Wavelength division (de)multiplexing devices (WDM) capable of splitting/combining the light into/from multiple wavelengths are components required for a wide variety of photonic applications, particularly to increase the capacity of high-speed telecommunication photonic integrated circuits. WDM devices demonstrated in literature include arrayed waveguide gratings (AWGs), planar concave gratings (PCGs), and micro-ring resonators [1–3].

All these devices have been realized in a variety of platforms, including silica and silicon-on-insulator (SOI), which pose different challenges that must be overcome to achieve competitive performances. On one hand, the low-index contrast silica platform has allowed fabricating devices with low insertion losses (ILs) and low cross-talk (XT) at the expense of increased footprints. On the other hand, devices on the SOI platform tend to be compact, but they exhibit higher losses and a higher sensitivity to both dimensional and temperature variations. To address this situation, Hu et al. proposed angled multimode interferometer (AMMI) (de)multiplexers based on multimode dispersive waveguides capable of providing low IL with a high tolerance to fabrication errors [4]. Nevertheless, SOI AMMIs are still prone to a low tolerance to temperature variations due to the large thermo-optic coefficient of $\mathrm{Si}\sim 1.8\times {10}^{-4}/°\mathrm{C}$.

Under this context, the silicon nitride (SiN) platform has proven to be a good compromise between footprint and spectral performance that enables the fabrication of WDM devices with low IL and a high tolerance to temperature changes [5–7]. In a previous paper, we demonstrated that stoichiometric SiN with a thickness of 300 nm and a refractive index $\sim 2.0$ can be used to fabricate AMMIs with a high tolerance to temperature changes using a relatively simple fabrication process [8]. Nonetheless, regardless of their low sensitivity to temperature variations, they exhibited IL and XT values close to the ones typically observed in the SOI platform.

We propose using a recently demonstrated N-rich SiN platform with a refractive index of 1.92 to improve the performance of AMMI structures in the O telecommunication band (1260–1320 nm) [9]. This material not only has the potential to reduce the XT and IL of the devices, but can also decrease their footprints as lower refractive indices tend to translate into shorter device lengths. In addition, it has processing temperatures $<400°\mathrm{C}$ that make its fabrication process compatible with back-end-of-line (BEOL) integration and, thus, it can potentially be used for multilayer integration schemes. In this Letter, we report the design, fabrication and characterization of a four-channel AMMI optimized to match the first four channels of the ITU CWDM standard G.694.2 using a 600 nm thick N-rich SiN platform. We discuss the spectral characteristics of the device and the effect that both temperature and dimensional variations have on its central wavelengths.

The basic structure of an AMMI consists of a multimode dispersive waveguide of width $W_{\mathrm{MDW}}$ with input/output waveguides of width $W_{\mathrm{IO}}$. The input/output waveguides are tilted at an angle ${\theta }_t$ and tapered from their single-mode width to $W_a$ before entering the multimode waveguide, as illustrated in Fig. 1. The input/output waveguides are placed along the multimode region to satisfy the inverted self-imaging condition described by Hu et al. [4]. This arrangement allows splitting the input signal into multiple wavelengths that are imaged at different axial positions ($L_i$) with respect to the input waveguide. These axial positions can be estimated using Eq. (1) which depends on the effective index of the fundamental mode in the multimode waveguide ($n_{\text{eff}}$) and the wavelength of the $i$th output channel (${\lambda }_i$) [10]:

 

Fig. 1. Schematic diagram of the four-channel AMMI (de)multiplexer.

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The maximum channel count ($N_{\text{max}}$) and the minimum channel spacing ($\mathrm{\Delta }{\lambda }_{\min }$) of the AMMI device are limited by Eqs. (2) and (3), where $x_{m}in$ is the minimum separation between the adjacent output waveguides required for a minimal cross-coupling:

These analytical equations were used to explore the design space to simplify the optimization process. In this case, Eq. (1) was used to set $W_{\mathrm{MDW}}$ to 18 μm, as it is the highest value that allows maintaining the overall length of the device well below 2 mm. This total length ensures that the footprint of the device is comparable to that of other WDM devices demonstrated on the SiN platform. Then Eqs. (2) and (3) were used to determine the range of $W_a$ and ${\theta }_t$ values that would provide the desired channel count of 4 and the channel spacing ($\mathrm{\Delta }\lambda$) of 20 nm. The selected $W_{\mathrm{MDW}}$ and the estimated ranges were carefully explored using FIMMWAVE to optimize the structural parameters of the device to provide spectral responses with a 3 dB bandwidth (${\mathrm{BW}}_{3\mathrm{dB}}$) of 10 nm, $\mathrm{ILs}<1\mathrm{dB}$, and XT between 15 and 20 dB. Table 1 summarizes the optimized parameters for the four-channel AMMI (de)multiplexer obtained from the simulations when using a refractive index of 1.92 for the N-rich SiN. The design was finalized by simulating separately the taper section used to convert $W_{\mathrm{IO}}=750\mathrm{nm}$ into $W_a=7.5\mathrm{\mu m}$ to determine its length of 300 μm.

