Nanophotonic Bragg grating assisted Mach–Zehnder interferometers for O-band add-drop filters

Abstract

Spectral filters are fundamental building blocks in integrated photonics. Bragg grating filters have been demonstrated in silicon waveguides with a wide range of spectral responses and are suitable for wavelength division multiplexing applications. However, retrieving Bragg grating reflections typically requires external components such as fiber optic circulators. In this work, we develop fully integrated add-drop filters based on cladding-modulated Bragg gratings incorporated in a Mach–Zehnder interferometer configuration. We design complex spectral filtering devices with single and dual-band flat-top responses for the specified bandwidth. Additionally, we propose a novel design methodology which aims to minimize phase errors within the filters. We experimentally demonstrate add-drop filters with single-band and two-band rejection spectra at the datacom O-band, fabricated on a 220-nm thick silicon-on-insulator platform. Our results show an insertion loss below 1 dB and a crosstalk of around −20 dB at the channel center for a 4.5-nm wavelength grid and 3-nm wide channels.

Introduction

Figure 1

(a) Schematic (top view) of the integrated interferometer-assisted cladding-modulated Bragg gratings. (b) Scanning electron microscope (SEM) image of an exemplary cladding-modulated Bragg grating that implements an arbitrary reflection response. (c) Detailed schematic of the cladding-modulated Bragg grating geometry. The proposed device operating as (d) a single-band add-drop filter and (e) a two-band interleaver.

Integrated spectral filters are important components used in many application areas, including quantum optics^1,2, biochemical sensing³, programmable⁴ and microwave⁵ photonics, and telecommunications^6,7,8. One of the main applications of spectral filters in telecom and datacom is wavelength division multiplexing (WDM), which underpins modern long-haul and high-capacity broadband access networks^9,10. Recently, attention has been drawn towards local area network wavelength division multiplexing (LAN-WDM), a potential standard for 25 Gbps optical modules in fronthaul connections of 5G networks and large datacenters^11,12,13,14. LAN-WDM¹⁵ requires a channel bandwidth ($\textrm{BW}$) of 3 $\text { nm }$, which places it between coarse WDM (CWDM, $\textrm{BW}\sim 20\ \text { nm }$) and dense WDM (DWDM, $\textrm{BW}\sim 0.4\ \text { nm }$). Wavelength multiplexers based on arrayed waveguide gratings (AWG) are typically used for DWDM applications, and allow multiplexing hundreds of channels over large operation bandwidths^16,17,18. Coupled micro-ring resonators, cascaded Mach–Zehnder interferometers, waveguide Bragg gratings, multimode Bragg gratings and contra-directional couplers have also been developed for WDM applications. Ring resonators are typically utilized in add-drop filter (ADF) devices, but they are inherently limited by their free spectral range (FSR)^19,20. Cascaded Mach–Zehnder interferometers have been demonstrated with multiplexing capability of over a dozen channels with moderate insertion loss (IL), but with comparatively large footprint^21,22. Waveguide Bragg gratings (WBGs) are appropriate for implementing flat responses with a virtually unlimited FSR, but their reflected drop bands need to be recovered using external circulators²³. Multimode Bragg gratings (MMBGs) reject specific bands by coupling them backwards to higher order modes, and additional components such as adiabatic directional couplers are needed for add-drop operation^24,25. Contra-directional couplers (CDCs) leverage a Bragg grating that directs its reflected signal to an exclusive drop port²⁶, but it is challenging to achieve narrow spectral features for CDCs implemented in silicon waveguides²⁷. A detailed comparison of existing design strategies can be found in Table 1. In this context, interferometer-assisted Bragg gratings appear as a promising alternative, allowing for precise spectral tailoring and at the same time providing an exclusive drop port without the need for external circulators²⁸.

Table 1 Summary of existing design approaches of silicon-on-insulator O-band add-drop filters.

In this work, we design and experimentally demonstrate add-drop filters based on interferometer-assisted Bragg gratings with arbitrary spectral response, leveraging the cladding-modulated grating comprising loading segments judiciously positioned in the evanescent field of a silicon wire waveguide^33,34,35,36. The schematic of the proposed device is illustrated in Fig. 1a. Two identical Bragg gratings are incorporated in the arms of a Mach–Zehnder interferometer. Fig. 1b shows a SEM image of a fabricated cladding-modulated Bragg grating implemented on the 220-nm thick silicon-on-insulator (SOI) platform, and details of the topology are presented in Fig. 1c. The reflection and transmission spectra of the interferometer with Bragg gratings phase-match at the drop and through ports of the device, respectively. This allows to utilize the filter without an external circulator and, at the same time, enables the add-drop operation. Furthermore, we develop a design methodology that optimizes filter dimensions while minimizing phase errors for given fabrication constraints. We focus here on two designs: a single-band add-drop filter and a two-band interleaver, shown in Fig. 1d and e. Both designs comply with the aforementioned LAN-WDM standard.

