1. Introduction

Silicon-on-insulator platform has shown a great potential for compact and monolithic integration of optics and electronics on a single chip. Optical filters of this technology have been developed in various structures based on Bragg gratings, ring resonators, arrayed waveguide gratings, Mach–Zehnder interferometers, etc. Those based on Bragg gratings have the advantage of free spectral range (FSR) free operation as well as great design flexibility to be engineered for desirable filtering characteristics [1–3].

However, two-port Bragg grating filters mostly operate in reflection mode, which usually translates to the need for optical circulators and increases the complexity of integration by requiring off-chip components or bonded nonreciprocal magneto-optic materials [4]. In this regard, integrated grating-assisted contradirectional couplers (Contra-DCs) have enabled researchers to successfully implement some of the wideband Bragg-grating-defined filtering requirements while their four-port structure (add-drop nature) circumvents the need for the circulation of optical power [5–8].

Grating-assisted Contra-DCs basically consist of two asymmetric waveguides and some form of refractive index perturbations along the waveguides; improving their performance lies in increasing the optical phase mismatch between the involved eigenmodes of the coupled waveguides. In our previous work, we demonstrated a new design approach whereby the need for two asymmetric waveguides and for a grating mechanism is simultaneously addressed by placing a subwavelength grating (SWG) waveguide next to a continuous waveguide [9].

In that SWG-based Contra-DC, the large optical phase mismatch between SWG and strip waveguides [in silicon-on-insulator (SOI)] enabled the device to operate over a 120 nm wavelength window free from the interference of intra-waveguide reflections, and to suppress the undesired codirectional coupling by 35 dB. At the same time, the strong on/off grating mechanism leads to high fabrication tolerance, short coupling length, and minor ripples in the pass-band. Those features show the potential of the device for broadband filtering applications (> 1 nm), such as integrated optical add-drop multiplexers (OADMs) in coarse wavelength division multiplexed (CWDM) networks [9].

For SWG-based Contra-DCs with uniform gratings and a fixed gap, strong sidelobes can cause difficulties such as cross-talk between adjacent channels in OADM applications. Recently, a high sidelobe suppression of 27 dB was experimentally demonstrated in an apodized SWG-based Contra-DC [10]. The apodization is employed with a Gaussian profile that tapers the gap between the two waveguides from 200 nm to ~900 nm for a 100 μm coupler. While the compact size and sidelobe rejection of the device is impressive, the rejection ratio of the through-port is limited to only ~5 dB within its stop-band and the pass-band of the drop-port shows a minimum of 2.5 dB insertion loss over its 8.8 nm 3 dB bandwidth. While such qualities make the device suitable as a two-port bandpass filter, its use as a four-port add-drop filter might be limited.

In this paper, we explore a stronger power coupling regime through an effectively narrower gap distance, and correspondingly, we adjust the coupling length to reach a compromise between sidelobe suppression and stop-band/pass-band extinction in favor of the four-port add-drop functionality of the filter for CWDM applications. We design apodized devices (using a raised cosine profile) with different pass-band bandwidths of 12 nm, 9 nm, and 6 nm, which show 10 dB to 20 dB sidelobe suppression ratio and 15 dB to 35 dB extinction ratio. However, the main objective of our work is not to compare explicitly nor optimize the different apodization functions (e.g., Gaussian, raised cosine, etc.).

We further tailor the spectral characteristics of the coupler by introducing a π phase shift into the gratings of the SWG waveguide. This way, a resonant peak appears in the stop-band spectrum of the through-port showing the feasibility of implementing a four-port photonic resonator. The location of the transmission peak with 7 dB extinction ratio and 1 nm bandwidth is highly sensitive to the refractive index of the surrounding cladding material since 50% of the SWG waveguide is occupied by cladding. Thus, the phase-shifted SWG-based Contra-DC takes advantage of the increased light-matter interaction and our analysis indicates a bulk sensitivity of 177 nm/RIU, which is of high interest in integrated optical sensing applications that require high sensitivity and efficient interaction between the light and the cladding material under test.

2. Device structures

The schematic diagram of the apodized SWG Contra-DC is illustrated in Fig. 1(a). A strip waveguide is first brought gradually to a gap distance, G_max, of a straight SWG waveguide with a period Λ (here set to 378 nm), to form the coupler waist over a coupling length L_C. Along the waist, the gap is tapered by a raised cosine profile described by Eq. (1), such that the minimum gap at the center, $Z=Lc/2$, is G_min [11]. It is worth noting that we taper the gap distance based on curving the strip waveguide; alternatively, the SWG waveguide might be curved as is the case in [10], but no significant difference in performance is expected nor observed in our simulations of both designs as long as the gap profile remains the same.

