1. Introduction

Silicon photonics integrated devices provide the opportunity to substantially miniaturize optics-based filters as compared to fiber-optics-based filters, and numerous companies are involved in silicon photonics research, see for example [1–9]. Resonator reflectors have been proposed for sensing applications [10–15], optical communication applications [15–17], optical feedback applications [16, 18–21], and have been experimentally demonstrated in a variety of configurations [10–16, 18–21, 23–25]. The features desired in a ring resonator reflector are application-dependent. For sensing applications, it is important that the free spectral range (FSR) of a ring resonator reflector be large enough so that a change in the ring’s resonance shift does not exceed its FSR [26]. A narrow bandwidth (large Q-factor) is also a desirable feature for sensing, as it allows smaller resonance shifts to be detected [26, 27]. In optical communications applications, a larger FSR allows more channels to be utilized for multiplexing and demultiplexing signals [28]. Also, in optical communications applications the required bandwidth is dependent upon a number of considerations, such as the operating data-rate. Therefore, flexibility in the design of the resonator’s bandwidth is necessary. In optical feedback applications involving narrow linewidth, single wavelength lasers, use of ring resonators can provide narrow bandwidths and large FSRs [29–32]. Therefore, in these applications, it is advantageous to eliminate the FSR. However, many of the ring resonator reflectors reported to date have FSRs, see for example [10–16, 18–20, 23, 25].

Nevertheless, reflector designs that eliminate the FSR have been reported [17,21,22,33–35]. For example, an all-pass silicon nitride microring resonator with a distributed Bragg reflector (DBR) has been experimentally demonstrated which showed suppression of minor notches in the through port and of minor peaks in the reflect port (i.e., no FSR) [21] and designs employing Fabry-Pérot structures composed of silicon directional couplers with silicon DBRs have also been experimentally demonstrated which showed elimination of the FSR [34,35]. Also, silicon Bragg grating reflectors, without ring resonators, have been experimentally demonstrated [12, 13, 36, 37].

In this paper, we experimentally demonstrate a grating-assisted silicon-on-insulator (SOI) racetrack resonator reflector by placing the racetrack resonator within a Mach-Zehnder interferometer (MZI) and adding contra-directional grating couplers (contra-DCs) to effectively eliminate the FSR. Our device is similar to those presented in [11, 16, 18], except that their devices do not use contra-DCs and their devices have FSRs.

2. Design

In order to eliminate the FSR of our device, we use contra-DCs [22, 38, 39]. Contra-DCs have been demonstrated to have highly wavelength-dependent coupling as compared to the coupling of co-directional couplers without gratings [40–47], and silicon racetrack resonators with contra-DCs have been experimentally demonstrated [38, 39, 45, 48] and have shown that the removal of the FSR is possible [38, 39, 45].

Figure 1(a) shows a diagram of our grating-assisted SOI racetrack resonator reflector where L_s is the length of the straight section of each of the branches of the MZI, L_b is the length of each S-bend, r is the radius of the bend regions of the racetrack resonator, and L_cd is the length of the contra-DC. Figure 1(b) shows a section of our contra-DC, where Λ is the grating period, G is the gap distance, w_a and w_b are the average waveguide widths of waveguide “a” and waveguide “b” of the coupler, respectively, and Δw_a and Δw_b are the corrugation widths for the gratings on waveguide “a” and waveguide “b” in the coupler, respectively [39, 47]. Also, we have chosen to use anti-reflection gratings to suppress the intra-waveguide Bragg reflections [39,41,44,47,49]. The bends of the racetrack resonator had widths equal to w_b. The input Y-branch of our device splits the light equally into the two MZI branches and the light couples into the racetrack resonator at wavelengths near the Bragg condition of the contra-DC while light at other wavelengths is not coupled into the ring but passes through the MZI and recombines at the output Y-branch. The major resonant peak will occur at that wavelength within the contra-DC passband that aligns with a resonance of the racetrack resonator [38, 39]. As a result, provided that only one resonance occurs within the passband of the contra-DC, all other resonant notches and peaks of the racetrack resonator can be suppressed. In this way, provided that the FSR of the racetrack resonator is sufficiently large, the FSR of our device can be effectively eliminated. The light that was coupled into the racetrack resonator from the top branch is coupled out of the racetrack resonator at the bottom branch and vice-versa. Hence, the light coupled out of the racetrack resonator in both branches is constructively recombined at the input Y-branch and can be detected at the reflect port [Fig. 1(a)].

 

Fig. 1 (a) Diagram of our reflector. (b) Diagram showing a section of our contra-DC with anti-reflection gratings [39].

