime. This waveguide coupler shows good energy transfer property, which is confirmed through measurement of transmission spectrum, internal field distribution and surface field distribution using Agilent microwave network analyzer.
© 2008 Optical Society of America
Photonic crystals (PCs) provide a promising prospect for optical integrated circuit. So far, a great amount of optical functional components that are of crucial importance for new telecommunications applications have been realized in PCs. Most of them are based on waveguides[1–5] or microcavities[6–9] which can control the propagation of light under the background of PCs. Recently, the power transfer properties of parallel coupled waveguides in PCs have been studied, and devices such as directional couplers [10–13], switches , and multiplexers/demultiplexers, [15,16] have been proposed using the waveguide coupling. Compared with multiplexers/demultiplexers based on the coupling between waveguides and microcavities, multiplexers/demultiplexers composed of waveguide couplers may avoid the adverse influence caused by the tiny change or the fabrication error of microcavities. On the other hand, PC waveguide couplers are natural grating-assisted waveguide couplers. The conventional waveguide-grating-based coupler-type filters [17, 18] usually require lengths in the range of several millimeters, which is far away from the demands of compact integrated photonic devices. Waveguide couplers employing PC technology achieve very short coupling lengths due to the large coupling coefficient, and this may allow highly compact devices. PC waveguide couplers may become a key building-block of complex ultra-compact optical integrated circuits. So far most of them are made in two-dimensional (2D) PCs, and few relevant reports are found in three-dimensional (3D) PCs. As optical integrated circuits and light propagation control in real 3D space depend on the development of 3D PCs and 3D PC devices, in this work we study the waveguide coupler in 3D woodpile structure PCs [19–21] at microwave regime. We investigate the power transfer properties of two parallel coupled waveguides through band diagram design, transmission spectrum measurement, internal field measurement in the waveguide and a surface-field-scanning measurement that is developed in reference .
2. Experimental sample
The photonic crystal shown in Fig. 1(a) consists of square shaped alumina rods with a refractive index of 3.0 and dimensions of 0.32cm×0.32cm×60cm. The center-to-center separation between the rods is a=1.1cm and the filling ratio of rods is about 0.29. The band gap along the rod extension direction extends from 10.9 to 13.5 GHz, and the complete band gap lies in the range between 11.1 and 13.3 GHz. As described in reference , waveguides in the 3D woodpile PC structure can be generally classified as 3 kinds: X-type, Y-type and Z-type. A type II Y waveguide, where the central axis of the Y waveguide (made by removing a segment of material from each rod) is located in a central-inversion symmetric line as shown in Fig. 1(b), has a single wide band within the band gap. Considering its single-mode superiority, we focus on waveguide coupler based on the type II Y waveguide. The waveguide coupler composed of two parallel straight type II Y waveguides in xy plane is schematically shown in Fig. 1(c). The two parallel waveguides are located in the 15th layer of a crystal platform with total 29 layers and the center-to-center space between them is d=2.75cm=2.5a. The width of both waveguides is w=0.75cm. Figure 2 shows the calculated dispersion relation of one type II Y waveguide in 3D PCs (the black circle) and two parallel type II Y waveguides (the red and blue circle) by means of the finite-difference time-domain (FDTD) method. We can see that the waveguide band splits from single to double as one waveguide changes into a double parallel waveguide coupler in the 3D PC. For the double waveguide bands, one is an even mode; the other is an odd mode. Coupling between two parallel waveguides can be understood by considering the supermodes in the coupling mode theory. For two identical waveguides, one may deal with the two lowest order modes having odd and even parity, respectively, with respect to the symmetry plane between the waveguides. These modes have different propagation constants, βodd≠βeven. A field injected into one waveguide switches entirely to the other one (“cross” state) if the coupler length is an odd multiple of half the beat length (or coupling length), LB=2π/Δβ≡2π/|βodd-βeven|(or Lc=LB/2). In contrast, the field comes out through the input waveguide (“bar” state) when the coupler length is an integer multiple of the beat length. If Δβ varies as a function of wavelength, a coupler of a given length L may become an important component for wavelength division multiplexer communications systems. According to the dispersion relation of our designed waveguide coupler shown in Fig. 2, we can obtain the coupling length as a function of frequency as shown in Fig. 3. We can see that the coupling length can reach a small value of several lattice constants long at some frequencies, which is much less than conventional dielectric waveguide coupler with weak coupling effect. From this point of view, the designed 3D PC waveguide coupler is favorable to realize high-density wavelength division multiplexer and compact integrated circuit.
