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We demonstrate that one can meet numerous commercial requirements for filters used in dense wavelength-division multiplexing applications using quadruple Vernier racetrack resonators in the silicon-on-insulator platform. Experimental performance shows a ripple of 0.2 dB, an interstitial peak suppression of 39.7 dB, an adjacent channel isolation of 37.2 dB, an express channel isolation of 10.2 dB, and a free spectral range of 37.52 nm.
© 2013 Optical Society of America
1. Introduction
The Vernier effect has been used extensively in the research community to expand the free spectral range (FSR) in ring resonators, and has been demonstrated both theoretically [1–10] and experimentally [11–28]. Ideally, one would like a box-like drop port spectral response, which can be achieved using series-coupled ring resonators [22]. Increasing the number of series-coupled rings, allows one to increase the clear window (channel bandwidth) and thus the data rate that the filter can handle. However, to date, no one has experimentally demonstrated the Vernier effect in more than three series-coupled rings and no one has experimentally shown whether series-coupled Vernier ring resonators can be used to meet typical commercial filter requirements. Timotijevic et al.[20] demonstrated double Vernier silicon-on-insulator (SOI) series-coupled ring resonators which had an FSR larger than the span of the C-band but minimal interstitial peak suppression (IPS). Fegadolli et al.[17] fabricated thermally tunable double Vernier SOI series-coupled ring resonators exhibiting the Vernier effect in the through port and drop port. Mancinelli et al.[21] used double Vernier SOI series-coupled resonators that had an extended FSR of 20 nm. Prabhathan et al.[16] fabricated double SOI cascaded ring resonators exhibiting the Vernier effect at the drop port for use as a thermally tunable wavelength selective switch. The authors’ device had an FSR of approximately 50 nm and a drop port out-of-band extinction greater than 15 dB [16]. However, ring resonators in cascaded configurations only exhibit the Vernier effect in the drop port response and not the through port response [11]. Yanagase et al.[22] have shown triple-ring resonators exhibiting the Vernier effect, where the coupling was done vertically and the material used for the waveguides was Ta2O5-SiO2. However, their devices show minimal IPS and their extended FSR was less than the span of the C-band. Also, they do not show the through port responses. Previously published research, both experimental and theoretical, show the benefit (FSR expansion) of using the Vernier effect within series-coupled ring resonators, as compared to the case where each resonator is identical, but minimal research has been done regarding meeting commercial requirements as regards to the IPS (see [3, 4, 10, 19]). Here, we experimentally demonstrate that it is, in fact, possible to meet many commercial requirements when using quadruple SOI series-coupled racetrack resonators exhibiting the Vernier effect including the necessary IPS. The commercial requirements that are met are the drop port ripple (Rdepth), the drop port adjacent channel isolation (Ai), the drop port non-adjacent channel isolation (nAi), and the express channel isolation (ECi). It should be noted that the ECi has the same definition as the through port channel extinction ratio and pass channel residual at express port. The IPS is similar to that of the nAi, however, since our device involves the Vernier effect there are multiple peaks between two dominant resonant peaks and, thus, it is important that the IPS meets the commercial specification for the nAi. The target specifications come from commercial dense wavelength-division multiplexing (DWDM) data sheets [29–31].
2. Theory
A schematic of our quadruple series-coupled racetrack resonators exhibiting the Vernier effect is shown in Fig. 1 which is similar to that found in [2–4] (same arrangement of the resonators but different resonator lengths, field transmission and coupling factors, and propagation loss). Here, La, Lb, Lc, and Ld are the total lengths of racetrack resonators a, b, c, and d, respectively. Ly is the length of the straight coupling regions, r is the radius of the racetrack resonators, and L is the length of the straight sections (other than those in the coupling regions) for racetrack resonators c and d. α is the total field loss coefficient for the racetracks resonators. κ1, κ2, κ3, κ4, and κ5 are the symmetric (real) point field coupling factors. t1, t2, t3, t4, and t5 are the straight through (real) point field transmission factors.
Fig. 1 Schematic of our quadruple series-coupled racetrack resonators exhibiting the Vernier effect.
