Oct 15, 2000 - bulk-crystal photonic bandgap and a rich resonance structure. The calculated ... fundamental and an applied perspective, has been the.
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Single-mode transmission in two-dimensional macroporous silicon photonic crystal waveguides S. W. Leonard and H. M. van Driel Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario M5S 1A7, Canada
A. Birner* and U. Gösele Max-Planck-Institute of Microstructure Physics, Weinberg 2, D-06120 Halle, Germany
P. R. Villeneuve† Department of Physics and Center for Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, 02139 Received June 19, 2000 We report the infrared operation of a two-dimensional photonic crystal waveguide fabricated in silicon. Measurements of the transmission spectrum reveal a large transmission bandwidth within the 3.1 5.5-mm bulk-crystal photonic bandgap and a rich resonance structure. The calculated transmission spectrum for this structure is in good agreement with the measured spectrum and predicts a 10% single-mode bandwidth for the waveguide. © 2000 Optical Society of America OCIS codes: 230.7370, 130.2790.
Since the conception of photonic crystals more than a decade ago,1,2 considerable interest has been shown in these materials and their ability to mold the f low of light. One of the main goals of the f ield, from both a fundamental and an applied perspective, has been the demonstration of single-mode light propagation in photonic crystal waveguides on a micrometer scale. If a linear defect is incorporated into a crystal, propagating modes confined within the defect can be created for frequencies within the photonic bandgap. A defect can therefore act as a waveguide, with the confinement achieved by means of the photonic bandgap and not by total internal ref lection as in traditional waveguides. Single-mode photonic crystal waveguides are expected to be one of the key elements of the all-optical microchip. Following initial theoretical predictions of photonic crystal waveguides,3,4 experiments in the microwave regime5,6 demonstrated waveguide confinement and efficient transmission around sharp bends. However, to achieve the goal of an infrared optical circuit constructed from single-mode photonic crystal waveguides it is necessary to fabricate photonic crystal waveguides on a micrometer scale and make detailed measurements of their transmission characteristics. A step toward this goal was recently taken by Hanaizumi et al.,7 Baba et al.,8 and Tokushima et al.,9 who performed experiments in the infrared that demonstrated evidence of propagation in photonic crystal waveguides. However, although these studies provided an interesting demonstration of waveguiding, because of the low coupling eff iciency and the fact that the transmission spectrum lacked quantitative detail they did not address single-mode guidance. Our photonic crystals were fabricated in macroporous silicon by the well-known techniques described in Refs. 10– 12. Lithography and alkaline etching were used to create pore nuclei in n-type silicon that were arranged in a two-dimensional triangular lattice with pitch a 苷 1.5 mm. After etching, 0146-9592/00/201550-03$15.00/0
cylindrical pores with radius r 苷 0.45 mm and a typical length of 100 mm were formed, inheriting the triangular order of the nuclei. The pore radius was widened by oxidation and wet-chemical etching to produce pores of radius r 苷 0.64 mm. By leaving out a row of etch pits during the prepatterning stage we created a line defect in the crystal, forming a 1.1-mm thin waveguide cladded by the surrounding crystal. Figure 1 shows a typical scanningelectron-microscope image of a microstructured photonic crystal bar, with a waveguide oriented in the G K direction. The pores adjacent to the waveguide had a radius of r 苷 0.75 mm and were slightly enlarged relative to the bulk crystal pores because of a local increase in a charge density (during etching, no carriers are consumed at the waveguide). The sample was mounted between two brass bars, and the cleaved edges of the substrate were coated with silver paint to prevent anomolous transmission within the substrate. The length of the waveguide used in the experiment was 27 mm (i.e., 18a). To couple light into the narrow waveguide (with a subwavelength width) with reasonable efficiency, we required a spatially coherent source of mid-IR light. A parametric source13 was used to produce a beam tunable from 3 to 6 mm, containing 200-fs pulses at a repetition rate of 250 kHz and a typical bandwidth of approximately 200 nm. The H -polarized beam was focused onto the sample by a 19-mm focal-length ZnSe lens to a spot size of approximately 25 mm. Because the waveguide width was 1.1 mm, this spot size provided a maximum coupling eff iciency of approximately 2%.14 The transmitted light was passed through a monochromator, chopped, and detected with a pyroelectric detector and a lock-in amplif ier. The transmission is defined as the ratio of the transmitted power to the total power incident upon the sample. Figure 2(a) shows the transmission spectrum of the G K-oriented waveguide. It was measured in 10 spectral segments, each corresponding to a different © 2000 Optical Society of America
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even and odd symmetry are shown by solid and dotted curves, respectively (the symmetry is def ined with respect to the vertical plane in the waveguide center, parallel to its axis). The shaded areas denote a continuum of modes and correspond to the projected band structure of the bulk crystal, where the propagating modes are no longer localized. As the incoming light has even symmetry, it couples only to the even waveguide modes. From Fig. 3 one observes that the even-mode transmission is single mode over a large spectral region that spans 0.37 , f , 0.46 c兾a. This observation is corroborated by the even spacing of the peaks in the measured and the calculated transmission spectra. However, to claim that the waveguide is single mode implies that only one mode, even or odd, exists over a given
Fig. 1. Microstructured bar of macroporous silicon photonic crystal with a waveguide oriented in the G K direction. The triangular lattice of air pores cladding the waveguide has a pitch of 1.5 mm and a depth of 100 mm. The wider areas of the bar provide mechanical stability when the structure is capped from above to prohibit extraneous transmission. The pores assume a cylindrical cross section within a depth of approximately 1 mm from the surface. The sample used for transmission experiments had larger pore radii than the sample shown in these images.
