1. INTRODUCTION

The rapid development of silicon photonics has stimulated broad interest in chip-scale photonic systems, such as on-chip signal processing [1,2], microwave photonics [3], and integrated quantum photonics [4,5]. As one of the fundamental building blocks, on-chip filters, including Bragg grating filters [4,6–8], micro-resonators [9–11], Mach–Zehnder interferometers (MZIs) [12,13], and contra-directional couplers [14–16], play a vital role in the performance of these systems. Among these filter structures, Bragg gratings have been widely used on many platforms for decades. Bragg grating filters couple optical signals near the Bragg wavelength into the backward-propagating mode, enabling a band-stop filter at the through port and a band-pass filter at the reflection port [17]. As a classic filter structure, the Bragg grating has a few distinct features, such as wide free spectral range (FSR) and low insertion loss [11,15,18], making it an appealing candidate for on-chip spectrum management.

However, achieving high rejection and narrow bandwidth simultaneously on silicon-on-insulator (SOI) is challenging due to the high index contrast. Based on the coupled mode theory, the rejection ($R$) and transmission spectrum bandwidth ($\mathrm{\Delta }\lambda$) of an ideal uniform Bragg grating filter are related to the coupling coefficient ($\kappa$) and filter length ($L_F$) by [19]

Besides, Eq. (2) suggests that to realize sub-nanometer bandwidth filters, the structural modulation of a conventional on-chip Bragg grating has to be within a few nanometers [30]. Recent research shows that the sidewall roughness is around a couple of nanometers (1.8 nm in Ref. [30] and 2.7 nm in Ref. [31]). It has been proven that such roughness can significantly distort the spectral response of Bragg gratings, especially long gratings [32]. It means that the dimension of the structure is in the same order as the sidewall roughness. Apparently, the required fabrication precision is far beyond the capability of currently commercialized silicon photonics foundries.

In this paper, we apply the coherency-broken configuration for cascaded cladding-modulated bimodal waveguide Bragg gratings to break the intrinsic limits on rejection and spectrum bandwidth. The coherency-broken cascade configuration mitigates the accumulation of phase errors, thus effectively suppressing the impact of fabrication imperfections on the rejection level. The narrow bandwidth is realized by employing the cladding-modulated grating structure, which significantly increases minimum feature sizes to tens of nanometers by avoiding directly modulating the waveguide [33–35]. This generic strategy paves the way towards on-chip integration of advanced nonlinear photonic systems.

2. WORKING PRINCIPLE

The schematic of the proposed coherency-broken cascaded cladding-modulated grating filter is illustrated in Fig. 1(a). A bimodal grating is leveraged to separate the forward- and backward-propagating optical waves into ${\mathrm{TE}}_0$ and ${\mathrm{TE}}_1$ modes, respectively. The filter comprises $N$ bimodal grating sections connected with mode-dependent attenuators. The structure of the asymmetric bimodal phase-shifted Bragg grating is shown in Fig. 1(b). Instead of directly modulating the waveguide core, e.g., sidewall corrugation, a cladding-modulated grating is formed by a periodic array of silicon blocks on both sides of the bimodal waveguide. As shown by the top left inset of Fig. 1(a), the blocks interact with the evanescent field of the guided modes. This configuration provides additional degrees of design freedom in tailoring the grating coupling coefficient $\kappa$. By adjusting the gap $G$ between silicon blocks and the central waveguide, a sufficiently small coupling coefficient can be generated with fabrication-friendly critical dimensions [36]. The period $\mathrm{\Lambda }$ of the bimodal waveguide Bragg grating can be calculated by the classic phase matching condition ${\lambda }_0=\mathrm{\Lambda }(n_{\mathrm{eff}1}+n_{\mathrm{eff}2})$, where $n_{\mathrm{eff}1}$ and $n_{\mathrm{eff}2}$ are the effective indices of the ${\mathrm{TE}}_0$ and ${\mathrm{TE}}_1$ modes of the bimodal waveguide, respectively. The silicon blocks on one side of the grating are shifted by half a period to assist the conversion of the forward-propagating ${\mathrm{TE}}_0$ mode to the backward-propagating ${\mathrm{TE}}_1$ mode [4]. As illustrated in Fig. 1(c), the single-section Bragg grating reflects light back into the input waveguide through constructive interference of partial reflections occurring in each period at Bragg wavelength. According to Eq. (1), for single-section grating filters, the rejection primarily depends on the grating-assisted coupling strength between the ${\mathrm{TE}}_0$ and the ${\mathrm{TE}}_1$ mode and the length of the grating. In the experiment, the presence of phase errors destroys the perfect coherent interference, leading to the forward-propagating photons in the stop-band and consequently compromising the rejection strength, as illustrated by the red lines in Fig. 1(c). Since the phase error accumulates with grating length, improving the rejection strength by increasing grating length becomes ineffective. Directly connecting multiple sections of filters also cannot avoid the accumulation of phase errors [37]. In the meantime, the phase errors distort the spectral response, resulting in the bandwidth broadening of the cascaded filter. Thus, even in the presence of negligible fabrication imperfections in the grating, the relative phase shift between two cascaded gratings still needs to be tightly controlled.

