1. Introduction

Multimode Interference (MMI) couplers [1] are an attractive alternative to directional couplers for power splitting in Photonics Integrated Circuits (PICs), as they typically ensure better tolerances to fabrication errors and significantly wider operation bandwidth. Right after their introduction in integrated optics, they have been adopted as power splitters in ring resonators and lasers, with significant advantages [2,3]. The feedback mechanism of ring resonators requires, by definition, the use of waveguide bends. Hence, the size of the resonator strongly depends on the minimum bending radii allowed by a given waveguide platform. A different feedback approach based on metal mirrors has been proposed for the first time by Bock et al. [4]. They simulated a device based on a 50:50 MMI splitter via 2-dimensional Finite Difference Time Domain (2D FDTD), assuming a micron-scale thick silicon waveguide (as we infer by the fact that the bulk silicon refractive index was assumed in 2D simulations) and perfect conductor mirrors. The choice of a 50:50 splitting ratio limited the quality factor to 516 and the finesse to 3.7. To the best of our knowledge, the concept has not been proven experimentally yet. Nevertheless, a similar resonator concept has been experimentally demonstrated based on a directional coupler with two gold reflectors on one of the two arms [5]. The device was fabricated on a submicron silicon photonics platform, and purposely designed to have low finesse and low quality factors. The measured mirror reflectivity was about 80%, with a quality factor of 260 and finesse 3.5. More recently a very similar concept based on Bragg mirrors has been demonstrated experimentally to have a single 15 GHz wide resonant peak [6]. The finesse was for sure at least one order of magnitude higher than in previous publications, even though the exact value cannot be easily deducted from the provided data. Compared to the commonly used ring-resonators, mirrored MMI splitters (or directional couplers) allow reducing the cavity length to a minimum, i.e. maximizing the free spectral range (FSR). Furthermore, when MMIs with uneven splitting ratios are used to build ring resonators, the through ports are in general not accessible [7], unless crossings are used, which would affect both losses and resonator length. Instead, this is not an issue for MMI resonators. On the other hand, unlike ring resonators, the challenge to achieve good MMI resonators is to minimize the loss of the mirrors providing the feedback mechanism.

In this paper we present the design, fabrication and characterization of MMI resonators designed to have significantly higher finesse (exceeding 16) and quality factors in the order of 10⁴. They are based on two different types of MMI splitters with splitting ratio 85:15 and 72:28 respectively [8,9] (in this paper we define the splitting ratio as the power in the cross port divided by the power in the bar port). The feedback mechanism of our resonators is based either on aluminum mirrors deposited on a silica layer covering the waveguide facet, or on purely dielectric MMI reflectors [10]. Cavity lengths vary from 95 μm to 348 μm, depending both on the MMI type and the reflector type. The paper is organized as follows: in Section 2 we present the MMI resonator concept and the equations describing its spectral response. In Section 3 we describe in details the different resonators that we designed for this work and their expected performances through numerical simulations. In Section 4 we describe the experimental results, including the fabrication process and the optical characterization. In Section 5 we present a detailed discussion of the results, by comparing the performances of the different designs with each other and with numerical simulations. In the last section we summarize the results and provide directions for future developments and potential applications.

2. MMI-resonators

The concept of MMI resonators has been introduced by Bock et al. [4]. They simulated a compact 2x2 50:50 MMI, which upper input and output ports were covered by a perfect conductor. Light launched from the lower input port was back-reflected in the same port when on-resonance and transmitted in the lower output port when off-resonance. In other words, the mirrored ports were collinear to each other as they were the free input and output ports. At variance with the original proposal, in this paper we will put the reflectors in non-collinear input and output ports, as shown in Fig. 1(d). This is because the shortest available MMI splitter with uneven power splitting have splitting ratios 85:15 and 72:28 respectively [8,9] i.e., unlike the lowest order directional couplers, they couple more in the cross port than in the bar port. Hence, since we aim at highest finesse and shortest resonator length, we have to switch the position of the mirrors on one side, as shown in Fig. 1(c) and Fig. 1(d). In both [4] and [5] an analytic model of the resonator has been derived in a way resembling the derivation for Fabry-Pérot interferometers [11]. Here we suggest an alternative approach, based on the topological equivalence explained in Fig. 1, where the perfect equivalence betweenan MMI-resonator and a ring resonator (i.e. a Fabry-Pérot resonator) is demonstrated, provided that the correct one-to-one transformation between the corresponding inputs and outputs is applied. The equivalence is easily showed by folding the microring resonator along the symmetry axis highlighted in Fig. 1(a). The resulting structure is perfectly equivalent to the micro-resonator of [5], and by moving one mirror from the upper to the lower port on the left-hand-side of the MMI splitter we finally show the equivalence with our MMI-resonators. It is worth noticing that the resulting structure can be interpreted as an “inverted” Fabry-Pérot interferometer. In fact, at variance with the Fabry-Pérot or the ring resonator in Fig. 1(a), the resonant wavelengths are reflected back and the non-resonant ones are transmitted. This proves that the MMI resonators can be effectively treated with the same equations already available for Fabry-Pérot resonators, once the role of each port is correctly identified. In particular the field reflection coefficient r can be expressed as

