A hitless wavelength-selective switch (WSS) based on InGaAs/InAlAs multiple quantum well (MQW) second-order series-coupled microring resonators is proposed and fabricated. In the core layer, a five-layer asymmetric coupled quantum well (FACQW) structure is employed. The WSS is driven by the electrorefractive index change in the FACQW core layer caused by the quantum-confined Stark effect (QCSE). The wafer for the WSS is grown by molecular beam epitaxy and waveguide structures are formed by dry etching. Boxlike spectrum responses and hitless switching characteristics of the WSS are successfully demonstrated for the first time. The change in coupling efficiency at a coupler between a ring and a busline and between rings and its effect on the switching characteristics are also discussed.
© 2013 OSA
A reconfigurable optical add–drop multiplexer (ROADM) [1,2] is one of the key components for the next-generation photonic network, and a hitless wavelength-selective switch (WSS) is an indispensable element for the ROADM. In particular, a series-coupled microring resonator is promising for the hitless WSS because a boxlike spectrum response can be achieved by optimizing the coupling efficiencies between a busline and a resonator and between resonators, and hitless switching characteristics are possible by shifting the resonant wavelengths of individual resonators independently. To date, various tunable filters and WSSs have been proposed and demonstrated using microring resonators based on a silica-based dielectric material [3–11], lithium niobate , and a polymer . They are mainly driven by the thermooptic (TO) effect. Although the tuning range of the resonant wavelength of a microring driven by the TO effect is wide and its tunable characteristics are stable, there are some problems, such as a low tuning speed and a large power consumption. Silicon microring resonators are also very promising for ultracompact and high-performance filters and switches [14–19]; however, their power consumption is also large because many of them are driven by current injection or the TO effect, and it is difficult to integrate them with other semiconductor active devices, such as laser diodes (LDs) and semiconductor optical amplifiers (SOAs).
One solution to these problems is to use an electrorefractive index change based on the quantum-confined Stark effect (QCSE)  in a multiple quantum well (MQW). Because the QCSE is a very fast phenomenon, high-speed and low-power-consumption operation is expected in optical devices driven by the QCSE. The devices based on MQWs are also suitable for integration with LDs and SOAs. Several types of compound semiconductor microring filters and switches have been proposed and investigated [21–25]. We have also demonstrated a single microring resonator wavelength-tunable filter and a low-voltage Mach-Zehnder modulator with a microring resonator using an InGaAs/InAlAs MQW [26, 27]. However, to our knowledge, a high-order series-coupled microring WSS based on the QCSE has never been demonstrated experimentally thus far, except for a short description on a WSS using an InGaAs/InAlAs MQW .
In this paper, we propose and demonstrate, for the first time, a hitless WSS based on InGaAs/InAlAs MQW second-order series-coupled microring resonators with a boxlike spectrum response and a high extinction ratio, as shown in Fig. 1 . As for the MQW in the core layer, we employed a five-layer asymmetric coupled quantum well (FACQW) [29,30], which is expected to exhibit a large electrorefractive index change.
2. Transfer function of series-coupled microring resonator
The transfer function of a series-coupled ring resonator can be obtained using transfer matrix methods [31–33]. In this section, we describe the derivation of the transfer function of a second-order series-coupled microring resonator with buslines .
The second-order series-coupled ring resonator consists of two microrings and coupling regions between waveguides. The field amplitudes at the output ports of the coupling region in Fig. 2(a) are expressed byEquation (1) can be rewritten as the relation between (Ec2, E′c2) and (Ec1, E′c1),Fig. 2(b) is expressed by
Figure 3 shows the calculation model for the transfer function of the second-order series-coupled ring resonator. By cascading Eqs. (2)–(5) at each stage and assuming the round-trip length of a microring to be L = 2l1 = 2l2, the transfer matrix is given by
3. Principle of hitless switching
The hitless WSS can be achieved using the electrorefractive index change in the MQW by controlling the individual resonant wavelengths of series-coupled microring resonators, Rings 1 an 2. When the resonant wavelengths of individual microrings in a series-coupled microring resonator are matched, the resonant wavelength channel is transmitted to the drop port. This is the initial ON state. When the resonant wavelengths of the microrings are not matched, all wavelength channels are transmitted to the through port and no spectrum response appears in the drop port. This is the OFF state. After shifting the resonant wavelengths of the two microrings, a new spectrum peak in the drop port response appears at another wavelength channel. This is the final ON state. As described above, the resonant wavelength can be shifted to another wavelength channel without blocking other wavelength channels. The operation principle and optimum design of a second-order series-coupled microring WSS is discussed in detail in [3,7,34].