 

Fig. 1. (a) Schematic of the proposed coherency-broken cascaded cladding-modulated Bragg grating filter. The incident fundamental mode (${\mathrm{TE}}_0$) converts into the backward-propagating first-order mode (${\mathrm{TE}}_1$) as it passes through each section of the grating. The adjacent sections of the grating are mode-dependent attenuators composed of tapers, single-mode waveguides, and bends, which efficiently radiate and dissipate the backward-propagating ${\mathrm{TE}}_1$ mode. Top left: electric field intensity distribution of ${\mathrm{TE}}_0$ and ${\mathrm{TE}}_1$ modes of the bimodal waveguide. Bottom right: schematic representation of the propagation characteristics of ${\mathrm{TE}}_0$ and ${\mathrm{TE}}_1$ modes in the mode-dependent attenuator. ${\mathrm{TE}}_1$ mode experiences significantly higher propagation loss than ${\mathrm{TE}}_0$ mode. (b) Schematic of the asymmetric Bragg grating geometry. (c) Diagram illustrating the effect of phase error on the grating operation of single-section Bragg grating and coherency-broken cascaded gratings.

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To overcome this limitation, it is of crucial importance to prevent the accumulation of phase errors. Thus, instead of directly connecting filters, mode-dependent attenuators are introduced in between filter sections to “drain” photons in the reflection band, as shown in Fig. 1(c). The mode-dependent attenuators can be built readily with bimodal-to-single-mode tapers and single-mode waveguide bend. In these waveguide structures, ${\mathrm{TE}}_1$ mode experiences significantly higher propagation loss than ${\mathrm{TE}}_0$ mode [as shown in the inset of Fig. 1(a)], thereby substantially attenuating the coherent interactions between adjacent grating sections and suppressing the accumulation of phase errors.

3. RESULTS

The proposed cladding-modulated Bragg filters are designed and fabricated on SOI with a 220-nm-thick single-crystal silicon device layer and a 2-μm-thick buried oxide (BOX) layer. Electron beam lithography (NanoBeam nB5) with diluted ZEP520A is leveraged for quick prototyping, while the critical dimension of the proposed filter is compatible with the multi-project wafer (MPW) in silicon photonics foundries. Then the designs are transferred into the single-crystal device layer by inductively coupled plasma (ICP) etching. Figure 2(a) shows the optical micrograph of a fabricated filter consisting of seven identical coherency-broken cascaded grating sections. The width of the single-mode waveguide $W_s$ is 450 nm to ensure low propagation loss transmission of the ${\mathrm{TE}}_0$ mode and the suppression of the ${\mathrm{TE}}_1$ mode. The width of the bimodal waveguide $W_m$ is 680 nm. The dimensions of silicon blocks are $W_g\times L_g=200\mathrm{nm}\times 175\mathrm{nm}$. The period of the grating $\mathrm{\Lambda }=350\mathrm{nm}$ is chosen to satisfy the Bragg condition at ${\lambda }_0=1550\mathrm{nm}$. The block array on one side of the grating is shifted by half a period (175 nm) relative to the other side [38]. Each section of the asymmetric bimodal grating has a taper with a length of $L_t=25\mathrm{\mu m}$ at both ends to achieve the adiabatic conversion of the ${\mathrm{TE}}_0$ mode from a single-mode waveguide to a bimodal waveguide and vice versa. Between every two grating sections, there is a 130-μm-long straight single-mode waveguide and two single-mode bends with a radius of 10 μm. These structures constitute the mode-dependent attenuator, enabling the radiation of ${\mathrm{TE}}_1$ mode. According to the simulation, the radiation ratio of ${\mathrm{TE}}_1$ mode when passing through the taper and a single-mode waveguide can reach at least 15 dB, ensuring the attenuation of phase errors caused by the subsequent filter. Figures 2(b) and 2(c) are the scanning electron microscopy (SEM) images of the single-mode waveguide bend and asymmetric bimodal grating, respectively.