 

Fig. 1 Topological equivalence between an MMI-resonator (d) and an add-drop ring-resonator (a), by suitably mirroring the ring along the highlighted symmetry axis (b) and switching the ports of the equivalent mirrored directional coupler (c).

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In order to effectively exploit these formulas in the analysis of the experimental results of Section 5, we introduce the following quantities, namely the reflection extinction ratio in dB

3. Design of the resonators

3.1 MMI splitters

We designed all resonators based either on 72:28 or 85:15 MMI splitters made of 4 μm thick silicon strip waveguides surrounded by a silica cladding as shown in Fig. 2(a). For both types of MMI the access waveguide width is w = 2 μm. The gap g between access waveguides and the MMI width W are 1.2 μm and 8 μm for the 72:28 MMI and 1.25 μm and 6.5 μm for the 85:15 MMI. The optimal MMI lengths have been determined using the commercial software FIMMPROP through 2D simulations based on local mode expansion (see Fig. 2), and found to be 114.0 μm and 94.3 μm respectively. All simulations assume 1.55 μm wavelength and TE polarization. For the first MMI we have found 72.5:27.5 splitting ratio with 0.05 dB overall loss. For the second MMI we have found 85.5:14.5 splitting ratio with 0.04 dB overall loss.

 

Fig. 2 (a) Cross-section of the silicon strip waveguide (b) top view of a 2D simulation of a 72:28 splitter and (c) of a 85:15 splitter.

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Simulations of our MMI splitters show significantly lower losses compared to the ones in [4]. Losses of MMIs can be minimized by maximizing the ratio w/g between the access waveguide width and the gap between the access waveguides or, equivalently, the ratio w/W. This is because the narrower is the input waveguide compared to the MMI width, the higher is the spatial resolution required, i.e. the number of MMI modes needed to resolve the input mode shape. But the higher is the number of modes significantly coupled, the higher is the impact of the non-ideal distribution of the propagation constants [1], which degrades the fidelity of the output image. In fact, the optimization of the angled facets presented in [4], can be alternatively interpreted as an up-tapering of the access waveguide width. We designed our MMIs to have no angled facets but input waveguide widths significantly larger than the gaps, leading to one order of magnitude smaller losses than in [4] and no significant spectral oscillations. We also relaxed all critical sizes to be compatible with our standard fabrication process (see Section 4) based on UV lithography and thermal oxidation. We stress here that, even if our access waveguides are highly multimode, in all practical implementations they are coupled to single-mode rib waveguides [14] through suitable converters [15]. Propagation in the rib waveguides radiates away any light possibly coupled to higher order modes.

