1. Introduction

Wavelength division multiplexing (WDM) is one of the most efficient multi-access techniques in optical communications, enhancing the data interconnections’ aggregated channel capacity. It is realized using multiplexing (MUX) and demultiplexing (DEMUX) optical filters in the optical transceiver system. Optical filters can be implemented at a low cost while attaining high performance using photonic integrated circuits on a silicon-on-insulator (SOI) platform. There are several different approaches, and system configuration setups of optical filters reported so far, including Mach-Zehnder Interferometer (MZI)-based [1–3], ring resonator-based [4,5], array waveguide grating (AWG)-based filters [6–9] and more. Filters based on MZI lattice structures studied in [2] and [3] can provide moderate spectral band and flat-top response, with 3 nm and 16 nm bandwidth (BW), respectively. Moreover, less than 1 dB and 1.6 dB insertion loss (IL) were obtained, along with an average channel crosstalk of 15 dB and 22 dB, respectively. However, these MZI-based lattice structures are generally large i.e., 0.022 × 10⁴ µm² and 3 × 10⁴ µm², respectively. This makes the MZI-based filter sensitive to fabrication variation-induced phase errors and would require thermal tuning or fabrication variation process (FVP) insensitive couplers [10]. On the other hand, ring resonators-based WDM reported in [4,5] is preferable regarding the footprint (especially when using high contrast SOI). However, ring resonator-based optical filters exhibit narrow bandwidth (less than 10 nm) and small free spectral range (FSR) and are unsuitable for wide-band data communications. In addition, the fact that they are resonant devices makes them inherently sensitive to fabrication variations. As a result, the micro-ring resonators (MRRs) reported in [4,5] require stringent spectral stability control mechanisms such as thermal tuning. According to work presented in [8] and the comprehensive study reported in [9], Echelle gratings are relatively less sensitive to fabrication errors. However, the Echelle gratings [8] still have a small FSR and a large footprint (2.16 × 10⁴ µm²). It can be understood from [7] that AWG-based filters offer relatively higher channel isolation (25 dB) and broadband BW (5 nm) but at the expense of a larger footprint (2.145 × 10⁶ µm²) and higher IL (5 dB). In addition, particular Multimode interference (MMI)-based filter [11] achieved less than 2 dB IL with a moderately large footprint (1.1 × 10⁵ µm²). However, it can be observed that it has a low sidelobe suppression ratio (SLSR) of <15 dB. In summary, a device that implements narrow BW and low FSR will either be limited in the number of usable channels due to significant channel crosstalk or require a large footprint. This makes these structures less attractive solutions for compact wide-band communication systems and restricts themselves to a low data rate application range.

A WDM (WDM) filter with a flat-top response, wide BW, and FSR-free can be efficiently designed using filters based on distributed Bragg reflectors (DBR) [12]. In [12], a two-port DBR based on reflection mode is reported. However, this device requires circulators and isolators, which are not CMOS-compatible. Another design [13] utilizes the π/2 phase difference of the MMI output ports to isolate the reflected optical signal from the Bragg reflector. However, its FVP sensitivity depends on the sensitivity of the MMI coupler.

The need for an optical circulator can be circumvented by employing grating-assisted contra-directional couplers (CDC) [14–18] or sub-wavelength grating (SWG) [19–21] in an add-drop filter configuration. In CDC or SWG, the wavelength selection through reflection is implemented using a pair of closely coupled grating waveguide structures where the forward mode of one waveguide is coupled into the backward mode of the other waveguide. Figure 1 shows the schematic of a CDC-based filter using two grating waveguides with a grating pitch (period) $\mathrm{\Lambda }$, widths W₁ and W₂, and corrugation width (depth) ΔW₁ and ΔW₂, respectively.

 

Fig. 1. Schematic of a wavelength selective Contra-Directional Coupler (CDC) (a) in phase grating: the fins of the grating are in phase such that there will be maximum mode coupling between the forward and backward propagation modes of the waveguide. Therefore, there will be a significant magnitude of back reflection/self-coupling (Eq. (1).) in each waveguide; (b) out of phase grating: The fins of the grating are out-of-phase such that there will be no power coupling between the backward and forward propagating mode. Consequently, the power of the back (self) reflected mode in each of the waveguides will be eliminated.

