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Abstract
This work demonstrates an integrated multimode interferometer (MMI) based on a fully polymeric platform and optimized for visible range operation. The dimensions of a 2×2 MMI are first calculated analytically and simulated using finite elements method. The devices are manufactured using two layers of negative tone photoresists. The top layer is patterned by e-beam lithography demonstrating the adaptability of this material, naturally designed to respond to UV radiation. Fabrication tolerance was smaller than 100 nm. Devices were optically characterized with a 635 nm input source and the best performance for a 3 dB power splitter was found at an interferometric cavity dimension of 10.5 × 190.68 µm. Other interferometric lengths were characterized to establish a process design kit that allows future use of this platform in more complex photonic integrated circuits architectures.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
For the past decades, photonic integrated circuits have been based on silicon-on-insulator (SOI) technology mainly because of compatibility with existing semiconductor industry. This platform is still the leading solution for applications working at telecom wavelengths due to low losses and high integration capabilities [1,2]. However, SOI cannot be employed for visible and near IR range which is relevant for some applications, such as high precision metrology [3,4], integrated optical coherence tomography [5,6], sensing and biosensing [7,8] or quantum photonics [9]. More recently, other materials have been studied for next generation photonic integrated circuits (PICs) allowing wideband operation including silicon nitride [10–12], indium phosphide [13] or lithium niobate [14–16]. Because of required equipment complexity and cost, researchers usually send the designs to manufacturing foundries that combine multiple designs on the same wafer layout. The typical processing time (excluding chip packaging) goes from 4-8 months making this option inconvenient for fast prototyping and limiting the accessibility of this technology.
On the other hand, optical polymers have demonstrated several unique advantages for PICs construction such as high transparency from visible to near IR wavelengths, refractive index tuneability, flexibility, temperature stability and fast production [17,18]. Nevertheless, the most advantageous characteristic is its cost-effective manufacturing processes. Photocurable polymers are mainly supplied as liquids, that can be directly sprayed, poured or spin coated on top of a flat surface. Deposited polymer can then be patterned in a single lithography step by several methods. Some of these processes need a mask or master, as conventional photolithography or nanoimprint lithography [19,20], and some others are maskless, as electron-beam lithography [21], direct laser writing [22,23] or 2-photon polymerization [24]. This structuring versatility makes polymers exceptional candidates for the whole fabrication cycle, from initial product prototyping to mass-production.
Polymer PICs operate at visible and near IR wavelengths, same as most used organic dyes. In optical biosensing field, dyes are employed both for light generation and detection [25]. Organic dye lasers can be integrated in the same polymeric platform to overcome fiber-to-chip coupling constraints [26]. Referring to light manipulation, it is a regular practice that dyes are used for sensor functionalization. Target molecules or pathogens are detected when bonded to a specific dye maximizing the optical change in the measuring medium. Moreover, common polymers used in microfabrication often are biocompatible, which is fundamental for building microfluidic channels, implants or living cell scaffolds. This results in polymer PICs as the best option to integrate next generation of biosensing platforms (lab-on-a-chip) [27–30].
2. MMI working principle and design
2.1 MMI working principle
Multimode interferometers (MMIs) are one of the basic building blocks in PICs of very purpose. They offer the highest efficiency in optical power splitting and adequate tolerance to fabrication errors. Here, a full polymeric integrated 2×2 MMI for visible operation has been designed, manufactured, and characterized.
The schematic structure of a 2×2 MMI is shown in Fig. 1. This integrated optical device is formed by a multimode region, where higher index guiding modes are allowed, connected to single mode waveguides. Single mode waveguides were built using a ridge waveguide architecture where three faces of the rectangular core are surrounded by a top-cladding material, air in this case ($n3 = nair \approx 1$).
Fig. 1. Schematic structure of the symmetric 2×2 MMI proposed. Ridge waveguides are grown in core polymer (yellow) on top of a flat polymer layer (green). Top cladding material is air. The fundamental and higher order modes interfere in the multimode region as shown. Only first and second order modes are considered for analytical calculations since higher order modes are poorly confined inside the structure. Cross-section normalized electric field distribution for TE polarization of fundamental (a) and second order (b) mode inside the interferometric region are shown. For mode simulation ${W_{MMI}} = 10.5\; \mu m,\; t = 1.7\; \mu m$ and a grid mesh of $\lambda /100$ are considered.