Figure 4 shows the theoretical hitless spectral response at the drop port of the WSS calculated using the transfer function discussed in Sect. 2 and the device parameters described in Sect. 4.1 (Table 1 ). Here, we assumed that the coupling efficiencies are constant. The hitless switching characteristics are obtained by controlling the changes in the refractive indices of the FACQW core layers of Rings 1 and 2 (Δn1 and Δn2). The extinction ratio is also defined as shown in Fig. 4.
4. Device design and fabrication
4.1. Design of ring resonator
Figure 5 shows the schematic top view of the WSS. The WSS is composed of two racetrack-shaped microring resonators and busline waveguides. The busline waveguides and microring resonators are coupled laterally. The designed and fabricated microring resonator has a symmetric structure, and we designed it as Ct1 = Ct2 and Rr1 = Rr2, that is, the coupling efficiency between the microrings Kb1 = Kb2≡Kb, the round-trip length of microrings L1 = L2≡L, and a1 = a2≡a1/2, where a is the transmittance per round.
A schematic cross-sectional view of the waveguide is shown in Fig. 6(a) . The waveguide consists of a core layer with 12 periods of an In0.53Ga0.47As/In0.52Al0.48As FACQW, 50 nm In0.52AlGa0.24As0.24 separate confinement heterostructure layers, and p/n-doped InP cladding layers (n = 3.17). The total thickness of the core layer is approximately 300 nm. To reduce the absorption loss caused by the p-doped upper cladding layer, a 200 nm undoped InP layer is inserted close to the core layer. The waveguide is buried with benzocyclobutene (BCB) (n = 1.543 at λ = 1550nm). The width of the waveguide, w, is 1.45 μm, which satisfies the single mode condition. The average refractive index of the FACQW layer is calculated to be 3.394 using a formula for calculating the average refractive index of dielectric multilayers . To obtain the propagation constant β ( = 2πneq/λ), the effective refractive index neff is used instead of neq, considering the dependence of refractive index on wavelength. In this design, neff is assumed to be 3.843.
In the coupling regions, we employed a directional coupler with a shallow gap  to control the coupling efficiencies easily. Figure 6(b) shows the schematic cross-sectional view of the coupling region. The width of the gap, wg, and the depth of the gap, dg, are 0.3 and 1.25 μm, respectively. The depth of the gap, dg, is slightly smaller than that in the previous WSS . The round-trip length of each ring resonator is 304.2 μm, which corresponds to the free spectral range (FSR) of 2.07 nm. The designed parameters of the proposed WSS are shown in Table 1.
4.2. InGaAs/InAlAs five-layer asymmetric coupled quantum well (FACQW)
As mentioned in Sect. 4.1, the multiple InGaAs/InAlAs FACQW  is used as the waveguide core of the device. The potential profile of the FACQW is shown in Fig. 7 . In0.53Ga0.47As and In0.52Al0.48As layers were employed as well and barrier layers, respectively. They are both lattice-matched to an InP substrate. The FACQW consists of a 19-monolayer (ML) well (QW1) and a 22-ML well (QW2) including a 3-ML barrier layer, and QW1 and QW2 are coupled through an 8-ML barrier layer. This structure shows a unique behavior of the QCSE, that is, the absorption peak intensity near the band edge increases without a redshift with an increase in applied electric field.
The refractive index change in the FACQW was theoretically investigated . The absorption coefficient was calculated using the k·p perturbation theory with the 4 × 4 Luttinger-Kohn Hamiltonian , considering the exciton effect. The electrorefractive index change Δn was calculated using the Kramers-Kronig relation. As a result, we found that an electrorefractive index change Δn/ΔF as large as 1.9 × 10−4 cm/kV can be expected in the ideal FACQW in the wavelength range of 100 nm from 1480 nm to 1580 nm. In addition, we have experimentally demonstrated a low-voltage InGaAs/InAlAs FACQW Mach-Zehnder modulator with the product of the half-wavelength voltage Vπ and phase shifter length Lp (VπLp) as low as 1.2 Vmm at a wavelength of 1.55 μm . This value corresponds to Δn/ΔF = 9.0 × 10−5 cm/kV. Using the InGaAs/InAlAs FACQW as the waveguide core of a microring resonator, a high-speed and low-voltage wavelength-tunable filter is expected to be realized.