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The Bragg condition of the CDC grating can be expressed as [14,15] [19]

Equation (1) represents the back coupled modes (reflection bands) of waveguide-i with width W_i (i:1,2). The cross-coupling mode between the two-grating waveguides will then have propagation constants expressed as in [14–16]:

Therefore, the drop wavelength will be:

Considering $\mathrm{\Delta }{\textrm{n}_{\textrm{eff}}} = ({\textrm{n}_{\textrm{ef}{\textrm{f}_1}}} - \textrm{}{\textrm{n}_{\textrm{ef}{\textrm{f}_2}}})$, the space (guard) band between the dropped wavelength and the reflection bands, ${\lambda _{{r_1}}}$ and ${\lambda _{{r_2}}}$, can be expressed as:

The DBR-based filter takes advantage of FSR-free operation and flat-top response that can be flexibly adjusted to achieve the desired filter specification. These can be attained by controlling the amplitude and phase response of the gratings by implementing a phase-modulated apodization profile [18], chirped gratings [22], phase-shifted gratings [23] and others.

In [16], the wavelength selection of the drop wavelength expressed in Eq. (4) is implemented via reflection using coupled waveguide grating structures and out-of-phase gratings to avoid any back reflection. However, the crosstalk (-13 dB) reported is significantly high. An attractive design modification was proposed in [19] to mitigate the effects of reflection bands by using high-index contrast waveguides. In [19], it was possible to achieve an extinction ratio (ER) as high as 30 dB; however, the SLSR and IL are still suboptimal at 8 dB and -1.2 dB, respectively. Similarly, it was shown [20] that a highly asymmetric waveguide can suppress co-propagating modes coupling by 35 dB and the back-reflected signal at the input by 15 dB. Despite this, the measured SLSR is below 10 dB, and the coupling length is 200 µm. Even though high-index contrast waveguide implementation mitigates some effects of back-reflected signals, these CDCs still exhibit high channel interference due to a strong sidelobe in the transmission spectrum. An SWG filter in [20] achieved moderately low IL (∼1 dB), ER, and co-propagating modes suppression levels as high as 30 dB and 35 dB, respectively but very low (7 dB) SLSR. A new and compact Bragg-grating-based contra-directional DCs is designed in [24] to suppress the sidelobe based on Kogelink's idea [25], and it was the only possible approach to achieve an SLSR of 12.93 dB and an ER of 14 dB.

A high channel interference due to a strong sidelobe in the transmission spectrum of the DBR [18] can be mitigated by suppressing the amplitude level of sidelobes. The amplitude of spectral modes of a DBR controlled by managing the coupling coefficient (k) expressed as

In [28], a dual-stage DBR configuration is employed to realize phase-modulated grating and was able to obtain a 23 dB SLSR but at the expense of a large coupling length of 900 µm and a footprint 2.4 × 10⁴ µm².

Furthermore, a quadrable CDC filter was implemented to enhance the SLSR and spectrum flatness further. By doing so, 37 dB SLSR was attained but still with a large footprint of 2.25 × 10⁴ µm². Another solution reported in [27], used apodization on the lateral space of the fins of the grating rather than on the grating width. In their design, they implement a multimode asymmetric waveguide Bragg grating where the reflected signal is extracted by coupling the transverse electric (TE) mode to the backward TE1 mode when the phase-match condition is satisfied. This mode coupling requires a long taper for smooth mode conversion, increasing the length (500 µm) to achieve an SLSR of only 18.5 dB.

Similarly, in [15], the waveguide perturbation was apodized instead of coupling gap apodization. Applying a Gaussian apodization to the waveguide corrugation generates a Gaussian like effective index distribution along the coupling length. This technique enables a gradual variation in the shape of the reflectivity profile with a minimum reflectivity at the stopband edges of the filter. These smooth and gradual variations of the spectral reflectivity profile of the DBR further reduce the reflection coefficient variation among the individual periods of the DBR periods. This will reduce the possible phase error introduced by the varying reflection coefficients of the DBR consecutive periods. As a result, the amplitude of the sidelobes usually created by the phase error will also be reduced. Therefore, the signal strength of the sidelobes will be weak and thus, SLSR will be higher. Therefore, if we combine both coupling gap apodization which induces a Gaussian like coupling profile and waveguide apodization which results weak sidelobe frequencies, a reduced SLSR than we could obtain from apodizing only one parameter.

In this work, we designed, simulated, and experimentally characterized two compact flat-top filters, a straight and a curved DBR thereafter named SDBR and CDBR, respectively. The footprint of each device is 130µm²/Ch (SDBR) and 3700µm²/Ch (CDBR). Both filters are experimentally verified to achieve SLSR of 32 dB and 25 dB. Furthermore, both filters showed little fabrication sensitivity across four wafer sites, with very low FVP-induced spectral shift of mean 0.7 nm (SDBR) and 1.3 nm (CDBR), as well as very low IL of 0.43 dB (SDBR) and 1.65 dB (CDBR) at the central wavelength of λ = 1290 nm (SDBR), λ = 1285 nm (CDBR). Both configurations make use of two closely spaced asymmetric waveguides with a sidewall corrugation on the drop waveguides, except in CDBR the waveguides are curved. The asymmetric waveguide is used to avoid channel interference induced due to the co-propagating and back-reflected modes during the add/drop filter operation. In addition, out-of-phase fins with misaligned gratings by $\wedge$/2 are used to avoid potential mode coupling between forward and backward modes within each waveguide.