tuning range of the parametric source. Because of differences in spot size, alignment, and collection efficiency, the nomalization of neighboring segments could not be standardized. The spectrum exhibits a detailed structure of Fabry – Perot resonances with a transmission bandwidth nearly covering the entire width of the bulk-crystal photonic bandgap, which lies in the wavelength range 3.3 , l , 5.5 mm (the stop band in the G K direction lies in the range 3.1 , l , 5.5 mm, as was experimentally confirmed). The Fabry – Perot resonances arise from multiple ref lections of Bloch modes at the waveguide facets. The maximum finesse is 3.4 6 0.2, and the highest peak transmission is 2.2%. The calculated H -polarized transmission spectrum for a waveguide with a length of 18a is shown in Fig. 2(b). The r兾a parameters were taken to be 0.43 for the bulk-crystal pores and 0.50 for overetched pores adjacent to the waveguide, in agreement with measured waveguide parameters. The results exhibit the same resonance structure and broad bandwidth as the measured spectrum.15 The calculated free spectral range of 1.34 6 0.04 THz is in excellent agreement with the measured value of 1.30 6 0.04 THz. The fact that the measured finesse compares well with (and in some spectral regions exceeds) the calculated finesse indicates that the losses are small. Many of the features of the transmission spectrum can be understood in terms of the waveguide band structure17,18 shown in Fig. 3. Guided modes with
Fig. 2. (a) Measured and (b) calculated H -polarized transmission spectrum of the waveguide shown in Fig. 1 with a length of 18a.
Fig. 3. Computed H -polarized band structure of the waveguide shown in Fig. 1. Solid and dotted curves correspond to even and odd modes, respectively. The bands at the right (labeled with arrows) appear to be due to the overetched pores on either side of the waveguide. The shaded areas correspond to the projected band structure of the bulk photonic crystal.
