3034 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 33, NO. 14, JULY 15, 2015 Silica-Clad Silicon Photonic Crystal Waveguides for Wideband Dispersion-Free Slow Light Takuya Tamura, Keisuke Kondo, Yosuke Terada, Yosuke Hinakura, Norihiro Ishikura, and Toshihiko Baba, Member, IEEE Abstract We comprehensively calculated the photonic bands of the waveguide modes in practical lattice-shifted photonic crystal waveguides, which are completely cladded by silica. We assumed various lattice shifts and found that the shift of the second rows and the mixed shift of the first and third rows along the waveguide generate low-dispersion slow light with group indices of 34 36, which is higher than those with a conventional shift of the third rows, maintaining a wide bandwidth over 10 nm at telecom wavelengths. We fabricated the waveguides using a CMOS-compatible process and confirmed correspondence with the calculation results. We also compared 25-Gb/s photonic crystal slow light Mach Zehnder modulators and confirmed the improvement of the modulation efficiency by second-row shifts. Index Terms Mach Zehnder modulator, photonic band, photonic crystal, silica clad, silicon photonics, slow light. I. INTRODUCTION PHOTONIC crystal (PC) waveguides consisting of a line defect in a high-index slab with hole arrays (PC slab) have been extensively studied for generating wideband lowdispersion (LD) slow light, which achieves slow propagation of short optical pulses, nonlinear enhancement, and size reduction of optical modulators [1] [5]. The LD slow light arises from partial distortion of the photonic band of the main waveguide mode, which is induced by local modulations of hole diameters and/or lattice points in a photonic crystal slab [6] [12] We have studied both types of modulations and mostly employed the latter for easier fabrication, calling it a lattice-shifted photonic crystal waveguide (LSPCW). In particular, we have employed the shift of the third rows along the line defect, because this shift produces a band distortion with a small shift in wavelengths of slow light. In other words, it is easy to set the wavelength range to target values experimentally. In recent years, using silicon (Si) photonics CMOS- compatible processes has become common worldwide, and we can fabricate LSPCWs with air cladding (i.e., air-bridge structure suspended on pedestals) and silica (SiO 2 ) cladding on a siliconon-insulator (SOI) wafer using this process [1], [13]. Moreover, with the air-clad design it is easy to obtain a high group index, Manuscript received February 22, 2015; revised April 1, 2015; accepted April 3, 2015. Date of publication April 6, 2015; date of current version June 3, 2015. This work was supported by New Energy and Industrial Technology Development Organization. The authors are with the Department of Electrical and Computer Engineering, Yokohama National University, Hodogaya-ku, Yokohama 240-8501, Japan (e-mail: tamura-takuya-nt@ynu.jp; kondo-keisuke-vs@ynu.jp; yterada@ynu.ac.jp; hinakura-yosuke-zm@ynu.jp; ishikura-norihiro-hv@ynu.jp; baba@ynu.ac.jp). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JLT.2015.2420685 Fig. 1. Structure and parameters of LSPCW. Left is the top view and right the cross-sectional view. Thick lines depict single cell model for photonic band calculation. i.e., n g > 50, with maintaining a bandwidth Δλ,forthe±10% change in n g, of wider than 10 nm at telecom wavelengths, because the strong optical confinement of the air-clad structure allows large design flexibility in LD slow light [4]. Therefore, such LSPCWs have been widely used in fundamental experiments even though they are typically not fabricated by CMOScompatible processes. In contrast, weaker optical confinement of waveguides clad with SiO 2 only achieves n g 20 when the third-row shifted LSPCW is used [1]. The extended light cone that couples with radiation modes in the SiO 2 cladding severely restricts the waveguide mode and n g of LD slow light. However, SiO 2 clad waveguides are more preferable in practical devices, because they are much more mechanically and chemically stable and the CMOS-compatible process is easier to apply. Recently, we have developed Si Mach Zehnder (MZ) modulators consisting of p/n-junction-loaded LSPCW phase shifters covered with SiO 2 cladding using a 180-nm CMOS-compatible process. Here, the phase shift is enhanced by a large n g of slow light in the LSPCW. By employing 200-μm-long phase shifters and an interleaved p/n junction giving efficient overlap with the waveguide mode, we succeeded in demonstrating 25-Gb/s operation with a passive insertion loss of 5 db, modulation loss of 0.8 db, drive voltage V pp =1.75 V, and extinction ratio ER =3dB. However, the large capacitance of the interleaved junction and electrical resistance of the LSPCW limit the frequency response and speed of operation. Reducing the capacitance would solve the problem, but it also reduces the phase shift and degrades all other performance metrics. Another candidate solution is to increase n g ; 40-Gb/s operation while maintaining the above ER will be possible if n g =35, which is difficult to achieve with the third-row-shifted LSPCW. Therefore, we have comprehensively investigated various lattice shifts in the SiO 2 -clad LSPCW to find a structure with such ahighn g. Here, we have imposed one constraint that is the 0733-8724 2015 IEEE. 