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Abstract
We present the design, modeling, fabrication, and characterization of grating coupler devices for z-cut lithium niobate near 1550 nm. We first experimentally measure the sensitivity of the insertion loss of a conventional grating coupler to translational misalignment through a three-factor full factorial design of experiment. Next, we design grating couplers that are significantly less sensitive to misalignment. The fabricated devices experienced less than 7 dB of excess insertion loss for combined misalignments of up to ± 5 μm in plane and up to −2 μm or + 10 μm out of plane.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The progressive growth of data centers and high-performance computing platforms requires novel data movement technologies with minimal energy expenditure for moving each bit of information from one node to the other in the network [1–3]. The emergence of photonics as a distance-independent solution for high-speed data movement prompts engineers to seek the solutions for integrated photonics that pave a path to high-quality photonic devices and high-volume production. Despite the success of Telecomm, its well-established photonic technologies are not readily transferrable to the Datacomm applications from an energy-per-transferred-bit perspective. That is why new integrated platforms such as silicon photonics (SiPh) have emerged to bridge this gap [4,5]. Although SiPh holds the highest promise in terms of scalability, its certain drawbacks such as reliance on carrier dynamics and excess optical loss of doped silicon fundamentally limit its capability for high throughput modulation [6–8].
Similar to SiPh, thin-film lithium niobate (LN) provides a high index contrast (HIC) platform (Δn ~0.7) for shrinking the size of photonic structures. Moreover, its linear electro-optic response [9] and larger transparency window (λ = 0.35−5.2 μm) make the LN platform superior to SiPh when very high performance modulation is demanded. Optical confinement in the thin-film LN platform can be realized by diffusion or proton exchange [10,11], loading the LN film with a rib of another dielectric (e.g., silicon [12] or silicon nitride [13]) or directly dry etching the LN film [14,15]. Although the rib-loaded waveguides are more convenient to make, directly etched waveguides provide the highest confinement of light. This can be done by partially etching [14] or fully etching the LN film.
The first step towards producing highly dense photonic circuits in the thin-film LN platform [16] is the demonstration of efficient coupling of light from a fiber into a LN thin film waveguide. An approach that moves beyond traditional 1-dimensional (1D) integration methods, such as edge coupling via spot-size converters with lensed fibers, into 2-dimensional (2D) scalability and increased flexibility for positioning of the optical I/O is to use vertical coupling [17–21]. Vertical grating couplers (VGC) provide several advantages including compactness and the ability to couple light from anywhere on the surface of the chip [22], thereby enabling rapid die/wafer testing. However, design and optimization of grating couplers is more challenging in LN due to its optical anisotropy [23]. Moreover, fiber misalignment is a major challenge that can rapidly degrade the coupling efficiency of VGCs. Due to the optical anisotropy of LN [23], the performance of the demonstrated structures based on X-cut or Y-cut crystals (in-plane extraordinary axis) [24] and TE optical mode (in-plane polarization) has an inherent dependence on their orientation. This is especially pronounced for microring-based structures [14], where their optical or electro-optic response can significantly degrade if the structures have some in-plane rotation or misplacement. This problem also exists for vertical grating couplers that have been so far demonstrated in LN platforms [18,25]. Although hybrid Si-LN grating couplers [26] might be a solution to this problem, their fabrication is more complex and challenging.
In this work, we examine the design and optimization of fully etched isotropic grating couplers in a thin film Z-cut LN platform. We further analyze the effect of misalignment and present the design and characterization of alignment-tolerant grating couplers.
2. Thin film waveguide modes
The waveguides are formed by fully etching a commercially available lithium niobate thin film from NanoLN. Inc. The nominal thickness of the film is 400 nm and the average variation of the thickness over the wafer brings it closer to 410 nm. The thin film is lying on top of a 2-μm thick buried oxide layer on top of a LN substrate. The single mode operation of the waveguide is determined by sweeping the width from 0.5 μm to 2 μm. As shown in Fig. 1, a width of 1 μm was chosen for our design so that only fundamental polarizations (TE00 and TM00) are supported. The optical effective index for the TE00 mode is 1.821 and for the TM00 is 1.655.
