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OPTICS LETTERS / Vol. 39, No. 21 / November 1, 2014
High-order microring resonators with bent couplers for a box-like filter response Pengxin Chen, Sitao Chen, Xiaowei Guan, Yaocheng Shi, and Daoxin Dai* Centre for Optical and Electromagnetic Research, State Key Laboratory for Modern Optical Instrumentation, Zhejiang Provincial Key Laboratory for Sensing Technologies, Zhejiang University, Zijingang Campus, Hangzhou 310058, China *Corresponding author: [email protected] Received September 1, 2014; revised October 5, 2014; accepted October 7, 2014; posted October 10, 2014 (Doc. ID 220205); published October 28, 2014 High-order microring resonator (MRR) filters with bent directional couplers are proposed and demonstrated to achieve a box-like filter response. When using bent couplers, the coupling ratio can be adjusted easily by choosing the length of the coupling region, and the excess loss is almost zero while the perimeter of the microring length is unchanged. For the present fabricated five-microring filters with bent directional couplers, the excess loss is less than 1.0 dB, the out-of-band extinction ratio is ∼36 dB, and the response has rising and falling edges as sharp as 48 dB∕nm. The thermal tunability of the high-order MRR filter with a Ti-microheater is also demonstrated and the thermally tuning efficiency is about 0.10 nm∕mW. © 2014 Optical Society of America OCIS codes: (130.3120) Integrated optics devices; (230.5750) Resonators; (230.4555) Coupled resonators. http://dx.doi.org/10.1364/OL.39.006304
Wavelength-division multiplexing (WDM) is a key technique developed to achieve high capacity for an optical interconnect link and a wavelength-division-multiplexer is one of the most important key components in a WDM system. In the past decades, various WDM filters have been demonstrated [1], such as Bragg gratings [2], microring resonators (MRRs) [3–8], Mach–Zehnder interferometers [9], and arrayed-waveguide gratings [10,11]. Among them, the MRR-based optical filter is one of the most popular choices because of the simple structure, the compact footprint, as well as the flexible scalability. For an optical filter, a box-like filtering response is often desired so that it can tolerate a wavelength shift due to any environmental change. For optical filters based on MMRs, this response can be synthesized with multiple rings [3–8,12,13]. When using multiple microrings to achieve a box-like filtering response, all the couplers involved should be designed optimally to achieve the coupling coefficients as desired [14]. For example, for the ultra-compact fifthorder MRR optical filters demonstrated in Ref. [4], the power coupling coefficients κ2 while κ itself defined as the field coupling coefficient for all the couplers are designed to be 0.45, 0.09, 0.05, 0.05, 0.09, and 0.45, respectively. With this design, the ripples in the passband of the fifth-order MRR filter are smaller than 0.15 dB, and the out-of-band rejection ratio is larger than 40 dB theoretically. In order to achieve the sufficient power coupling coefficient of 0.45 between the access waveguide and the side-microring, one usually has to use the design of race-track resonators so that the coupling can be enhanced by increasing the length L of the coupling region or reducing the gap wgap in the coupling region. However, a longer coupling region causes a smaller free-spectral range (FSR), which limits the channel number available in WDM systems and consequently is not desired. Alternatively, when choosing a narrow gap (e.g., ∼20 nm), the beating length becomes small to realize a large FSR. However, the fabrication (e.g., the lithography and etching processes) becomes difficult, and the coupling ratio is very sensitive to the beating length 0146-9592/14/216304-04$15.00/0
