We propose the hybrid integration of conventional index-guided waveguides (CWGs) and photonic crystal (PhC) regions of very limited spatial extent as a promising path toward large-scale planar lightwave circuit (PLC) integration. In CWG/PhC structures the PhC regions do not perform the function of waveguiding, but instead augment the CWGs to permit a drastic reduction in the size of photonic components. For single mode waveguides with a refractive index contrast of only 2.3%, simulation results show a 90 degree bend with 98.7% efficiency, a compact beamsplitter with 99.4% total efficiency, and a planar Mach-Zender interferometer (MZI) with 97.8% efficiency. The MZI occupies an area of only 18 μm × 18 μm.
© 2002 Optical Society of America
Photonic crystal (PhC) structures have been the focus of intense research in recent years  in part because of their potential to realize ultracompact planar lightwave circuits (PLCs). Two-dimensional (2-D) PhCs implemented in an index guiding slab that confines light within the slab through total internal reflection (TIR) have received particular attention [2–23] owing to their relative ease of fabrication compared to 3-D PhCs. Much of the work reported in the literature on 2-D PhC structures has focused on creating fundamental elements of PLCs such as waveguides [3–11,19–23], bends [8,12–14,24], splitters [15–16], and resonators [17,18,25,26]. The common theme for the vast majority of this work is to implement these functions with a 2-D PhC containing suitable lattice defects such that light is laterally confined by the photonic bandgap of the periodic structure. For this approach issues such as scattering loss [19,20,21], relationship of defect waveguide modes to the light line [8,22,23], single mode versus multimode waveguide operation [6,8,11], and flatness of the dispersion relation of the fundamental guided mode  are problematic and require careful design consideration.
In this paper we present an alternate vision for how to use 2-D PhC structures to achieve the goal of realizing ultracompact PLCs. Our approach is based on the hybrid integration of conventional waveguides (CWGs) and PhC structures of limited spatial extent. The PhC regions augment the CWGs to reduce overall device size while preserving the traditional advantages of CWGs such as straightforward design for single mode operation, low propagation loss, and low dispersion. We demonstrate the potential of this approach by investigating high efficiency 90-degree bends and beam splitters, and, as an example, show how these elements can be combined to form a very compact, high efficiency planar Mach-Zender interferometer.
2. High efficiency hybrid 90-degree bend
First let us consider the geometry shown in Fig. 1(a) in which a small 2-D PhC region forms a 90-degree corner for a CWG. The CWG has core and clad refractive indices of n1=1.500 and n2=1.465, respectively, for a refractive index contrast, Δ = (n1-n2)/n1, of 2.3%. (Note: since our analysis is 2-D in nature, these refractive indices are for 2-D waveguides. A similar approach may be taken to approximate 3-D channel waveguides if effective indices are used.) The CWG has a width of 2 microns so it supports a single guided mode for wavelengths in the telecommunication band near 1.55 μm. The PhC lattice is composed of a square array of silicon posts (refractive index 3.481) with a lattice constant, a, of 380 nm and a post radius, r, of 86.8 nm.
We use a 2-D finite difference time domain (FDTD) method  with Berenger perfectly matched layer boundary conditions  to numerically calculate the optical properties of the structure shown in Fig. 1(a). The fundamental waveguide mode is sourced along an 8 μm wide line centered on the input waveguide and directed toward the PhC region as indicated in the figure. The light is TM polarized (electric field orientation parallel to the posts). The field is monitored along 8 μm wide detector lines for light that is transmitted through the PhC region, reflected by the structure toward the input waveguide, and deflected into the output waveguide.
Figure 1(b) shows a plot as a function of wavelength of the fraction of the incident light that is deflected into the output waveguide (which we term bending efficiency), reflected back toward the input waveguide, and lost through the top of the PhC region. For wavelengths between 1.23 μm and 1.68 μm very little light is lost through the PhC structure. Instead, most of it is either reflected back in the direction of the source or deflected into the output waveguide. Note that there is a broad wavelength region (~1.43 to 1.64 μm, Δλ/λ = 13.5%) in which the bending efficiency is greater than 95%. In Fig. 1(c) the magnitude squared of the time-average electric field is shown for a wavelength of 1.55 μm. The bending efficiency for this case is 98.7%, while only 0.14% of the incident light is reflected back in the direction of the input waveguide. The bend radius for a curved waveguide with the same bending efficiency is 2.5 mm. Insertion of the PhC region essentially introduces a high efficiency, mode-matched mirror into the waveguide to achieve a dramatic reduction in the area required to realize a 90-degree bend.