Fig. 1 (a) Top view of the grating coupler and the calculated optical polarizations (E-field) of the waveguide of size 1 μm × 0.41 μm. (b) Effective index of the first three polarizations of the waveguide. The single mode operation is supported up to ~1 μm in width.
3. Initial design of the LN grating coupler
The three key design parameters of the grating coupler as shown in Fig. 2 are: (1) grating pitch, Λ, (2) duty cycle or fill factor, FF, and (3) etch depth, e. They determine the diffraction angle, peak wavelength, and coupling efficiency of the grating coupler. Three other parameters that are less influential are: (1) number of periods, N, (2) waveguide height, h, and (3) top cladding thickness, ttop.
Fig. 2 Schematic diagram, design parameters, and coordinate system for the LN grating coupler. The z-axis is the extraordinary axis of the LN crystal.
The grating equation gives the diffraction angle, θm (with respect to the z-axis), of the mth diffraction order as [27]:
where neff is the average effective index of the waveguide considering both the etched and unetched sections, nclad is the refractive index of the cladding material above the grating, and λ is the wavelength.We design for 1550-nm light with transverse electric (TE) polarization of the waveguide, i.e., polarized along the y-direction. Considering an incident angle of 8° which corresponds to the angle of the fiber array V-groove used in our experimental setup, a first order diffraction grating (m = 1), and the effective index computed by the Lumerical finite difference eigenmode (FDE) solver for a 1-μm wide and 410-nm thick LN core with a 2-μm thick bottom SiO2 cladding, we estimated the grating coupler period to be ~1 μm using Eq. (1).
The grating equation assumes an infinitely long grating section in an isotropic material. Neither assumption is applicable in our case. Because of its crystal symmetry, z-cut lithium niobate is a uniaxial birefringent material. Light polarized along x or y has ordinary refractive index, no, while light polarized along z has extraordinary refractive index, ne. The following empirical relationships are excellent fits to the dispersion of the refractive indices as measured by the manufacturer (NanoLN) over the wavelength range 1200 nm < λ < 1900 nm:
where λ0 = 1550 nm and λ is in nanometers. Because of the birefringence, the finite grating length, and our choice of fully-etched gratings (etch depth = film thickness), the initial design based on Eq. (1) did not yield a high coupling efficiency in a 2D FDTD simulation. Hence, we replaced neff in Eq. (1) with the average indices of the 2D waveguide and air ((1.936 + 1)/2 = 1.468) and recalculated the grating pitch to be 1.1664 μm and then ran a particle-swarm optimization algorithm [28] to find a combination of grating period and fill factor that maximizes the average coupling efficiency. Figure 3(a) shows the two-dimensional (2D) finite difference time domain (FDTD) grating coupler model created in Lumerical. We assume an optical fiber is placed 2 μm above the top of the LN thin-film in the simulation and the coupling efficiency is calculated by projecting the diffracted light onto the mode of the fiber. Figure 3(b) shows the field profile along with the calculated far field radiation as a function of diffraction angle. The grating diffracts the light and couples it from the LN waveguide into the fiber. Figure 3(c) shows the transmission spectrum of the grating coupler with the optimized period and fill factor. We chose a full etch of the LN thin film (e = 410 nm) to simplify fabrication by allowing the waveguide and grating coupler to be defined in a single etch step. The 8° incident angle is an industry standard for reducing back reflections. We used a top SiO2 cladding for index matching to the optical fiber to further reduce back reflections. The particle-swarm optimization gave a value of 500 nm for the top cladding thickness. Because the top cladding redshifts the transmission curve, we needed to re-optimize the grating parameters. Table 1 presents the final design parameters from the 2D FDTD model. The expected insertion loss is 6.6 dB.Fig. 3 2D FDTD grating coupler design in Lumerical. (a) Schematic diagram. (b) Power profile (in dB) and far field radiation pattern at 1550 nm. (c) Grating coupler transmission with and without top oxide cladding.