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TAMURA et al.: SILICA-CLAD SILICON PHOTONIC CRYSTAL WAVEGUIDES FOR WIDEBAND DISPERSION-FREE SLOW LIGHT 3035 Fig. 2. (a) Calculated photonic bands with no lattice shifts and (b) modal magnetic fields in the y direction at points A D. Here, 2r = 212 nm (2r/a =0.531). The gray area shows the SiO 2 light cone. Closed circles show the main waveguide mode, and open circles show higher order modes and slab modes. In the modal fields, profiles in the unit cell every five time steps are aligned. minimum inter-hole spacing, which is modified by the lattice shifts, should satisfy the process rule in the 180-nm CMOScompatible process, such that the spacing must be no smaller than 140 nm. This constraint could be relaxed using a more advanced 90 130 nm process, but it would increase the production cost. In this paper, we first present the photonic band of the waveguide mode, and its n g and Δλ for lattice shifts at different rows and in the different directions. We discuss the behaviors of bands and optimization toward larger n g with a sufficient Δλ. Then, we compare the calculated results with the experimental ones for a LSPCW fabricated by 180-nm CMOS-compatible process. Finally we report its application to a MZ modulator, which exhibits better performance because of the high n g. II. CALCULATION AND DESIGN Photonic bands were calculated for a single cell model of the LSPCW, as shown in Fig. 1. Here, we used a threedimensional finite-difference time-domain method in which a periodic boundary condition was applied to the longitudinal direction (z direction) and a perfectly matched layer condition to the lateral directions (x and y directions) [14]. The thickness of the Si layer (index n =3.43) was set to 210 nm, which corresponds to the experimental value, as shown later. For this thickness, we set the Yee cell size to 21 nm and the time step Δt =0.039 fs so as to satisfy the Courant stability condition. Regarding holes of the photonic crystal slab, various complicated shapes and/or lattices have been studied to date [6] [12]. However, it is the easiest to achieve an accurate shape with circular holes, and the requirement for the inter-hole spacing is the most relaxed for a triangle lattice. Thus, we assumed circular holes with a diameter 2r and a triangular lattice with lattice constant a = 399 nm, which is an integer multiple of the Yee cell size. For 2r, we first set a value, then count the number of Yee cells inside one hole to calculate the hole area S, and finally estimate the actual 2r from 2 S/π. Fundamentally, the waveguide comprises one line defect, and one pair of rows, similarly separated from the line defect, were shifted. Let us define the amount of longitudinal and lateral shifts in first to fourth rows to be s z1 s z4 and s x1 s x4, respectively. We also defined Δw as a small increment of the line defect. We assumed SiO 2 (n =1.444) as the medium above and below the Si layer and inside the holes. The total thickness of the model in the y direction, t all, is 2394 nm, and the total number of hole rows is 11 on each side of the line defect so that the modal evanescent field converges sufficiently. An excitation was applied to the electric field vector oriented inside the xz plane at the center of the slab (TElike polarization). The number of time steps is set to 131 072, which corresponds to the wavelength resolution of 1.377 nm. This resolution creates an error in the calculated bands. Therefore, we approximated them by a sixth-order function using the least squares method. The n g spectrum was calculated from n g = c(dk/dω), where c is the vacuum velocity of light, k is the wavenumber, and ω is the frequency. Fig. 2 shows the total view of the photonic bands of the main guided mode (closed circles), higher order mode and slab modes (open circles) and their field profiles, assuming 2r = 212 nm (2r/a =0.531). The guided mode band is formed by the anticrossing of a steep index-guided mode band (blue line), which is folded back into the Brillouin zone at the band edge and a Bragg-guided mode band (red line), which is flatter than the index-guided mode band [15], [16]. As observed in the field profiles, point A on the index-guided mode band penetrates broadly into the photonic crystal with a relatively slow exponential decay. On the other hand, point C on the Bragg-guided mode band penetrates a shorter distance and exhibits a standing wave oscillation in the lateral direction. Point B exhibits an intermediate stage between these two profiles. As mentioned above, LD slow light is generated in the guided mode band distorted by the frequency shift of the slab mode band below the waveguide mode band in the presence of some lattice shifts.