Table 1. Optimized Design Parameters for the Four-Channel AMMI

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Figure 2 illustrates the spectral response simulated for the AMMI (de)multiplexer with the optimized parameters that exhibits $\mathrm{IL}<1\mathrm{dB}$, ${\mathrm{BW}}_{3\mathrm{dB}}=10\mathrm{nm}$, and $\mathrm{XT}<20\mathrm{dB}$ which meet the requirements originally set for the design.

 

Fig. 2. Simulated spectral response for the four-channel AMMI with optimized parameters ${\theta }_t=0.3\mathrm{rad}$, $W_a=7.5\mathrm{\mu m}$, and $W_{\mathrm{MDW}}=18\mathrm{\mu m}$.

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The layout used to characterize the spectral response of the device included an array of with $W_{\mathrm{MDW}}$ variations of $\pm 20$ and $\pm 40\mathrm{nm}$ to study their sensitivity to dimensional variations. All the AMMI structures had a grating coupler consisting of a single-mode waveguide tapered up to a 10 μm surface grating with a period of 950 nm as a means to couple light in the O-band. It is important to mention that a separate structure with two tapered grating couplers connected back-to-back was also fabricated for normalization purposes.

The structures were fabricated on a $6^{\prime \prime }$ (150 mm) Si wafer with a 2 μm thermally grown ${\mathrm{SiO}}_2$ layer and a 600 nm N-rich SiN film deposited at 350°C using a ${\mathrm{NH}}_3$-free plasma enhanced chemical vapor deposition (PECVD) process detailed in Ref. [9]. The layout was defined on the wafers using electron beam lithography with a high-resolution 850 nm ZEP520A resist. The design was then transferred onto the N-rich SiN layer using ICP etching with an etch depth of 600 nm using a ${\mathrm{SF}}_6\text{:}{\mathrm{CHF}}_3$ chemistry. A 1 μm thick layer of PECVD ${\mathrm{SiO}}_2$ was finally deposited at 350°C on top of the devices as cladding. Figure 3 shows microscopic images of the fabricated AMMI devices.

 

Fig. 3. Microscopic images of the fabricated AMMI at the (a) input waveguides and (b) output waveguides.

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The spectral response of the device was characterized using an Agilent 8164B tunable laser source with a wavelength tuning range between 1260 and 1360 nm. The polarization of the light was controlled to ensure that only TE modes could propagate on the structures. Additionally, the temperature of the measurements was controlled with a thermal stage to study the effect of the temperature on the spectral response of the devices.

Figure 4 shows the measured spectral response of the fabricated AMMI for TE polarization. The oscillations present in the spectra are the combined result of the Fabry–Perot effect produced by the presence of the grating couplers and the polarization state of the measurement setup. Regardless of these oscillations, it can be observed that the experimental result is in good agreement with the simulation. The channel spacing matches closely the required 20 nm specification with $\mathrm{\Delta }\lambda =19.9\pm 0.5\mathrm{nm}$, and the central wavelength of all the channels only deviates by $<1\mathrm{nm}$ from the desired ${\lambda }_i$. The ${\mathrm{BW}}_{3\mathrm{dB}}$ for all the channels is $\sim 11.0\pm 0.4\mathrm{nm}$ which is well within the initial specifications and covers almost 55% of the total $\mathrm{\Delta }\lambda$. In addition, the mean IL after normalizing the spectrum to that of the grating couplers with losses of 14 dB/grating is estimated to be $\sim 1.3\mathrm{dB}$ with a maximum non-uniformity of 0.4 dB across the channels. Finally, the mean XT between adjacent channels is $\sim 21\mathrm{dB}$ with a maximum XT non-uniformity of 11 dB. This strong XT non-uniformity is produced by the difference in the free spectral range (FSR) of the channels. In this case, Ch4 has a FSR of only $\sim 68\mathrm{nm}$ which limits the XT of Ch1 to values $<16\mathrm{dB}$, while Ch1 has a larger FSR $\sim 94\mathrm{nm}$ which reduces the XT of Ch4 to values $<27\mathrm{dB}$. The overall XT of the device could be reduced $<30\mathrm{dB}$ by increasing the $W_{\mathrm{MDW}}$ to reduce the $\mathrm{\Delta }{\lambda }_{\min }$ or by reducing $W_a$ to increase $N_{\max }$. However, either solution will come at the expense of increased device footprint or higher IL, respectively.

 

Fig. 4. Spectral response of the demonstrated four-channel AMMI on the N-rich SiN platform measured at 20°C.