Table 1. Simulated design parameters for a LN grating coupler
4. Round 1 device fabrication
We fabricated devices using the process steps shown in Fig. 4(a). A 900-nm thick layer of SiO2 is chosen as the hard mask for dry-etching LN (LN:SiO2 etch rate ~0.9:1) and is deposited using standard PECVD (~115 nm/min). To pattern the SiO2 mask, an 80-nm thick chromium layer patterned via an e-beam-lithography based lift-off process is chosen as the mask (SiO2:Cr rate ~20:1) due to the lack of sufficient etch selectivity between the e-beam photoresist and SiO2. Once the SiO2 mask is defined via a CHF3-based reactive ion etching (RIE) process, the LN thin film is etched using chlorine-based chemistry in the RIE tool with inductively coupled plasma (ICP) at a rate of 200 nm/min. The gas mixture in the etching process is as follows: 5 sccm Cl2, 15 sccm BCl3, and 18 sccm Ar under a chamber pressure of 5 mT. The RIE and ICP powers are set to 280 and 900 W, respectively. More details about the development of this etch recipe can be found in [29]. Figure 4(b) is a scanning electron microscope (SEM) image of the fabricated device. We set the grating coupler dimensions to be 13.92 μm (12 × 1.16 μm) in the x-direction and 10.8 μm in the y-direction to be comparable to the spot size of a single mode fiber. We used an adiabatic 45-μm long linear taper to direct the light into the 1-μm wide waveguide. We did not perform optimization for the taper length.
Fig. 4 (a) Side view schematic of the fabrication flow. (b) Top view SEM image of LN grating coupler.
There were a number of fabrication errors. The cross-sectional profile of the grating was trapezoidal rather than rectangular, the fill factor at the bottom was 74% instead of 65%, and the etch depth was close to 500 nm instead of 410 nm. We measured the transmission spectrum using a light emitting diode and an optical spectrum analyzer and observed that these three errors shifted the peak wavelength to 1450 nm and increased the coupling loss to 15 dB.
5. Misalignment study
We performed a three-level, four-factor full factorial experiment to quantify the effect of misalignment in the x, y, and z Cartesian directions and in the θ-rotation. Table 2 shows the low, center, and high settings. The zero positions for x, y, z, and θ are defined as those that give the maximal coupling. We define these to be the center setting for x, y, and θ, but the low setting for z because it is not physically possible to move the fiber into the device under test (DUT). The DUT is a back-to-back LN grating coupler with a 1.39-mm long waveguide in between. One channel of a polarization maintaining optical fiber array (from OzOptics) sends light at 8° to the input grating coupler. Light then propagates in an on-chip waveguide before coupling through a second grating coupler back into a separate channel of the fiber array. A photodetector and logarithmic amplifier convert the transmitted light into a voltage that is proportional to the transmission in dB, i.e., a 200 mV change corresponds to 10 dB. An oscilloscope measures this voltage. We align the input and output fibers to the DUT using a manual goniometer for θ-rotation and Thorlabs PT3 translation stages with motorized ZST225B actuators for x, y, and z translation. As previously mentioned, the peak wavelength was significantly blueshifted because of the fabrication errors. To get accurate results in this misalignment study, we needed much more power than the LED (broadband source) could provide. Thus, we switched to a tunable laser source (Santec TSL 710, 1480 - 1640 nm). We set the laser to its minimum wavelength of λ = 1480 nm and used 2 mW of optical power.
Table 2. Factors studied and their low, center, and high values
We examined the collected data for outliers and time drift and the results are plotted in Fig. 5(a). The normal probability plot showed that all raw data points lie within a 95% confidence interval, indicating no apparent outliers. The time series plot of the residuals in Fig. 5(b) shows a mostly random distribution with some slight auto-correlation. The variability gauge plots in Fig. 6 indicate the dependence of the response on the level of each factor. The plots are visually consistent with the overall expected trend. That is, for misalignment in x, y, and θ, the center points give the highest reading, whereas for misalignment in z, the low setting gives the highest voltage.
