Design of SWG-based spatial mode filters. MDM has been developed for increasing the data capacity of optical interconnects by multiplexing different spatial modes in a multimode waveguide. As only a single-wavelength laser source is needed, MDM has attracted wide-spread attention due to its low cost, good system scalability and small footprint24. However, one of the main challenges for the MDM systems is the superposition of inter-modal crosstalk when dozens to hundreds of devices are cascaded, resulting in serious signal degradation. Mode filters are a type of devices which can filter the undesired modes out of the system, and thus help to improve the signal-to-noise ratio performance6. Since high-order modes have weaker confinement, they can easily be filtered out by means of tapering the waveguide to a cutoff width, hence mode filters provide usually solutions for blocking the low-order modes in a multimode waveguide25. Owing to the importance of the devices, several demonstrations have been reported on other material platforms6, 25–28. However, there are still no demonstartions for mode filters on the LNOI platform.
Figure 1a shows the schematic diagram of a proposed SWG-based TE1-mode-pass filter. The device is designed along the crystallographic Z direction on a X-cut LNOI platform with a 300-nm-thick lithium niobate thin film on top of a 4.7-µm-thick buried oxide layer, following our previous work23. The birefringence of lithium niobate is considered in the design, which means the crystallographic Z direction has an extraordinary refractive index (ne) of ∼2.14, the crystallographic Y/X directions have an ordinary refractive index (no) of ∼2.21, at a wavelength of 1550 nm. The SWG structure is designed on a silicon nitride thin film on the surface of the LNOI platform, whose thickness is chosen to be 300 nm as well, for a strong mode confinement in the hybrid waveguide and a considerable mode confinement factor in the lithium niobate slab29. As silicon nitride has similar but slightly lower refractive index to lithium niobate (~1.99), the input optical mode is partially confined in the silicon nitride rib, which is important for the interaction between the optical mode and SWG structure.
For a TE1-mode-pass filter, the hybrid SWG waveguide is expected to work in the Bragg regime for TE0 mode and the subwavelength regime for TE1 mode. Thus, the input TE0 mode is reflected whereas the TE1 mode is converted to the localized Bloch mode and propagates with low loss. It means that the Bragg conditions should be satisfied, which are expressed as30:
where Λ1 is the grating pitch, λ0 is the central wavelength of photonic stop band for TE0 mode, neff0 and neff1 are the effective indices of TE0 and TE1 modes in the hybrid SWG waveguide.
The SWG structure is optically equivalent to a homogeneous medium with a refractive index given by1:
$${n_{SWG}}^{2}={n_{SiN}}^{2}\cdot ff+{n_{air}}^{2}\cdot (1 - ff)$$
2
where nSiN and nair are the refractive indices of silicon nitride and air clad, respectively. The ff is the filling factor of the SWG, which is expressed as ff=wt/Λ1 where wt is the width of the SWG segment. Here, the ff is designed to be 0.7, for an easy-to-fabricate minimum feature size as well as a relatively large effective index difference between different modes. Then, the effective refractive indices of the Bloch modes in the hybrid SWG waveguide are calculated by using a full-vector eigenmode solver31, as shown in Figure 1b. According to the results, the width of the SWG is designed to be w1=2 µm for low-loss propagation of TE1 mode, and the grating pitch is designed to be Λ1 = 413 nm for a photonic stopband of TE0 mode around 1550 nm. The transmission of TE0 and TE1 modes as a function of grating period number is simulated at a wavelength of 1550 nm, by using the three-dimensional finite-difference time domain (3D-FDTD) method32, as shown in Figure 1c. To achieve both low loss and high mode extinction ratio (MER), the grating period number is chosen to be 120. The simulated insertion loss for TE1 mode is 1.7 dB and the MER between TE0 and TE1 modes is about 48 dB. The total length of our SWG-based TE1-mode-pass filter is 49.56 µm. Figure 1d shows the simulated electric field profiles for TE0 and TE1 modes input into the device, at a wavelength of 1550 nm. It can be seen that the TE1 mode passes through the device with low loss whereas the TE0 mode is blocked. We also simulate the transmission spectra of different modes as a function of the input wavelength, as shown in Figure 1e. The designed device shows a bandwidth of about 46 nm (from 1524 nm to 1570 nm) for a MER larger than 20 dB, while the insertion loss for TE1 mode stays below 3.5 dB.
Most of the demonstrated mode filters block only one specific low-order mode, generally TE0 mode. It is still difficult to deal with the case that multiple modes need to be filtered out simultaneously, however, this function is important for the real-world application of the devices. Researchers proposed a few methods to solve this problem, such as cascading multiple directional couplers26, or introducing graphene as auxiliary material27, however, such devices have typically large footprint and relatively low extinction ratio. Thus, a compact and high-extinction-ratio mode filter which can filter out multiple optical modes simultaneously is still missing as a photonic circuit component. To fill this gap, we demonstrate our SWGs as an attractive choice to realize such a mode filter on the LNOI platform. For proof-of-concept, a TE2-mode-pass filter is designed here.