variation [4]. In order to overcome these issues, multimode interference (MMI) couplers were used as the coupler with a power ratio of 45∶55 between the two output ports in Ref. [4]. One should note that there are some disadvantages when introducing MMI couplers. First, an MMI coupler usually has a few percent of excess loss during this splitting process [4], and there is also mode conversion loss between the straight section and the bending section of a microring. This might introduce some notable excess loss for an MRR filter, particularly for the case with utlrasharp bending. Second, the power splitting ratio of an MMI coupler is fixed [15], and thus it is not available when one wants to choose another value for the power splitting ratio. Third, the length LMMI of the MMI section is usually several microns (e.g., LMMI ∼3.5 μm [4]), and the cavity length is increased by 2 LMMI , which increases the microring length and thus reduces the FSR in some degree. In order to solve these problems, in this Letter, we introduce bent directional couplers for high-order MRR optical filters to have a box-like filtering response. The SEM image of five-microring filter with bent coupler as shown in Fig. 1(a). In the present design, bent couplers are used for light coupling between the access waveguides and the side-microring. With bent couplers, the coupling ratio can be chosen flexibly by choosing the length of the coupling region appropriately even when Input W2 R1
R2
W1 (a) Drop
Bent coupler
Wgap (b)
Bent coupler
Fig. 1. (a) SEM image of the present five-microring filter with bent couplers. (b) SEM image of the bent coupler used here. © 2014 Optical Society of America
the gap width is relatively large. Furthermore, there is no excess loss theoretically, and the cavity length is the same as a regular microring. Figure 1(b) shows the structure of the bent couplers, in the coupling region of which there are two parallel bent waveguides, i.e., the bent access waveguide and the microring waveguide. In order to have efficient coupling between the access waveguide and the microring, the two parallel bent waveguides are designed to be with different widths w1 ; w2 according to the phase matching condition [16], neff1 R1 neff2 R2 , where neff1 and neff2 are the effective indices of the fundamental modes of the two bent waveguides, respectively, R1 and R2 are the corresponding bending radii, and R1 R2 w1 w2 ∕2 wgap . In our design, a relatively large gap (wgap > 150 nm) is chosen so that the fabrication is not difficult. The design with the phase matching condition also helps minimize the excitation of higher-order modes in the microring waveguides (which might be multimode). In this Letter a silicon-on-insulator (SOI) wafer with a 220-nm-thick top silicon and a 2-μm-thick buried-oxide layer is used, and there is a 1-μm-thick SiO2 uppercladding layer for the SOI nanowires used here. The refractive indices of Si and SiO2 are nSi 3.45 and nSiO2 1.45, respectively. As an example, we choose the widths w1 ; w2 to be around 450 nm and the radii R1 ; R2 to be around 5 μm regarding the single-mode condition as well as the bending loss. Figure 2 shows the calculated value of neff R for bending waveguides with different core widths (w 350; 375; …; 500 nm) as the radius R increases. Here the effective index neff is obtained by using a full-vectorial finite-difference method (FV-FDM) mode-solver numerically. According to the resonant equation for MRRs 2πneff R mλ, where m is the resonant order of the microring and λ is the wavelength in the vacuum, one has the product neff2 R2 11.1 μm (as indicated by the dash-dotted line in Fig. 2) when assuming that the resonant order m 45 and λ 1.55 μm. From this figure, one can easily have many solutions for w2 ; R2 to satisfy the equation neff2 R2 11.1 μm. According to phase matching condition, finally we choose the parameters w1 0.35 μm, R1 5.455 μm, w2 0.425 μm, and R2 4.886 μm for the bent coupler so that the gap is relatively large (wgap ∼182 nm) to make the fabrication not difficult. Figure 3(a) shows the simulated power coupling coefficients of the designed bent coupler for the case with light launched from the access waveguide as the angle
Power coupling ratio
November 1, 2014 / Vol. 39, No. 21 / OPTICS LETTERS 1.0 Total
0.8 0.6
0.8
Thru Cross
Thru
0.2
8 6 3
4
5
6
7
R (µm)
Fig. 2. Calculated value of neff R for the bent waveguides with different core widths (w 350; 375; …; 500 nm) as the radius R increases.