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For the fabricated device that we present here, our mask layout for the device had the following design parameters: w_a was 450 nm and w_b was 550 nm [22,39,44,47], Δw_a was 30 nm and Δw_b was 40 nm [39,44,47], the waveguide heights were 220 nm [22,39,44,47], the bends of the racetrack resonator had widths of 550 nm [22, 39], G was 300 nm, r was 3 μm, L_cd was 56.784 μm (the number of grating periods was 182 and Λ was 312 nm), L_s was 156.784 μm, and L_b was 10.705 μm. Each MZI S-bend had a waveguide width of 500 nm which was then tapered to 450 nm [the tapered waveguide regions are shown in blue in Fig. 1(a)]. The reflector design was fabricated using electron beam lithography [50] and the device was covered with an oxide cladding. Shallow-etched fiber grating couplers were used for coupling light into and out of the device [51]. For testing purposes, we added an extra Y-branch before the input port shown in Fig. 1(a) so that we could separate the reflected light from the light injected into the device and, thus, be able to measure the reflect port spectrum. The designs of the Y-branch junctions were based on [52, 53].

3. Principle of operation

In this section, we conceptually describe the principle of operation of our reflector design. Figures 2(a) and 2(b) show the theoretical contra-DC power coupling and power transmission factors versus wavelength, respectively, for the straight sections of the racetrack resonator. Figure 2(c) shows the theoretical spectrum for the reflect port when using contra-DCs, as well as when using co-directional couplers without gratings, to couple the light into and out of the racetrack resonator. We can clearly see that our device suppresses all but one of the peaks and, therefore, effectively eliminates the FSR. Figure 2(d) shows the theoretical through port spectrum when using contra-DCs, as well as when using co-directional couplers without gratings, which shows that the FSR is also effectively eliminated at the through port when contra-DCs are used. For these figures, we have assumed the following values: the coupling coefficient is 2000 m⁻¹; the Y-branch junction loss is 0.28 dB [52]; and the propagation loss for the racetrack resonator and MZI branches is 3 dB/cm. It should be noted that these theoretical results will not exactly match the experimental results since we have assumed values for the coupling coefficient and losses and we have ignored all scattering, e.g., backscattering and scattering from dielectric discontinuities. For the contra-DCs, we have assumed no co-directional coupling due to the large difference in the waveguide widths of the contra-DCs [38, 39, 44, 54]. For example, [44] experimentally demonstrates a contra-DC (average waveguide widths of 450 nm and 550 nm) that has small co-directional coupling. Also, the phases of the MZI branches, including propagation through the contra-DCs, were calculated assuming waveguide widths of 450 nm. For the modeling of the reflector without gratings (i.e., using normal co-directional couplers), the co-directional power coupling factor was set to the maximum contra-DC power coupling factor that was used for the device with gratings [see red dot in Fig. 2(a)]. Also, the co-directional power transmission factor was set to the minimum contra-DC power transmission factor that was used for the device with gratings [see red dot in Fig. 2(b)]. The phases of the MZI branches, including the co-directional coupling regions, were calculated assuming waveguide widths of 550 nm. The modeling of the racetrack resonator with and without contra-DCs is similar to the model used in [39]. The effective indices of the waveguides were calculated using MODE Solutions by Lumerical Solutions, Inc., [39, 47, 55]. The reflect port transfer function (Eq. 8) and the through port transfer function (Eq. (15)) are derived and given in the appendix for the device with gratings.

 

Fig. 2 (a) Theoretical contra-DC power coupling factor versus wavelength (the red dot indicates the value used for the co-directional power coupling factor of the reflector without gratings). (b) Theoretical contra-DC power transmission factor versus wavelength (the red dot indicates the value used for the co-directional power transmission factor of the reflector without gratings). Theoretical comparison of (c) the reflect port spectrum and (d) the through port spectrum of our reflector with contra-DCs and with co-directional couplers without gratings.

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4. Measurement results

Here we present experimental results for our device. Figures 3(a) and 3(b) show the experimental reflect port spectrum (normalized to its maximum power) measured at a temperature of 25°C, which show the elimination of the FSR. For the reflect port spectrum, the reflect port peak suppression is 10.3 dB and the 3-dB bandwidth is 0.147 nm. The red dot in Fig. 3(b) represents the wavelength at which data was sent through the device to its reflect port (as described below). Figure 4(a) shows the experimental through port spectrum [normalized to the maximum power within the wavelength region shown in Fig. 4(a)] measured at a temperature of 25°C, which also shows the elimination of the FSR. The extinction ratio of the major notch is about 7 dB and the extinction ratio of the largest minor notch is about 1 dB. Improved performance, in terms of increased reflect port suppression, is likely achievable by thermally tuning the contra-DCs and/or the bend regions of the racetrack resonator to compensate for fabrication variations (see experimental results in [39]). Although there is significant suppression of the minor notches, it is still important to determine the extent of the through port dispersion within the regions of the suppressed minor notches (for example, see [56]). Figure 4(b) shows the measured through port dispersion at wavelengths near the first minor notch to the right of the major notch. The green dot in Fig. 4(b) represents the wavelength at which data was sent through the device to its through port (as described below). The through port dispersion is the average of 300 measurements using an Optical Vector Analyzer™ STe by Luna Innovations, Inc., [47].