3. Transmission spectra and field distributions
Figure 4 shows the calculated field distributions of waveguide coupler at frequency 12.4437 GHz in 3D woodpile PCs by means of the FDTD technique: (a) shows the internal field distribution situation in two nearby waveguides; (b) shows the surface field distribution situation with 7 layers above the layer containing the two parallel waveguides. In Fig. 4(a) and (b), the bottom sections show the field distribution of the xy plane; and the black and blue curves in the upper sections give the field distribution along the black and blue lines in the bottom sections. The black and blue curves in the upper sections of Fig. 4(a) and (b) are smoothed as red and green curves, respectively. From the upper sections of Fig. 4(a) and (b), it can be seen that the strong and weak field intensity alternately emerge in the two parallel waveguides and the coupling length is about 11a. The energy transfer process is clearly demonstrated by both the internal and surface field distribution. The surface field distribution also shows strong radiation field. That is because the surface scanning plane is in the air. The radiation field doesn’t influence the exhibition of energy transfer process. On the contrary, it is auxiliary to show more clearly the back and forth transfer process of energy between the two parallel waveguides. Whenever energy power transfers from one waveguide to the other, strong radiation will occur. According to the calculated results, we applied a surface-field-scanning method developed in reference  which can combine with the transmission measurement to reveal richer and more all-around information of our research objects.
We performed both the internal field and surface field measurement by an Agilent microwave network analyzer. The surface field measurement was performed as described in detail in reference . When measuring the internal field, we put a source, a dipole antenna connected with network analyzer, at Port 1, and a detector, another dipole antenna that feeds back signal to network analyzer, into the waveguides. Because of the small size of the waveguide cross section opening, it is hard to insert the coaxial-cable detector into the waveguide to scan the field without causing significant disturbance to the field. To overcome this difficulty, we increase gradually the length of the waveguide with a step of 0.5a and always place the detector at the exit end of the waveguide. In this way, the detector can measure the field distribution along the central axis of waveguides with remarkable stability. At every step, the transmission spectrum is recorded from 11 GHz to 13.5 GHz automatically. Figure 5 shows the transmission spectra at Port 2 (black line) and Port 3 (red line). It can be seen that electromagnetic wave outputs from Port 2 in the frequency range 12.2438~12.5875 GHz and from Port 3 in the range 12.5875~12.8656 GHz.
We extract the transmission coefficients for each frequency at all the scanning steps in W1 and W2 and then assemble them as a function of the propagation distance of electromagnetic wave. Thus we can obtain the internal field distribution curves as shown in Fig. 6(a) and (b) by the original data curves (black line) for 12.4437GHz. The oscillation of electromagnetic waves is clearly shown by the smoothed curves of the original data curves. Comparing the smoothed curves in W1 and W2 as shown in Fig. 6(c), we can see that the strong field and weak field alternately emerge in two waveguides, which means that the energy transfers back and forth between two waveguides. The experimental result is consonant with the theoretical results in the upper sections in Fig. 4(a) and (b). The coupling length can be found from the peak-to-peak (or dip-to-dip) distance in Fig. 6(c) to be about 10~11a. Although the experimental data of coupling length exhibit some fluctuation in, the result agrees well with the theoretical result in Fig. 3 and Fig. 4. The scanned surface field with the 7 layers above the layer containing two parallel waveguides shows the energy transfer process more directly. From Fig.6(c) and (d), it can also been seen that the electromagnetic wave outputs from Port 2, which agrees with the transmission spectra shown in Fig. 5. We also show the measured internal field distribution and surface field distribution of 12.6406 and 12.8843GHz in Fig. 7 and Fig. 8, respectively. Figure 7(a) shows more regular oscillation like Fig. 6(c), and Fig. 7(b) shows obviously energy transfer between waveguide. But it differs from Fig. 6 in that the electromagnetic wave outputs from Port 3, which is also consistent with the transmission spectra in Fig. 5. From Fig. 8, we can see that the internal field does not oscillate regularly any more and the surface field doesn’t show clear energy transfer between two waveguides. The transmission efficiency is similar at Port 2 and Port 3. It can be explained by the dispersion relation. For 12.8843 GHz, the coupled system only supports a single mode, and the mode field homogeneously distributes in two waveguides.
In summary, we designed and realized a waveguide coupler in 3D woodpile PCs at microwave regime. Through extensive measurement of the transmission spectrum, internal field distribution and surface field distribution, the designed waveguide coupler shows good energy transfer property. As many optical devices used in integrated circuit and optical communication such as directional couplers, switches, and multiplexers/demultiplexers are based on waveguide coupler, the realization of waveguide coupler in 3D PCs can find potential applications in ultracompact optical integrated circuit and communication devices.