An interesting feature of this result is illustrated in the band diagram for the PhC region, which is shown in Fig. 2(a). Note that a wavelength of 1.55 μm (normalized frequency of 0.243) does not lie in the bandgap, but rather is just below it. However, as seen in Fig. 1(c), light does not couple into a propagating mode of the PhC and instead is reflected with great efficiency into the output waveguide.
This can be understood by examination of the wave vector diagram [29, 30] in Fig. 2(b) in which the horizontal axis is the Γ-M direction, which coincides with the direction of the PhC surface that is at 45 degrees to the input and output waveguides. For λ = 1.55 μm, the black circle indicates the allowed wave vectors in the core and clad regions (which we treat as homogeneous for simplicity in constructing the wave vector diagram), while the dotted black curves denote the wave vectors for allowable propagation modes in the PhC region. Note that for light incident from the input waveguide at 45 degrees to the PhC surface (green arrow) there are no allowed states in the PhC that the light can couple into (i.e., the black dashed vertical line does not intersect the allowed PhC wave vector curves). Therefore it is not necessary that the PhC be designed such that the wavelengths of interest for device operation fall strictly within the PhCs photonic bandgap.
Alternatively, consider propagation at λ = 1.75 μm, which, from Fig. 2(a), is considerably below the low frequency edge of the photonic bandgap. As shown in Fig. 2(c), much of the light is coupled into the PhC structure. Referring to the blue wave vector curves in Fig. 2(b), it is clear that the incident light can directly couple into an allowed PhC propagating mode. Moreover, the first diffraction order (with a wave vector component in the Γ-M direction given by the end of the blue arrow) couples into a PhC propagating mode as well.
It is also useful to understand why such a large fraction of light within the bandgap in the 1.23 – 1.32 μm wavelength range is reflected toward the input waveguide rather than deflected into the output waveguide. From Fig. 1(b), the peak reflection efficiency occurs at a wavelength of 1.24 μm. As seen in Fig. 2(a), this wavelength is just below the high frequency edge of the bandgap. As shown in Fig. 2(d) the reflected light is not directed exactly back along the input waveguide. The red curves in Fig. 2(b) show the corresponding wave vector diagram, in which there are no allowed propagating modes in the PhC. However, the first diffraction order (with wave vector shown by the heavy red arrow) is not evanescent, but propagates at an angle of 9 degrees relative to the input waveguide. This diffraction order contains most of optical power that is redirected by the PhC region. Thus the existence of allowed diffraction orders in the nearly homogeneous CWG areas due to diffraction from the periodic PhC interface is a critical design consideration when integrating limited PhC regions with CWGs.
3. High efficiency beamsplitter
We now consider beamsplitters. Our basic geometry is shown in Fig. 3(a) in which, as an example, two layers of a square lattice of Si posts cross a CWG intersection at 45 degrees.
Figure 3(b) shows the efficiency with which light is split into the two output ports as a function of wavelength for both single and double layers of Si posts. In each case the Si post arrays have been designed to yield equal splitting of the incident power into the two output waveguides at a wavelength of 1.55 μm. For the single layer of posts, the fraction of the incident optical power directed into each waveguide is 49.7% (for 99.4% total efficiency) and only 0.012% is reflected back into the input waveguide. For the double layer of posts, 50.2% of the incident light is directed into the horizontal output waveguide, 49.2% into the vertical output waveguide (for, again, 99.4% total efficiency), and 0.05% is reflected. As one would expect, when the number of Si post layers is increased beyond two the total efficiency of directing light into the output waveguides rapidly decreases.