 

Fig. 3 (a) Measured reflect port spectrum and (b) the spectrum at wavelengths near the major peak (the red dot indicates the wavelength at which the data in Fig. 5(a) was sent through the device).

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Fig. 4 (a) Measured through port spectrum at wavelengths containing the major notch and one of the minor notches. (b) Measured through port dispersion at wavelengths near the minor notch (the green dot indicates the wavelength at which the data in Fig. 5(b) was sent through the device).

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Previously, we demonstrated a method to determine the coupling coefficients of fabricated contra-DCs and verified the approach using contra-DCs fabricated on three separate fabrication runs [47]. One of our fabricated contra-DCs in [47] had the same as-designed average waveguide widths, waveguide corrugation widths, grating period, and gap distance as the contra-DC we use in this paper. Also, the same fabrication process was used for the contra-DCs in this paper as the one used in [47]. The average extracted coupling coefficient for contra-DCs with gap distances of 300 nm based on the results of the three fabrication runs in [47] is 4139 m⁻¹. Using this extracted coupling coefficient, we have simulated the power coupling factor versus wavelength of the contra-DC as well as the reflect port spectrum of the reflector. The simulated 3-dB bandwidth of the contra-DC is 4.450 nm. The value for the maximum reflectivity, R, in dB [R_dB = 10log₁₀(R)] of the reflector based on the simulated results is −1.28 dB. However, the maximum, inherent R_dB (removing all loss mechanisms) is 0.00 dB, therefore, as SOI processing methods improve, e.g., reductions in waveguide propagation losses [57], the reflectivity of our device should only improve and will be limited only by the losses in the Y-branch junctions and the radiation losses in the ring.

Next, data was sent through the device using an external MZI modulator and eye diagrams were obtained (we used a set-up similar to the ones in [44,56,58]) at the reflect port and through port of our device. Figure 5(a) shows an open eye diagram (extinction ratio, ER, is 13.0 dB) at the reflect port for a 12.5 Gbps NRZ PRBS-31 signal operating at a wavelength of 1535.08 nm. Next, we sent a 12.5 Gbps NRZ PRBS-31 signal operating at a wavelength of 1539.42 nm, corresponding to the center of one of the through port minor notches, through our device and measured the eye diagram at the through port. Figure 5(b) shows that an open eye diagram (ER = 14.0 dB) is achievable at the through port when operating at the center of the minor notch. Since the dispersion within the through port minor notch is highly wavelength-dependent [as shown in Fig. 4(b)], it is expected that a change in the operating wavelength will affect the extent of achievable eye opening (a similar trend has been experimentally demonstrated within one of the minor notches of a quadruple Vernier racetrack resonator [56]). As compared to the reflectors presented in [21, 34, 35] which also have no FSRs, here, we have verified that our reflector can be used to transmit data.

 

Fig. 5 (a) Measured reflect port eye diagram for a 12.5 Gbps signal operating at a wavelength of 1535.08 nm. (b) Measured through port eye diagram for a 12.5 Gbps signal operating at a wavelength of 1539.42 nm.

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Also, of interest is investigating the residual signal at the major notch of the through port, i.e., when the signal is being reflected. Hence, we measured eye diagrams for a 12.5 Gbps NRZ PRBS-31 signal operating at the wavelength corresponding to the center of the major notch for both the through and reflect ports. Figures 6(a) and 6(b) show the two eye diagrams side-by-side. As expected, the eye diagram at the through port major notch is more closed as compared to the eye diagram at the reflect port major peak.

 

Fig. 6 (a) Measured through port eye diagram for a 12.5 Gbps signal and (b) measured reflect port eye diagram for a 12.5 Gbps signal both operating at the wavelength corresponding to the center of the major notch and are on the same scale.