The advantages of our designed filters originate from the apodization approach, which is implemented for both the coupling gap as well as the sidewall grating widths in contrast to most of the reported papers, which implement apodization in only one of the filter parameters on either gap or grating widths. Both filter configurations enhance the SLSR and crosstalk by controlling the energy exchange between the coupled modes of the two waveguides using grating and gap apodization to effectively suppress the sidelobes. Furthermore, the devices are fabricated in a state-of-the-art monolithic silicon photonics platform [29,30] which enables on-chip integration of a variety of best-in-class electronic and photonic devices.

The structure of the paper is described as follows. The design and principle of operation of the proposed design as well as the approach taken to circumvent the high interference challenge in conventional filters will be briefly explained in section 2. Subsequently, the experimental characterization and obtained results will be statistically analyzed and presented in section 3. Finally, section 4 concludes and summarizes the filter performance.

2. Principle of operation and structure design

The proposed SDBR and CDBR filters are schematically shown in Fig. 2 . The designed DBR filter consists of two parallel asymmetric waveguides, named bus, and drop waveguides, with 250 nm and 400 nm widths separated by a gap of 250 nm. The sidewall width of the drop waveguide is corrugated to form gratings with a corrugation width of ΔW. The waveguide grating's period is made to be constant with a pitch of $\mathrm{\Lambda }$ and a uniform duty cycle of 50%.

 

Fig. 2. Design schematic for (a) apodized straight distributed Bragg reflector (SDBR); (b) curved distributed Bragg reflector (CDBR). In both design variations, the coupling gap, and the corrugation width of the DBR (drop waveguide) are apodized to tailor the spectral shape of the transmission spectrum. The gap and corrugation width apodization would make the effective index across the drop waveguide vary in a gaussian form and, consequently the transmission spectrums.

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As mentioned in the introduction section, an adverse factor of the CDC design is the strong reflection band (Eq. (1)) and co-propagating modes that occurred at the waveguides (bus and drop) mode coupling. This effect has to be addressed; otherwise, these reflection bands and co-propagating modes will cause interference during the add/drop operation if their strength is significant and channel spacing Δλ is not large enough. In addition to using high-index contrast coupling waveguides, the effective coupling efficiency between the forward and backward modes of grating waveguides can be controlled by utilizing phase mismatched gratings [31]. This can be mathematically expressed as:

In our design, high-index contrast waveguides and drop grating fins offset by Λ/2, are implemented for both methods to mitigate the effect of back-reflections and the co-propagating modes. By doing so, the possible interferences due to co-propagating modes and the reflection bands is solved.

Furthermore, a phase-modulated grating is produced by gradually varying the width of the corrugation and the coupling gap in the filter. This results in an apodized coupling strength that can be controlled to manage the SLSR and, consequently, the inter-channel crosstalk. Considering a constant period perturbed waveguide, the coupling coefficient, which is determined by the grating fins depth, dictates the local coupling between the forward and backward modes of a grating waveguide (Eq. (6)). The peak reflectivity and coupling strength (k­_s) can be related according to Eq . 7 [25]:

According to the analysis in [25], and Eq. (8), the spectral shape of the reflected signal depends on the shape of the function used to apodize the corrugations as well as the coupling strength. If we consider a rectangular shaping function, k_s would have a sinc like function profile with high sidelobes.

Accordingly, the SLSR and the crosstalk of our system are controlled by exploiting the energy exchange between the coupled waveguides using grating as well as gap apodization. In our design, a gaussian function profile is used to manipulate the coupling coefficient by gradually modifying both the gap (G) and corrugation width (ΔW) according to Eq. (9), and Eq. (100), respectively:

2.1 Apodization factor optimization

To investigate the impact of different apodization factors on the coupling gap and corrugation width for the WDM spectral response, VarFDTD LUMERICAL simulations were performed [32], and the outcomes are displayed in Fig. 3(a). Notably, a uniform grating and coupling gap over the coupling length resulted in a considerably strong and symmetrical sidelobe strength compared to the apodized ones. In order to enhance the SLSR of the system, a gaussian apodization profile was implemented in Eq. (9) and Eq. (10), where the coupling gap and corrugation width were gradually varied. As mentioned in section 2, this gaussian apodization profile induces a spectral shape spectral strength that resembles a gaussian function. The degree of apodization determines the steepness of the guassian function and therefore; steepness of spectrum strength profile and consequently the suppression level of the sidelobe. In Fig. 3(a), an apodization factor of 2.5 led to a significant improvement in SLSR by 34 dB compared to the uniform grating. These results highlight the crucial role of carefully selecting the apodization factor to optimize the performance of the DBR-based WDM system. Accordingly, a sweep run for different coupling gap and corrugation width appodization level combinations is conducted.