Also, as shown in Fig. 3(b), the ratio of power split between the two output waveguides is less sensitive to wavelength for a single layer of Si posts. In essence, this structure is a subwavelength diffraction grating for which all of the diffraction orders are evanescent except the reflected and transmitted zero orders, and the grating structure is tuned to direct equal power into these two orders.
4. Mach-Zender interferometer using hybrid bends and beamsplitters
As shown in Fig. 4, the single layer beamsplitter can be combined with the waveguide bend from Fig. 1(a) to form a compact (18 μm × 18 μm), high efficiency, planar Mach-Zender interferometer. For the particular simulation result shown in the figure (λ = 1.55 μm), the fraction of the incident optical power that is directed into the horizontal output waveguide is 97.8%, while only 0.6% is coupled into the vertical output waveguide and 0.08% is reflected back into the input waveguide.
As one would expect, simulation results show that arbitrary power splitting between the two output waveguides occurs when the optical path lengths of the two interferometer legs are changed by small shifts in the position of the bend elements. If a phase modulator is introduced in one leg of the interferometer, the overall interferometer footprint will be limited by the phase modulator length (for phase modulators with refractive index modulation of ~10-2 or less) rather than the size of the bend and beamsplitting regions.
In summary, CWGs augmented by small PhC regions offer a potential path to dramatically reduce the size of PLC components and thereby permit the realization of compact, highly integrated photonic circuits. An important next step in evaluating this path is to extend the 2D results presented in this paper to a 3-D analysis of CWG/PhC structures. Additional areas to address in future research include polarization dependence and fabrication approaches and tolerances.
This work was supported in part by DARPA Grant N66001-01-1-8938 and National Science Foundation Grant EPS-0091853.
References and links
1. See for example the special issue on photonic crystals in IEEE J. Quant. Elect.38 (2002).
2. H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. D. L. Rue, R. Houdre, U. Oesterle, C. Jouanin, and D. Cassagne, “Optical and Confinement Properties of Two-Dimensional Photonic Crystals” J. Lightwave Technol. 172063 (1999). [CrossRef]
3. S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs” Phys. Rev. B 628212 (2000). [CrossRef]
4. T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, and A. Sakai, “Light Propagation Characteristics of Straight Single-Line-Defect Waveguides in Photonic Crystal Slabs Fabricated Into a Silicon-on-Insulator Substrate” IEEE J. Quantum Electron. 38743 (2002). [CrossRef]
5. Y. Sugimoto, N. Ikeda, N. Carlsson, K. Asakawa, N. Kawai, and K. Inoue, “AlGaAs-Based Two-Dimensional Photonic Crystal Slab With Defect Waveguides for Planar Lightwave Circuit Applications” IEEE J. Quantum Electron. 38760 (2002). [CrossRef]
6. A. Adibi, Y. Xu, R. K. Lee, A. Yariv, and A. Scherer, “Properties of the Slab Modes in Photonic Crystal Optical Waveguides” J. Lightwave Technol. 181554 (2000). [CrossRef]
7. M. Loncar, T. Doll, J. Vuckovic, and A. Scherer, “Design and fabrication of silicon photonic crystal optical waveguides,” J. Lightwave Techn. 181402 (2000). [CrossRef]
8. A. Chutinan and S. Noda, “Waveguides and Waveguide Bends in Two-Dimensional Photonic Crystal Slabs”, Phys. Rev. B Condens. Matter 624488 (2000). [CrossRef]
9. S. Y. Lin, E. Chow, S. G. Johnson, and J. D. Joannopoulos, “Demonstration of highly efficient waveguiding in a photonic crystal slab at the 1.5- μm wavelength” Opt. Lett. 251297 (2000). [CrossRef]
10. A. Talneau, L. L. Gouezigou, and N. Bouadma, “Quantitative measurement of low propagation losses at 1.55 μm on planar photonic crystal waveguides” Opt. Lett. 261259 (2001). [CrossRef]