The resulting high contrast between core and top cladding refractive indices improves mode confinement and allows for compact device integration. Addition of higher order modes with different propagation constants creates a periodic interference pattern. Any desired power splitting ratio at the output ports may be obtained, generated at a specific length from the input ports. This is known as self-imaging and is the general working principle of power splitters based on MMIs [31].
2.2 MMI simulation and design
MMIs can be classified as symmetric and paired imaging devices depending on the position of input waveguide. Here, paired devices are selected to allow reversible operation and obtain more characterization data. Inputs and outputs are located symmetrically along the device’s long axis as indicated in Fig. 1. Distance between port centers is established as one third of MMI width (${W_{MMI}}/3$). MMI length is determined by number of ports, targeted splitting ratio and beat length. Beat length Lπ, is described by formula (1) and defined as the distance from input port where self-image is periodically replicated,
If 2×2 (2 input and 2 output ports) case is studied, then $N = 2$ and first balanced power splitting ratio is found at a distance ${L_{MMI}} = {L_\pi }/2$ from input source. Note that MMI ports are tapered to gradually adapt modes from single-mode waveguide to MMI region and vice versa and hence reduce insertion losses. It must be considered this taper length as part of Lπ. Linear tapers (with a maximum width of 5 μm and 25 μm length) are also allocated in the fiber-PIC interface with same purpose. Separation between tapers connected with the MMI must be large enough to avoid port crosstalk by evanescent wave coupling. This value constraints MMI width and hence integration capability.
A finite-difference method mode solver [32] designed for the 2D infinite rectangular waveguide case was applied to solve transverse electric and magnetic field components, besides the waveguide propagation constant. A MATLAB toolbox calculate then the waveguide effective refractive index to determine the initial cross-section dimensions for input and output waveguides. The objective is to guarantee single-mode operation under working conditions. To define the range where single-mode operation is accomplished, effective refractive index was calculated for waveguide widths ranging from 1.5 to 5.5 µm and shown in Fig. 2. Source wavelength, core and cladding refractive indices and waveguide core dimensions are defined as input variables. Geometries were discretized using a uniform rectangular mesh where element size was at least ten times smaller than the input source wavelength. Note that above 4 µm, the wave equation has four possible solutions, two for TE and two for TM, meaning that the waveguide becomes multimode. Also note that for widths smaller than 1.8 µm the wave equation has no solution, thus the energy is not confined in the waveguide. This means the fabricated WG width must be bigger than 1.8 µm and smaller than 4 µm to meet single mode operation. The final waveguide width selected was 2.5 µm, while the length of the linear in and output ports was not considered a crucial parameter and was spanning till the chip’s edges. Losses on the length scale of our chips (1 cm) were found to be negligible for the visible range in the Epocore material [33].
Fig. 2. Waveguide effective refractive index vs waveguide width. Input parameters are λ = 635 nm, cladding material refractive index n1 = 1.5804, core material refractive index n2 = 1.5937, air refractive index n3 = 1 and core thickness t = 1.7 µm. Each propagating mode inside the waveguide has an effective refractive index, and this is strongly reliant on the waveguide width. First mode cutoff in blue line for TE and dashed for TM. Second mode cutoff in red line for TE and dashed for TM. Electromagnetic field 2D-distribution for TE polarization is included in this figure to illustrate non-guiding, single-mode guiding and bimodal guiding conditions.
Mode analysis and electromagnetic field distribution on waveguides was used to determine the minimum distance between two waveguides, so energy is not coupled from one MMI port to the adjacent one. The same toolbox was then used to calculate the interferometric cavity dimension. Applying formula (1) MMI beat length Lπ was then calculated analytically. COMSOL Multiphysics was used to perform finite elements method (FEM) simulations and then compare with the analytical Lπ result. To optimize computing time, the 3D waveguide problem was reduced to an analogous 2D model by implementing effective refractive index method (EIM) [34]. Since this model is time independent, simulations were done in the frequency domain. By applying variable sweeping to MMI length, the relation between length and output power splitting ratio was verified.