 

Fig. 1 (a) Schematic top view of the apodized and (b) phase-shifted SWG Contra-DC in SOI platform.

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Figure 1(b) shows the schematic diagram of a phase-shifted device. In this case, the gap G is fixed and a phase shift of $\pi$ is introduced at the center of the SWG waveguide. In all designs, the duty cycle of the SWG waveguide is η = 50%.

SWG tapers [Fig. 2(a)] at the input and output of the SWG waveguides are responsible for adiabatic mode transition by incorporating a fixed period of 250 nm, but a width variation in their connecting bridges between 500 nm and 150 nm over a length of 15 µm [12]. The height and width of the strip waveguides are 220 nm and 500 nm, respectively, as shown in the cross-section view in Fig. 2(b). The waveguides sit on a 3 µm thick buried oxide (BOX) layer and a 2.5 μm thick cladding of SiO₂ is deposited on top. Focusing vertical grating couplers (VGCs) optimized for TE operation are used to couple light into and out of the chip [13]. The devices were fabricated using electron beam lithography in a single, full, plasma etching process, at the University of Washington Nanofabrication Facility (WNF) [14].

 

Fig. 2 (a) schematic top view of the SWG taper; (b) cross-section of the strip waveguide.

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3. Results

Figure 3(a) in [9] shows the spectral responses of a compact device with a coupling length $L_C$ of 100 μm and a fixed gap G of 150 nm. We re-fabricated the device and obtained similar spectral responses as shown in Fig. 3(a) (all the reported spectra are normalized to the back-to-back insertion loss of a test pair of VGCs with a central loss of 15 dB and a 3 dB bandwidth of 30 nm).

 

Fig. 3 (a) Measured drop-port (red) and through-port (blue) spectra for a device with L_C = 100 μm and a fixed gap of G = 150; (b) simulated responses of two gap-tapered devices having G_min = 150 and G_max = 450 nm with (dotted) and without (solid) width compensation.

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3.1 Apodized coupler

To suppress the strong sidelobes in Fig. 3(a), we taper the gap of the device by preserving the central gap G_min equal to 150 nm, but increasing it up to G_max = 450 nm at the two ends of the coupler waist with the profile described by Eq. (1). The solid lines of Fig. 3(b) show the through-port (blue) and drop-port (red) spectra of the device obtained through a 3D FDTD solver (from Lumerical). The simulated response is asymmetric and the main sidelobes are on the short-wavelength side of the spectrum while the sidelobes on the long-wavelength side are better apodized and suppressed. The same observation holds true in Fig. 2 of [10] and is worth further attention.

We believe that the nature of the stronger sidelobes on the left-hand of the spectrum (i.e., at shorter wavelengths) is the same as that of apodized Bragg gratings with “dc” effective refractive index change [11, 15]. In this gap-tapered coupler, at the two ends of the coupler waist, the gap is larger, and therefore, the phase-match condition of contradirectional coupling is satisfied at a shorter wavelength. Accordingly, the short wavelengths are contra-coupled more strongly at the two ends compared with the center of the coupler with a narrower gap such that the two ends of the apodized coupler form a Fabry-Pérot cavity at short wavelengths and create strong sidelobes.

A possible solution is to change the width of the strip waveguide (or alternatively SWG waveguide) along the length of the coupler in order to counteract the effects of the tapered gap on the phase-match condition letting it be satisfied at the same wavelength along the length. It is similar to the idea of apodized Bragg gratings with no “dc” index change meaning that the average effective refractive index is meant to remain constant lengthwise to make sure the Bragg condition is met at a fixed wavelength [11].

To investigate this solution, we simulate the response of a device with a similarly tapered gap, but a compensated width of the strip waveguide, such that it changes from 500 nm at the two ends of the coupler waist down to 475 nm at its center, in correspondence to the tapered gap, to ensure that the phase-match condition is always met at the same wavelength along the coupler based on the formulation of the phase-matched coupling condition provided in [9]. The dotted lines in Fig. 3(b) demonstrate the simulation results of such a device showing that this idea can effectively suppress the main left-hand sidelobes favoring a more symmetric spectrum.

