1. Introduction

Optical stopband filters (OSBF) in silicon photonics have gained research interest due to their importance in several fields [1,2]. As more channels are used in optical communications and on-chip spectroscopy applications keep increasing, the necessity of broadband OSBF and periodical transmission peaks are required. These photonic integrated devices should possess tunable stopbands, small footprints and low reflections [3]. One of the most common method to realize OSBF has been with periodical structures such as Bragg gratings (BG) as they can be fabricated by modulating the surface of the waveguide [4], the sidewalls [5,6] the cladding [7,8] or the core of a single mode waveguide [9].

For applications that require high Q transmission peaks, an OSBF with defect in one of the periods can be used and depending on the length of the defect, one, or several transmission peaks is obtained [10]. A long defect can also be considered as a Fabry-Perot (FP) cavity that utilizes BGs as the reflective ends. These FP filters have been proposed in systems that require several narrow bandwidth pass channels, to characterize the group index and waveguide losses [11]. Nevertheless, since the transmission peaks only appear within the stopband of the BG, the total bandwidth that is covered by the FP filter is limited to a few 10ths of nanometers [12]. Therefore, in order for the FP filter to cover a wider range, it is desired to obtain a larger stopband. Broadband OSBF can be fabricated using one dimensional (1D) photonic crystal (PhC) etched on the waveguide core [13], however, the reflected wave is detrimental in several applications.

In recent years, broadband OSBF with the possibility to filter out the returning wave have been suggested using multimode waveguides with conjunction of linear tapers. In these types of filters, the stopband is achieved by coupling the fundamental mode into a higher order mode and then, filtering out the reflected higher order mode with the tapers. They have been proposed with asymmetric Bragg sidewall gratings [14–18] and 1D photonic crystal etched in the waveguide core. Stopbands in the order of 84 nm are expected with low back reflections [19]. Additionally, two parallel rows of a 1D PhC etched on the core of the waveguide have been used as degenerate band edge resonators [20,21]. However, multimode broadband OSBF based on two parallel rows of a 1D PhC with defect have not been fully studied and thoroughly experimental characterizations are missing.

In this paper, we propose and demonstrate an OSBF with transmission peaks based on a multimode waveguide with two rows of a 1D PhC with defect. By using two rows of the PhC we broaden the stopband of the device in comparison to a single row and reduce the footprint [19]. The parallel rows of the PhC are asymmetric to serve as a TE₀ to TE₁ mode coupler for the wavelengths that satisfy the phase matching condition and the defect in the photonic crystal allows us to have a number of localized states in the bandgap. By directly etching the PhC in the core of the waveguide, we show that few periods are needed to achieve high efficiency conversion, thus keeping the device very compact. Additionally, by combining this structure with linear tapers, we can remove the reflected wave that would otherwise travel backwards. The application of this structure lies in its ability to achieve high Q transmission peaks throughout the S, C and L optical bands when a long defect is inserted. The device is fully compatible with standard fabrication techniques and the material used is Silicon-on-Insulator.

2. Design

The schematic of the device is shown in Fig. 1(a). The input and output consist of single mode waveguides of 440 nm width connected via 8 μm long linear tapers to a multimode waveguide with a wider width of W = 1000 nm. In the multimode waveguide, a PhC is fully etched consisting of two rows of two sections of N holes separated by a defect length L. Both rows of holes have a period Λ and diameter d, separated in the x direction by Δx and displaced by Δz with respect to each other.

 

Fig. 1 (a) Schematic of the proposed device and SEM image with Λ = 330 nm, d = 140 nm, L = Λ, W = 1000 nm, Δx = 500 nm, Δz = Λ/2, (b) mode profiles of the two existing modes in the unpatterned U and patterned P regions, (c) effective refractive index for the two TE modes considering dispersion.

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Using a 3D mode solver, we computed the E_x mode profiles of the existing TE modes in the cross section of the unpatterned region (U) and patterned region (P) of the multimode waveguide and are shown in Fig. 1(b). Therefore, the effective refractive index (N_eff) of the structure can be calculated by integrating the refractive indices of each mode through both sections, and their values for the 1440 – 1640 nm wavelengths are shown in Fig. 1(c). The results were obtained considering a Si height of 250 nm, SiO₂ as substrate (n = 1.44), air as cladding (n = 1), d = 140 nm and Λ = 330 nm.