Cross
0.2
Input
Input
Cross
0.0
(a)
15 30 (degree)
45
0
(b)
0.2
0.4
0.6
wgap ( m)
Fig. 3. (a) Simulated power coupling ratio of the bent coupler as the angle θ of the coupling region increases when w1 0.35 μm, R1 5.455 μm, w2 0.425 μm, and R2 4.886 μm. (b) Coupling ratio of the inter-ring coupler as the gap width wgap varies when choosing R 4.886 μm and w 0.425 μm.
θ of the coupling region increases. Here the light propagation is simulated with a three-dimensional finite-difference time-domain (3D-FDTD) method. The simulation shows that the excess loss of this structure is as low as ∼0.04 dB in theory. The coupling ratio between the access waveguide and the microring is 0.45 as required when choosing θ 13.7°. As indicated by Ref. [3], the power coupling coefficients should be [0.45, 0.09, 0.45] for a two-ring filter, [0.45, 0.09, 0.09, 0.45] for a three-ring filter and [0.45, 0.09, 0.05, 0.05, 0.09, 0.45] for a five-ring filter, respectively. For the inter-ring coupler between two adjacent microrings, the coupling coefficients can be controlled by adjusting the gap between them, as shown in Fig. 3(b). For example, the gap widths are about 116 and 156 nm to achieve the power coupling coefficients of 0.09 and 0.05, respectively. The sensitivity of the power coupling ratios to the core/gap width deviation is also analyzed with a 3DFDTD simulation for the designed three couplers for the five-ring filter as an example (see Fig. 4). Assuming that there is a deviation Δw for the waveguides, one has w w0 Δw and wgap wgap0 –Δw for the waveguide width and the gap width, respectively, where w0 and wgap0 are the designed values. From Fig. 4(a) (see the curve with circles), the power coupling ratio for the bent coupler is not sensitive to the deviation Δw, which is an advantage and has been also proposed to realize a broad-band 3 dB coupler in Ref. [17] recently. In contrast, the inter-ring coupler is more sensitive to the deviation Δw (see the curves with squares and diamonds). When jΔwj < 20 nm, the coupling ratios 0
0.45
Bent coupler
-10
0.44
0.13
Power (dB)
w=350:25:500nm
wgap
0.4
0
Power coupling ratio
10
Thru Cross
2
0.4
0.46
12
Thru Total
0.6
0.0
14 neffR (µm)
1.0
6305
Inter-ring coupler #1
0.08 Inter-ring coupler #2
0.03 -0.02
(a)
-0.01
0
Δ w (µm)
0.01
0.02
Δw=20, 10, 0, -10, -20nm
-20 -30
-40 1548 (b)
1549.5 1551 1552.5 Wavelength (nm)
Fig. 4. (a) Sensitivity of the coupling ratio to the waveguide deviation Δw. (b) Calculated spectral responses for a five-ring filter when there is a deviation Δw.