Experimental measurements of the fabricated device with L_C = 100 μm, G_min = 150 nm, G_max = 450 nm, and without width compensation are plotted by solid lines in Fig. 4(a). Interestingly, the response does not suffer from asymmetric sidelobes with strong sidelobes on the short-wavelength side as expected form the 3D FDTD simulation of the same device shown by solid lines in Fig. 3(b). This can be explained by a fact described in [9] and implicit in Fig. 3(a) that, for the original device with a fixed gap, the side lobes at longer wavelengths are stronger than their counterparts at shorter wavelengths since the coupling coefficient is wavelength dependent and, at longer wavelengths, involved supermodes of the coupled waveguide system are less confined to the waveguide cores, which leads to higher coupling coefficient, and consequently, stronger side lobes at longer wavelengths. Now, in the gap-tapered device, this fact counteracts the aforementioned Fabry-Pérot effect and allows the spectrum to show more equalized sidelobes on the two sides.

 

Fig. 4 Measured drop-port and through-port spectra for (a) devices with G_min = 150 nm, and G_max = 450 nm but with different L_C of 100 μm (solid lines) and 200 μm (dotted lines), and (b) devices with L_C = 100 μm, G_min = 200 nm, G_max = 450 nm (solid lines) and L_C = 400 μm, G_min = 250 nm, G_max = 650 nm (dotted lines).

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It should be noted that the simulation of the apodized device is not able to fully reflect the balance between the above two effects. An explanation of this could be the fact that the optical source in the 3D FDTD solver is implemented as a 2D plane that crosses the input waveguide and injects an optical pulse with time-varying amplitude but a fixed field profile calculated at the central frequency over the frequency range of interest; we believe that the fixed profile of the injected optical pulse does not allow the simulation to fully account for the wavelength dependence of the coupling coefficient [16].

The fabricated SWG-based Contra-DC shows 19 dB suppression of the main sidelobe and 14 dB pass-band/stop-band extinction ratio with a 3 dB bandwidth of 12 nm. For an enhanced extinction ratio, a device with the same gap variation but doubled L_C is measured and shown as dotted lines in Fig. 4(a). The extinction ratio increases to 33 dB and the flatness of the pass-band is improved while the 3 dB bandwidth is almost the same. In comparison, the apodized Bragg grating-assisted Contra-DCs in [17] show ~10 dB suppression of the main sidelobe and have 320 μm coupling length to demultiplex a CDWM channel with similar 3 dB bandwidths.

To adjust the bandwidth of the filter, one can change the gap; however, increasing the gap without appropriately increasing the coupling length will cause weak power coupling and therefore, high insertion loss of the dropped signal and its low extinction ratio compared to the remaining power at the through-port. Thus, to reduce the 3 dB bandwidth, we consider a device with G_min = 200 nm and a longer coupling length of L_C = 200 μm. The 3 dB bandwidth shrinks down to 9 nm, as shown in solid lines in Fig. 4(b). To reduce the bandwidth even further, we consider a device with L_C = 400 μm, G_min = 250 nm, and G_max = 650 nm; the 3 dB bandwidth is now 6 nm, as illustrated by dotted lines in Fig. 4(b).

In our previous work on couplers with a fixed gap [9], we developed a coupled-mode analysis for SWG-based Contra-DCs and reported the effective coupling coefficients. This model provides a basic understanding of the principle of operation for devices with a fixed gap; however, it ignores the wavelength dependence of the coupling coefficient. Thus, the model cannot explain qualities such as the asymmetry of the spectral responses around the central coupling wavelength, and consequently, quantities such as the strength of the main sidelobes on either side of the spectrum. The practical implementation of coupled-mode theory for analyzing tapered grating-assisted coupling (e.g., in [18] for the case of tapered Bragg gratings or in [5] for the case of tapered Bragg grating-assisted Contra-DCs) considers the coupling coefficient as a function of coupling length z calculated at the central coupling wavelength 𝜆_C and ignores the exact dependence of κ on wavelength 𝜆 [i.e., κ = κ(z,𝜆_C) but not κ(z,𝜆)]. This simplifying assumption is very useful for analysis of narrowband grating filters (e.g., < 1 nm). However, an analysis that is aimed at designing the spectral response of broadband grating filters (e.g., > 1 nm) needs to take into account the dependence of κ to both z and 𝜆, which makes the analysis computationally intensive, especially since there is no analytical solution for κ of coupled channel waveguides as a function of wavelength and gap distance, and numerically, a modal solver needs to return the complex κ at appropriately quantized points in the two dimensional space of z and 𝜆.