The working principle of the device is that the input travelling wave in the single mode waveguide is expanded to the fundamental TE₀ mode of the multimode waveguide via a linear taper. In the multimode waveguide, the PhC creates a bandgap, or as it can also be explained from the BG point of view, the asymmetric holes serve as refractive gratings to achieve mode coupling and reflection from the TE₀ mode to the TE₁ mode for the wavelengths that satisfy the phase matching condition given by ${\lambda }_B=\Lambda \left(N_1+N_0\right)$ where λ_B is the Bragg wavelength, N₁ and N₀ are the effective refractive indices of the coupled modes. The returning TE₁ waves are filtered by the linear taper as they return as shown by the blue lines in Fig. 1(a). The stopband of the OSBF is given by Eq. (1) [19]:

Now, by inserting a defect in the middle of the PhC, a localized state is allowed in the band gap [22], so a transmission peak is detected at the output. This condition is of great interest as it is easy to experimentally characterize the impact of the design parameters by measuring the effects on the transmission peak. In our main design, we set the diameter of the holes of the PhC to d = 140 nm as this size is easily achieved by electron-beam lithography (EBL). The distance between the center of the rows was set to Δx = 500 nm and the bottom row was shifted Λ/2 to the right with respect to the top one to get an anti-symmetric structure with the highest coupling coefficient. To get a λ_B = 1550 nm, we computed the effective refractive indices to be N₀ = 2.72 and N₁ = 1.95, from Fig. 1(c). Then, we solved for the period and obtained Λ = 330 nm. Each section of rows consisted of 10 periods.

The behavior of such device and the effects of the different design parameters were studied using the FDTD algorithm. In order to save computational time, 2D simulations were carried out where the 3D projection into a 2D structure was taken into account by rotating the input polarization and using the effective index method. So first, we set the Ex component of the 2D TM-polarized light as input because its field profile matches the 3D Ex profile of the TE₀ mode as shown in Fig. 2(a). Then, we set a 2D dispersive material whose 2D N_eff best matches the 3D N_eff. The values of the refractive indices used in the 2D simulation are shown in Fig. 2(b). By doing this procedure, we can simulate the top view of the device. Although it is also possible to simulate the side view of the device without needing to change the polarization of the input light [23], it is more difficult to account for variations in the design in terms of size and displacement of the holes.

 

Fig. 2 (a) Input field for the 2D simulation, (b) refractive indices, (c) transmission spectra for a 2D and a 3D FDTD simulation with Λ = 330 nm, d = 140 nm, W = 1000 nm, N = 10. The optical stopband of 205 nm is seen with center at around 1550 nm.

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For validation, a 3D and a 2D simulations of the device without defect are displayed in Fig. 2(c). A mesh size of Δm_z = Δm_x = Δm_y = 40 nm for the 3D case, and Δm_z = 5 nm and Δm_x = 2 nm for the 2D case were used. From the figure, we are able to identify a stopband of about 205 nm, which corresponds to the mode conversion due to the PhC. From the bandwidth, we can calculate the coupling coefficient to be κ = 1.01 μm⁻¹ given the group indices n_g0 = 3.87 and n_g1 = 4.29. Therefore, by using two rows of air holes, a very strong coupling is obtained and the grating periods N can be minimized. However, we can observe large fluctuations outside the stopband, which can be flattened by apodizing the size of the holes as in [19]. However, even with large fluctuations, the device is useful when transmission peaks are found within the stopband by introducing a defect in the photonic crystal as they can be used as reference for refractive index sensors or narrowband filters. Also, there is a small shift between both simulations of about 20 nm due to a small discrepancy in the N_eff and a difference about 10 dB in the power level. Nevertheless, the computation time for 2D is in orders of magnitude much faster than the 3D simulations and is enough to analyze the effects of the PhC.

Then, we introduce a defect in the photonic crystal that has a length equal to one period to obtain a single resonant peak, just like the case of a phase shifter in BGs [24]. The computed transmission of the device using the 3D and 2D model are shown in Fig. 3(a). The mode profiles at the output of the PhC for different wavelengths, i.e., 1550 nm (transmission peak), 1700 nm (passband) and the reflected wave before the linear tapers i.e., 1510 nm (stopband) are shown in Fig. 3(b) using the 2D model. The mode profiles of the respective wavelengths reveal that the 1700 nm passes through the crystal unaffected with the original mode profile. For the 1550 nm, the defect allows for the wave to pass through in a similar shape as the input, but losses are expected from the PhC. In the stopband, very less power is allowed to pass as most of it was reflected back with a TE₁ profile. With the simulations, we can confirm mode coupling and that we obtain a single transmission peak in the stopband.

 

Fig. 3 (a) Transmission of the device with a defect L = Λ, Λ = 330 nm, d = 140 nm, N = 10, W = 1000 nm and (b) mode profiles for the reflected and transmitted waves using the 2D model. Corresponding wavelengths are indicated by dotted lines in (a).