 

Fig. 3. Performance evaluation of the DBR filter for different apodization factors, Eq. (9) and Eq. (10), (a) on the transmission spectrum. Increasing the apodization factor reduces the amplitude of the sidelobes. (b) extinction ratio; (c) sidelobe suppression ratio; the waveguide widths for the bus and drop waveguides are chosen to be 250 nm and 400 nm, respectively. The coupling gap is set at 250 nm and the corrugation width is chosen to be 80 nm.

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Implementing an apodization technique by modifying the reflectivity of the filter non-uniformly can suppress undesired sidelobes [33,34]. This allows for a smooth variation in the shape of the reflectivity profile with minimal reflectivity at the stopband edges of the filter. This smooth, gradually varying spectral reflectivity profile of the DBR further reduces the reflection coefficient variation among the individual periods of the DBR periods. The will in return reduce the possible phase error introduced by reflection coefficients of the DBR consecutive periods. As a result, the amplitude of the sidelobes usually created by the phase error will also be reduced. Therefore, the signal strength of the sidelobes will be weak and the SLSR will be higher. Figure 3(b, c) illustrates the performance variation of ER and SLSR as a function of apodization of the coupling gap and corrugation width.

The results presented in Fig. 3(b) and (c) demonstrate that apodization can improve SLSR in the DBR-based WDM system. However, apodizing either the coupling gap or corrugation width alone produces limited SLSR of approximately 14 dB. Increasing the apodization factor beyond 3 can enhance SLSR further, but it will also suppress the corrugation width over a significant fraction of the DBR length, leading to weaker power coupling and increased crosstalk during the add operation. To avoid these issues, a larger corrugation width and longer coupling length can be employed, but they come at the cost of a larger footprint. Figure 3(c) indicates that simultaneous apodization of both geometric parameters, ΔW0 and G0, leads to a higher SLSR compared to apodization of the parameters individually. Specifically, apodizing both the coupling gap and corrugation width can increase SLSR while reducing ER, but a trade-off between SLSR and ER exists. Thus, a moderate apodization factor for both parameters (rather than a large apodization factor for either of them) can achieve better performance. Based on the results in Fig. 3(b, c), an optimal apodization factor of 2 is selected to achieve relatively high ER and SLSR. The above statement confirms that a moderate apodization magnitude applied to the coupling gap and corrugation width simultaneously can effectively improve the system's performance.

2.2. Filter geometric dimensions optimization

Having decided the optimal apodization factor, we will need to optimize the geometric dimensions of the DBR, corrugation width and coupling gap.

Figure 4(a)-(d) show the simulated (varFDTD) results of the DBR filter performance metrics as a function of corrugation width and coupling gap, which reveals the effect of the geometrical dimensions of the DBR filters (SDBR and CDBR) on SLSR, ER, BW, and IL.

 

Fig. 4. Corrugation width and coupling gap optimization and performance comparison for: (a) bandwidth, (b) extinction ratio, (c) insertion loss, and (d) suppression ratio.

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Looking into Fig. 4(a, b), low coupling gap and large corrugation width generally exhibit high BW and ER. A small coupling gap enhances mode coupling from the bus to the drop waveguide. This will increase the signal strength of the dropped signal as it is strongly reflected by the large corrugation width of the drop waveguide gratings. Consequently, low power of the target wavelength will exit across the through port (Fig. 2), and therefore, high ER will be yielded. Similarly, as shown in Fig. 4(c), the IL for small coupling gaps and large corrugation widths is extremely low. At a small coupling gap, a large fraction of the input power at a specific wavelength will be coupled, and then a significant amount of the power is reflected by large corrugation width at the drop waveguide. This will enable high dropped power at the drop port and so less IL (<0.05 dB). As it can be understood from [35] and Eq. (11), the bandwidth of the reflected signal is linearly proportional to the coupled power of the reflected modes’ k’. For longer gratings, the coupling coefficient in the DBR (reflection amount per unit length) is related to the BW according to the expression [35]:

The varFDTD simulations gave us general information on the effects of the corrugation width and coupling gap on the BW, IL, and SLSR performance metrics of the DBR filter. After obtaining the optimal filter dimensions, a final verification simulation run using 3D FDTD was conducted. This rigorous 3D simulation was conducted for two channels centered at wavelengths of λ₁ = 1274 nm and λ₂ = 1290 nm (SDBR), and λ₁ = 1269 nm and λ₂ = 1285 nm (CDBR) with grating periods of $\wedge$₁ = 307 nm, $\wedge$₂ = 314 nm respectively. The obtained BW, IL, crosstalk, SLSR and channel spacing in 3D FDTD are very similar to varFDTD with insignificant deviation in BW and spectral shifts. Considering the same geometrical specifications, Fig. 5(a, b) shows the filter response for both SDBR and CDBR. The crosstalk in CDBR is larger by 6 dB compared to the SDBR. Furthermore, apodizing both the corrugation width of the grating and waveguide gap improves the SLSR from 2 dB in the non-apodized structure to 32 dB and 39 dB for SDBR and CDBR, respectively. Additionally, the CDBR exhibits 1.5 nm lower BW and ∼5 nm spectral shift compared to the SDBR. The difference in BW is due to the curved structure's lower coupling coefficient, which affects the signal BW (Eq. (11)).

 

Fig. 5. Transmission spectrum for the optimized geometrical dimensions of the DBR structure apodization factor $({a\; = \; 2} )$, $coupling\; gap\; ({G = 250\; nm} ),\; $ bus waveguide width (W1 = 250 nm) drop waveguide with (W2 = 400 nm), corrugation width ($\Delta W = 80\; nm$), pitch periods of $\wedge$1 = 307 nm, $\wedge$2 = 314 nm a) SDBR, λ1 = 1274 nm and λ2 = 1290 nm b) CDBR, λ1 = 1269 nm and λ2 = 1285 nm (CDBR). The CDBR outperforms the SDBR in terms of SLSR and crosstalk (6 dB more). The BW obtained by the CDBR is slightly lower (${\sim} $1.5 nm) than that of the straight, and it has ∼5 nm spectral shift due to the curved structure effect on the effective index of the waveguide.

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Furthermore, as shown in Fig. 5, the central wavelengths in CDBR are slightly blue-shifted (∼5 nm) compared to the central wavelength of the SDBR. One possible reason could be that the curved waveguide's guided mode is more delocalized from the waveguide center, making the less-confined mode interact more strongly with the oxide cladding. Thus, the effective index of the mode is reduced, which causes a slight blue shift according to Eq. (4). In general, both designed filter types perform better, with slight differences, and offer state-of-the-art performance with a compact footprint.

Looking in to Fig. 5 (a) and (b), the SLSR and the bandwidth of the curves of the two filters is slightly difference with better SLSR but narrower spectrum in the CDBR than the SDBR. in the curved. This could be happened due to the curvature structure of the curved DBR filter effect on the number of permitted modes(frequencies) of the waveguide, phase shift and effective index change of the propagating modes. The number of allowed modes in the waveguide reduces as the waveguide's curvature rises. This is due to the waveguide's curvature, which provides additional curvature-induced dispersion and may reduce the waveguide's supported mode count. Thus, when the number of possible resonant modes of the waveguide coupling to the incoming light decreases, the energy previously dispersed across a large number of modes is now focused in a smaller number of modes. This might enhance the central lobe's strength and can lessen the amplitude of the sidelobes. Contrarily, the fact that the energy is distributed across the number of modes is now concentrated in smaller signal frequencies, it results in a narrow spectrum. In addition, the curved structure of the CDBR causes more phase shifts and changes in the effective refractive index, which might influence the filter's dispersion characteristics. For instance, the group delay dispersion might be much higher for a curved DBR filter, leading to a smaller bandwidth.

Furthermore, one can observe from Fig. 5 that filter characteristics such as ER, SLSR and BW of the filters are slightly affected by the operating wavelength due to the wavelength dependent nature of the mode coupling and dispersion which can lead to varying reflectivity and phase shifts at various wavelengths. As a result, the ER, SLSR and BW at various wavelengths may vary, with some wavelengths having a higher or lower SLSR or a narrower or wider BW than others.

2.3. Performance analysis of Curved DBR filter for radius of curvature and fabrication process variations

Generally, the radius of curvature of the CDBR or the length of the SDBR is determined by the number of periods within the structure. The period of the DBR filter greatly impacts the performance of the DBR, including parameters SLSR and BW. We have conducted an analysis of the number of periods (radius) for the Curved DBR and have plotted the results in Fig. 6(a). A comprehensive analysis is provided in the following section. The overall radius of curvature is large enough such that bend loss is insignificant. However, the SLSR and BW are the main filter parameters that are directly influenced by the number of reflective interfaces and the resulting interference. These findings are detailed in the following section.