Design and experimental results

Figure 2

(a) Strongest coupling synthesizable by the grating, $\kappa (s_\mathrm{min})$, and maximum coupling coefficients required by the 1-band (blue line) and the 2-band (magenta line) spectra, $\max {(\kappa _n)}$. The segment separation was fixed to $s=s_\mathrm{min}$, and the rest of the geometry parameters were tuned at each point to $\Lambda =\Lambda _\mathrm{Bragg}(\lambda _0)$, $L_\mathrm{S}=\textrm{DC}\cdot \Lambda _\mathrm{Bragg}$ and $W_\mathrm{S}=2/3W_\mathrm{c}$, for different values of the duty cycle. (b, c) 2-band and 1-band target reflection spectrum definition, respectively. (d) Final profiles of coupling coefficients for the 1-band (blue line) and 2-band (magenta line) target reflection spectra. These profiles were calculated using the layer-peeling algorithm, and their maxima correspond to intersection points of blue and magenta lines with the black line for $\textrm{DC}=0.4$ in Fig. 2a.

The reflection spectrum of a uniform Bragg grating is a single pass band whose bandwidth is mainly determined by its coupling coefficient, $\kappa$³⁷. Any other arbitrary reflection spectrum $\varGamma (\lambda )$ can be achieved by adequately adjusting the coupling coefficient at each period along the grating. The layer-peeling algorithm³⁸ is a well-known method for transforming $\varGamma (\lambda )$ into a spatial profile of coupling coefficients, $\kappa _n$. The topology of the Bragg grating needs to be selected to allow for the synthesis of the entire $\kappa _n$ range. In a cladding-modulated Bragg grating (Fig. 1a–c), reflections are due to evanescent field interaction with lateral loading segments. The strength of this interaction determines the coupling coefficient, which can be tuned for each period by adjusting the segment separation ($s_n$) for given segment size ($L_\mathrm{S}\times W_\mathrm{S}$) and waveguide core width ($W_\mathrm{c}$). The selection of geometrical parameters must ensure that minimum feature size (MFS) is respected for the full design range of coupling coefficients. Since segments can be placed several micrometers apart from the waveguide core, low coupling strengths can be readily synthesized. This strategy overcomes the fabrication limitations of sidewall-modulated Bragg gratings, which typically require very small feature sizes or the use of multi-level etching processes^26,39,40. On the other hand, the maximum coupling coefficient is limited by the minimum segment separation, $s_\mathrm{min}$, which depends on foundry design rules. In order to accommodate this constraint, we start our design by determining dimensions of $L_\mathrm{S}\times W_\mathrm{S}$ and $W_\mathrm{c}$ to ensure that the strongest coupling our specific geometry allows matches the maximum coupling required to implement the target reflection spectrum, i.e. $\kappa (s_\mathrm{min})=\max {(\kappa _n)}$.

In our design flow, we first calculate the strongest coupling, $\kappa (s_\mathrm{min})$, as a function of the waveguide core width, $W_\mathrm{c}$. For this purpose, we choose the target central wavelength to match a specific LAN-WDM channel, $\lambda _0=1309\ \text { nm }$, and fix the segment separation to $s_\mathrm{min}=100\ \text { nm }$ to maximize field interaction with the loading segments. Then, for each waveguide core width, we tune the grating period ($\Lambda$) to meet the Bragg condition at the central wavelength, rescale segment size to $W_\mathrm{S}=2/3W_\mathrm{c}$ and $L_\mathrm{S}=\textrm{DC}\cdot \Lambda _\mathrm{Bragg}$, and evaluate the coupling coefficient with MIT Photonic Bands solver^41,42 (see Methods). Calculated coupling coefficients are shown in Fig. 2a (black lines), for TM polarization and several duty cycles. TM-polarized modes are less affected by sidewall imperfections thus improving phase coherence along the grating. The $\kappa (s_\mathrm{min})$ decreases as the waveguide core widens, due to an increasingly confined grating mode hence its reduced interaction with loading segments. In the next step, we calculate the layer-peeling transforms of target reflection spectra (shown in Fig. 2b and c) as a function of $W_\mathrm{c}$. Then, we select the maximum required coupling coefficient of each transform, $\max {(\kappa _n)}$, as exemplified in Fig. 2d. Blue and magenta curves of Fig. 2a correspond to maximum coupling coefficients required by 1-band and 2-band reflection spectra, respectively. We chose a duty cycle of $\textrm{DC}=0.4$ and the maximum waveguide core width ($W_\mathrm{c}$) for each filter. This strategy helps improve the fabricability of the gratings, because this duty cycle maximizes field interaction with the loading segments, and wide waveguide cores are generally less sensitive to fabrication imperfections^23,43. Figure 2d shows the obtained coupling coefficient profiles for our final designs. Note that $\max {(\kappa _n)}$ of the 2-band grating is two times larger compared to the 1-band grating, since the 2-band reflection spectrum covers twice as much bandwidth as the 1-band reflection spectrum.