3.2 MMIs with reflectors

We have designed different types of reflecting elements, either based on aluminum mirrors or on purely dielectric waveguides. Three types of aluminum mirrors and two types of all-dielectric mirrors have been tested both on 72:28 and 85:15 MMI splitters, amounting to 10 different designs overall. The simplest designs are based on MMIs missing two non-collinear ports, let’s say the lower on the left hand side and the upper on the right hand side, like the one shown in Fig. 3(f). The silicon waveguides and MMIs are first covered with a 265 nm thick silica cladding, and then with a 200 nm thick aluminum layer that, at last, is selectively removed to cover the input and output regions only, as shown in Fig. 3(a)–3(c). Another layer of silica with thickness of 500 nm is then deposited to protect the metal from later process steps. Aluminum has been chosen mainly because it is the best reflecting CMOS compatible metal. The drawback is that aluminum has non-negligible absorption in the infrared. Even ifgold would have significantly lower losses, it is not only not CMOS compatible, but also, unlike aluminum, it doesn’t stick when deposited direct on silica or on silicon. From Fresnel equation, aluminum deposited direct on silicon, would give 92% reflectivity, in contrast to 97.7% in principle achievable with a hypothetic gold mirror (based on the refractive index data reported in [16]). But if a 265 nm thick quarter-wave of silica is placed between silicon and aluminum, transfer matrix calculations show that 98.4% reflectivity is achievable for a plane wave, while 2D numerical simulations of a 2 μm wide waveguide show that reflectivity in the fundamental mode is limited to 97.1% by diffraction losses. Depositing aluminum on silica solves also the additional issue of aluminum diffusion in silicon, which would lead to alloys and spikes at the interface, further worsening the mirror performances. We stress that the short (about 10 μm long) MMI and waveguide sections covered by aluminum are not significantly affected by the metal losses, thanks to both the thick silica interlayer and the high confinement in micron-scale silicon waveguides.

 

Fig. 3 (a) Metal mirror of type M1: the lower MMI waveguide is missing and the silica cladding around the input/output regions is covered by aluminum; (b) metal mirror of type M2, similar to M1, but with a thin non-etched trapezoidal shape in the bottom corner of the MMI, preventing corner rounding during fabrication; (c) metal mirror of type M3: the waveguide is not removed but tapered up to 4.5 μm and terminated in an aluminum coated T-shape to avoid corner rounding; (d) dielectric mirror of type D1; (e) dielectric mirror of type D2, with input waveguide tapered up and small non-etched triangles in the 45° mirrors to prevent corner rounding; (f) example of a 72:28 MMI resonator with M2-type mirrors; (g) detail of the left-hand-side of a 72:28 MMI resonator with M3-type mirror; (h) example of a 85:15 MMI resonator with D1-type mirrors.

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The MMI facets to be covered with aluminum have been designed in two different ways. The basic design is shown in Fig. 3(a) (type M1), and it is simply a standard MMI facet missing one of the two waveguides. A possible fabrication issue with this design is the rounding of the corner where one waveguide is missing. A rounded corner could distort the reflected phase front, leading to additional losses. This is why we designed the alternative MMI facet shown in Fig. 3(b) (type M2), where the corner is avoided by not etching the MMI side wall completely till the MMI facet. This ensures no rounding during the fabrication process and a perfectly straight mirror facet. The last reflector design based on aluminum is shown in Fig. 3(g) (type M3) and it is closer to the original proposal [4], as it relies on an MMI splitter with no access waveguide removed, with the only difference that, in our case, the aluminum mirrors are placed on two non-collinear waveguides. The mirrored waveguides Fig. 3(c) are tapered up to 4.5 μm width, in order to minimize diffraction effects, and the facet ends with a 500 nm thick T-shape, in order to prevent rounding during fabrication. Even if numerical simulations predict 98.3% reflectivity with an ideal waveguide facet, unfortunately the T facet induces diffraction losses and degrades the reflectivity to 91.5%.

We adopted as all-dielectric mirrors the MMI reflectors recently proposed by Kleijn et al. [10], and experimentally demonstrated on indium phosphide waveguides. To the best of our knowledge, we are the first to demonstrate this device on a silicon platform. An all-dielectric resonator is shown in Fig. 3(h), based on the MMI reflector highlighted in Fig. 3(d) (type D1). The MMI is 6.25 μm wide and 45.25 μm long. An alternative arrow-shaped design is shown in Fig. 3(e) (type D2), where two small triangles are added sideways in order to prevent rounding of the reflection facets during fabrication. In this second design the access waveguide was tapered up to 2.6 μm, in order to test possible benefits of a wider input mode. In fact, if on one hand enlarging the input mode improves the MMI image fidelity, on the other hand a wider mode will be more affected by the corner rounding in the arrow section. The MMI reflectors have been simulated and optimized with the 2D finite element method of COMSOL, and predicted to achieve up to 98.4% reflection in the fundamental mode. An example simulation is shown in Fig. 4, together with the simulated wavelength dependence and length tolerance of the device.