 

Fig. 2. (a) Microscope image of one of the fabricated coherency-broken cascaded grating filters comprising seven Bragg grating filters. Scanning electron microscope image of (b) single-mode waveguide bend and (c) cladding-modulated grating filter.

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The filters are characterized by a C-band narrow linewidth tunable laser (Santec TSL-550, with a linewidth of 400 kHz) and a power meter (Santec MPM-210). The minimum detectable power of the power meter is approximately $-80\mathrm{dBm}$, which determines the maximum rejection strength that could be measured with the experiment setup. A polarization-maintaining fixture is employed to ensure the input light is with the transverse-electric (TE) polarization. To demonstrate the coupling strength tuning capability of cladding modulation, the transmission spectra of single-section bimodal Bragg grating filters with three different gaps $G=80$, 90, and 110 nm are collected and shown in Fig. 3(a). Each filter includes 1700 periods, corresponding to a total length of around 600 μm. For clarity of discussion, the rejection of a filter is defined as the ratio of the off-band transmission to the minimum inside the stop-band. As shown in Fig. 3(a), the rejection strength decreases from 37 to 27 dB as the gap $G$ increases from 80 to 110 nm. The null-to-null bandwidths are 2.06, 1.89, and 1.62 nm for $G=80$, 90, and 110 nm, respectively. These results, together with our previous demonstration of ultra-long grating antennas [35], have shown that evanescent field modulation is a powerful tool in tailoring the spectral response of gratings.

 

Fig. 3. Measured transmission spectra of single-section Bragg filter with (a) different gap widths ranging from 80 to 110 nm, and (b) single-section filters with different grating lengths ranging from 400 to 2000 μm while gap $G$ equals 90 nm. The red solid line in (b) indicates the rejection of the air cladding grating, and the blue solid line indicates the grating covered by SU-8.

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Figure 3(b) shows the rejection in relation to grating length for a fixed gap $G=90\mathrm{nm}$. The grating length varies from 400 to 2000 μm. As shown by the red solid line in Fig. 3(b), the rejection of the grating filter with air cladding increases quickly with the grating length. When the grating length reaches 1000 μm, the growth rate starts to decrease. When the filter length exceeds 1500 μm, the rejection saturates at around 45 dB, as indicated by the red dashed line in Fig. 3(b). It indicates that the maximum rejection strength is ultimately limited by the fabrication quality. The high-refractive-index contrast between silicon and air exacerbates the deleterious effects of fabrication imperfections. Intuitively, the phase errors can be reduced by decreasing the index contrast. Thus, a 1.8-μm-thick layer of SU-8 is spin-coated on the chip, reducing the index contrast from 2.47 to 1.89. In the meantime, due to the reduced index contrast, the evanescent wave extends further into the cladding, resulting in the increase of coupling coefficient $\kappa$. The rejection of single-section gratings with a gap width of 100 nm and grating lengths varying from 200 to 2000 μm is shown by the blue solid line in Fig. 3(b). It is evident that the SU-8-coated grating filters exhibit significantly higher rejection compared to air-clad gratings when the grating length is relatively short. The rejection approaches saturation when the grating length reaches 600 μm. Even when the grating length increases to 2000 μm, the rejection of a single-section grating filter remains around 50 dB without significant increase. The saturation value is indicated by the blue dashed line in Fig. 3(b). The experimental results have proven the previous discussion that the fabrication sets the upper limit of the rejection strength. Furthermore, when SU-8 cladding is introduced, the stop-band shifts towards longer wavelengths ($\sim 30\mathrm{nm}$) compared to the filter with air cladding.