Fig. 6 Variability gauge plots showing the distributions of each factor versus voltage measured. Plots show the effect of factors (a) X1, (b) X2, (c) X3, and (d) X4.
A full model that incorporates the expected quadratic dependence of voltage on misalignment would contain 81 terms. However, most terms are not statistically significant at the α = 5% level. Table 3 shows the statistically significant terms. The final model is:
Table 3. Statistically significant model coefficients (unitless) and their 95% confidence intervals
Because we chose the center point for x, y, and θ to produce maximum transmission, the first derivative, i.e., the linear terms, were not statistically significant. The 2° θ-rotation had no effect even including the quadratic term. However, the 2-μm misalignment in x or y, produced a statistically significant change in transmission due to the quadratic term. For z-translation, both the linear and quadratic terms are important. The linear term exists because the maximum occurs at the low setting rather than the center setting. Overall, the equation predicts a whopping 18 dB of excess loss when the misalignment in z is as small as 10 μm.
6. Alignment-tolerant grating couplers
The tight translational tolerance is unacceptable both for wafer-scale testing and for packaging. Thus, we designed and fabricated couplers that were less sensitive to alignment by increasing the grating coupler width and length to 24 μm and 23.2 μm, respectively. This required us to increase the number of grating pairs from 12 to 20. To preserve good coupling efficiency, we used three-dimensional (3D) FDTD simulations and optimized the length of the linear taper to match the field profile of the larger area grating coupler. The result was a slightly non-linear taper of length 23 μm. Figure 7 shows the results. The optimized taper adds 0.6 dB of loss compared to 3.8 dB loss for the original 45-μm long linear taper. The improvement of the non-linear taper (order > 1) over the linear taper (order = 1) was negligible so we adopted a linear taper for simplicity.
Fig. 7 (a) Optimization of the taper order for maximum focusing of the optical beam for L = 23 μm. (b) Top view of the field profile showing transmission through the taper.
The larger grating coupler area naturally increases the tolerance in x, y and θ. However, a less obvious but more prominent effect is that it significantly increases the tolerance in z as well. We performed 3D FDTD simulations using the schematic in Fig. 8(a) as we varied the z position of the fiber. Figure 8(b) illustrates the results. The predicted excess loss is only ~2.2 dB for a + 10-μm misalignment in z, i.e., z = 12 μm versus z = 2 μm. Because the beam from a single mode fiber diverges very slowly (Rayleigh length is zR = πω02/λ > 40μm), the fiber can be placed farther away and still produce a beam that overlaps well with the large area coupler. This facilitates testing because it reduces the chances of the fiber contacting the wafer, which often has several microns of total thickness variation due to bow and warp. We now fix z = 12 μm and place the fiber at the optimal in-plane position (denoted by x = 0 and y = 0) in order to study the effect of misalignment in x and y. Figure 8(c) shows that less than 1.6 dB and 4.4 dB of additional excess loss is added when the in-plane misalignment is 2 μm and 5 μm, respectively. Thus, we conclude that the device design is alignment-tolerant because the total excess loss is 3.8 dB for a combined misalignment of + 10 μm or −2 μm out-of-plane and ± 2 μm in-plane and 6.6 dB for a combined misalignment of + 10 μm or −2 μm out-of-plane and ± 5 μm in-plane.
Fig. 8 3D FDTD simulations showing the effect of fiber position on transmission. (a) Schematic of the 3D FDTD simulation. (b) z is varied for x = y = 0 μm. (c) x or y is varied for z = 12 μm.