The wavelength of the absorption edge of the InGaAs/InAlAs FACQW is approximately 1420 nm, which is 130 nm away from the operation wavelength of 1550 nm. Therefore, it makes the absorption loss of the MQW waveguides very low compared with that of a conventional MQW.
An epitaxial wafer was grown by solid-source molecular beam epitaxy (MBE). To fabricate a directional coupler with a shallow gap, we adopted a two-step etching technique . First, by electron beam (EB) lithography, the gaps in coupling regions were formed by inductively coupled plasma reactive ion etching (ICP-RIE) using on a Br-based gas. Next, by photolithography, high-mesa waveguides were formed by ICP-RIE. Electrodes were formed on top of the waveguides of the microrings and on the back of the wafer. Since the microrings and buslines are electrically isolated by the gap in directional couplers, reverse voltages are only applied to the microrings.
Figure 8(a) shows the microscopic image of the top of the fabricated WSS. Figure 8(b) shows the scanning electron microscopic (SEM) image of the sidewalls of the waveguides at around a coupler of another WSS without BCB, fabricated by the same process as that for the device with the device parameters in Table 1. The sidewalls are successfully formed without noticeable roughness.
Figure 8(c) shows the SEM image of a cross section of the coupler between the microring and the busline. The sidewalls of the waveguides are almost vertical. In this sample, the width of the bottom of the gap is smaller (approximately 0.24-0.27 μm) than the designed (0.3 μm), and the depth of the gap is slightly larger (1.26 μm) than the designed (1.25 μm). The fabrication errors of the gap lead to the difference between the coupling efficiencies of the fabricated and designed couplers. In particular, the coupling efficiency is very sensitive to the depth of the gap. For example, when the depth of the gap becomes 0.01 μm larger, the coupling efficiency is reduced by approximately 34%. On the other hand, the coupling efficiency increases by approximately 12% when the width of the gap becomes 0.03 μm smaller. In addition, the position of the gap is slightly off-centered. The effect of this off-centered position of the gap on the coupling efficiency is also discussed in Sect. 5.1.
5. Switching characteristics
5.1. Single ring filter
First, to evaluate the device parameters of the microring resonator and the electrorefractive index change in the FACQW core layer, we measured through-port spectrum responses of a single-microring resonator with the same waveguide structure as the WSS under reverse voltages, as shown in Fig. 9(a) . The coupling efficiencies Kb1 and Kb2 are defined in the figure. The depth of the gap in the directional couplers, the round-trip length of the microrings, and the length of the coupling regions are 1.25, 316.7, and 95.5 μm, respectively. The designed coupling efficiency between the buslines and the microring is 0.542. The electrodes were formed only on the microring resonators. Therefore, the microrings are electrically separated from the other waveguides.
Figure 9(b) shows the measured drop-port spectrum responses of the single-microring resonator for TE-polarized input lights under various reverse voltages. A marked shift in wavelength and no increase in propagation loss were observed. Figure 10(a) shows the evaluated refractive index change in the core layer of the microring waveguide Δncore at the resonant wavelengths of 1547.6, 1549.6, and 1551.6 nm as a function of applied dc reverse bias voltage Va, considering the optical confinement factor (0.527). Considering the filling factor p of the FACQW in the core layer (p = 0.574), the electrorefractive index change in the FACQW at V = −14 V is evaluated to be approximately 7.3 × 10−3. This result shows that the refractive index change of the FACQW is almost constant in this wavelength region, which is consistent with the discussion in .