The following assumptions are made for the design: La,b = 2πr+2Ly and Lc,d = (4/3)La,b = 2πr+2L+2Ly, where r = 5 μm, Ly = 7 μm and L = 7.569 μm. κ1 = κ5, κ2 = κ4, t1 = t5, and t2 = t4. The waveguides are strip waveguides with a top silicon dioxide cladding having widths and heights of 502 nm and 220 nm, respectively. The propagation loss for each ring was assumed to be 2.4 dB/cm [32]. The modeling and analysis of the quadruple Vernier racetrack resonator was done using a mixture of numeric and analytic methods. Specifically, the effective index of the strip waveguides and the field coupling and transmission factors were determined using MODE Solutions by Lumerical Solutions, Inc., and everything else was done analytically. The gap distances are g1 = 125 nm, g2 = 350 nm, g3 = 410 nm, g4 = 350 nm, and g5 =125 nm, respectively. The value of their field coupling and field transmission factors were determined by applying a third order polynomial curve-fit to the wavelength dependent even and odd effective indices. At 1550 nm, the field coupling factors are κ1 = κ5 = 0.5446, κ2 = κ4 = 0.0771, and κ3 = 0.0460 and their slopes are dκ1/dλ = dκ5/dλ = 1.72×10−3 [/nm], dκ2/dλ = dκ4/dλ = 4.58×10−4 [/nm], dκ3/dλ = 3.03×10−4 [/nm]. Also at 1550 nm, the effective index is 2.4464 and the slope is −1.12×10−3 [/nm]. The theoretical drop port and through port responses are shown in Figs. 2(a) and 2(b). The derivation of the drop port and through port transfer functions can be found in the Appendix. The spectral characteristics are defined based on typical commercial definitions that describe the performance of DWDM filters. We choose a 100 GHz (≈ 0.8 nm) channel spacing and a 6 GHz (≈ 0.048 nm) clear window centered at a desired wavelength (our choice of clear window assumes there will be no laser wavelength drift). The FSR should be greater than or equal to 35.89 nm (the span of the C-band, 1528.77 nm to 1563.86 nm [33], plus one adjacent channel). The definitions for Ai[34, 35], nAi[34, 35], Rdepth[33, 34], and ECi[34] can be found in the citations given. The spectral characteristics are determined within the clear windows of the desired channel and the 44 clear windows to the left and right of the desired channel. The spectra shown in Fig. 2(a) and 2(b) meet the typical commercial values for the target specifications as shown in Table 1. It should be noted that there is some variance in target values depending on the DWDM vendor. For example, [29] specifies an ECi value of 12 dB whereas [30] specifies a value of 10 dB.
Table 1. Theoretical and Target Specifications
3. Fabrication results and discussion
The device was fabricated at the University of Washington using electron beam lithography, as described in [36]. Figures 3(a) and 3(b) show the experimental through port and drop port responses of one of our quadruple Vernier racetrack resonators. Figure 3(a) clearly shows significant IPS. The maximum through port insertion loss (ILthru) [34] and the drop port insertion loss (ILdrop) [33–35] have not been included since we were unable to measure them accurately. The spectral characteristics meet numerous commercial requirements as shown in Table 2. The ECi, Rdepth, and IPS are within 0.9 dB of the theoretical results. The experimental Ai is 37.2 dB whereas the theoretical Ai is 52.7 dB, which is likely due to the experimental filter line shape being asymmetric and to increased field coupling factors due to the bend regions of the couplers. To be able to simultaneously drop and add signals using just one instance of the device shown in Fig. 1, the target values shown in Table 2 would be needed except that ECi would need to be greater than or equal to 25 dB [37]. Here, we have defined the IPS as the contrast between the minimum transmission within the clear window of the desired channel and the maximum transmission within the clear windows of all non-adjacent channels. However, it should be noted that in [19], the IPS was defined as the difference (in dB) between the maximum value of a major peak and the maximum value of the largest interstitial peak. Based on this definition, our measured IPS would be 37.1 dB. The much larger notches within the pass band of the through port as compared to the theoretical results are possibly due to fabrication variations and coupling-induced frequency shifts (CIFS) [38, 39], which can be corrected by thermally tuning each racetrack resonator [39]. However, the notches are not located within any of the adjacent or non-adjacent channels as shown in Figs. 3(c) and 3(d). The passband of the through port to the left of the major peak shows that there are actually 4 notches (two small notches and two large notches) as shown in Fig. 3(c). However, our theoretical results showed that there are only two small notches as shown in Fig. 2(a). The likely reasons for this difference between the theory and experimental results are fabrication variations, in which the effective indices of the resonators are not all exactly the same, and CIFS. For example, if the effective index of racetrack resonator a is decreased by 0.003 (as shown in Fig. 3(e)) each of the notches separates into 2 notches (one small and one large), where the larger notch is located to the right of the smaller notch (as shown in Fig. 3(f)), which is in agreement with the experimental results. In addition to the device presented here, we fabricated 48 other devices in which the gap distances were varied. The device presented here showed the best performance. However, future designs based on this device can be made to be thermally tunable to compensate for fabrication variations and effects such as CIFS.