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3. Fabrication

Next, we experimentally studied the influence of the different parameter variations, namely the period, hole size, waveguide width, number of periods, displacement, cladding refractive index and defect length. We fabricated our devices in a SOI wafer with 250 nm thick silicon and 2 μm buried SiO₂ with EBL technology in the positive resist ZEP520A. A large voltage of 75 kV was used to thoroughly pattern the holes. The resist was developed with the high contrast developer ZED50 for 1 minute at room temperature. Then, we used a single dry etching step to transfer the resist pattern into the silicon layer with inductive coupled plasma reactive ion etching (ICP-RIE) using low pressures of SF₆ gas to achieve smooth sidewalls. In order to keep the complete fabrication process to a single etching step, all waveguides are strip waveguides and fully-etched grating couplers at both ends of the single mode waveguide are used to couple the TE polarized light in and out of the device [25]. No upper cladding is deposited.

The experimental setup consists of six-axis alignment stages to position and tilt two independent single mode fibers (SMF) by 10 degrees above the grating couplers to avoid second order reflections. A tunable laser with wide range 1440-1640 nm was used as light source with a polarization controller to input the TE mode into the device. The chip was thermally stabilized at 25 °C and the output was detected with an optical power meter. The 3 dB bandwidth of the diffraction grating couplers is about 45 nm at a central wavelength of 1560 nm with a total insertion loss of 9 dB. Nevertheless, it is feasible to analyze the behavior of the device because the minimum power detected throughout the 200 nm laser range is approximately −40 dBm which is well above the noise level of the power meter.

4. Measurements

First, we verified that the linear tapers and multimode waveguide did not incur extra losses by comparing the transmission spectrum to that of a single mode nano waveguide. After confirming that the linear tapers are long enough to neglect losses. We chose to mainly characterize a device with a defect equal to one period since the unique peak falls into the 3 dB bandwidth of the diffraction grating couplers and thus, we can correctly measure the extinction ratio and Q values. We normalized the results of the devices with a reference waveguide that consists of an input grating coupler, followed by a 200 μm long taper that ends in a 440 nm single mode waveguide. Then, we insert our proposed multimode waveguide without PhC, and at the output of the device we have a similar grating coupler structure to extract the light from the SOI chip. The normalized results are shown in the following graphs.

The transmission spectrum of a device with the same design parameters as the one presented in the previous section is shown in Fig. 4(a) labeled with Λ = 330. We can observe a peak at the wavelength 1570 nm due to the photonic crystal defect, and a wide stopband of about 200 nm. There is approximately 20 nm difference with the 2D simulation results in terms of the position of the peak, but the same order of difference was found from the projection of the 3D model into the 2D model. Thus, the differences may be attributed to the discrepancy between the effective refractive indices which we can calculate to be 0.09 refractive index units (RIU) between experiment and simulations. Furthermore, from the experimental results, we can see a high extinction ratio of 25 dB. The actual TE₀-TE₁ conversion efficiency is lower than that estimated from this value as this includes both, the TE₀-TE₀ reflection and the TE₀-TE₁ conversion. By using the simulation results at the wavelength of 1500 nm, there is about 9% reflected in the same mode.

 

Fig. 4 Experimental characterization of a 2D PhC with defect Δz = 1Λ for different (a) Period, d = 140 nm, W = 1000 nm, N = 10 (b) hole diameter Λ = 330 nm, N = 10, W = 1000 nm (c) waveguide width, Λ = 320 nm, d = 140 nm, N = 10 (d) number of periods, Λ = 320 nm, d = 140 nm, W = 1000 nm (e) row displacement Λ = 330 nm, d = 140 nm, N = 10 and (f) cladding refractive index.

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Also, in the same figure, we show the transmission spectrum of five devices with different periods, and we get a linear relationship as expected from the Bragg equation of δλ/δΛ = 3.05 nm/nm. It is important to say that only for the case of Λ = 320 we are able to see the complete stopband, and for the other periods, only one side lies within the spectrum range of the tunable laser. Nevertheless, a similar bandwidth of 200 nm is confirmed if we take half the bandwidth (from the peak to one side of the stopband 100 nm) and assume a symmetric spectrum, which confirms our large coupling coefficient of κ = 1 μm⁻¹ that is consistent with the 2D-FDTD simulations.

Then, we studied the effects of the hole size while keeping a constant period of 330 nm, and found out that as the size of the hole increases, there is a shift to the left of the Bragg wavelength as shown in Fig. 4(b) because the N_eff of the modes is reduced as there is more air in the structure. We calculated the relationship δλ/δd = 1.23 nm/nm which is about one third the effect of the period. The peaks in the experimental results have a loss of approximately 7 dB and a full width at half maximum (FWHM) of 5.2 nm.

Figure 4(c) shows the effect of the multimode waveguide width because this parameter also determines the value of N_eff of the guided modes. We studied the case when the waveguide is 1000 nm and 1100 nm wide with a period of 320 nm and a d = 140 nm. From the transmission spectrum, we can conclude that the stopband is red shifted due to the increase of the N_eff mostly governed by the increase of the N₁ value as the N₀ is approaching the slab waveguide limit.