This refractive index change is mainly caused by the QCSE in the FACQW. Although the Pockels effect in the FACQW also contributes to the index change, it is evaluated to 4.3 × 10−5 at Va = −14 V . This value is smaller by two orders of magnitude than the QCSE. The TO and carrier injection effects are also negligible because the dark current is very small (approximately 10 μA/350 μm2 at −18 V). Therefore, the main cause of the change in refractive index is the QCSE in the FACQW core layer. Unfortunately, the refractive index change of the core layer is smaller than that theoretically predicted even though the index change in the FACQW is still three times larger than that in a conventional square QW with the same wavelength of the absorption edge. The cause of this deterioration in the electrorefractive index change is considered to be the nonuniform electric field in the core layer .
In the microring resonator with buslines, the coupling efficiencies change when the reverse voltages applied to the microring are altered. This is due to the change in the effective refractive index of the waveguide on the side of the microring in the directional couplers, resulting in the change in the propagation constant of this waveguide.
The coupling efficiencies can be evaluated using the spectrum responses of the through and drop ports. That is, using the transfer matrix for a single microring resonator with two buslines, the transmissions from the input port to through port, TT, and that from the input port to the drop port, TD, can be calculated byEq. (11), the full width at half-maximum (FWHM) of the drop-port resonant peak is calculated to beEqs. (12)-(14), a, Kb1, and Kb2 are obtained.
The round-trip propagation loss was evaluated to be approximately 1.3 dB/round by solving Eqs. (12)-(14) for the single microring resonator, shown in Fig. 9(a). In this propagation loss, the coupling losses at the couplers are also included. Because the coupling loss is calculated to be approximately 0.20 dB/coupler using a mode expansion of the even and odd modes in the directional coupler, the propagation loss except the coupling losses at the couplers in a microring waveguide is evaluated to be approximately 0.91 dB/round (2.87 dB/mm). The main reasons for the propagation loss in the microring are free carrier absorption in the upper p-cladding layer and the electrodes, and scattering loss due to the sidewall roughness of the waveguide. Residual absorption in the multiple FACQW core layer is considered to be much smaller than the free carrier absorption loss, as discussed in Sect. 4.2.We have not investigated the effect of the sidewall roughness on the propagation loss. This issue will be studied and discussed elsewhere.
The dependence of the evaluated coupling efficiencies Kb1 and Kb2 on the applied reverse voltage is shown in Fig. 10(b). As shown in the figure, Kb1 increases by approximately 0.06 when the applied reverse voltage is changed from 0 to −15 V. On the other hand, Kb2 decreases by approximately 0.04 with the change in the applied reverse voltage. The reason for these changes in coupling efficiency can be explained as follows; in the fabrication process of the WSS, the resist patterns for the gaps in the directional couplers are drawn by EB lithography and those for the waveguides are drawn by photolithography. In this device, it is considered that the positions of the whole EB resist patterns for the gaps were slightly shifted downward in Fig. 9(a) from the center of the directional coupler, as shown in Fig. 8(c). This off-centered position of the gap results in the degradation of the symmetry of the directional couplers. That is, for example, the busline waveguide becomes wider than the microring waveguide in Directional Coupler 1 (DC1). Therefore, when the voltage was applied to the microring and its equivalent refractive index increased, the symmetry of DC1 was recovered, leading to the increase in Kb1. On the other hand, the situation for Directional Coupler 2 (DC2) was opposite, leading to the decrease in Kb2. This change in coupling efficiency has an effect on the switching characteristics of the WSS.
5.2. Second-order series-coupled microring WSS
The measured drop port spectrum responses of the second-order series-coupled microring resonator are shown in Fig. 11(a) . The solid and broken lines represent the ON and OFF state responses, respectively. For the initial ON state at λ = 1549.1 nm, a reverse voltage V1 of 3.0 V was applied to Ring 1 to match the resonant wavelength of Ring 1 with that of Ring 2 because there was a difference of approximately 0.10 nm between the resonant wavelengths of the two microrings. Next, V2 of −14 V was applied to Ring 2 for the OFF state. Finally, V1 of −15 V was applied to Ring 1 for the ON state at λ = 1550.1 nm. As shown in Fig. 11(a), the hitless switching of approximately 1.0 nm owing to the electrorefractive index change in the MQW core layer was successfully demonstrated. The FSR and full FWHM of the bandwidth are approximately 2.1 and 0.25 nm, respectively. The extinction ratios of the drop-port response of the initial and final ON states are 8.7 and 11.5 dB, respectively. A boxlike spectrum response was obtained, as shown in Fig. 11(b) owing to the second-order series-coupled microrings. The shape factor defined as 
The coupling efficiencies between the input busline and Ring 1, Rings 1 and 2, and Ring 2 and the output busline, that is, Kb1, Kr and Kb2, respectively, of the WSS were evaluated by fitting the theoretical spectrum responses of the through and drop ports to the measured spectra. The evaluated coupling efficiencies in the WSS are shown in Table 2 . The coupling efficiencies for the initial ON state are evaluated by the fitting, and those for the OFF and final ON states were calculated by considering of the change in coupling efficiency discussed in Sect. 5.1. As shown in Table 2, there are large discrepancies between the designed and measured coupling efficiencies. The reason for the discrepancies is thought to be the depth of the fabricated gaps in the directional couplers was larger than that designed (1.25 μm) and/or the gaps in the couplers are off-centered, as shown in Fig. 8(c).