Fig. 3 (a) measured through port and drop port spectral response. (b) zoom-in of the measured major resonance. (c) zoom-in of the measured through port passband to the left of the major peak. (d) zoom-in of the measured through port passband to the right of the major peak. (e) zoom-in of the theoretical notch splitting when the effective index of racetrack resonator a decreases and (f) zoom-out of Fig. 3(e) (showing the increase in notch depth as the effective index of racetrack resonator a decreases).
Table 2. Experimental and Target Specifications
4. Summary
In summary, we have experimentally shown that it is possible to meet numerous commercial requirements for dense wavelength-division multiplexing filters using quadruple series-coupled racetrack resonators exhibiting the Vernier effect. We have demonstrated a Vernier filter having a free spectral range greater than the span of the C-band (37.52 nm), a ripple of 0.2 dB, an adjacent channel isolation of 37.2 dB, an interstitial peak suppression of 39.7 dB, and an express channel isolation of 10.2 dB.
Appendices
Appendix: Quadruple series-coupled racetrack resonator transfer functions
Here, we will derive the drop port and through port transfer functions of quadruple series-coupled racetrack resonators using Mason’s rule [40]. In [5], Dey et al. derived the drop port transfer function using Mason’s rule [40] but did not derive nor present the through port transfer function. For completeness, here we have re-derived the drop port transfer function as well as derived the through port transfer function. Since in our configuration, there are four racetrack resonators coupled in series, there are 33 loop gains. There are 10 loop gains of the 10 possible combinations of 1 non-touching loop,
where Xa,b,c,d = exp(−αa,b,c,dLa,b,c,d − jβa,b,c,dLa,b,c,d), where the field loss coefficients and propagations constants for the racetrack resonators are represented by αa,b,c,d, and βa,b,c,d, respectively. κ1, κ2, κ3, κ4, and κ5 are the symmetric (real) point field coupling factors. t1, t2, t3, t4, and t5 are the straight through (real) point field transmission factors. There are 15 loop gains of the 15 possible combinations of 2 non-touching loops, There are 7 loop gains of the 7 possible combinations of 3 non-touching loops, There is 1 loop gain of the 1 possible combination of 4 non-touching loops, The gain and co-factor of the first forward path that is used to determine the drop port transfer function is, The determinant for the entire system is given by, Thus, the transfer function for the drop port is given by [5], The gains of the second to sixth forward path that are used to determine the through port transfer function are , and the corresponding co-factors are, Thus, the transfer function for the through port is given by,Acknowledgments
We would like to thank the Natural Sciences and Engineering Research Council of Canada for partial support of this project. Also, we wish to thank Lumerical Solutions, Inc., for providing the numerical software MODE Solutions. Part of this work was conducted at the University of Washington Microfabrication Facility, a member of the NSF National Nanotechnology Infrastructure Network. We would also like to thank Yun Wang for the design of the grating couplers.
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