One of the best advantages of using such a structure is that the high index contrast between Si and the air holes translate into a high κ coefficient that allows the required number of periods to be kept to a few numbers, thus maintaining a very compact device in comparison to other topologies [17]. Additionally, it has been shown that the Q factor of band edge resonators based on two rows of a 1D PhC increases to the fifth power with the number of periods [26]. However, the effects on the transmission with a defect have not been reported. We found that the FWHM of the transmission peak are 20.6 nm, 5.2 nm and 3.0 nm for N = 5, 10 and 15 respectively which follows a quadratic relationship. However, losses of the device are also increased and for the case where N = 20, the peak is buried in the noise level of the rejection band as shown in Fig. 4(d).

Next, we studied the effects of the displacement between the two rows of holes Δz. It was said that if there is no displacement between the holes, the mode-conversion integral is zero and there is no coupling between modes, so all the power is transmitted to the output. In this case, the periodical device can be treated as a BG with the N_eff given only by the fundamental mode, which would correspond to a λ_B = 1700 nm for our case. However, when there is a displacement, two resonant peaks appear and they become closer to each other and finally, they merge into one, as the displacement approaches the maximum value of half a period as shown in Fig. 4(e). We attribute this effect to the coupling between forward and backward propagating waves of the same mode when the device is not perfectly anti-symmetrical.

We also verified the effect of the cladding in the position of the transmission peak. To modify the refractive index of the cladding, different concentrations of salt in deionized water were prepared knowing that the refractive index varies with 0.0018 RIU per mass % [27]. With the help of a microfluidic channel manually mounted on the surface of the chip, the device was exposed to the different solutions. Figure 4(f) shows the linear fitting between the refractive index of the cladding and the Bragg wavelength for simulations and experimental results. The simulations have a sensitivity of 72 nm/RIU, whereas the measurements show 54 nm/RIU. The differences may be due to an inhomogeneous solution and inaccurate salt concentrations.

Finally, longer defect lengths were investigated, being 50Λ and 100Λ long, so that multiple transmission peaks could be detected at the output while still maintaining a maximum total footprint size of 40 μm² with Λ = 330 nm. These two cases can be studied as a dielectric FP filter whose mirror ends are given by 10 periods of the PhC structure. The number of localized states increases throughout the whole bandgap following the free spectral range (FSR) of the FP equation for multimode waveguides written as [28]:

 

Fig. 5 Experimental results for photonic crystals with long defects with Λ = 330 nm, d = 140 nm, W = 1000 nm (a) Transmission spectrum for the whole stopband, (b) close up on the transmission for the 100Λ device, (c) measured group index

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The FWHM of each peak is measured to be 0.4 nm when they are spectrally resolved, and 0.66 nm when they are closely spaced that they cannot be resolved with our measurement setup. From the fact that we can only see one set of peaks, we suspect that there is only one mode resonating in the cavity. As we are able to directly measure the λe through the complete band, we can calculate the wavelength-dependent group index and is shown in Fig. 5(c). From the measured value, we can find that is very close to the group index of TE₁ of 4.29 at 1550 nm and thus, the mode that resonates is the TE₁ mode. The small difference of 0.12 may be due to the length the light penetrates into the PhC before being reflected back that was not taken into account in the computation of L. When using the measured values with Eq. (2), we obtain an effective length of 17.2 μm instead of the designed 16.5 μm. The losses throughout the stopband for both devices is relatively constant, as the losses of the multimode cavity are low.

5. Conclusion

In summary, we demonstrated and characterized a broadband OSBF with transmission peaks based on a multimode waveguide and two parallel rows of a 1D photonic crystal with defect. We focused our discussion on the case of having a defect in the photonic crystal to obtain a single transmission peak to easily quantify the effects of each design parameter. By directly modulating the refractive index of the waveguide with the proposed anti-symmetric PhC, the coupling coefficient is enhanced which allows us to create a very compact mode converter from TE₀ to TE₁ that is compatible with standard fabrication technologies. We achieved a high extinction ratio of 25 dB and a wide stopband of 200 nm. We showed how to tune the position of the transmission peaks with the design parameters and proposed the usage of longer defects to obtain multiple transmission peaks across the stopband. According to our results, the length of the Fabry-Perot cavity can be tailored to suit the required FSR and FWHM because the cavity losses are very low due to the fact that a wide multimode waveguide makes up the cavity so sidewall roughness are not as detrimental as the case of nanowire waveguides. We showed a very compact device with a footprint of 7 μm². We believe that this device can become a fundamental photonic device with applications in sensing, optical communications and on-chip spectroscopy.