 

Fig. 6. Transmission spectrum (a) for different period number (radius); (b) ± 5 nm variations on corrugation width

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The period of the DBR filter significantly affects the stopband width and, therefore, the SLSR performance. The stopband width is defined as the range of wavelengths that are strongly reflected by the DBR filter. A longer (more number of gratings) DBR filter results in a narrower stopband and better sidelobe suppression because it increases the number of layers in the filter, which improves its reflectivity. A longer period results in a narrower stopband because it creates more reflective interfaces, increasing the number of optical interference effects.Fig. 6(a) demonstrates that a shorter DBR (few number of gratings) corresponding to a smaller radius of curvature, results in a wider spectrum but a lower SLSR than a longer period. When the length of the Bragg grating structure is short, the coupling length and the number of reflective elements decrease. This affects the signal strength of the main lobe and results in a small SLSR.

In summary, a longer DBR filter (i.e., longer DBR length in the case of SDBR or larger radius in the case of CDBR) leads to a narrower stopband and better sidelobe suppression because it increases the number of reflective interfaces and the number of optical interference effects, resulting in higher reflectivity and a narrower stopband width. The curvature can affect the coupling efficiency in a curved waveguide by changing the overlap between the two waveguides. A larger radius of curvature which includes more grating structure induces a higher coupling efficiency. Figure 6(a) illustrates this fact. higher period (N = 450) or larger curvature results in higher coupling efficiency (lower insertion loss) and wide spectral width. Therefore, a period of 450 was selected, as there was only minimal performance improvement beyond this number of periods. Furthermore, the radius of curvature of a curved optical waveguide can have significant effects on the co-directional coupling and the Bragg phase match condition. A co-directional coupling refers to the transfer of light from one waveguide to another parallel waveguide and traveling in the same direction. One technique implemented to avoid the effect of co-propagating signals on the target drop wavelength is, using asymmetric coupling waveguides. One can observe from Eq. (4) (section 1), asymmetric waveguides will have high index contrast so that the band separation of the drop wavelength and the co-propagating bands will be large enough to interfere each other.

The Bragg phase match condition refers to the state where the phase difference between the forward- and backwards-propagating waves in a Distributed Bragg Reflector (DBR) or other photonic structure is an integer multiple of 2π. This condition is necessary for maximum reflection of the incident light at the resonant frequency. In a curved DBR, the curvature can affect the Bragg phase match condition by changing the effective refractive index of the waveguide, which impacts the resonant frequencies. A larger radius of curvature can result in a larger effective refractive index, which can shift the resonant frequencies to higher values and result in a better Bragg phase match condition. Unlike to some of the designs as in [36] where, the radius of curvature determines the nulls of CDC and the MRR FSR, increasing radius of curvature will not affect the FSR, as a half ring DBR is used and DBR is FSR-free.

In summary, the radius of curvature of a curved optical waveguide can affect the co-directional coupling and the Bragg phase match condition, which are essential parameters for the performance of optical devices. A larger radius of curvature can result in higher coupling efficiency and a better Bragg phase match condition, leading to improved device performance.

A core analysis for fabrication induced geometrical variations is conducted and result is depicted in Fig. 6(b). The geometrical variation during the fabrication will induce change in the effective index, which causes a spectral shift. Looking into Fig. 6(b) a -5 nm reduces the reflectivity of the filter which reduces bandwidth (Eq. (11)) and +5 nm is vice versa. Therefore, there will be spectral shift as well as change in spectral width. Furthermore, the spectral shift introduced is significantly low and it will not affect the filter performance, as it is within the passband range of the filter. Therefore, the ±5 nm error during fabrication may not affect the filter performance. In general, the slight performance deviation we see in the simulated spectrum of Fig. 6(a) (b) and the measured spectra obtained from 4 different wafer sites of Fig. 8(a) show our filter's robustness. Thus, the DBR is robust.

3. Experimental results and discussions

3.1. Experimental setup

The SDBR and CDBR devices were fabricated, and their performance was experimentally verified. The chip measurements were performed by an automated probe station [37] at GlobalFoundries (GF). The experimental setup is depicted in Fig. 7. (a). The extracted data was analyzed using MATLAB software [38] to evaluate the performance of different filter metrics such as IL, SLSR, BW and ER.

 

Fig. 7. (a) Image of the automated probe station setup for optical characterization of the devices described proposed in this work [37]. (b) GDS layout of the curved structure that is oriented in directions not normal to the x-y axis.