3036 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 33, NO. 14, JULY 15, 2015 Fig. 3. Longitudinal shift models (left), photonic bands (center), and n g spectra (right) for 2r = 212 nm (2r/a =0.531). Solid and dashed lines show the conditions that do and do not satisfy the requirement for inter-hole spacing, respectively. Gray area shows SiO 2 lightcone, and n g spectra for bands in this area are eliminated. The n g spectra near the band edge are also eliminated, because the bands near the band edge exhibit the delicate behaviors but they are outside the scope of this study. Fig. 4. n g, Δλ, and NDBP for first- and third-row shifts. Other details are the same as for Fig. 3. Next, let us focus on the guided mode band and its changes for longitudinal shifts. The guided mode band and n g spectrum for the same 2r are shown in Fig. 3(a) (d). With no lattice shifts (black line), the band slopes toward the band edge and n g increases monotonically from 20 to 40 followed by a rapid increase at the band edge. This behavior is different from the air clad case, where n g is mostly unchanged but has a rapid increase near the band edge. The band slope with the SiO 2 cladding is due to the smaller index contrast that gives a narrower photonic band gap, resulting in weaker band flattening. When the first rows are
TAMURA et al.: SILICA-CLAD SILICON PHOTONIC CRYSTAL WAVEGUIDES FOR WIDEBAND DISPERSION-FREE SLOW LIGHT 3037 Fig. 5. Lateral shift models (left), and photonic bands (center) and n g spectrum (right). Shifts in the direction away from line defect are defined as positive and shown by red lines, while in opposite direction negative and shown by blue lines. Other details are the same as for Fig. 3. Fig. 6. Photonic bands (upper) and n g spectra (lower) after final optimization. Gray areas in n g spectrum show LD bands. shifted, the band edge with the mode profile more concentrated into the line defect moves to the high frequency side. Because the steeper band near the light cone shifts very slightly, the band becomes flatter and a narrow LD band is produced with a high n g. Conversely, for the conventional third-row shifts, the band near the light cone that exhibits a deep mode penetration moves, and a wide LD band appears with a relatively low n g. The second-row shifts show more balanced results, i.e., the band edge and the region near the light cone move together and the central part also moves, largely producing a wide LD band with
3038 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 33, NO. 14, JULY 15, 2015 Fig. 7. Scanning electron micrograph of fabricated Si LSPCW with longitudinal shifts in second rows. Top SiO 2 cladding is removed. a larger n g. The fourth-row shifts are too far from the line defect and do not result in a significant change unless the shift amount is particularly large. Meanwhile, the second-row shifts are identical to simultaneous and equal shifts of the first and third rows if we only look near the line defect. Therefore, we expect that such mixed shifts move bands similar to the second-row shifts. The calculation results in Fig. 3(e) have similar behaviors to those in Fig. 3(b). If the band edge and the region near the light cone are controlled independently by the shifts to the first and third rows, respectively, the linearity of the LD band will be improved and n g and Δλ can be maximized. To investigate this, we calculated n g, Δλ, and normalized delay-bandwidth product NDBP n g (Δλ/λ), which is often used as a figure-of-merit of slow light [3] for various s z1 and s z3, as shown in Fig. 4. Here, the bandwidth Δλ is defined as the range where the change of n g is within ±10% as mentioned above. The color maps exhibit complex distributions, but we can see that n g and Δλ have a trade-off relationship, and optimum shifts are determined by the parameter that one considers more important. The highest NDBP is given by s z1 = 120 nm and s z3 =90nm. Similarly, in Fig. 5, calculation results for the lateral shifts are shown. Note that the positive and negative shifts are equivalent in the longitudinal shifts; however, they are not equivalent in the lateral shifts. When the first or second rows are shifted, the band moves entirely, because the lateral shift changes the effective core width of