3.2 Phase-shifted coupler

To further investigate the potential of SWG-based Contra-DCs, a resonant filter is created by introducing a π phase shift into the grating phase at the center of the coupler, as schematically illustrated in Fig. 1(b). Two devices with L_C = 100 μm having a uniform gap of 200 nm with (solid lines) and without (dotted lines) a $\pi$ phase shift are compared in Fig. 5(a). The phase-shifted device shows a transmission resonant peak within its broadened stop-band with diminished rejection ratio.

 

Fig. 5 Measured drop-port and through-port spectra for devices with (a) L_C = 100 μm, G = 200 nm with (solid lines) and without (dotted lines) a $\pi$ phase shift, (b) and $\pi$ phase-shifted devices with L_C = 100 μm but different gaps of G = 225 nm (solid lines) and G = 125 nm (dotted lines).

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The peak shows 7 dB extinction ratio and a 3 dB bandwidth of 1 nm corresponding to a quality factor ($Q$) of ~1,500. Devices with wider (G = 225 nm) and narrower (G = 125 nm) gap are considered in solid and dotted lines in Fig. 5(b) enabling the resonant peak within weakly and highly rejected stop-bands of the through port spectrum, respectively. The resonant peak for a device with a wider gap exhibits lower insertion loss. However, for a device with a fixed length, a wider gap translates into lower stop-band rejection. Thus, if an application requires both a resonant peak with low insertion loss and high rejection in the stop-band, widening the coupling gap while appropriately increasing the coupling length should offer a good solution, but at the expense of increased device footprint.

In comparison, phase-shifted Bragg grating-assisted Contra-DCs have enabled four-port photonic resonators with a $Q$ factor of 7,000 [5, 19]. The optical field of that type of device is highly confined to the silicon cores of the asymmetric rib waveguides of the coupler, and in case of sensing applications, this limits the interaction of the light with the cladding material. However, intuitively, since the SWG waveguide allows the light to pass through the cladding material half of its propagation time, the wavelength and intensity of the resonant peak of the phase-shifted SWG-based Contra-DC is expected to be highly sensitive to the refractive index of the cladding [20].

In theory, this fact can be explained as follows: the resonant peak appears at the central coupling wavelength, λ_C, in the middle of the stop-band [5]. The central coupling wavelength, λ_C, satisfies the phase-matched coupling condition between the two lowest-order transverse TE-like supermodes of the coupler waist (E₁ and E₂) according to Eq. (2) [9]:

To quantify the sensitivity of the resonant peak to the change in the refractive index of the cladding material, we consider two claddings with wavelength-independent refractive indices of 1.444 and 1.494, and find λ_C by using Eq. (2) where β ₁, β ₂ are extracted from a mode solver while the SWG waveguide is replaced with an equivalent strip waveguide with the average permittivity given by Eq. (3). Figure 6 shows that such change of the cladding shifts λ_C by 8.85 nm and 8.87 nm for the devices with 200 nm and 225 nm gap distances, respectively. It concludes that the bulk sensitivity S_b of the device described by Eq. (4) is 177 nm/RIU. This result indicates a 4.6-fold and 1.3-fold increase in sensitivity compared to the standard 220 nm thick and 90 nm ultrathin TE silicon ring resonators, respectively [21]; and is comparable to TM ring resonators [22]. However, SWG ring resonators with bulk sensitivity of 490 nm/RIU have been reported in [20]; and this superior sensitivity can be attributed to the fact that the resonance in a SWG ring resonator is mainly controlled by the characteristics of SWG waveguides, but the resonance in a phase-shifted SWG-based Contra-DC relies on a balanced interaction between SWG waveguides and solid waveguides.

 

Fig. 6 Graphical solution of the phase-matched coupling condition given by Eq. (2) as the cross points of β₁ + β₂ curves by the horizontal dotted line indicating the wavenumber of the grating 2π/Λ. The four cross points correspond to two cladding materials with refractive indices of 1.444 (solid lines) and 1.494 (dashed lines) and two gap distances of 200 nm (blue) and 225 nm (red).

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4. Summary

We designed, fabricated, and characterized silicon photonic SWG-based Contra-DCs with tailored spectral responses. In gap-tapered devices, we demonstrated compact add-drop filters that reached a compromise between sidelobe suppression and pass-band/stop-band extinction ratio to be better qualified for applications such as (de)multiplexers of CWDM networks. We also demonstrated a four-port filter with a resonant transmission peak in its spectrum. Use of the SWG waveguide in the structure of such coupler allows the characteristics of the resonant peak to be highly sensitive to the cladding material, and makes it useful for integrated sensing applications.