11. M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama, ”Structural Tuning of Guiding Modes of Line-Defect Waveguides of Silicon-on-Insulator Photonic Crystal Slabs” IEEE J. Quantum Electron. 38736 (2002). [CrossRef]
12. A. Talneau, L. L. Gouezigou, N. Bouadma, M. Kafesaki, C. M. Soukoulis, and M. Agio, “Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55 μm” Appl. Phys. Lett. 80547 (2002). [CrossRef]
13. H. Benisty, S. Olivier, C. Weisbuch, M. Agio, M. Kafesaki, C. M. Soukoulis, M. Qiu, M. Swillo, A. Karlsson, B. Jaskorzynska, A. Talneau, J. Moosburger, M. Kamp, A. Forchel, R. Ferrini, R. Houdre, and U. Oesterle, “Models and Measurements for the Transmission of Submicron- Width Waveguide Bends Defined in Two-Dimensional Photonic Crystals” IEEE J. Quantum Electron. 38770 (2002). [CrossRef]
14. S. Olivier, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, R. Houdre, and U. Oesterle., “Improved 60° Bend Transmission of Submicron-Width Waveguides Defined in Two-Dimensional Photonic Crystals” J. Lightwave Technol. 201198 (2002). [CrossRef]
15. Y. Sugimoto, N. Ikeda, N. Carlsson, K. Asakawa, N. Kawai, and K. Inoue, “Light-propagation characteristics of Y-branch defect waveguides in AlGaAs-based air-bridge-type two-dimensional photonic crystal slabs” Opt. Lett. 27388 (2002). [CrossRef]
16. S. Boscolo, M. Midrio, and T. F. Krauss, “Y junctions in photonic crystal channel waveguides: high transmission and impedance matching” Opt. Lett. 271001 (2002). [CrossRef]
17. O. Painter, A. Husain, A. Scherer, P. T. Lee, I. Kim, J. D. O’Brien, and P. D. Dapkus, ”Lithographic Tuning of a Two-Dimensional Photonic Crystal Laser Array” IEEE Photon. Technol. Lett. 121126 (2000). [CrossRef]
18. S. Y. Lin, E. Chow, S. G. Johnson, and J. D. Joannopoulos, “Direct measurement of the quality factor in a two-dimensional photonic-crystal microcavity” Opt. Lett. 261903 (2001). [CrossRef]
19. H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Beraud, and C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: Positive role of the substrate” Appl. Phys. Lett. 76532 (2000). [CrossRef]
20. W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, and D. D. Zutter, “Out-of-plane Scattering in Photonic Crystal Slabs” IEEE Photon. Technol. Lett. 13565 (2001). [CrossRef]
21. P. Lalanne and H. Benisty, “Out-of-plane losses of two-dimensional photonic crystals waveguides: Electromagnetic analysis” J. Appl. Phys. 891512 (2001). [CrossRef]
22. P. Lalanne, “Electromagnetic Analysis of Photonic Crystal Waveguides Operating Above the Light Cone” IEEE J. Quantum Electron. 38800 (2002). [CrossRef]
23. M. Tokushima and H. Yamada, “Light Propagation in a Photonic-Crystal-Slab Line-Defect Waveguide” IEEE J. Quantum Electron. 38753 (2002). [CrossRef]
24. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High Transmission through Sharp Bends in Photonic Crystal Waveguides” Phys. Rev. Lett. 773787 (1996). [CrossRef] [PubMed]
25. A. Sharkawy, S. Shi, and D. W. Prather, “Multichannel wavelength division multiplexing with photonic crystals” Appl. Opt. 402247 (2001). [CrossRef]
26. S. Olivier, C. Smith, M. Rattier, H. Benisty, C. Weisbuch, T. Krauss, R. Houdre, and U. Oesterle, “Miniband transmission in a photonic crystal coupled-resonator optical waveguide” Opt. Lett. 261019 (2001). [CrossRef]
27. A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method, (Artech House, Boston, Mass.,1995).
28. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994). [CrossRef]
29. P. S. J. Russell, T. A. Birks, and F. D. L. Lucas, “Photonic bloch waves and photonic band gaps” in Confined Electrons and Photonics: New Physics and Applications, E. Burstein and C. Weisbuch, eds. (Plenum Press, New York, 1995). [CrossRef]
30. M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap” Phys. Rev. B 62 10,696 (2000). [CrossRef]