Table 2 Parameters summary of the designed cladding-modulated Bragg gratings.

Figure 3

(a) Coupling coefficient as a function of segment separation, $\kappa (s)$, for the cladding-modulated Bragg gratings implemented in the 1-band (blue line) and the 2-band (magenta line) filter configurations. (b) Separation distance, $s_n$, optimized for the 1-band (blue curve) and the 2-band (magenta curve) target reflection spectra (insets, orange curves). Insets also show the synthesized reflectance spectra (black curves).

In the subsequent simulations, both $W_\mathrm{c}$ and $L_\mathrm{S}\times W_\mathrm{S}$ of the gratings remained fixed at the nominal values (see Table 2), and the grating length was limited to 300 $\upmu {\textrm{m}}$ or less to minimize phase decoherence arising from fabrication imperfections⁴⁴. The segment separation was adjusted to match the required coupling coefficient at each period of the gratings, $\kappa _n$. To this end, we calculated coupling coefficient as a function of segment separation for both 1-band and 2-band gratings. In a cladding-modulated Bragg grating the coupling coefficient exponentially decays with segment separation³³, $\kappa (s)=\kappa _0\exp (-\gamma _\mathrm{e}s)$. Both $\gamma _\mathrm{e}$ and $\kappa _0$ of each grating were calculated based on band diagram simulations with varying s. Then, the inverse of the resulting exponential functions (Fig. 3a) were used for mapping $\kappa _n$ to $s_n$. The separation profiles ($s_n$) shown in Fig. 3b and c correspond to layer-peeling transformation of 1-band and 2-band target reflection spectra (Fig. 3b and c insets, orange curves) and subsequent mapping through calculated exponential functions. Due to the design length of the filters, their synthesized reflection spectra (Fig. 3b and c insets, black curves) differ slightly from the ideal target curves (Fig. 3b and c insets, orange bands). Note that both gratings meet the same minimum segment separation, $s_\mathrm{min}$, constrained by design.

The designed cladding-modulated Bragg gratings were incorporated in a Mach–Zehnder interferometer configuration (Fig. 1a). The input signal is evenly divided by the first multi-mode interference device (MMI) into two arms with a phase difference of 90$^\circ$ and coupled to a pair of identical cladding-modulated Bragg gratings. After being reflected by the Bragg gratings with identical reflection spectrum, $\varGamma (\lambda )$ , the split signals recombine constructively at the drop port and destructively at the input port due to the 180$^\circ$ phase difference at the latter caused by back-and-forth propagation through the MMI. A similar behaviour is observed at the through and add ports: the former exhibits the transmission spectrum of the Bragg gratings, $T (\lambda )$ , and, ideally, no power is transmitted to the latter. MMIs were used at the input and output stages, with optimized MMI width and length of $W_\mathrm{MMI}=6.25\ \upmu {\textrm{m}}$ and $L_\mathrm{MMI}=147.5 \upmu {\textrm{m}}$, respectively. The calculated insertion loss and imbalance of the MMI were less than 0.4 dB and phase error lied below 0.3$^\circ$ in the wavelength range 1270 nm − 1330 nm. We obtained the expected frequency responses of the drop and through ports, with identical gratings incorporated in both interferometer arms, combining the simulated S-matrices of the corresponding structures. These responses are represented with dashed lines in Fig. 4a and b, for both add-drop filter designs. The proposed MZI configuration is robust to fabrication impairments, primarily because MMI devices are tolerant to waveguide dimensions bias and the pair of gratings are located close to each other to minimize differential fabrication bias. Bragg gratings can detune due to waveguide width and wafer height variations. This effect is particularly noticeable in SOI Bragg filters because of the high refractive index contrast. We adjusted the central wavelength by thermo-optic tuning via titanium-tungsten (TiW) heaters located on top of the gratings.