2.3 Predicting MMI splitting behavior in dependence of MMI length
All simulations are based on a 635 nm light source for the MMIs specifically designed for single wavelength operation. Waveguide height used in simulations was fixed at 1.7 µm after coating deposition protocol was stablished and repeatable. Waveguide width was set to 2.5 µm after calculating single-mode operation by modal analysis method. Minimum distance between waveguides was stablished as 1 µm to avoid wave overlapping. The resulting minimum width for 2×2 MMI was calculated to be 10.5 µm. This was the MMI width selected for all fabricated devices since minimizing footprint is essential. From the analytical method the MMI beat length is initially determined to be ${L_{\pi ,TE}} = 373.4$ µm and ${L_{\pi ,TM}} = 379.8$µm for TE and TM polarization respectively. FEM simulations were performed using COMSOL to validate the analytical result.
Figure 3 shows simulated power density from each output port. Interferometric lengths ranging from 186 µm to 560 µm were simulated to cover one beat length period. The central region corresponds to the self-image operation where the input power coming from input 1 is redirected to output 2 and the device works as a switch. In contrast, in the edges of the range the input power is distributed among the two output ports and the device works as a splitter. Once the optimal range of lengths under study was selected the manufacturing design was generated in GDSII file extension using Nazca Design [35] libraries for Python.
Fig. 3. Power density at output port 1 (red) and output port 2 (blue) for MMI lengths ranging from 186 µm to 560 µm. 2D-FEM simulation was performed for TE and TM polarizations. It is verified that the beat length reached by analytical method (373.4 µm) corresponds to switching operation where FEM simulation shows most of the power is transferred from input 1 to output 2. In the same way, 186.7 µm and 560.1 µm (0.5·Lπ and 1.5·Lπ respectively) corresponds to interferometric lengths where FEM simulations results show input power is split uniformly.
3. MMI fabrication and morphological characterization
Samples fabricated in this study combined E-Beam lithography, with polymer spin-coating and other conventional polymer processing steps described in more detail below. This fabrication protocol was implemented at INL clean room and chips only left the clean environment when ready for optical characterization. A 200 mm silicon wafer was diced into 25×25 mm pieces and then rinsed with acetone and treated by plasma ashing. Plasma ashing removes organic residues on the silicon surface and significantly improves surface adhesion. We observed coated material uniformity was enhanced after plasma ashing was incorporated to the protocol and less material was needed for the same desired coating thickness. Polymer layers were fabricated using Epoclad and Epocore (Micro Resist Technology GmbH) negative photoresists for cladding and core coating respectively. These epoxy materials were selected because their optical properties; they offer low refractive index contrast ($\underline{\mathrm{\Delta n}} = 0.014$) and high transparency at visible wavelengths [36]. Silicon samples were first spin-coated with Epoclad and soft baked on a hotplate. Then samples were flood-exposed to UV light in a mask aligner and hard baked in an oven for several hours. This created a uniform 20 µm cladding layer covering the sample surface. Likewise, 1.7 µm of Epocore was then spin-coated and soft baked on top of the first layer. The designed patterns are then transferred to the Epocore layer via e-beam lithography, at 100 kV of acceleration voltage using a dose of 6 µC/cm2 and a beam step size of 20 nm, showing that this material is a perfect candidate for electron radiation curing. Note that the spinning and baking recipes provided by the polymer supplier were optimized to reach the desired layer thickness and correct e-beam dose is reached by previous dose tests. Right after e-beam lithography is completed, samples were baked on a hotplate at 120°C for 2 min to finish the polymerization process. When samples were at room temperature, they were immersed in developer mr-Dev 600 during 30 sec for pattern developing. After developing step, chips’ edges area diced in an automatic dicing saw tool (DAD3350, Disco) matching with tapered waveguide ports’ location so that light can be coupled directly from the fiber output to the waveguide.
Devices were fabricated according to the simulated designs and a selection of samples was characterized by profilometry to determine the average layer thickness. Both Epocore and Epoclad coating thickness differed from nominal values provided by the manufacturer [36]. The original Epoclad deposition protocol was adapted to obtain layer thickness greater than 20 µm. The Epocore layer protocol was optimized, and the measured thickness was $1.68 \pm 0.02$µm. Both the surface and the edges of the chips were inspected by SEM to determine the difference between designed and fabricated structures. Polymer structures were coated with 20 nm of gold before SEM inspection. Waveguide and MMI width were inspected by top and tilted view in a SEM (Fig. 4(a)). Deviation from designed dimensions was smaller than 100 nm after the fabrication protocol and e-beam dose were optimized. Lowest resolution for polymer patterning achieved with this EBL equipment was 60 nm, nevertheless we attribute this larger deviation mainly because of cladding thickness variability and hence fluctuating material dose absorption. Note that EBL high resolution capabilities (≈ 10 nm) cannot be applied to this experiment since structures are several millimeters long and EBL writing field is necessarily big (60-120 µm). This particularly affects to critical parts of the design where structures are close to each other, i. e. MMI coupling ports.