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spectral responses are also calculated by using the analytical formulas given in Ref. [18] (see the thick curves). For this calculation, the coupling ratios are chosen as the values designed above. It can be seen that the measured results agree well with the calculated results. Their FSRs are about 18.4 nm, and the 3-dB bandwidths are 2.0, 2.6, and 2.38 nm, respectively. The measured out-of-band rejection ratios for the fabricated two-microring, threemicroring, and five-microring filters are about 25, 30, and 36 dB, respectively. The out-of-band rejection ratio of five-microring filter might be higher than the measurement result shown in Fig. 5(c) due to the limit of the sensitivity of the powermeter used in our measurement setup. Nevertheless, it can be seen that higher out-ofband rejection ratio is obtained by introducing more microrings. Both the measurement and simulation results also show that the spectral response is more box-like (with sharp transitions) when more microrings are cascaded. The response for the five-microring filter has rising and falling edges as sharp as 48 dB∕nm. From the measured spectral responses, one can also see that the fabricated two-microring, three-microring, and fivemicroring filters have an excess loss of
OPTICS LETTERS / Vol. 39, No. 21 / November 1, 2014
High-order microring resonators with bent couplers for a box-like filter response Pengxin Chen, Sitao Chen, Xiaowei Guan, Yaocheng Shi, and Daoxin Dai* Centre for Optical and Electromagnetic Research, State Key Laboratory for Modern Optical Instrumentation, Zhejiang Provincial Key Laboratory for Sensing Technologies, Zhejiang University, Zijingang Campus, Hangzhou 310058, China *Corresponding author: [email protected] Received September 1, 2014; revised October 5, 2014; accepted October 7, 2014; posted October 10, 2014 (Doc. ID 220205); published October 28, 2014 High-order microring resonator (MRR) filters with bent directional couplers are proposed and demonstrated to achieve a box-like filter response. When using bent couplers, the coupling ratio can be adjusted easily by choosing the length of the coupling region, and the excess loss is almost zero while the perimeter of the microring length is unchanged. For the present fabricated five-microring filters with bent directional couplers, the excess loss is less than 1.0 dB, the out-of-band extinction ratio is ∼36 dB, and the response has rising and falling edges as sharp as 48 dB∕nm. The thermal tunability of the high-order MRR filter with a Ti-microheater is also demonstrated and the thermally tuning efficiency is about 0.10 nm∕mW. © 2014 Optical Society of America OCIS codes: (130.3120) Integrated optics devices; (230.5750) Resonators; (230.4555) Coupled resonators. http://dx.doi.org/10.1364/OL.39.006304
Wavelength-division multiplexing (WDM) is a key technique developed to achieve high capacity for an optical interconnect link and a wavelength-division-multiplexer is one of the most important key components in a WDM system. In the past decades, various WDM filters have been demonstrated [1], such as Bragg gratings [2], microring resonators (MRRs) [3–8], Mach–Zehnder interferometers [9], and arrayed-waveguide gratings [10,11]. Among them, the MRR-based optical filter is one of the most popular choices because of the simple structure, the compact footprint, as well as the flexible scalability. For an optical filter, a box-like filtering response is often desired so that it can tolerate a wavelength shift due to any environmental change. For optical filters based on MMRs, this response can be synthesized with multiple rings [3–8,12,13]. When using multiple microrings to achieve a box-like filtering response, all the couplers involved should be designed optimally to achieve the coupling coefficients as desired [14]. For example, for the ultra-compact fifthorder MRR optical filters demonstrated in Ref. [4], the power coupling coefficients κ2 while κ itself defined as the field coupling coefficient for all the couplers are designed to be 0.45, 0.09, 0.05, 0.05, 0.09, and 0.45, respectively. With this design, the ripples in the passband of the fifth-order MRR filter are smaller than 0.15 dB, and the out-of-band rejection ratio is larger than 40 dB theoretically. In order to achieve the sufficient power coupling coefficient of 0.45 between the access waveguide and the side-microring, one usually has to use the design of race-track resonators so that the coupling can be enhanced by increasing the length L of the coupling region or reducing the gap wgap in the coupling region. However, a longer coupling region causes a smaller free-spectral range (FSR), which limits the channel number available in WDM systems and consequently is not desired. Alternatively, when choosing a narrow gap (e.g., ∼20 nm), the beating length becomes small to realize a large FSR. However, the fabrication (e.g., the lithography and etching processes) becomes difficult, and the coupling ratio is very sensitive to the beating length 0146-9592/14/216304-04$15.00/0