Figure 12 shows the theoretical switching characteristics calculated using the device parameters in Table 2 and the change in the refractive index of the MQW core layer in Fig. 10(a). In this calculation, the refractive index change of the multiple FACQW core layer is constant in this wavelength region, as mentioned in Sect. 5.1. As can be seen, the theoretical spectrum responses well reproduce the measured responses. Therefore, we should consider the change in coupling efficiency in directional couplers when we design microring-resonator-based wavelength-tunable filters and switches.
Finally we discuss the propagation loss of the proposed WSS. As mentioned in Sect. 5.1, the propagation loss in the microring waveguide and the coupling loss at the coupler were evaluated to be approximately 0.91 dB/round and 0.20 dB/coupler, respectively. Using these values and the coupling efficiencies shown in Table 2, the difference in insertion loss between the drop and through ports for the initial ON state of the second-order series coupled WSS is calculated to be approximately 16.5 dB. This large insertion loss at the drop port is due to the small coupling efficiencies and it needs to be reduced by improving the design of the WSS.
We proposed and fabricated a hitless WSS based on MQW second-order series-coupled microring resonators. In the core layer, multiple InGaAs/InAlAs FACQW structure was employed. The WSS was driven by the electrorefractive index change in the FACQW core layer caused by the QCSE. The directional coupler with a shallow gap was employed to control the coupling parameters between busline and microring waveguides. By adjusting the gap depth of the coupling region, the coupling coefficient between the busline and microring waveguides was controlled more easily and precisely than that of the device with a deep gap. We grew an epitaxial wafer by solid-source MBE and fabricated the WSS by ICP dry etching.
The through-port response and wavelength switching characteristics of the WSS were measured, and boxlike spectrum responses and hitless switching were successfully demonstrated for the first time by controlling the voltages applied to the ring resonators. The FSR and FWHM were approximately 2.1 and 0.25 nm, respectively. The wavelength shift was approximately 1.0 nm at a driving voltage of 14 V. The extinction ratios of the drop-port response of the initial and final ON states were 8.7 and 11.5 dB, respectively. In addition, it was revealed that the coupling efficiencies in the couplers change by more than 0.04 when the reverse voltage applied to the ring resonators is changed from 0 to −15 V, and such change affects the switching characteristics. The proposed WSS is very promising for high-speed and low-power-consumption operation.
The authors express sincere thanks to Dr. R. Katouf for experiments and fruitful discussion. This work is supported by SCOPE, Ministry of Internal Affairs and Communications, and by a Grant-in-Aid for Scientific Research B, Ministry of Education, Culture, Sports, Science and Technology, Japan (No. 21360030).