 

Fig. 4 (a) Electric field plot of a 2D simulation of an MMI reflector; (b) power back-reflected in the fundamental mode as a function of wavelength; (c) similar plot as a function of the MMI length change at 1.55 μm wavelength.

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3.3 Numerical simulations

We made some 2D numerical simulation of the simplest designed MMI resonators, i.e. the ones with only one access waveguide per side and covered with metal. Also in this case, we used the commercial software FIMMPROP, based on local mode expansion. The mirrors are simulated as a 500 nm thick aluminum layer on top of a 265 nm silica layer. In Fig. 5(a) and 5(b) we show the intensity pattern of the MMI resonators on resonance for the 72:28 MMI and the 85:15 MMI respectively. The corresponding spectral responses are shown in Fig. 5(c) and 5(d), in terms of transmission and reflection in the fundamental mode.

 

Fig. 5 (a) Intensity distribution of a 72:28 MMI resonance in a 2D simulation; (b) the same for a 85:15 MMI resonance; (c), transmission (blue) and reflection (green) spectra of the 72:28 MMI resonator; (d) the same for the 85:15 MMI resonator.

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Peak values and corresponding extinction values vary from resonance to resonance, as an effect of beatings of MMI modes. The 72:28 MMI resonances have a FWHM of 0.34 nm and FSR of 3.0 nm, leading to a finesse of 8.9. The best minimum and maximum losses are 0.2 dB and 21.2 dB in transmission, and 0.8 dB and 15.9 dB in reflection respectively. The 85:15 MMI resonances have a FWHM of 0.22 nm and FSR of 3.7 nm, leading to a finesse of 16.8. The minimum and maximum losses are 0.1 dB and 16.6 dB in transmission and 1.4 dB and 22.1 dB in reflection respectively. Due to its higher finesse, the 85:15 MMI has higher field enhancement in the cavity, so that the input and reflected intensities are significantly weaker than the intensity peaks in the resonator. Now we compare the found finesse values with predictions of (5). For the 72:28 MMI resonator we know from simulations that C = 0.717 (see Fig. 2) and R = 0.971, which, assuming no extra losses, leads to F = 8.7. Similarly for the other MMI resonator we find F = 16.2. These values are smaller than those found in the numerical simulations. The problem is that we are overestimating the mirror losses, assuming that they are placed on 2 μm wide waveguides. Instead, in these particular designs we have removed the output waveguides, and placed the mirrors on the MMI itself, leading to reduced diffraction losses. From (5), assuming A = 1, 8.9 finesse and C = 0.717 correspond to R = 0.980. Similarly, for the 85:15 MMI resonator the found 16.8 finesse corresponds to R = 0.978 assuming C = 0.848. This explanation is supported by the lower finesse values found in simulations of MMIs with all access waveguides, and mirrors placed on two non-collinear waveguides.

4. Experimental results

4.1 Fabrication

We have fabricated the designed structures on 4 µm thick SOI wafers based on the well assessed VTT silicon waveguide technology. The devices were fabricated using smart-cut silicon-on-insulator wafers from SOITEC. Initial SOI layer thickness was increased with epitaxial silicon growth. FilmTek 4000 spectrophotometer was used to measure the thicknesses of the SOI layer (4.25 ± 0.05 µm) and the underlying buried oxide (2.997 ± 0.002 µm). A 500 nm thick Tetraethyl orthosilicate (TEOS) layer was deposited on the wafer in LPCVD diffusion furnace to work as a hard mask in silicon etching. Waveguide fabrication was done using our standard double-masking multi-step process [17]. In the process, two mask layers are passively aligned with respect to each other, and two separate silicon etch-steps form the rib and strip waveguide structures and waveguide facets. Lithography steps were done using FPA-2500i4 i-line wafer stepper from Canon Inc. and pattern transfer to oxide hard mask was done using LAM 4520 reactive ion etcher with CF₄ and CHF₃ chemistry. Waveguides were etched into silicon using Omega i2l ICP etcher from SPTS Technologies. The etching was done with a modified Bosch process [18] using SF₆ and C₄F₈ as etch and passivation gases, respectively, and O₂ as an etch gas to break passivation polymer formed by C₄F₈. After silicon etching, TEOS hard mask was removed with buffered oxide etch (BOE). Hard mask removal was followed by wet thermal oxidation consuming 225 nm of silicon, and thermal oxide removal with BOE. This was done to smoothen the etched surfaces, and to thin the SOI-layer to its final thickness of approximately 4 µm. A 0.17 µm thick silicon nitride layer was then deposited on the wafer with LPCVD as an antireflection coating and to prevent the etching of buried oxide in later oxide wet etch process steps. This layer was patterned in hot phosphoric acid using a hard mask made of 0.25 µm thick LPCVD TEOS patterned with BOE. After silicon nitride layer patterning, 265 nm of LPCVD TEOS was deposited as a cladding layer for the waveguides. The cladding deposition was followed with sputtering of 200 nm of pure aluminum, in a MRC 903M sputtering system. Aluminum was then protected with 500 nm thick PECVD TEOS. As a last step, the oxide layers were removed from the waveguide facets with BOE etch, and wafer was diced into chips