variation [4]. In order to overcome these issues, multimode interference (MMI) couplers were used as the coupler with a power ratio of 45∶55 between the two output ports in Ref. [4]. One should note that there are some disadvantages when introducing MMI couplers. First, an MMI coupler usually has a few percent of excess loss during this splitting process [4], and there is also mode conversion loss between the straight section and the bending section of a microring. This might introduce some notable excess loss for an MRR filter, particularly for the case with utlrasharp bending. Second, the power splitting ratio of an MMI coupler is fixed [15], and thus it is not available when one wants to choose another value for the power splitting ratio. Third, the length LMMI of the MMI section is usually several microns (e.g., LMMI ∼3.5 μm [4]), and the cavity length is increased by 2 LMMI , which increases the microring length and thus reduces the FSR in some degree. In order to solve these problems, in this Letter, we introduce bent directional couplers for high-order MRR optical filters to have a box-like filtering response. The SEM image of five-microring filter with bent coupler as shown in Fig. 1(a). In the present design, bent couplers are used for light coupling between the access waveguides and the side-microring. With bent couplers, the coupling ratio can be chosen flexibly by choosing the length of the coupling region appropriately even when Input W2 R1
R2
W1 (a) Drop
Bent coupler
Wgap (b)
Bent coupler
Fig. 1. (a) SEM image of the present five-microring filter with bent couplers. (b) SEM image of the bent coupler used here. © 2014 Optical Society of America
the gap width is relatively large. Furthermore, there is no excess loss theoretically, and the cavity length is the same as a regular microring. Figure 1(b) shows the structure of the bent couplers, in the coupling region of which there are two parallel bent waveguides, i.e., the bent access waveguide and the microring waveguide. In order to have efficient coupling between the access waveguide and the microring, the two parallel bent waveguides are designed to be with different widths w1 ; w2 according to the phase matching condition [16], neff1 R1 neff2 R2 , where neff1 and neff2 are the effective indices of the fundamental modes of the two bent waveguides, respectively, R1 and R2 are the corresponding bending radii, and R1 R2 w1 w2 ∕2 wgap . In our design, a relatively large gap (wgap > 150 nm) is chosen so that the fabrication is not difficult. The design with the phase matching condition also helps minimize the excitation of higher-order modes in the microring waveguides (which might be multimode). In this Letter a silicon-on-insulator (SOI) wafer with a 220-nm-thick top silicon and a 2-μm-thick buried-oxide layer is used, and there is a 1-μm-thick SiO2 uppercladding layer for the SOI nanowires used here. The refractive indices of Si and SiO2 are nSi 3.45 and nSiO2 1.45, respectively. As an example, we choose the widths w1 ; w2 to be around 450 nm and the radii R1 ; R2 to be around 5 μm regarding the single-mode condition as well as the bending loss. Figure 2 shows the calculated value of neff R for bending waveguides with different core widths (w 350; 375; …; 500 nm) as the radius R increases. Here the effective index neff is obtained by using a full-vectorial finite-difference method (FV-FDM) mode-solver numerically. According to the resonant equation for MRRs 2πneff R mλ, where m is the resonant order of the microring and λ is the wavelength in the vacuum, one has the product neff2 R2 11.1 μm (as indicated by the dash-dotted line in Fig. 2) when assuming that the resonant order m 45 and λ 1.55 μm. From this figure, one can easily have many solutions for w2 ; R2 to satisfy the equation neff2 R2 11.1 μm. According to phase matching condition, finally we choose the parameters w1 0.35 μm, R1 5.455 μm, w2 0.425 μm, and R2 4.886 μm for the bent coupler so that the gap is relatively large (wgap ∼182 nm) to make the fabrication not difficult. Figure 3(a) shows the simulated power coupling coefficients of the designed bent coupler for the case with light launched from the access waveguide as the angle
Power coupling ratio
November 1, 2014 / Vol. 39, No. 21 / OPTICS LETTERS 1.0 Total
0.8 0.6
0.8
Thru Cross
Thru
0.2
8 6 3
4
5
6
7
R (µm)
Fig. 2. Calculated value of neff R for the bent waveguides with different core widths (w 350; 375; …; 500 nm) as the radius R increases.