Figure 2a shows the schematic diagram of the proposed TE2-mode-pass filter. The hybrid SWG waveguide is designed to work in the subwavelength regime for TE2 mode, while work in the Bragg regime for TE0 and TE1 modes simultaneously. The Bragg conditions have been revised as:
where Λ2 is the grating pitch, λ1 is the working wavelength, neff0, neff1 and neff2 are the effective indices of TE0, TE1 and TE2 modes in the hybrid SWG waveguide. For simplicity, we also design the ff to be 0.7, while the width of SWG is chosen to be w2= 3.5 µm to support low-loss propagation of TE2 mode, as shown in Figure 2b. It can also be seen that the effective index difference between TE0 and TE1 modes is smaller than that between TE1 and TE2 modes. Thus, it can be predicted that the photonic stopbands of TE0 and TE1 modes are located closely to each other whereas well separated from that of TE2 mode, which is important for filtering out the TE0 and TE1 modes simultaneously. According to the results, the grating pitch is designed to be Λ = 415 nm for a device working at around 1550 nm. We also simulated the power transmission for different modes as a function of the grating period number at a wavelength of 1550 nm, by using 3D-FDTD method again, as shown in Figure 2c. According to the results, the grating period number is chosen to be 120 as well, resulting in the total length of the device to be 49.8 µm. The insertion loss for TE2 mode is 1.2 dB and the MER between TE2 and the low-order modes is larger than 41 dB. Figure 2d shows the simulated electric field profiles for TE0, TE1 and TE2 modes input into the device, at a wavelength of 1550 nm. It can be seen that TE2 mode passes through the device with low loss whereas the low-order modes are blocked. Similarly, Figure 2e shows the transmission spectra of different modes as a function of the input wavelength. The designed device shows a bandwidth of 33 nm (from 1533nm to 1566 nm) for a MER larger than 20 dB, while the insertion loss for TE2 mode stays below 4.2 dB.
Design of SWG-based TM-pass polarizer. Similar to spatial mode filters, polarizer can stop one of the two polarization modes while let the other one pass, and it plays a key role in PDM systems to reduce the crosstalk. Due to its attractive function, TE/TM-pass polarizers have been widely investigated based on different structures on the SOI platform9, 33–35. Fortunately, there are also a few works reported previously on the LNOI platform. For example, hybrid plasmonic gratings (HPG) have been proposed and numerically demonstrated for TE/TM-pass polarizers on the LNOI platform36, 37. The proposed devices are compact with only several to tens of micros length, and broadband with high polarization extinction ratio (PER). However, the metal deposition requires high alignment accuracy, which is not easy in the real-world fabrication. Furthermore, the devices will suffer high additional absorption loss from the metal. On the other hand, lateral leakage has also been proposed to realize TE/TM-pass polarizers by differentiating the propagation loss of TE and TM modes in a waveguide38, 39. This kind of device is expected to have low loss and high PER. However, the devices are usually required to be from hundreds of micros to one millimeter long, which are somewhat bulky for large-scale integration. Thus, there is still a gap to realize a polarizer with compact size, low loss and high PER simultaneously based on the LNOI platform. To address this gap, we demonstrate a compact, low-loss and high-PER TM-pass polarizer by using our SWGs.
Figure 3a shows the schematic diagram of the proposed SWG-based TM-pass polarizer which is designed along the crystallographic Y direction on the same platform as the mode filters. The width of the silicon nitride stripe is set to be w3=1 µm, which can support low loss propagation for both TE0 and TM0 modes while the high-order modes are cut-off in the hybrid waveguide. For a TM-pass polarizer, the SWG waveguide is expected to work in the Bragg regime for TE0 mode while work in the subwavelength regime for TM0 mode. It means that the Bragg conditions should be expressed as:
where λ0 is the central wavelength of photonic stopband for TE0 mode, neffTE and neffTM are the effective indices of TE0 and TM0 modes in the hybrid SWG waveguide. To avoid the mode hybridization in the Y propagating waveguide, the ff is chosen to be 0.8 and a nanobridge with a width of w4= 100 nm is designed to connect the segments (refer to Supporting Information, S1 for details).