To demonstrate the effectiveness of the coherency-broken cascading architecture in minimizing the impact of phase errors, artificial fabrication errors are introduced into a single-section filter with a length of 2000 μm. For comparison, the transmission spectrum of the filter without artificial defects is shown in Fig. 4(a). The maximum rejection reaches 46 dB. The 3, 20, and 40 dB bandwidths are 1.13, 0.55, and 0.29 nm, respectively. These results are competitive with state-of-the-art single-section grating filters. The defects are created by randomly selecting several silicon blocks and changing their $L_g$ (reduced to random lengths such as 120, 130, or 140 nm), as shown in the inset of Fig. 4(b). Due to the phase errors induced by the artificial defects, the filter exhibits entirely different transmission characteristics. As shown in Fig. 4(b), typical features in the spectral response of Bragg gratings disappear due to the accumulation of phase errors. In Fig. 4(c), the single-section 2000-μm-long grating with the same artificial fabrication errors is divided into two 1000-μm-long sections connected with a mode-dependent attenuator. The transmission spectrum shows that a significant stop-band appears in the spectrum with a rejection strength of 44 dB. The results show that the utilization of the coherency-broken cascade structure can substantially ameliorate the impact of phase errors and improve the spectral response.

 

Fig. 4. Measured transmission spectra of (a) single-section 2000-μm-long Bragg filter without artificial imperfections, (b) single-section 2000-μm-long Bragg filters with artificial imperfections, and (c) two sections of cascaded 1000-μm-long Bragg filters with artificial imperfections. The insets of (b) show the grating structure in three different cases, where the introduced imperfections are denoted by red dots.

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To find the number of sections yielding the maximum rejection strength, we divide the 2000-μm-long filter with a gap width of 90 nm into 4, 8, 16, and 20 sections with equivalent length. The measured spectra are shown in Fig. 5(a). It can be observed that the distortion in the transmission spectrum of the single-section 2000 μm grating is prominent compared to the spectrum shown in Fig. 4(a), indicating the fabrication error varies from chip to chip. Therefore, to systematically study the impact of the number of sections on the rejection level, filters fabricated side-by-side on the same chip are measured. As proved in Fig. 5(a) once again, the coherency-broken cascading effectively suppresses the accumulation of phase errors. The blue plot in Fig. 5(a) (right and top axes) summarizes the measured rejection of filters with different numbers of sections while the total grating length is kept at 2000 μm. It can be observed that there exists the optimal number of sections that maximizes the rejection. Additionally, the filter bandwidth increases as the length of single grating sections decreases, and even the total length of the filter remains the same. This is because the spectral bandwidth is primarily determined by the bandwidth of the single grating sections rather than the total filter length [39].

 

Fig. 5. (a) Measured transmission spectra of $2000\mathrm{\mu m}\times 1$, $500\mathrm{\mu m}\times 4$, $250\mathrm{\mu m}\times 8$, $125\mathrm{\mu m}\times 16$, and $100\mathrm{\mu m}\times 20$ gratings (left and bottom axes). The blue plot (right and top axes) summarizes the change of the rejection as the number of sections increases. The total grating length is fixed at 2000 μm. (b) Comparison of the rejection of single-section (red square) and coherency-broken cascaded (blue circle) strategy as a function of the filter length. (c) Measured transmission spectrum of the coherency-broken cascaded filter consisting of seven 400 μm Bragg grating sections.