the waveguide, and so the modal equivalent index. With these lateral shifts, the Bragg-guided mode is influenced more directly than with longitudinal shifts. Because the central part does not move with the longitudinal shifts, the LD band does not appear. Negative shifts of the third rows show a wide LD band; however, n g > 30 cannot be obtained, because the band edge does not move at all. Furthermore, this condition is close to the requirement for inter-hole spacing. For the fourth row positive shifts, the band edge and the region near the light cone moves, whereas the central region does not. Such behaviors form a flat band, which generates dispersion compensated (DC) slow light, although it does not satisfy the requirement for interhole spacing. All the above results indicate that the longitudinal first-row shifts are suitable for n g > 40 and Δλ 5 nm; the second-row shifts for n g > 30 and Δλ 10 nm; and the thirdrow shifts for n g > 20 and Δλ 15 nm. The lateral thirdrow shifts exhibit similar values, but fabrication will be more difficult. They also indicate that the longitudinal second-row shifts and mixed shifts of the first and third rows are promising approaches for our current purpose. As the final step, we optimized these two structures so as to give a larger n g and/or wider Δλ, by fine tuning 2r and adjusting Δw, as shown in Fig. 6. In (a) and (b), we assumed s z2 =0.21a and a =84nm. In (a), n g 20 is obtained with Δλ =26nm by reducing 2r, which shifts the band edge to the low frequency side. Although this n g is smaller than our target, such a wide Δλ will be useful for covering most of the C band at telecom wavelengths (λ = 1530 1565 nm). The NDBP n g (Δλ/λ) is 0.33, which is 1.65-fold higher than that for conventional thirdrow shifts. In (b), 2r is not changed, whereas Δw is adjusted and n g =35, Δλ =12nm, and n g (Δλ/λ) =0.27 are obtained, which satisfy our targets. In (c) (e), we employ mixed shifts and additional Δw.In(c),n g 40, Δλ =12nm and n g (Δλ/λ) = 0.31, which is better than second-row shifts. In (d) and (e), Δλ is as narrow as 5 and 3 nm, while n g is as high as 54 and 68 (n g (Δλ/λ) =0.17 and 0.13), respectively. III. EXPERIMENT The calculation results indicate that optimized structures are the second-row shifts and the mixed shifts of the first and third rows. In this study, we fabricated the former by a 180-nm Si CMOS-compatible process [1], as shown in Fig. 7. We did not fabricate the latter because the latter needs two variable parameters for optimization while the wafer area we could use for this study was limited. We rather fabricated the conventional third-row shifts simultaneously for comparison. The Si layer is 210 nm thick and each of the SiO 2 layers above and below Si are 2 μm thick. Because the fabrication area assigned for this study was limited in the wafer, we fixed a = 400 nm, and only prepared two 2r = 200 and 210 nm samples, taking fabrication errors into consideration. For second-row shifts, we also set Δw =30nm and s z2 =70, 80, and 90 nm. For third-row shifts, we set Δw =0and s z3 =80, 105, and 135 nm. The n g spectrum was measured by modulation phase shift method [17], as shown in Fig. 8. As s z2 increased, the n g spectrum is gradually flattened and a wide LD band appeared. At 2r = 200 nm and s z2 =90nm, n g =34and Δλ =16nm were obtained, which agrees approximately with the calculation in Fig. 6(b). When 2r is increased to 210 nm, n g increases to 40 with Δλ decreasing to 7 nm. These results differ from the behaviors for third-row shifts; n g is decreased gradually as s z3 is increased. The second-row shifts give 1.7-fold higher n g than that of the third-row shifts for the same bandwidth Δλ =16nm, which also agrees with calculation results. Let us briefly discuss the influence of fabrication errors, which mainly occur in hole diameter. As observed in Fig. 8(a), 10 nm change in hole diameter significantly changes the n g spectrum. The accuracy in absolute operating wavelength is similarly severer; 10-nm change in hole diameter results in a 15 20 nm error in the wavelength, which completely shifts the slow light band. Therefore, the target accuracy of the hole diameter will be less than 5 nm, which can be achieved by optimizing the lithography, optimizing the diameter.