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3.2. Straight distributed Bragg reflector for WDM system

Figure 8 (a) shows the transmission spectrum of the fabricated SDBR WDM device depicted in Fig. 2 (a), obtained from 4 different wafers for the O-band. The measured spectrum of channels centered at λ₁ = 1274 nm and λ₂ = 1290 nm can be observed in Fig. 8(b). The transmission spectrum for the designed SDBR WDM configuration has an average BW of 7.2 nm, 0.43 dB IL and 15.8 nm channel spacing. Comparing the measured and simulated transmission spectrum Fig. 5 (a) we can observe a good agreement with regards to the SLSR (<1 dB deviation) and IL. More importantly, apodizing the corrugation width of the grating and the coupling gap has significantly suppressed the sidelobe amplitude by 32 dB, reducing the corresponding 3dB-crosstalk level to -32 dB.

 

Fig. 8. Transmission spectrum of SDBR WDM filter device: (a) measured transmission of one channel for 4 different wafer sites. Very small performance variation with a spectral shift of only 0.7 nm on average and 0.34 nm SD is observed. (b) Measured transmission spectra for 2 channels centered at λ₁ = 1274 nm and λ₂ = 1290 nm. The measured spectrum is slightly blue-shifted (less than 1 nm) and has almost the same SLSR and insertion ratio with respect to the 3D FDTD simulated spectrum.

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Additionally, based on the results obtained from the four wafers, Fig. 8 (a), one might observe almost similar performance among the wafer test sites with a very small variation of only 0.34 nm SD among each other.

Noticeably, there is a very small performance variation among the 4 wafer test sites due to the inevitable fabrication process variation (FPV) with 0.7 nm spectral shift deviation from the simulation.

3.3. Curved distributed Bragg reflector for WDM filter

Figure 9 (a, b) illustrates the experimentally measured channel transmission of the CDBR - WDM filters recoded in 4-wafer test site. Figure 9 (a) shows that almost all the obtained results from the 4 different wafer sites exhibit similar spectral shift performance of SD of 0.54 nm among each other and ∼2 nm compared to the simulation.

 

Fig. 9. Transmission spectrum of CDBR WDM filter device: (a) measured transmission of one channel for 4 different wafer sites. Very small performance variation (spectral shift of only 1.3 nm on average and 0.54 nm SD) is observed. (b) Measured transmission spectra of two channels. The measured spectrum is slightly blue-shifted (less than 1 nm) comparing with the simulated one. The SLSR appears to be significantly lower (25 dB) for the fabricated device compared to the simulated device.

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Figure 9 (b), depicts the transmission spectrum of the individual WDM channels of the CDBR-based WDM filter. A 7.1 nm BW, 1.65 dB IL, 15.8 nm channel spacing, and 25 dB SLSR is obtained for the CDBR. On average, there is ${\sim} $1.3 nm blue shift of the center wavelength as depicted in Fig. 9 (b) and this is 0.6 nm more spectral shift compared to what we obtained in the SDBR. In our opinion, the main reason for this shift is due to the change in the effective index induced by the curved waveguide used in the CDBR filter.The effective index in the curved waveguide tends to decrease as the guided mode is delocalized and interacts more strongly with the cladding due to lower mode confinement. Therefore, according to Eq. (4), the reduced effective index results in a shorter drop wavelength, and therefore, the spectrum will be blue-shifted.

Figure 9 (a, b) shows that there is some signal distortion in the longer wavelengths which creates the asymmetric spectrum transmission with respect to the center wavelength of each channel. This might be caused due to two main reasons; one possible reason might be due to the wavelength-dependent nature of the mode coupling [39]. As a result, larger power fraction is coupled for longer wavelengths compared to shorter wavelengths. This results in relatively stronger sidelobes in the longer wavelength region than the short wavelength.

The other reason could be due to noise or phase variations induced by the apodization scheme. The apodization of the coupling gap and corrugation width of the grating creates a finite minimum step size between consecutive gratings that create an offset step size from the normal x-y plane because it is curved, Fig. 7 (b). This may create a variation in the average effective index along the coupling length, as explained well in [40], which could possibly lead to phase variations created by a kind of Fabry-Perot type response, created by the two ends of the DBR, resonating at longer wavelengths with respect to the target wavelength.

Moreover, in contrast to the obtained 3D FDTD simulation results, the measured crosstalk of the CDBR WDM (Fig. 9 (b)) is relatively lower compared to the obtained values of the SDBR. This result contradicts what was obtained in the 3D FDTD simulations, where the CDBR outperforms the SDBR in-terms of crosstalk as shown in Fig. 5. The small deviation on the performance of the measured CDBR compared to the simulation could be related to the very fine step size implemented in our design. The implemented apodization scheme is done by modulating the sidewall corrugation width of the waveguide. Since our design is based on single mode operation, the strip waveguide which is small restricts/limits the resolution step and dynamic ranges of the apodization applied to the waveguide. Therefore, a potential geometric precision error might be present for the case of the curved waveguide due to lithography limitations.