Figure 4

(a, b) Simulated (dotted curves) and measured transmittances (solid curves) of the single-band add-drop filter and the two-band interleaver. (c) Add-drop filter wavelength tunability measurement. (d, e) Close-up SEM images of the 1-band and 2-band cladding-modulated Bragg gratings in the MZI arms.

The experimental results for both the single-band add-drop and the two-band interleaver showed good agreement with calculated performance, exhibiting 0.6 dB and 0.9 dB insertion loss, respectively (Fig. 4a and b, solid lines). The main contribution to the insertion loss comes from MMIs; experimental characterization yielded an excess loss of 0.25 dB per MMI. Since both through and drop signals propagate through two MMI splitters, their contribution to the total insertion loss is 0.5 dB. An increased power loss is observed at the two-band interleaver due to the narrower waveguide needed for the multi-band operation of the gratings. The single-band add-drop filter preserved its line shape well because it uses a wider core hence being less affected by the fabrication imperfections. Interchannel crosstalk (CT in Fig. 1d and e) degraded compared to simulation results likely due to phase errors of the gratings in the MZI arms. The crosstalk at the channel center was −22.3 dB for the single-band add-drop filter and −18.3 dB for the two-band interleaver, both in compliance with the LAN-WDM standard. An increased crosstalk penalty was observed for the two-band interleaver, arguably as a consequence of the narrower waveguide core with higher sensitivity to fabrication deviations and sidewall roughness. Overall, the measured drop port frequency responses remained flat in the bands of interest. Channel bandwidth (BW) and spacing ($\Delta \lambda$) showed good resilience to fabrication deviations. These two parameters primarily depend on the accurate control of the coupling coefficients along the filter, implemented through judicious adjustment of the positions of the lateral segments. This showcases the advantage of cladding-modulated Bragg gratings for the realization of complex optical filters. The centers of reflection spectra were blue-shifted around 13 nm, due to an estimated fabrication over-etch of 15 nm, a value confirmed by SEM inspection (Fig. 4d and e). To compensate for the fabrication bias, we included thermo-optic phase shifters (heaters) on top of each grating. By feeding the heaters with varying currents we estimated a maximum red-shift of around 16 nm, limited by a breakage current density of $J_\mathrm{max}=45\ \textrm{mA}/\upmu {\textrm{m}}^2$. The thermal tuning efficiency inferred from Fig. 4c data is 40 nm/W, which allows fine-tuning of the filter frequency response to match the LAN-WDM channel grid.

Conclusion

We have demonstrated a single-band add-drop filter and a two-band interleaver for the datacom O-band on the 220-nm SOI platform. Both devices are based on an interferometer-assisted Bragg grating architecture which enables an independent on-chip drop port. By using cladding-modulated Bragg gratings, we were able to cover a wide range of grating strengths for a minimum feature size of 100 nm, compatible with deep-UV fabrication processes. The phase decoherence arising from fabrication imperfections was mitigated by i) limiting grating length to 300 $\upmu {\textrm{m}}$ or less, ii) using TM (out-of-plane) polarization and iii) optimizing waveguide width to reduce field interaction with sidewall imperfections. The add-drop filters achieved channel characteristics that comply with the LAN-WDM standard¹⁵. As reported in Table 1, we experimentally demonstrated an insertion loss below 1 dB and a crosstalk lower than −18 dB for both desings. While single-band add-drop filters based on Bragg gratings have been reported^{28,45,46,47,48}, this is the first time, to the best of our knowledge, that a multi-band add-drop filter leveraging cladding-modulated Bragg gratings and Mach–Zehnder interferometers has been demonstrated. Furthermore, the proposed design technique can be readily applied to waveguide platforms with lower index contrast, such as silicon nitride, with the potential advantage of reduced influence of fabrication errors and phase decoherence. This work paves the way for development of advanced multi-channel WDM filters based on silicon-on-insulator waveguides, while it can also be readily adapted to other integrated photonics platforms, including silica-on-silicon and silicon nitride.