TAMURA et al.: SILICA-CLAD SILICON PHOTONIC CRYSTAL WAVEGUIDES FOR WIDEBAND DISPERSION-FREE SLOW LIGHT 3039 Fig. 8. Measured n g spectrum (wavelength resolution is 0.6 nm.) for longitudinal shifts. (a) Second-row longitudinal shifts, (b) Third-row shifts. Fig. 9. MZ modulator structure (a) Structure with linear p/n junction. (b) Eye pattern for device with the second-row shifted LSPCW. (c) That for the third-row shifted LSPCW. As first mentioned the current target is to use the high n g for MZ modulators. In general, the efficiency of the phase shifter is considered to increase in proportion to n g, although the overlap of the modal field with the p/n junction further modifies it [18]. Therefore, we compared the second- and third-row shifts in MZ modulators of Fig. 9(a). Because of the limited area available in this fabrication, the phase shifter length was shortened to 90 μm. Other details are the same as those in Ref. [18]. We applied a 25-Gb/s non-return-to-zero pseudo-random-bit-sequence signal voltage of V pp =1.75 V and V DC = 0.9 V from a pulse pattern generator (Anritsu MP1800A) to the RF electrodes under push pull configuration, and observed the modulated light output using a sampling oscilloscope (Keysight 86100C). Fig. 9(b) and (c) show the eye patterns observed for the second- and third-row shifts, respectively. Neglecting the large noise caused by the short phase shifters, the second-row shifts obviously exhibit a clearer open eye. For this device, ER =3.2 db at ML = 4.2 db, which is better than ER =2.9 db at ML =6.8 db obtained for the third-row shifts. The phase shift estimated from these values based on the calculation in Ref. [18] is 0.136π and 0.090π for the second- and third-row shifts, respectively, and the enhancement is 1.5 times. This agrees well with the enhancement of n g, which means that the modal field overlaps with the p/n junction are comparable between these lattice shifts. IV. CONCLUSION Aiming at improving SiO 2 -clad Si photonic crystal waveguide MZ modulators, we investigated lattice-shifted structures that generate wideband low-dispersion slow light with a group index n g higher than 30. We found that second-row longitudinal shifts and mixed longitudinal shifts of the first and third rows give such high n g and a bandwidth Δλ over 10 nm at telecom wavelengths, which corresponds to the 1.5-fold enhancement
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Yokohama, Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs, Phys. Rev. Lett., vol. 87, no. 25, p. 253902, 2001. [16] A. Yu. Petrov, and M. Eich, Zero dispersion at small group velocities in photonic crystal waveguides, Appl. Phys. Lett., vol. 85, no. 21, pp. 4866 4868, 2004. Takuya Tamura received the B.E. degree from the Department of Electrical and Computer Engineering, Yokohama National University, Yokohama, Japan, in 2014, where he is currently working toward the M.D. degree in the same university. He has been working on the design of photonic crystal slow light waveguides. He is a Member of the Japan Society of Applied Physics (JSAP). Keisuke Kondo received the B.E. and M.E. degrees from the Department of Electrical and Computer Engineering, Yokohama National University, Yokohama, Japan, in 2012 and 2013, respectively, where he is currently working toward the Ph.D. degree in the same university. He has studied copropagating slow light pulses, receiving the Research Fellowship from JSPS. He is a member of JSAP. Yosuke Terada received the B.E., M.E., and Ph.D. degrees, all from the Graduate School of Arts and Sciences, University of Tokyo, Tokyo, Japan, in 2007, 2010, and 2013, respectively. During his Ph.D., he focused mainly in material physics on Ge light emitters. He is currently working toward Si photonic crystal slow light modulators. He is a Member of JSAP. Yosuke Hinakura received the B.E. degree from Yokohama National University, Yokohama, Japan, in 2015. He has studied Si photonic crystal slow light modulators. He is currently working toward Si photonic crystal optical modulators as a master course student in the same university. He is a Member of JSAP. Norihiro Ishikura received the B.E., M.E., and Ph.D. degrees, all from the Department of Electrical and Computer Engineering, Yokohama National University, Yokohama, Japan, in 2009, 2011, and 2014, respectively. During his Ph.D., he focused mainly on Si photonics slow light devices fabricated by CMOS-compatible process, and for this he received the Research Fellowship from JSPS. He is currently working with Fujikura Ltd. He is a Member of JSAP. He received the Paper Award at MOC 2011. Toshihiko Baba (M 93) received the Ph.D. degree from the Division of Electrical and Computer Engineering, Yokohama National University (YNU), Japan, in 1990, respectively. Then he became a Research Associate of Tokyo Institute of Technology in 1990, and an Associate Professor and a Full Professor of YNU in 1994 and 2005, respectively. He has studied ARROWwaveguides, VCSELs, photonic crystals, Si photonics and bio-sensing. He is the coauthor of more than 170 papers. He is a Member of JSAP, IEICE and OSA. He received 14 academic awards including IEEE/LEOS Distinguished Lecturer in 2006/2007.