3.4. Fabrication process variation analysis

Table 1 shows the statistical analysis of the measured IL, spectral shift, BW, and SLSR for both fabricated devices obtained from 4 different wafer test sites at wavelength ${\mathrm{\lambda }_1}$.

Table 1. Statistical analysis of measured filter parameters

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As for the IL, the mean and SD at the central wavelength of $\lambda = 1290\; nm\; $ for the SDBR is only 0.43 dB and 0.077 dB, respectively, whereas a mean of 1.65 dB and SD of 0.095 dB is obtained for the CDBR. Furthermore, the SDBR WDM filter shows FPV-induced spectral shift with a mean of 0.7 nm and SD of 0.34 nm. This is relatively lower compared to the CDBR which exhibits a 1.3 nm mean with SD of 0.54 nm. However, the obtained spectral shift in both filters is low and tolerable for a wide BW channel spectrum, which is more than 7.2 nm in our case. In general, there is insignificant performance deviation among the test sites for both the SDBR and CDBR filters with slightly higher IL and spectral shift in the CDBR filter than in SDBR. The induced IL and spectral shift observed in both filter types could be due to the smoothing effect during lithography. The smoothing effect might make the fabricated DBR appear more rounded; therefore, the coupling gap will be increased and the grating depth will be reduced. This will reduce the coupling coefficient and reflection strength as well. In effect to this, there will not be efficient coupled back-reflected modes in the drop waveguide. Consequently, less amount of power exits through the drop port leading to higher IL. This smoothing effect applies to both filter types, which is why both filters exhibit higher IL compared to the simulation results. Furthermore, the IL is higher in the CDBR filter than in the SDBR as shown in Table 1, due to lossy radiative modes present in the curved waveguide that contribute to an additional loss. The spectral shift of the measured spectra compared to the simulated ones is also observed in both filters. This might be due to the effective index change which is caused by the smoothing effect. If the waveguide width is reduced by a few nanometers due to the FPV, it will induce a change in effective index and shift the drop wavelength according to Eq. (4).

Table 1 shows the statistical analysis of the measured BW and SLSR for both devices, SDBR and CDBR, obtained from the four wafer sites at ${\mathrm{\lambda }_1}$. We observe minimal BW variation, with SD of 0.2 nm for both devices. However, the measured BW deviates more (∼4 nm) from the simulated one. The BW reduction after fabrication might have been caused by the reduction in amplitude of the grating fins (sidewall corrugation width), which dictates the coupling efficiency. Small perturbations of the waveguide sidewall result in weak reflection and, therefore, weaker forward-to-backward coupling, which in return affects the BW of the spectrum, Eq. (11). This can be observed and explained by looking into Fig. 4 (a) and Eq. (11) and the analysis made in section 2.2. When the sidewall corrugation is reduced, the coupling is decreased, thus the BW will be reduced. Nevertheless, both filters still exhibit less deviation among all wafer sites with SD of 0.38 dB and 0.73 dB from their respective measured mean of 32 dB (SDBR) and 25 dB (CDBR), respectively.

Lastly, Table 2 shows a detailed comparison of each performance metric between the fabricated devices and the filters presented in the literature. One can observe from Table 2 that our design (SDBR) is very compact compared to the rest and it has better SLSR and IL than the others except in [15] where they achieved 5 dB more SLSR but at 200x footprint.

Table 2. Performance comparison of different filter type

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4. Conclusion

In this work, we have designed, simulated, and experimentally demonstrated a grating-based contra-directional coupler WDM in two different configuration setups, straight DBR and curved DBR. The devices were fabricated in a GlobalFoundries CMOS compatible monolithic silicon photonics platform, enabling on-chip integration of electronics and photonic devices. Interference due to the co-propagating modes and reflection bands during filter operation is circumvented by employing asymmetric parallel waveguides at close proximity. Dissimilar parallel waveguides allow us to realize high effective index contrast between the waveguides so that the reflection bands will be located outside the target center wavelengths. In addition, the possible coupling between the forward and backward modes within the grating waveguide is reduced by using out-of-phase fins of the gratings. Furthermore, the crosstalk is significantly minimized to 32 dB for the SDBR and 25 dB for the CDBR through the apodization of both the coupling gap and the grating corrugation width of the waveguide. The experimental measurements showed excellent performance stability across all wafer sites with very low standard deviation in BW (0.2 nm), IL (0.077 dB), SLSR (0.38 dB) and spectral shift (0.34 nm). The design was implemented in a compact device dimension footprint with only 130 µm² / Ch (140 µm x0.93 µm) and 3700 µm² / Ch (86 µm x43 µm) for SDBR and CDBR, respectively.