The authors would like to acknowledge the financial support of the National Natural Science Foundation of China at No. 10525419, and the National Key Basic Research Special Foundation of China at No. 2006CB921702 and No. 2007CB613205.
References and Links
1. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Vileneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996). [CrossRef] [PubMed]
2. A. Mekis, S. Fan, and J. D. Joannopoulos, “Bound states in photonic crystal waveguides and waveguide bends,” Phys. Rev. B 58, 4809–4817 (1998). [CrossRef]
3. E. Chow, S. Y. Lin, J. R. Wendt, S. G. Johnson, and J. D. Jouannopoulos, “Quantitative analysis of bending efficiency in photonic-crystal waveguide bends at λ=1.55 µm wavelengths,” Opt. Lett. 26, 286–288 (2001). [CrossRef]
5. M. Galli, D. Bajoni, M. Patrini, G. Guizzetti, D. Gerace, L. C. Andreani, and M. Belotti, “Single-mode versus multimode behavior in silicon photonic crystal waveguides measured by attenuated total reflectance,” Phys. Rev. B. 72, 125322 (2005). [CrossRef]
7. R. K. Lee, O. J. Painter, B. D’Urso, A. Scherer, and A. Yariv, “Measurement of spontaneous emission from a two-dimensional photonic band gap defined microcavity at near-infrared wavelengths,” Appl. Phys. Lett. 74, 1522–1524 (1999). [CrossRef]
8. P. Pottier, C. Seassal, X. Letartre, J. L. Leclercq, P. Viktorovitch, D. Cassagne, and C. Jouanin, “Triangular and hexagonal high Q-factor 2-D photonic bandgap cavities on III-V suspended membranes,” J. Lightwave Technol. 17, 2058–2062 (1999). [CrossRef]
9. J. Hwang, H. Ryu, D. Song, I. Han, H. Song, H. Park, Y. Lee, and D. Jang, “Room-temperature triangular-lattice two-dimensional photonic band gap lasers operating at 1.54 µm,” Appl. Phys. Lett. 76, 2982–2984 (2000). [CrossRef]
10. A. Martinez, F. Cuesta, and J. Marti, “Ultrashort 2-D photonic crystal directional couplers,” IEEE Photon Technol. Lett. 15, 694–696 (2003) [CrossRef]
11. S. Kuchinsky, V. Y. Golyatin, A. Y. Kutikov, T. P. Pearsall, and D. Nedeljkovic, “Coupling between photonic crystal waveguides,” IEEE J. Quantum Electron. 38, 1349–1352 (2002) [CrossRef]
12. S. Boscolo, M. Midrio, and C. G. Someda, “Coupling and decoupling of electromagnetic waves in parallel 2D photonic crystal waveguides,” IEEE J. Quantum Electron. 38, 47–53 (2002). [CrossRef]
13. Y. Sugimoto, Y. Tanaka, N. Ikeda, T. Yang, H. Nakamura, K. Asakawa, K. Inoue, T. Maruyama, K. Miyashita, K. Ishida, and Y. Watanabe, “Design, fabrication, and characterization of coupling-strength-controlled directional coupler based on two-dimensional photonic-crystal slab waveguides,” Appl. Phys. Lett. 83, 3236–3238, (2003) [CrossRef]
14. A. Sharkawy, S. Shi, and D. W. Prather, “Electro-optical switching using coupled photonic crystal waveguides,” Opt. Express 10, 1048–1059 (2002) [PubMed]
15. M. Koshiba, “Wavelength division multiplexing and demultiplexing with photonic crystal waveguide couplers,” J. Lightwave Technol. 19, 1970–1975 (2001) [CrossRef]
16. A. Sharkawy, S. Shi, and D. W. Prather, “Multichannel wavelength division multiplexing with photonic crystals,” Appl. Opt. 40, 2247–2252 (2001). [CrossRef]
18. T. Erdogan, “Optical add-drop multiplexer based on an asymmetric Bragg coupler,” Opt Commun. 157, 249–264 (1998) [CrossRef]
19. E. Ozbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and K. M. Ho, “Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945–1948 (1994). [CrossRef]
20. E. Ozbay, G. Tuttle, M Sigalas, C. M. Soukoulis, and K. M. Ho, “Defect structures in a layer-by-layer photonic band-gap crystal,” Phys. Rev. B 51, 13961–13965 (1995). [CrossRef]
21. E. Ozbay and B. Temelkuran, “Reflection properties and defect formation in photonic crystals,” Appl. Phys. Lett. 69, 743–745 (1996) [CrossRef]
23. Z. Y. Li and K. M. Ho, “Waveguides in three-dimensional layer-by-layer photonic crystals,” J. Opt. Soc. Am. B 20, 801 (2003) [CrossRef]