References and links
1. K. Suzuki, T. Mizuno, M. Oguma, T. Shibata, H. Takahashi, Y. Hibino, and A. Himeno, “Low loss fully reconfigurable wavelength-selective optical 1× N switch based on transversal filter configuration using silica-based planar lightwave circuit,” IEEE Photon. Technol. Lett. 16(6), 1480–1482 (2004). [CrossRef]
2. S. J. Emelett and R. Soref, “Design and simulation of silicon microring optical routing switches,” J. Lightwave Technol. 23(4), 1800–1807 (2005). [CrossRef]
3. Y. Goebuchi, T. Ka, and Y. Kokubun, “Fast and stable wavelength-selective switch using double-series coupled dielectric microring resonator,” IEEE Photon. Technol. Lett. 18(3), 538–540 (2006). [CrossRef]
4. T. Kato and Y. Kokubun, “Optimum coupling coefficients in second-order series-coupled ring resonator for nonblocking wavelength channel switch,” J. Lightwave Technol. 24(2), 991–999 (2006). [CrossRef]
5. S. Suzuki, Y. Kokubun, and S. T. Chu; “Box-like filter response and expansion of FSR by a vertically triple coupled microring resonator filter,” J. Lightwave Technol. 20(8), 1525–1529 (2002). [CrossRef]
6. S. Xiao, M. H. Khan, H. Shen, and M. Qi, “A highly compact third-order silicon microring add-drop filter with a very large free spectral range, a flat passband and a low delay dispersion,” Opt. Express 15(22), 14765–14771 (2007). [CrossRef] [PubMed]
7. Y. Yanagase, S. Yamagata, and Y. Kokubun, “Wavelength tunable polymer microring resonator filter with 9.4 nm tuning range,” Electron. Lett. 39(12), 922–924 (2003). [CrossRef]
8. B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,” IEEE Photon. Technol. Lett. 16(10), 2263–2265 (2004). [CrossRef]
9. T. Kato, Y. Goebuchi, and Y. Kokubun, “Improvement of switching characteristics of hitless wavelength-selective switch with double-series-coupled microring resonators,” Jpn. J. Appl. Phys. 46(6A), 3428–3432 (2007). [CrossRef]
10. O. Tsilipakos, T. V. Yioultsis, and E. E. Kriezis, “Theoretical analysis of thermally tunable microring resonator filters made of dielectric-loaded plasmonic waveguides,” J. Appl. Phys. 106(9), 093109 (2009). [CrossRef]
11. S.-J. Chang, C.-Y. Ni, Z. Wang, and Y.-J. Chen, “A compact and low power consumption optical switch based on microrings,” IEEE Photon. Technol. Lett. 20(12), 1021–1023 (2008). [CrossRef]
12. T.-J. Wang and C.-H. Chu, “Wavelength-tunable microring resonator on lithium niobate,” IEEE Photon. Technol. Lett. 19(23), 1904–1906 (2007). [CrossRef]
13. J.-H. Song, D.-H. Kim, and S.-S. Lee, “Polymeric microring resonator enabling variable extinction ratio,” Jpn. J. Appl. Phys. 46(7), L145–L147 (2007). [CrossRef]
14. D. Geuzebroek, E. Klein, H. Kelderman, N. Baker, and A. Driessen, “Compact wavelength-selective switch for gigabit filtering in access networks,” IEEE Photon. Technol. Lett. 17(2), 336–338 (2005). [CrossRef]
15. M. S. Nawrocka, T. Liu, X. Wang, and R. R. Panepucci, “Tunable silicon microring resonator with wide free spectral range,” Appl. Phys. Lett. 89(7), 071110 (2006). [CrossRef]
16. C. Li, L. Zhou, and A. W. Poon, “Silicon microring carrier-injection-based modulators/switches with tunable extinction ratios and OR-logic switching by using waveguide cross-coupling,” Opt. Express 15(8), 5069–5076 (2007). [CrossRef] [PubMed]
17. R. Amatya, C. W. Holzwarth, H. I. Smith, and R. J. Ram, “Precision tunable silicon compatible microring filters,” IEEE Photon. Technol. Lett. 20(20), 1739–1741 (2008). [CrossRef]
18. T. Hu, W. Wang, C. Qiu, P. Yu, H. Qiu, Y. Zhao, X. Jiang, and J. Yang, “Thermally tunable filters based on third-order microring resonators for WDM applications,” IEEE Photon. Technol. Lett. 24(6), 524–526 (2012). [CrossRef]