To compensate for fabrication errors in the round 2 devices, we studied how grating period, fill factor, etch depth, and film thickness shift the transmission peak using 2D FDTD. The 2D analysis is adequately accurate for capturing the general trends. We set the nominal design parameters for the grating coupler to the values in Table 1, but increased the number of grating pairs from N = 10 to N = 20. Next, we adjusted each parameter individually in each plot of Fig. 9. From this analysis, we designed and fabricated three separate grating couplers with a peak wavelength of 1550 nm and first order diffraction angle of 8°. Table 4 shows these designs.
Fig. 9 2D FDTD simulation results showing how transmission changes with the (a) grating period, (b) fill factor, (c) etch depth, and (d) LN film thickness.
Table 4. Designed and fabricated period and fill factor for the three 1550-nm grating coupler designs
We then performed 3D FDTD for more accurate estimates of the performance of these designs. The predicted insertion losses for the devices in the 3D simulation as designed are 7.7, 7.1, and 8.2 dB for the low, center, and high designs, respectively, when z = 2 μm. However, the fabricated devices had periods that were slightly smaller and fill factors that were slightly larger than designed. These errors blueshift and redshift the spectrum, respectively. This results in almost no change in the peak wavelength, but a decrease in the coupling efficiency. Additionally, the sample was over-etched by about 20 nm into the bottom oxide layer during the final LN etch step. This also increases the loss and blueshifts the spectrum. Simulations predict that these three fabrication errors would increase the insertion loss by 2.7, 0.2, and 0.7 dB for the low, center, and high grating couplers, respectively.
The larger area grating coupler produces more pronounced electron-beam proximity effects that deteriorate pattern fidelity. Thus, we used Beamer software (GenISys GmbH) to perform proximity effect correction and mask fracturing. Figure 10 shows a patterned device.
Fig. 10 Top view SEM images of an LN grating coupler. (a) Full device. (b) Zoomed-in view of the grating section.
To validate the prediction of relaxed alignment constraints, we measured the three devices using a separation of z = 12 μm. The low setting grating coupler did not produce a measurable response, possibly because of damage to the particular device. Figure 11 shows the experimental and simulation results for the center and high setting devices. The measured data is a little noisy because of Fabry-Perot resonances in the waveguide. There is a weak cavity with a free spectral range (FSR) of 0.5 nm formed by the back-to-back grating couplers separated by the 1.39-mm long waveguide in between. The simulations in Fig. 11 include the optimal case (z = 2 μm with designed parameters) and the actual case (z = 12 μm with actual fabrication parameters). We observe excellent agreement for both the spectral shape and the peak coupling efficiency. We attribute the slight discrepancy to waveguide loss and uncertainty in some of the dimensions of the fabricated sample (e.g., LN film thickness). Next, we studied x and y misalignment on each coupler. Rather than repeating a full factorial study, we simply observed that the voltage change was not statistically significant compared to the measurement noise when we scanned x and y through the 10 μm by 10 μm square region centered on the optimally aligned position. In summary, there is less than 7 dB of excess insertion loss when the fiber is within the 10 μm by 10 μm by 12 μm volume adjacent to the device under test. Therefore, we have validated our key assertion that the new grating couplers are adequately insensitive to misalignment.
Fig. 11 Simulated, measured, and corrected transmission spectra for the (a) center and (b) high designs.
7. Conclusions
We designed and demonstrated vertical grating couplers in z-cut thin film lithium niobate platform. Our analysis of the misalignment of the fiber relative to the grating area shows that the coupling efficiency deteriorates by < 7 dB for the combined movements of ± 5-μm in-plane and −2/+10-μm vertically. Considering that the extraordinary axis of the z-cut LN crystal is normal to the structure, our analysis of the misalignment tolerance remains valid regardless of the orientation of the grating couplers on the die.
Funding
Sandia National Laboratories (contract number 1672814), NASA Early Career Faculty award (ECF) (contract number 80NSSC17K052)
Acknowledgments
The authors thank Doc Daugherty and Roger McCay at GenISys for e-beam proximity correction and Edmond Chow at the University of Illinois Urbana-Champaign for e-beam patterning.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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