Methods

Calculation of the Bragg coupling coefficient

The calculation of the coupling coefficient for every Bragg grating period was performed using MPB (MIT Photonic Bands)^41,42, an open-source software package for computing band diagrams of periodic dielectric structures. We used material refractive indexes of silicon and silica of $n_\mathrm{Si}=3.500$ and $n_\mathrm {SiO_2}=1.447$ at a target central wavelength of $\lambda _0=1309\ \text { nm }$. We first calculated the period of the grating by setting $\Lambda _\mathrm{Bragg}=\lambda _0/2n_\mathrm{eff}$, where $n_\mathrm{eff}$ is the effective index of the fundamental mode of the unperturbed waveguide, i.e. the solid waveguide without the lateral loading segments. Then, we set the 3D simulation box dimensions to $S_x=10\ \upmu {\textrm{m}}$, $S_y=4\ \upmu {\textrm{m}}$ and $S_z=\Lambda _\mathrm{Bragg}$, and incorporated the loading segments. At a normalized wavevector of $\hat{k}_z=0.5$ and using odd parity in the y-axis, the first two bands correspond to the lower ($\hat{\omega }_\mathrm{lo}$) and upper ($\hat{\omega }_\mathrm{up}$) normalized frequencies of the first order TM-polarized Bragg reflection of an infinite grating in the propagation direction (z-axis). The bandwidth was calculated as $\Delta \lambda =1/\hat{\omega }_\mathrm{lo}-1/\hat{\omega }_\mathrm{up}$, and the central wavelength as $\lambda _c=(1/\hat{\omega }_\mathrm{lo}+1/\hat{\omega }_\mathrm{up})/2$. The calculated central wavelength would differ from the target value, because the Bragg condition holded for a waveguide core with no lateral loading segments. To compensate for this effect, we iteratively adjusted the grating period until they matched. Finally, the coupling coefficient was determined from the expression $\kappa =\Delta \lambda \pi n_\mathrm{g}/\lambda _\mathrm{c}^2\$³⁷, where $n_\mathrm{g}$ is the group index of the unperturbed waveguide at $\lambda _0$ (Fig. 5).

Figure 5

(a) Band diagram of a uniform cladding-modulated Bragg grating with infinite length and $\Lambda _\mathrm{Bragg}=322\ \text { nm }$, $W_\mathrm{c}=370\ \text { nm }$, $W_\mathrm{S}=246\ \text { nm }$, $L_\mathrm{S}=129\ \text { nm }$ and $s=100\ \text { nm }$. (b) Definition of the simulation region used to compute band diagrams.

Synthesis of a Bragg grating with an arbitrary reflection spectrum

We used the layer peeling algorithm³⁸ to synthesize our distributed reflection gratings. Starting from the target spectral response of the entire grating, the algorithm propagates fields using the dispersion relation of the unperturbed waveguide and calculates the required reflectivity at each period, $\rho _n$. In a single-mode Bragg grating, reflectivity is determined by the coupling coefficient, $\kappa _n$. The synthesized grating reflection spectrum closely fits the target reflection spectrum with increasing number of periods, N. In our designs, the number of periods is calculated as $N=\lceil L/\Lambda _\mathrm{Bragg}\rceil$, where L is the grating length, and we use the transfer matrix method to calculate the spectral response of the designed grating. The profile of coupling coefficients that the algorithm generates depends on the dispersion relation of the unperturbed waveguide, as previously mentioned. This is also the reason why the largest required coupling coefficient varies with waveguide core width in Fig. 2a (blue and magenta curves).

Device fabrication

The devices were fabricated by Applied Nanotools in a multi-project wafer run⁴⁹. The structures were patterned by e-beam lithography and anisotropic ICP-RIE etching. SEM images of the fabricated structures are shown in Figs. 1b and 4c and d. We used buried oxide (BOX) and $\mathrm {SiO_{2}}$ cladding layers both 2-$\upmu {\textrm{m}}$ thick. On top of the cladding layer, 200-nm thick and 4-$\upmu {\textrm{m}}$ wide titanium-tungsten alloy (TiW) heaters were fabricated, spanning accross the Bragg gratings of both interferometer arms. Tracks of 500-nm thick and 25-$\upmu {\textrm{m}}$ wide aluminum were patterned using photolithography and connected TiW heaters to air-exposed pads. All the metal except for the pads was covered with a 300-nm thick oxide passivation layer.

Device measurements

For the measurements, light was coupled through the chip facet using lensed fibers and subwavelength grating (SWG) edge couplers⁵⁰. A half-wave plate polarization controller was used to inject TM polarized light into the chip from a tunable laser source (Agilent 81672B). Transmitted light was directed to a lightwave multimeter (Agilent 81642B). All measurements were referenced to the straight waveguide transmittance.