Fig. 4. Morphological characterization. Tilted view SEM images from a MMI coupling region and coupling ports used for characterizing fabrication tolerances. Dimensions observed in (a) differed from the original design less than 100 nm in any device when final fabrication protocol was settled. Two cases of port quality are shown in (b) and (c). SEM images of coupling ports were inspected to optimize dicing parameters and test several dicing saws. However, following present dicing protocol a variable number of ports are damaged in every chip. Thus, fabricating multiple identical devices in the same chip is required.
Selected samples were diced into smaller chips, cutting through the waveguides and exposing their extremities before optical characterization so end-fire coupling method can be applied. This was the most critical part of the fabrication process. Polymer layers were found to present strata that were more evident after dicing (Figs. 4(b) and 4(c)). These strata affect light coupling adding losses and noise to the measurement. Polymers are also softer materials compared with conventional inorganic platforms used in integrated photonics. This means that ports are more likely to be damaged during the dicing process. Baking final devices and manual polishing (20 nm grain films) steps were investigated to improve the uniformity of port’s surface without any success, mostly because polishing debris would contaminate the chips. To ensure best facet finish, brand-new precision blades (FTB-Q46, Accretech, Japan) were used for this job. For all this reason, end-fire method efficiency was critically dependent in the condition of input and output ports affecting the consistency of the measurements. We determined $1/5$ of ports were completely broken after dicing and non-usable, and at least $1/2$ of them present some kind of damage.
4. Optical characterization
Chips were characterized by end-fire coupling method [37] in an optical lab at INL facilities. Source light was a 635 nm laser (HLS635 Thorlabs, Inc.) coupled into a single-mode fiber (780HP Thorlabs, Inc.). The beam was then passed through a polarizer and coupled into a lensed tip fiber (LFM1F-1 Thorlabs, Inc.). A digital microscope (Dino-Lite) is used as top-view camera to assist the alignment and a monochrome CMOS camera (CS2100M Thorlabs, Inc.) is used as optical output detector. The image captured in the CMOS camera is first augmented by a ×4 objective. The tip of the lensed fiber, the characterized sample and the CMOS camera are all mounted independently on 3-axes motion stages for optimal alignment and coupling. Thorcam was employed as capturing software, adapting exposure time and sensor sensitivity to the measure. An in-house software toolbox was employed for detecting the maximum intensity peak of every captured image and summing intensity values inside the region of interest around it. MATLAB was used to analyze and manage the dataset, and to plot the information.
Output power ratio of 2×2 MMIs was inspected following the method and setup previously described. Four independently fabricated chips were selected for characterization. Each contains 81 interferometric lengths varying equidistantly from 186 µm to 560 µm. In each chip, devices were duplicated and placed in opposite areas of the chip in case there was damage or a fabrication error affecting one area of the sample. Since coupling light in the PIC is achieved manually, and hence human dependent, two researchers repeated the same characterization process to reduce measurement error.
The measured power splitting ratio ($\frac{{|{{\underline{O}_1} - {\underline{O}_2}} |}}{{{\underline{O}_1} + {\underline{O}_2}}}$) obtained from these devices is plotted in Fig. 5(a). A relative measure of the outputs power allows us to compare the performance of the MMI splitters, not being impacted by variations in in-coupling due to alignment variations or due to different input facet morphologies. Experimental data (blue) is represented as an average of power splitting ratio calculation (30 data points per interferometric length) and its standard deviation. This is compared with 2D FEM simulation for TE polarization (black) for the same interferometric length. Interferometric response was also inspected for TM polarization, but no significant difference was found. In a preliminary result, the experimental curve deviated horizontally from the curve expected from simulation at least in 20 µm shift. After inspecting all the parameters involved both in characterization and simulation, a considerable shift in the central wavelength of the laser source compared with its nominal value was found. FEM simulations were adapted to the new source wavelength and the refractive indices of Epocore and Epoclad (wavelength dependent) were modified accordingly [36], leading to a better fit between experimental and simulated curve as shown in Fig. 5.