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We then measured the spectrum of our device at different temperatures by heating the entire device. Figure 7(a) shows the experimental results when the temperature is changed from 15°C to 55°C (each measurement was normalized to its maximum power). Since our device suppresses all but one of the major peaks, we could adjust the temperature such that the major peak shifts over a wavelength range larger than the wavelength range that would correspond to the FSR of our device without gratings, i.e., the racetrack resonator’s FSR which we call FSR_rr [Fig. 7(b)]. The resonant peak wavelength temperature dependence of our device is 0.0703 nm/°C [Fig. 7(b)], which provides the potential for our device to be used in temperature sensing applications, see [10, 14, 59–63].

 

Fig. 7 (a) The reflect port spectrum of our device that has a gap distance of 300 nm measured at different temperatures where from left to right the peaks correspond to 15°C, 25°C, 35°C, 45°C, and 55°C. (b) Resonant peak wavelength versus temperature (dots indicate the measured results and the red line is the fit).

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Table 1 shows a comparison between previously reported on FSR-free reflectors [21, 34–36] and our reflector. Our reflector is substantially smaller than the reflectors presented in [21] and [34]. The reflectors in [35] and [36] are more compact than our device, however, our 3-dB bandwidth is much smaller than theirs. Although our device does not have the smallest footprint, it can be re-designed to optimize the footprint by using contra-DC bus waveguides that have widths of 500 nm, which would enable us to remove the tapered waveguide sections and, therefore, our device could have a footprint of 80.8 μm × 8.1 μm. The reflectivities presented in [21] and [36] are higher than our device’s reflectivity, however, the reflect port suppression (suppression is defined as the difference between the maximum intensity of the major peak and the maximum intensity of the largest minor peak) of our device is larger and the bandwidth is smaller as compared to those in [21] and [36]. Also, our reflect port suppression is comparable to the suppressions seen in [34] and in [35]. Additionally, [21, 34–36] provide no theoretical or experimental results for the dispersion of their devices and, thus, it is not possible to determine the extent to which the signal may be degraded by these reflectors. We, however, have experimentally demonstrated the through port dispersion at one of the minor through port notches as well as verified that our reflector can operate on PRBS data.

Table 1. Comparison of FSR-free reflectors.

View Table

5. Conclusion

We have presented conceptual, theoretical (see appendix), and experimental results that show that it is possible to effectively eliminate the FSR of a SOI racetrack resonator reflector by using contra-DCs. The experimental results show a reflect port suppression of 10.3 dB. Also, open eye diagrams were measured at the reflect port and the through port of our device. Our reflector can also be used as a temperature sensor with a temperature-dependent spectral shift of 0.0703 nm/°C.

Appendix

To determine the transfer functions of our reflector, we used Mason’s rule [64–68]. Our reflector has two loop gains, G_L1 and G_L2, which are shown graphically in Fig. 8 and given by,

(1)$$G_{L1}=G_{L2}=t_{\mathit{cd}}^2{X}_r,$$

where t_cd is the contra-DC field transmission factor [54] (we have included the loss and the phase due to the length of the coupler [39]) for the straight sections of the racetrack resonator. X_r = exp(− jβ_rL_r − α_rL_r) where β_r is the propagation constant of the bend regions of the racetrack resonator, α_r is the field loss coefficient of the bend regions of the racetrack resonator, and L_r is the length of the racetrack resonator excluding the lengths of the contra-DCs. t_cd is given by [39, 54],

(2)$$t_{\mathit{cd}}=\frac{s{e}^{\frac{j\mathrm{\Delta }\beta }{2}{L}_{\mathit{cd}}}}{s\text{cosh}(s{L}_{\mathit{cd}})+\frac{j\mathrm{\Delta }\beta }{2}\text{sinh}(s{L}_{\mathit{cd}})}{e}^{-j{\beta }_b{L}_{\mathit{cd}}-{\alpha }_b{L}_{\mathit{cd}}},$$

where Δβ = β_a + β_b − 2π/Λ [54], β_a is the propagation constant of the portion of the contra-DC within the racetrack resonator’s bus waveguide, β_b is the propagation constant of the portion of the contra-DC within the racetrack resonator, Λ is the grating period, $s={\left({\left|\kappa \right|}^2-\mathrm{\Delta }{\beta }^2/4\right)}^{\frac{1}{2}}$ [54], κ is the coupling coefficient, α_b is the field loss coefficient of the portion of the contra-DC within the racetrack resonator, and L_cd is the length of the contra-DC. In our model, we have assumed κ is real-valued since a complex-valued κ would only result in additional phase terms in the numerator of the reflect port transfer function (Eq. 8).

 

Fig. 8 Diagram showing the loop gains, G_L1 and G_L2.