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spectral range. The band structure reveals that, for 0.37 , f , 0.41 c兾a, there exists only a single, even mode and no odd modes. Of course, it is difficult to prove experimentally that, of an infinite variety of odd-order incident beam prof iles, none of them would experience transmission. However, based on the agreement between the calculated and the measured transmission spectra, we infer a large 10% single-mode bandwidth for the waveguide. Further corroboration of the agreement between theory and experiment is provided by the existence of an even-mode waveguide bandgap at a frequency near 0.45 c兾a, which can be observed in Fig. 2 as a stop band. The resonant structure can be understood in terms of multiple ref lections of Bloch modes at the waveguide facets. As described in Ref. 19, the resonances satisfy the condition 2Nka 苷 2mp, where N is the number of pores along the length of the waveguide and m is an integer. The resonances have a constant wave-vector spacing of Dk 苷 p兾Na, and there are N 1 1 resonances that occur when the Brillouin zone boundary is reached at p兾a. Therefore there are N 1 1 resonances per band, and we would expect to observe 19 resonances for the complete band in Fig. 3. However, only 11 peaks are counted in the transmission spectrum of this band, which lies in the frequency range 0.36 0.44 c兾a [see Fig. 2(b)]. The reason for the smaller number of peaks is that the band f lattens at k 苷 11p兾18a, resulting in the accumulation of the remaining seven peaks in a narrow spectral range. Our results indicate that photonic crystal waveguides can effectively confine and guide light on a micrometer scale. To create an optical chip with a network of such waveguides will require further study of the eff icient propagation of light around bends and the use of an additional vertical confinement mechanism to provide total mode confinement. If bends were introduced into the two-dimensional waveguides studied here, coupling between even and odd modes would likely occur. However, within the spectral region 0.37 , f , 0.41 c兾a, the absence of odd modes would preserve single-mode operation. Furthermore, this single-mode bandwidth of 10% is much larger than the current optical communications bandwidth of 2%. We also note that, even though these waveguides were designed with a thick cladding layer of bulk crystal, it was shown recently13 that only a few crystal rows are necessary for a high degree of conf inement. Finally, we point out that one can easily avoid the resonant spectral structure and the diffraction losses by eliminating the waveguide facets, i.e., by connecting the waveguide to other optical circuit elements directly. In summary, we have measured the H -polarized transmission spectrum of a two-dimensional photonic crystal waveguide fabricated in macroporous silicon. The spectrum showed a detailed structure of Fabry– Perot resonances and a large transmission bandwidth. Calculations of the transmission spectrum and band structure accurately accounted for many of the observed features and predicted a 10% single-mode bandwidth. The results demonstrate the feasibility of single-mode photonic crystal waveguides operating in the infrared.
Part of this research was funded by the Natural Sciences and by the Engineering Research Council of Canada and Photonics Research Ontario. Financial support by the Deutsche Forschungsgemeinschaft (project GO 704兾2-1) is acknowledged by A. Birner. S. W. Leonard’s e-mail address is leonard@physics. utoronto.ca. *Present address, Infineon Technologies AG, Königsbrücker Strasse 180, D-01099 Dresden, Germany. † Present address, Clarendon Photonics, Inc., Suite 724, 100 Boylston Street, Boston, Massachusetts 02116. References 1. S. John, Phys. Rev. Lett. 58, 2486 (1987). 2. E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987). 3. R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Olerhand, D. A. Smith, and K. Kash, J. Appl. Phys. 75, 4753 (1994). 4. A. Mekis, J. C. Chen, I. Kurland, S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996). 5. S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, Science 282, 274 (1998). 6. B. Temelkuran and E. Ozbay, Appl. Phys. Lett. 74, 486 (1999). 7. O. Hanaizumi, Y. Ohtera, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 777 (1999). 8. T. Baba, N. Fukaya, and J. Yonekura, Electron. Lett. 35, 654 (1999). 9. M. Tokushima, H. Kosaka, A. Tomita, and H. Yamada, Appl. Phys. Lett. 76, 952 (2000). 10. V. Lehmann, J. Electrochem. Soc. 140, 2836 (1993). 11. U. Grüning, V. Lehmann, S. Ottow, and K. Busch, Appl. Phys. Lett. 68, 747 (1996). 12. A. Birner, U. Grüning, S. Otto, A. Schneider, F. Müller, V. Lehmann, H. Foll, and U. Gösele, Phy. Status Solidi A 165, 111 (1998). 13. S. W. Leonard, H. M. van Driel, K. Busch, S. John, A. Birner, A. P. Li, F. Müller, U. Gösele, and V. Lehmann, Appl. Phys. Lett. 75, 3063 (1999). 14. This transmission is less than that obtained with an estimate based on the measured spot size of 25 mm and a waveguide width of 1.1 mm (the approximate distance between pores adjacent to the waveguide), which gives a transmission of 4.8%. The transmission deficit is attributed to the clipping of the beam by the substrate and to diffraction losses in the emergent beam. 15. The difference between the calculated and the measured spectral envelopes is caused by imperfect normalization of the experimental data and also by a difference in the termination of the crystal at the waveguide facets, which was recently shown16 to have a signif icant effect on the transmission spectrum. 16. J. Yonekura, M. Ikeda, and T. Baba, IEEE J. Lightwave Technol. 178, 1500 (1999). 17. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995). 18. A. Mekis, S. Fan, and J. D. Joannopoulos, Phys. Rev. B 58, 4809 (1998). 19. D. Labilloy, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, R. Houdré, and U. Oesterle, Phys. Rev. B 59, 1649 (1999).