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The comparison of experimentally measured rejection for the single-section and coherency-broken cascaded grating filters is shown in Fig. 5(b). Both sets of filters are fabricated on the same chip and have the same gap $G=90\mathrm{nm}$. The rejection of the single-section grating filters saturates when the grating length reaches $\sim 1600\mathrm{\mu m}$, as indicated by the red dashed line. This phenomenon accompanied by the spectral disturbance has been observed frequently in our in-house fabricated single-section filters. The rejection of the coherency-broken cascaded filters with total length varying from 400 to 2800 μm is shown by the blue dots in Fig. 5(b). Each of these coherency-broken cascaded filters consists of a different number of grating sections with a length of 400 μm, as illustrated in Fig. 2(a). The experimental results demonstrate that the coherency-broken cascading approach is effective in making the rejection improve with total grating length. The rejection reaches at least 74 dB when the total grating length is 2800 μm and has surpassed the maximum value that can be measured by the testing setup, as indicated by the gray region in Fig. 5(b).

Figure 5(c) shows the transmission spectrum of the filter with a total length of 2800 μm and consisting of seven 400 μm bimodal Bragg grating sections. The rejection of the cascaded filter reaches 74 dB, which is limited by our measurement setup. The filter also has narrow bandwidths of 2.89, 1.39, 0.44, and 0.16 nm when the rejection reaches about 3, 20, 40, and 60 dB, respectively. The rejection band of the output spectrum is located at the noise floor of the power meter ($-80\mathrm{dBm}$). This result is close to, to the best of our knowledge, the largest rejection experimentally demonstrated for the silicon Bragg grating filters (80 dB). However, due to the utilization of cladding-modulated gratings, our filter exhibits a significantly narrower rejection bandwidth compared to that work ($\sim 10\mathrm{nm}$) [39].

Table 1 summarizes the Bragg grating filters reported in recent years. The strip waveguide sidewall corrugation design reaches 34 dB rejection with a 3 dB bandwidth of 6 nm, but the corrugation is only a few nanometers [38]. The filter using a cladding-modulated grating structure can achieve a bandwidth as narrow as 1.7 nm (with a rejection of 23 dB) owing to the reduced coupling coefficient [40]. An alternative to reducing the coupling coefficient is using a thin waveguide core. For instance, Bragg gratings on 60-nm-thick silicon strip waveguides can achieve a narrow bandwidth of 0.94 nm (with a rejection of 43 dB). Compared to the typical 220-nm-thick strip waveguide, the thin waveguide supports a fundamental mode with much lower optical confinement in the waveguide core [41]. Overall, cascaded gratings exhibit significantly higher rejection. The highest rejection achieved so far is approximately 80 dB (6 nm bandwidth) by coherency-broken cascaded 10 Bragg gratings, each with a length of 250 μm [39]. Filters based on Bragg grating geometry have the advantages of subwavelength engineering and coherency-broken cascading to implement narrow bandwidths (3.3 nm) with high rejection levels (60 dB) [44]. In this work, we realize high rejection and narrow bandwidth filters by introducing the coherency-broken cascaded cladding-modulated grating. The present silicon photonic filter has a narrow 40 dB bandwidth of $\approx 0.44\mathrm{nm}$ and a high rejection of 74 dB, which is better than most silicon filters based on gratings. Besides, the present silicon photonic filter has a large feature of 90 nm.

Table 1. Recent Results of On-Chip Silicon Filters Based on Bragg Gratings

View Table

4. CONCLUSION

In summary, we exploit a coherency-broken cascade configuration and cladding-modulated bimodal waveguide Bragg gratings to break the intrinsic limits on rejection and spectrum bandwidth. The coherency-broken configuration effectively suppresses the accumulation of phase errors, thereby significantly improving the rejection. By employing the cladding-modulated grating structure, small coupling coefficients can be achieved with a large gap width, which is compatible with photolithography. This research also demonstrates that cladding modulation is an effective approach to break the design constraints of high-index-contrast waveguides, which can give rise to a new category of on-chip devices, such as filters [21,45], sensing [46,47], and antennas [35,48].