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The determinant, Δ, of our reflector is given by,

(3)$$\mathrm{\Delta }=1-(G_{L1}+G_{L2})+G_{L1}{G}_{L2}.$$

The reflect port has two forward path gains, G_P1 and G_P2, (shown graphically in Fig. 9) and two co-factors, Δ_P1 and Δ_P2,

(4)$$G_{P1}=G_{P2}=\frac{{\kappa }_{\mathit{cd}}^2{X}_r^{\frac{1}{2}}{X}_{mzi}^2{K}^2}{2},$$

(5)$${\mathrm{\Delta }}_{P1}=1-G_{L2},$$

(6)$${\mathrm{\Delta }}_{P2}=1-G_{L1},$$

where κ_cd is contra-DC field coupling factor [54], X_mzi = exp(− jβ_mziL_mzi − α_mziL_mzi), β_mzi is the propagation constant of the MZI branch, α_mzi is the field loss coefficient of the MZI branch, L_mzi is the length of one of the MZI S-bends plus the length of one of the tapered waveguide regions of the MZI branch, and K accounts for the field reduction going through each of the Y-branch junctions. κ_cd is defined as [54],

(7)$${\kappa }_{\mathit{cd}}=\frac{-j\kappa \text{sinh}(s{L}_{\mathit{cd}})}{s\text{cosh}(s{L}_{\mathit{cd}})+j\frac{\mathrm{\Delta }\beta }{2}\text{sinh}(s{L}_{\mathit{cd}})}.$$

 

Fig. 9 Diagrams showing the two forward path gains, G_P1 and G_P2, from input port to reflect port.

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Therefore, the reflect port transfer function is,

(8)$$T{F}_{\mathit{reflect}}=\frac{G_{P1}{\mathrm{\Delta }}_{P1}+G_{P2}{\mathrm{\Delta }}_{P2}}{\mathrm{\Delta }}.$$

The through port has four forward path gains, G_P3, G_P4, G_P5, and G_P6, (shown graphically in Fig. 10) and four co-factors, Δ_P3, Δ_P4, Δ_P5, and Δ_P6,

(9)$$G_{P3}=G_{P4}=\frac{t_{cd-bus}{X}_{mzi}^2{K}^2}{2},$$

(10)$${\mathrm{\Delta }}_{P3}={\mathrm{\Delta }}_{P4}=\mathrm{\Delta },$$

(11)$$G_{P5}=G_{P6}=\frac{{\kappa }_{\mathit{cd}}^2{t}_{\mathit{cd}}{X}_r{X}_{mzi}^2{K}^2}{2},$$

(12)$${\mathrm{\Delta }}_{P5}=1-G_{L2},$$

(13)$${\mathrm{\Delta }}_{P6}=1-G_{L1}.$$

In Eq. (9), t_cd–bus is defined as the contra-DC bus waveguide field transmission factor [54] (we have included the loss and the phase due to the length of the coupler [39]),

(14)$$t_{\mathit{cd}–\mathit{bus}}=\frac{s{e}^{\frac{j\mathrm{\Delta }\beta }{2}{L}_{\mathit{cd}}}}{s\text{cosh}(s{L}_{\mathit{cd}})+\frac{j\mathrm{\Delta }\beta }{2}\text{sinh}(s{L}_{\mathit{cd}})}{e}^{-j{\beta }_a{L}_{\mathit{cd}}-{\alpha }_a{L}_{\mathit{cd}}},$$

where α_a is the field loss coefficient of the portion of the contra-DC within the racetrack resonator’s bus waveguide. In our model we have set α_r = α_mzi = α_a = α_b, β_r = β_b, and β_mzi = β_a.

 

Fig. 10 Diagrams showing the four forward path gains, G_P3, G_P4, G_P5, and G_P6, from input port to through port.

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Therefore, the through port transfer function is,

(15)$${\mathit{TF}}_{\mathit{through}}=\frac{G_{P3}{\mathrm{\Delta }}_{P3}+G_{P4}{\mathrm{\Delta }}_{P4}+G_{P5}{\mathrm{\Delta }}_{P5}+G_{P6}{\mathrm{\Delta }}_{P6}}{\mathrm{\Delta }}.$$

Acknowledgments

We acknowledge the Natural Sciences and Engineering Research Council of Canada, CMC Microsystems, the SiEPIC program, Lumerical Solutions, Inc., and Mentor Graphics. We thank Anritsu for the use of their MP1800A Signal Quality Analyzer and Richard Bojko for fabrication of the device. We thank Dr. Wei Shi, Han Yun, Alex MacKay, Yun Wang, and Jonas Flueckiger for their help. Part of this work was conducted at the University of Washington Nanofabrication Facility, a member of the NSF National Nanotechnology Infrastructure Network.

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