19. X. Luo, J. Song, S. Feng, A. W. Poon, T.-Y. Liow, M. Yu, G.-Q. Lo, and D.-L. Kwong, “Silicon high-order coupled-microring-based electro-optical switches for on-chip optical interconnects,” IEEE Photon. Technol. Lett. 24(10), 821–823 (2012). [CrossRef]
20. D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, and C. A. Burrus, “Band-edge absorption in quantum well structures: The quantum-confined Stark effect,” Phys. Rev. Lett. 53(22), 2173–2176 (1984). [CrossRef]
21. J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, “Higher order filter response in coupled microring resonators,” IEEE Photon. Technol. Lett. 12(3), 320–322 (2000). [CrossRef]
22. V. Van, T. A. Ibrahim, K. Ritter, P. P. Absil, F. G. Johnson, R. Grover, J. Goldhar, and P.-T. Ho, “All-optical nonlinear switching in GaAs-AlGaAs microring resonators,” IEEE Photon. Technol. Lett. 14(1), 74–76 (2002). [CrossRef]
23. R. Grover, Member, IEEET. A. Ibrahim, S. Kanakaraju, L. Lucas, L. C. Calhoun, and P.-T. Ho, “A tunable GaInAsP–InP optical microring notch filter,” IEEE Photon. Technol. Lett. 16(2), 467–469 (2004). [CrossRef]
24. H. Simos, A. Bogris, N. Raptis, and D. Syvridis, “Dynamic properties of a WDM switching module based on active microring resonators,” IEEE Photon. Technol. Lett. 22(4), 206–208 (2010). [CrossRef]
25. S. Ravindran, A. Datta, K. Alameh, and Y. T. Lee, “GaAs based long-wavelength microring resonator optical switches utilising bias assisted carrier-injection induced refractive index change,” Opt. Express 20(14), 15610–15627 (2012). [CrossRef] [PubMed]
26. T. Makino, T. Gotoh, R. Hasegawa, T. Arakawa, and Y. Kokubun, “Microring resonator wavelength tunable filter using five-layer asymmetric coupled quantum well,” J. Lightwave Technol. 29(16), 2387–2393 (2011). [CrossRef]
27. H. Kaneshige, Y. Ueyama, H. Yamada, H. Yajima, T. Arakawa, and Y. Kokubun, “InGaAs/InAlAs multiple quantum well Mach-Zehnder modulator with single microring resonator,” Jpn. J. Appl. Phys. 51(2), 02BG01 (2012). [CrossRef]
28. H. Ikehara, T. Goto, H. Kamiya, T. Arakawa, and Y. Kokubun, “Hitless wavelength-selective switch using multiple quantum well second-order series coupled microring resonators,” Photonics in Switching (PS) 2012, Th-S24–O07 (2012).
29. H. Feng, J. P. Pang, M. Sugiyama, K. Tada, and Y. Nakano, “Field-induced optical effect in a five-step asymmetric coupled quantum well with modified potential,” IEEE J. Quantum Electron. 34(7), 1197–1208 (1998). [CrossRef]
30. T. Arakawa, T. Toya, M. Ushigome, K. Yamaguchi, T. Ide, and K. Tada, “InGaAs/InAlAs five-layer asymmetric coupled quantum well exhibiting giant electrorefractive index change,” Jpn. J. Appl. Phys. 50, 032204 (2011). [CrossRef]
31. G. Barbarossa, A. M. Matteo, and M. N. Armenise, “Theoretical analysis of triple-coupler ring-based optitacl guided-wave resonator,” J. Lightwave Technol. 13(2), 148–157 (1995). [CrossRef]
32. R. Orta, P. Savi, R. Rascone, and D. Trinchero, “Synthesis of multiple-ring-resonator filters for optical systems,” IEEE Photon. Technol. Lett. 7(12), 1447–1449 (1995). [CrossRef]
33. C. K. Madsen and J. H. Zhao, “A general planar waveguide autoregressive optical filter,” J. Lightwave Technol. 14(3), 437–447 (1996). [CrossRef]
34. T. Kato, Y. Goebuchi, and Y. Kokubun, “Experimental study of optimum coupling efficiency of double series coupled microring resonator,” Jpn. J. Appl. Phys. 45(10A), 7741–7745 (2006). [CrossRef]
35. M. Born and E. Wolf, Principles of Optics, 7th Ed. (Cambridge University Press, 1999), p.838.
37. T. Arakawa, T. Hariki, Y. Amma, M. Fukuoka, M. Ushigome, and K. Tada, “Low-voltage Mach-Zehnder modulator with InGaAs/InAlAs five-layer asymmetric coupled quantum well,” Jpn. J. Appl. Phys. 51, 042203 (2012). [CrossRef]