Cross
0.2
Input
Input
Cross
0.0
(a)
15 30 (degree)
45
0
(b)
0.2
0.4
0.6
wgap ( m)
Fig. 3. (a) Simulated power coupling ratio of the bent coupler as the angle θ of the coupling region increases when w1 0.35 μm, R1 5.455 μm, w2 0.425 μm, and R2 4.886 μm. (b) Coupling ratio of the inter-ring coupler as the gap width wgap varies when choosing R 4.886 μm and w 0.425 μm.
θ of the coupling region increases. Here the light propagation is simulated with a three-dimensional finite-difference time-domain (3D-FDTD) method. The simulation shows that the excess loss of this structure is as low as ∼0.04 dB in theory. The coupling ratio between the access waveguide and the microring is 0.45 as required when choosing θ 13.7°. As indicated by Ref. [3], the power coupling coefficients should be [0.45, 0.09, 0.45] for a two-ring filter, [0.45, 0.09, 0.09, 0.45] for a three-ring filter and [0.45, 0.09, 0.05, 0.05, 0.09, 0.45] for a five-ring filter, respectively. For the inter-ring coupler between two adjacent microrings, the coupling coefficients can be controlled by adjusting the gap between them, as shown in Fig. 3(b). For example, the gap widths are about 116 and 156 nm to achieve the power coupling coefficients of 0.09 and 0.05, respectively. The sensitivity of the power coupling ratios to the core/gap width deviation is also analyzed with a 3DFDTD simulation for the designed three couplers for the five-ring filter as an example (see Fig. 4). Assuming that there is a deviation Δw for the waveguides, one has w w0 Δw and wgap wgap0 –Δw for the waveguide width and the gap width, respectively, where w0 and wgap0 are the designed values. From Fig. 4(a) (see the curve with circles), the power coupling ratio for the bent coupler is not sensitive to the deviation Δw, which is an advantage and has been also proposed to realize a broad-band 3 dB coupler in Ref. [17] recently. In contrast, the inter-ring coupler is more sensitive to the deviation Δw (see the curves with squares and diamonds). When jΔwj < 20 nm, the coupling ratios 0
0.45
Bent coupler
-10
0.44
0.13
Power (dB)
w=350:25:500nm
wgap
0.4
0
Power coupling ratio
10
Thru Cross
2
0.4
0.46
12
Thru Total
0.6
0.0
14 neffR (µm)
1.0
6305
Inter-ring coupler #1
0.08 Inter-ring coupler #2
0.03 -0.02
(a)
-0.01
0
Δ w (µm)
0.01
0.02
Δw=20, 10, 0, -10, -20nm
-20 -30
-40 1548 (b)
1549.5 1551 1552.5 Wavelength (nm)
Fig. 4. (a) Sensitivity of the coupling ratio to the waveguide deviation Δw. (b) Calculated spectral responses for a five-ring filter when there is a deviation Δw.
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spectral responses are also calculated by using the analytical formulas given in Ref. [18] (see the thick curves). For this calculation, the coupling ratios are chosen as the values designed above. It can be seen that the measured results agree well with the calculated results. Their FSRs are about 18.4 nm, and the 3-dB bandwidths are 2.0, 2.6, and 2.38 nm, respectively. The measured out-of-band rejection ratios for the fabricated two-microring, threemicroring, and five-microring filters are about 25, 30, and 36 dB, respectively. The out-of-band rejection ratio of five-microring filter might be higher than the measurement result shown in Fig. 5(c) due to the limit of the sensitivity of the powermeter used in our measurement setup. Nevertheless, it can be seen that higher out-ofband rejection ratio is obtained by introducing more microrings. Both the measurement and simulation results also show that the spectral response is more box-like (with sharp transitions) when more microrings are cascaded. The response for the five-microring filter has rising and falling edges as sharp as 48 dB∕nm. From the measured spectral responses, one can also see that the fabricated two-microring, three-microring, and fivemicroring filters have an excess loss of