Figure 3b shows the calculated effective indices of Bloch modes in the hybrid SWG waveguide. It can be seen that the TM0 mode is cutoff when the SWG width is below 1.75 µm. Thus, the width of the SWG is chosen to be w5=1.8 µm for low loss propagation of TM0 mode, as well as a large effective index difference between TE0 and TM0 modes. According to the results, the grating pitch is chosen to be Λ3 = 422 nm in this work, for a central wavelength around 1550 nm. Figure 3c shows the simulated transmission of TE0 and TM0 modes as a function of grating period number is simulated at a wavelength of 1550 nm. The input and output modes are designed to converted to and from the Bloch modes gradually by means of SWG tapers, for reducing mode conversion loss. According to the simulated results, the number of grating periods is chosen to be 110 for both low loss and high PER. It can be seen that the simulated insertion loss for TM0 mode is about 0.5 dB, and the PER is about 38 dB. The SWGs are designed to connect with the silicon nitride stripes by using a pair of tapers with a length of Lt=4.5 µm. The total length of the device is ~55 µm, with the length of taper waveguides included, which is reduced greatly compared to that reported in previous work on the same platform (~1000 µm)38. Figure 3d shows the simulated electric field profiles for TE0 and TM0 modes input into the device, at a wavelength of 1550 nm. Figure 3e shows the simulated transmission spectra of different light polarization modes as a function of the input wavelength. It can be seen that the designed device shows a bandwidth of about 39 nm (from 1526-1565 nm) for a 20 dB PER, and the insertion loss for TM0 mode is below 0.6 dB within this wavelength range.
Device characteristics. Figure 4a shows the microscope image of the fabricated devices for TE1-mode-pass filter, with a close-up scanning electron microscope (SEM) image of the SWGs. For the convenience of measurement, TE0-TE1 mode (de)multiplexers (MMUXs) are fabricated and connected to the TE1-mode-pass filter23. The input and output ports for TE0 mode are denoted as I0-O0, while those for TE1 mode are denoted as I1-O1, respectively. In order to eliminate the effects from the MMUXs to the device performance, a reference device with the SWGs replaced by silicon nitride stripe is fabricated closely on the same chip (refer to Supporting Information, S2 for details). The corresponding ports are denoted as I2-O2 and I3-O3 for TE0 and TE1 modes, respectively. Figure 4b shows the microscope image of the fabricated devices for TE2-mode-pass filter, with the SWGs shown in a SEM image as well. Similarly, TE0-TE1-TE2 MMUXs are fabricated and connected to the filter for the convenience of multimode input and output23. The input and output ports are denoted as I0-O0, I1-O1 and I2-O2 for TE0, TE1 and TE2 modes, respectively. The experimental results are also normalized to that of the reference device without SWGs (refer to Supporting Information, S3 for details). The devices are interfaced by grating couplers with a grating period of 920 nm and duty circle of 0.4. The details of grating couplers can be found in our previous work40.
Figure 4c shows the measured results of the TE1-mode-pass filter which are normalized to the reference device without SWGs. At a wavelength of 1550 nm, the device show insertion loss for TE1 mode of 1.9 dB and a MER of about 43 dB. Moreover, the experimental results exhibit a bandwidth of ~44 nm (from 1515-1559 nm) for a MER of 20 dB, and the insertion loss for TE1 mode is lower than 3.2 dB within the wavelength range. Figure 4d shows the measured results of the TE2-mode-pass filter. The measured insertion loss for TE2 mode is 3.1 dB, and the MER is about 34 dB, at a wavelength of 1550 nm. Moreover, the device shows a bandwidth of ~29 nm (from 1525-1554 nm) for a MER of 20 dB, and the insertion loss for TE2 mode is lower than 6 dB within this wavelength range.
Figure 5a shows the microscope image of the fabricated devices for TM-pass polarizer, including the SEM image of the SWGs with a nanobridge. We use the polarization splitter and rotator (PSR) to input and output different polarization modes for the ease of measurement23. The input and output ports for TE0 mode are denoted as I0 and O0, while those for TM0 mode are denoted as I1 and O1, respectively. The reference device without the SWGs is also fabricated (refer to Supporting Information, S4 for details). The devices are interfaced by grating couplers with a grating period of 940 nm and duty circle of 0.440. The normalized results are shown in Figure 5b. The measured insertion loss for TM0 mode is about 1.3 dB, and the PER is about 30.6 dB, at a wavelength of 1550 nm. The fabricated device shows a bandwidth of ~36 nm (from 1521-1557 nm) for a PER of 20 dB, and the insertion loss for TM0 mode is lower than 1.5 dB within the 36 nm wavelength range.
Overall, the measured results are close to our simulation. We have noted the measured central wavelengths of the photonic stopbands are blue shifted compared with the design. This can be attributed to the slight deviations in the fabrication. Even so, the fabricated devices still provide good performance in the C band. The central wavelengths can be tuned to desired wavelengths by a precompensation of the structural parameters in the future.