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Figure 5 presents the sensitivity of the spectral shift ($\delta {\lambda }_i$) with respect to the fabrication error in the width of the multimode waveguide ($\delta W_{\mathrm{MDW}}$). This result reveals that the AMMI exhibits an almost linear sensitivity of 114 pm/nm, which is consistent with the values observed in SOI AMMIs [11]. This value is almost one order of magnitude lower than the sensitivity exhibited by other SOI WDM devices. This improved tolerance can be attributed to the negligible shift experience by the $n_{\text{eff}}$ of the multimode waveguide with fabrication errors due to its increased dimensions compared to single-mode waveguides.

 

Fig. 5. Sensitivity of the spectral shift as a function of the fabrication error in the width of the AMMI multimode waveguide observed in the O-band.

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The $\delta {\lambda }_i$ as a function of the temperature variation $\delta T$ is illustrated in Fig. 6. In this case, it can be observed that $\delta {\lambda }_i$ is directly proportional to the temperature variation with a sensitivity of 18 pm/°C. This sensitivity can be described as a function of the thermally induced changes on the $n_{\text{eff}}$ of the AMMI structure ($\delta n_{\text{eff}}/\delta T$) using Eq. (4) [10]. This last value can be directly linked to the thermo-optic coefficient of the SiN layer ($\delta n_{\mathrm{SiN}}/\delta T$) using Eq. (5), where $\delta n_{{\mathrm{SiO}}_2}/\delta T$ is the thermo-optic coefficient of the ${\mathrm{SiO}}_2$ cladding, $\delta n_{\text{eff}}/\delta n_{\mathrm{SiN}}$ is the sensitivity of the $n_{\text{eff}}$ of the multimode waveguide to $n_{\mathrm{SiN}}$, and $\delta n_{\text{eff}}/\delta n_{{\mathrm{SiO}}_2}$ is the $n_{\text{eff}}$ sensitivity to $n_{{\mathrm{SiO}}_2}$:

 

Fig. 6. Sensitivity of the spectral shift as a function of temperature variations exhibited by the AMMI in the O-band.

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These two equations were used to estimate the thermo-optic coefficient of the N-rich SiN layer using $\delta n_{{\mathrm{SiO}}_2}/\delta T=0.95\times {10}^{-5}$ [12] after extracting $\delta n_{\text{eff}}/\delta n_{\mathrm{SiN}}=0.98$ and $\delta n_{\text{eff}}/\delta n_{{\mathrm{SiO}}_2}=0.11$ from simulations. The computed results reveal that the N-rich layers with a $n=1.92$ have a thermo-optic coefficient $\sim 2.2\times {10}^{-5}$ which is similar to the values reported for other SiN platforms in the literature [12].

Table 2 compares the characteristics of the N-rich SiN AMMI with other CWDM devices available in the literature. It can be observed that the performance of the AMMI in terms of XT and IL is comparable to other published devices, such as AWGs and PCG on SOI and SiN. Furthermore, its XT is closer to values $\sim 40\mathrm{dB}$ exhibited by silica AWGs [14]. In terms of footprint, the proposed AMMI is larger than SOI devices which are in the order of ${\mathrm{\mu m}}^2$, but it still maintains the higher tolerance to dimensional and temperature variations characteristic of SiN devices with a more compact design than that of silica devices.

Table 2. Summary of the Characteristics of WDM Devices Operating in the Near-Infrared, Including Footprint, Channel Spacing, ILs, XT, Sensitivity to Dimensional Variations, and Sensitivity to Temperature^a

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One of the major limitations of the AMMI is its reduced channel count, which makes it hardly scalable to dense WDM application, where AWGs and PCGs offer a better performance. Furthermore, the proposed structure is polarization dependent, whereas silica AWGs present an almost polarization-independent operation. However, the 600 nm thickness of the N-rich layer offers the possibility of fabricating polarization-independent AMMIs, as it is possible to design waveguides with the same effective index for both polarizations by carefully selecting their widths. Still, the polarization independent operation of the devices must be studied further, as the width of the multimode waveguide required for polarization independence may limit the amount of channels and the channel spacing supported by the structure.

We have demonstrated a four-channel AMMI (de)multiplexer for CWDM with $\mathrm{\Delta }\lambda =20\mathrm{nm}$, ${\mathrm{BW}}_{3\mathrm{dB}}\sim 11\mathrm{nm}$, $\mathrm{IL}<1.5\mathrm{dB}$, and $\mathrm{XT}<20\mathrm{dB}$. This performance is comparable to the state-of-the-art in SOI and SiN CWDM devices. Nevertheless, the AMMI structure allows taking advantage of the higher tolerance of SiN to fabrication and temperature variations with a more compact design than typical AWGs and PCGs devised for SiN. In addition, the low processing temperature of the N-rich layer makes this device compatible with multilayer CMOS BEOL integration. As a result, the demonstrated AMMI is an ideal candidate for commercial CWDM applications that require compactness with stability to temperature changes.