4.2 Optical characterization

In order to characterize the losses of the fabricated MMI splitters we designed cascades of 1, 11, and 21 72:28 MMIs and 1, 9, and 17 85:15 MMIs. We didn’t use the standard binary tree approach both because of lack of space in the mask layout and because too high noise levels would affect the low power levels after several splits through the bar ports. Instead we exploited the cyclic property of the MMIs under study: cascading 5k + 1 identical 72:28 MMIs (k integer) still gives 72:28 splitting ratio, while cascading 4k + 1 identical 85:15 MMIs still gives 85:15 splitting ratio. Characterization at 1.55 µm wavelength of the first type of splitters resulted in 69.7:26.4 splitting ratio, i.e. 72.5:27.5 with 0.17 dB overall loss. The second type of splitters resulted in 82.4:14.7 splitting ratio, i.e. 84.9:15.1 with 0.13 dB overall loss. The splitting ratios are in good agreement with the numerical simulations, but the losses are significantly higher than predicted. This is due to fabrication imperfections, especially in the access waveguide region.

The spectral characterizations of the resonator transmissions are shown in Fig. 6. All curves are based on 1000 sample points, which are enough to properly resolve the narrow resonance dips. The plots correspond to the five different types of mirrors shown in Fig. 3(a)–3(e) and to the two types of MMIs. Blue continuous lines and red dashed lines are the data from 72:28 MMI resonators and 85:15 MMI resonators respectively. Best extinction values are found in the resonators with removed waveguides Fig. 6(a) and 6(b), while worst ones are found in those with aluminum mirrors placed on the waveguides Fig. 6(c). Similar to the simulation results of Fig. 5(c) and 5(d), all the experiments show significant variations from peak to peak of the same resonator. We didn’t measure the reflection spectra, since they are much affected by a relatively high level of back-reflection from the chip facet. Furthermore, as we will show in the next section, the transmission spectrum is more reliable than the reflection spectrum to estimate the resonator finesse and the mirror reflectivity in our experiments. In fact all experimental results are affected by spurious reflections from the input and output waveguide interfaces, leading to high frequency spectral oscillations of the order of ± 0.5 dB. These oscillations are due to non-ideal anti-reflection coating and would induce too high uncertainties trying to estimate the linewidths of resonant peaks in reflection. Instead using the extinction in transmission (4) can provide a more reliable estimation of the mirror reflectivity and of the resonator finesse through (5).

 

Fig. 6 (a) Experimental transmission spectra of 72:28 (blue solid line) and 85:15 (red dashed line) MMI resonators with M1-type mirrors; (b) same for the resonators with M2-type mirrors; (c) same for the resonators with M3-type mirrors; (d) same for the resonators with D1-type mirrors; (e) same for the resonators with D2-type mirrors.

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Measured maximum extinction values for the different resonators are reported in the first row of Table 1.