Fig. 5. Comparison between experimental and simulated optical outputs of the MMIs for various interferometric lengths. (a) 2×2 MMI output power ratio vs MMI interferometric length. Blue line represents the average power splitting ratio for every interferometric length described by $\frac{{|{{{O}_1} - {{O}_2}} |}}{{{{O}_1} + {{O}_2}}}$ where O1 and O2 are power density values in each MMI output respectively. Each blue data point is an average of 30 independent measurements, and error bars represent symmetrically the standard deviation. Black line represents results of FEM simulations (TE polarization) for the same interferometric lengths. (b) 2×2 MMI total output power vs MMI interferometric length. Red line represents the average total output power for every interferometric length. Error bars represent the standard deviation and black line represents FEM simulation (TE polarization).
The experimental data presented in the graphs of Fig. 5 show good agreement with the simulated data comparing relative (a) and absolute (b) output power in dependence of the MMI lengths. Deviations are observed at low relative output power, which is a result from leakage of light from the core material into the cladding, which always lead to increased relative output power values, as observed for the MMI lengths ranges from 300 μm to 350 μm and from 450 μm to 500 μm.
The peaks in Fig. 5(a) correspond to the interferometric lengths in which power is unbalanced between outputs and the ratio tends to 1. The valleys correspond to interferometric lengths that equally split the input light between the two output ports and the ratio tends to 0. However, this graph is not enough to describe the performance of the manufactured MMIs. Figure 5(a) shows valleys in the 310 µm and 460 µm regions, however, these devices cannot be considered optimal 3 dB splitters since the total output power is low both in measurements and simulations as can be seen in Fig. 5(b). This is also observable in FEM simulation results shown in Fig. 3, where high total output power is found at 190 µm, 390 µm and 550 µm interferometric lengths. MMIs in the 186-200 µm length range can split the input power in two, without significant power loss, where 190.68 µm was found as the best interferometric length. Any other power splitting ratio can be achieved by using the data in Fig. 5 and stablish a generic process for MMIs fabrication.
5. Conclusions
An integrated optical power splitter based on a 2×2 MMI built on an all-polymeric platform, optimized for 635 nm light sources has been presented. A complete in-house process design kit was developed facilitating future manufacture of more complex photonic structures based in MMIs, such as integrated Mach-Zehnder interferometers.
The analytical and FEM simulations were validated by the manufactured devices characterization. The fabrication protocol demonstrated that Epocore and Epoclad are perfect candidates for polymer integrated photonics fabrication using e-beam lithography. Fabrication tolerance smaller than 100 nm was obtained after optimization of the lithography process.
Single mode waveguides employed were dimensioned as 2.5 µm wide and 1.8 µm high. Interferometric lengths ranging from 186 µm to 560 µm were studied and confirmed experimentally the simulated power splitting ratio. The optimal MMI length for the 3 dB power splitter was found to be 190.68 µm for the 10.5 µm wide structure.
Dicing process needs to be thoroughly optimized in the future to obtain more uniform chip edges and better coupling. Damages caused while dicing meant that a big population of samples were needed to get reliable data. A total of 30 measurements for each interferometric length was considered.
This work shows that polymeric materials are a promising alternative to traditional PIC platforms, offering fast and cost-effective prototyping allowing single-step lithography and being exceptionally suitable for applications in the visible region. Furthermore, polymeric waveguide technology has the future projection of roll-to-roll manufacture using low-cost flexible substrates and nano-imprint technology.
Funding
European Commission (713640, 828841); Ministerio de Ciencia e Innovación (PID2020-114172RB-C22); Comunidad de Madrid (BG20/00136, S2018/NMT-4326); CCDR-N (NORTE-01-0145-FEDER-000019).
Acknowledgments
The authors wish to acknowledge Ricardo Adão for providing the MATLAB based custom data acquisition and analysis software used for the optical characterization studies, Bejoys Jacob for supporting SEM characterization, and Rafael Casquel from Technical University Madrid for fruitful discussions. This work benefitted from the access to and support by the Micro- and Nanofabrication, Nanophotonics and Bioimaging Core Research Facilities of INL.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper may be obtained from the authors upon reasonable request.
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