Table 1. Summary of the resonator properties

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5. Discussion

We now aim to exploit the experimental results to assess the quality of the fabricated mirror and the finesse of the resonators made out of them. As anticipated in the previous section, we can use the transmission extinction defined in (4) to evaluate the effective reflectivity $R\sqrt{A}$ of the mirrors, i.e. the reflectivity times the attenuation in half round trip for given values of the cross and bar MMI coupling C and B. We have plotted in Fig. 7 both the transmission and reflection extinction ratios E_r and E_t when B and C equal the simulated values Fig. 7(a) and 7(b) and the measured values Fig. 7(c) and 7(d). The figures clearly show that the transmission extinction has stronger dependence on effective reflectivity. Therefore, transmission spectra can give more accurate information than reflection spectra. In order to check the reliability of this approach, we apply this method to the simulations of Fig. 5(c) and 5(d), which correspond to extinction 21.0 dB and 16.5 dB. In Fig. 7(a) and 7(b) these values correspond to $R\sqrt{A}=\text{}0.980$ and $R\sqrt{A}=\text{}0.981$ respectively, which match very well the valuespreviously found, namely 0.980 and 0.978. These last two values were derived by inserting into (5) the finesse calculated as the ratio FSR/FWHM. Using the experimental extinction of the different resonators we can now determine the corresponding $R\sqrt{A}$values. For the ones with removed access waveguides we will use Fig. 7(a) and 7(b), because no loss can be ascribed to coupling to the access waveguides. For all the other ones we will take into account the additional loss and use Fig. 7(c) and 7(d) instead. The effective reflectivity of the mirrors is reported in Table 1 together with the corresponding finesse F and quality factor Q. For each type of resonator we have considered the resonance with the best measured extinction ratio in Fig. 6, and then used Fig. 7 to evaluate the corresponding $R\sqrt{A}$ value. From this value, F is easily calculated from (5) and Q is derived from F using (6). Finesse values as high as 13.1 have been found in resonators with metal mirrors directly deposited on the MMI facets. The best all-dielectric resonators achieved finesse as high as 9.9 and outperformed the resonators with metal mirrors placed on waveguides. Quality factors as high as 12.5⋅10³ have been measured in longer resonators.

 

Fig. 7 (a) Transmission (green) and reflection (blue) extinction of a 72:28 MMI resonator as a function of the effective reflectivity $R\sqrt{A}$ assuming the losses and splitting ratio found in numerical simulations; (b) the same for a 85:15 MMI resonator; (c) the same for a 72:28 MMI resonator, but assuming the losses and splitting ratio measured in the fabricated MMIs; (d) the same for the 85:15 MMI resonator.

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When comparing the found reflection values with the 2D numerical simulations, it should be taken into account that, in a real 3D device, diffraction losses can occur also in the vertical direction. Luckily, 2D simulations of a 4 um thick silicon slab waveguide with a quarter wave of silica predict 98.4% reflectivity for TE polarization, i.e. the same as a plane wave. Hence, we can straightforwardly apply the results found in 2D simulations to the 3D case. From Table 1 it can be seen that the experimentally found $R\sqrt{A}$ values are always significantly lower than the numerical estimated R values. The additional losses can come from non-ideal operation of the MMI splitters (which explain the different extinction ratios from resonance to resonance found both in Fig. 5 and Fig. 6), non-vertical mirror facets and corner rounding. For all 72:28 MMI resonators the discrepancy between simulations and experiment is systematically worse, hinting at the non-ideal MMI operation as one of the main causes. The almost identical effective reflectivity found for both resonators of type M3, hints at non-idealities in the facet itself, but also excitation of higher order modes in the waveguide bends and in the tapers could contribute. Rounding of the corner tip and non-vertical facets could be the reason why all the MMI mirrors do not perform as good as expected [10]. But, also in this case, the bent waveguides and the tapers could play a role. The best reflectivity and finesse are achieved by 85:15 MMI resonators with M2-type mirrors.

6. Conclusion

We have designed and fabricated MMI resonators with both metal mirrors and MMI mirrors on a micron-scale silicon photonics platform. Best dielectric mirrors reached up to 88.5% reflectivity (i.e. 0.5 dB loss), in line with previous results reported for similar structures in indium phosphide [10]. Best metal mirror reached up to 92.7% reflectivity (i.e. 0.3 dB loss). To the best of our knowledge, this represents the highest reflectivity achieved by a metal mirror on a PIC, leading to the highest finesse ever reported for an integrated resonator with metal mirrors. Significant improvements can come from optimization of the verticality of the waveguide etch process and from implementation of suitable optical proximity corrections to prevent corner rounding. Higher finesse can be achieved in principle by using more unbalanced splitting ratios like the ones demonstrated in [19], provided that the round-trip losses are significantly smaller than the bar-coupling coefficient B. The proposed resonators are promising candidates for optical filtering, external laser cavities and tunable wavelength selective laser mirrors. The proposed broadband reflectors can also find applications in reflective arrayed waveguide gratings.