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Abstract
We propose a novel integrated micro-opto-mechanical-system spectrometer design in a monochromator setup. It consists of a concave grating fabricated in a planar waveguide that is connected to a rotational electrostatic actuator, which enables angular tuning of the grating. The spectrometer covers a wide operational wavelength range (>100 nm), covering partially the E-band and fully covering the S, C, and L-bands (1416.6 nm - 1696.6 nm), and requires a single photodetector to acquire the spectrum. The spectrometer is designed to exhibit low optical losses throughout the range of motion. The spectrum can be acquired at a frequency of 1.76 kHz. The simulated acquired spectrum features an average insertion loss of −1.8 dB and a crosstalk better than −70 dB with a resolution as low as 1.62 nm. The entire device covers an area of 4 mm x 4 mm and is based on a thick silicon-on-insulator platform.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The integration of wavelength discrimination functionalities on chips is key for wavelength-division-multiplexing networks, sensing, and spectroscopy. Among sensing techniques, spectroscopy has the advantage of high selectivity stemming from the unique “fingerprint” of molecules. This feature makes optical spectroscopy a favored choice for a wide range of applications including agriculture, water quality and forest disaster monitoring, and bio-chemical sensing [1–3]. In addition, it is also used to investigate and characterize the structure and dynamics of biological macromolecules, tissues, materials and gazes. However, traditional infrared spectroscopic systems are bulky, table-mounted, complex and expensive, which limits their accessibility. The growing demand for sensing systems, especially in hand-held and point-of-care diagnostic devices, is driving the realization of mini and micro-spectrometers. There is also a need to miniaturize spectrometers for astronomical spectroscopy [4]. Two technologies enabled by micro-fabrication can advance the development of miniaturized on-chip spectrometers: microelectromechanical systems (MEMS) and integrated photonics. Photonic integrated circuits (PICs) are a promising technology for the next generation of high-speed, low-loss, low power-consumption, high-performance and low-cost optical devices. Similarly, advancement in MEMS enabled the miniaturization of many optical systems on-chip such as scanning mirrors [5–7], tunable filters [8–10], tunable lasers [11–13] and beam steering devices [5,14,15] and gratings [16–18]. Systems combining both functionalities are known as micro-opto-mechanical systems (MOEMS). The integration of these two technologies is promising for the development of spectrometers with high resolution, high sensitivity, small footprint and low cost. Accordingly, this work leverages the benefits of these two technologies to design a compact integrated MOEMS spectrometer fabricated on a micron-scale silicon photonics platform based on a tunable planar concave grating (PCG) and requiring only a single photodetector.
Miniaturized optical spectrometers have been implemented with various technologies. These include Fourier-transform (FT), integrated optical filters and tunable optics. FT spectrometers provide wide operational bandwidth and address broadband applications. However, most of the proposed MEMS-based FT proposed systems are not fully integrated and offer modest resolution [19,20]. On the other hand, silicon photonics-based Fourier transform spectrometers (Si-FTS) offers higher resolution at the price of a smaller free spectral range (FSR) [19]. Nevertheless, these systems encounter some challenges such as thermo-optic non-linearity, waveguide thermal expansion and dispersions that become significant for high temperature tuning [21].
As for spectrometers implemented with static optical filters, many approaches were explored and demonstrated. These include integrated optical filters such as Bragg grating filters [22,23], series of Fabry-Perot resonators with different center wavelength [24], cascaded Mach-Zehnder interferometers [25], and ring resonators (RR) arrays [26–28]. These approaches can achieve relatively high resolutions but suffers from a narrow operational wavelength range, and in some cases, such as for RR arrays and interferometers, they necessitate active tuning to compensate for wavelength shifts due to environmental changes or fabrication variations.
Another appealing approach for on-chip spectrometers is multi-channel filters that are based on a single component including photonic crystal superprisms [29,30], echelle grating (EG) and arrayed waveguide gratings (AWG) [31–33]. They can provide higher performance, resolution and channel counts (i.e. operational bandwidth). Efficient AWG-based spectrometer designs can be found in literature with a high resolution and wide operational bandwidth [31,34]. The group in [34] developed a miniaturized AWG spectrometer fabricated in a low index material platform with a resolution of ∼1300 that covers the H band and has a peak throughput of ∼23%. However, all of these approaches require an array of highly sensitive photodetectors. Therefore, their implementation for systems operating at wavelengths above the absorption limit of silicon (∼1.2 µm) often require expensive III-V photodetector arrays [32,35,36] with a limited integration density [37], which increases dramatically the price of the device, limits the number of wavelengths that can be measured, requires complex read-out and further processing of the data. Less expensive germanium photodetectors can be used for wavelengths up to 1.7 µm but they are less sensitive than III-V photodetectors.
Conversely, another attractive approach is to use high-speed tunable optical filters. The advantages of this approach are compactness, eliminating the need for an array of detectors and acquiring the spectrum of the signal over a short time interval. Different designs were developed and exploited, including tunable diffraction gratings [16,18,38,39], continuously tunable Fabry-Perot interferometers [40–42], tunable fiber Bragg gratings [43], thin-film tunable filters [44] and volume holographic grating-based filters [45]. Various tuning mechanisms were adopted to adjust the filter response either in-plane or out-of-plane; these include light valve [46], microfluidic actuation [47], thermal actuation [48], piezoelectric actuation [49], and electrostatic actuation [38]. Among all these approaches, grating-based MEMS spectrometers are particularly appealing because of their small size, weight, power consumption, and cost, and their high temperature and pressure stability [39,50]. Grade and his group [51] developed a MEMS tunable diffraction-grating filter based on free-space optics. The filter can acquire a spectrum of 40 nm for a ±1.8° rotation of the MEMS actuator about its center pivot point with a 140 V actuation voltage. In [17], a continuously tunable grating mounted in a Littrow configuration was designed to implement an external cavity tunable laser. The design is based on a microlens-grating, has an experimental tuning range limited to 30.3 nm over an angular range of ±0.97°. The acquired spectra have a full width at half maximum (FWHM) ($\Delta \lambda $) of about 5 nm with a wavelength repeatability of ±0.1 nm. The output signal power drops from an initial maximum of −0.4 dBm to −11.8 dBm over the full scan range. The grating is tuned by a rotary comb drive that provides unidirectional motion only. Lammel et. al. [8] demonstrated a spectrometer where the grating was replaced by a micromachined interference filter that is angularly tuned through thermal actuation. The system works in free-space, has a high resolution of 1.16 nm for a bandwidth ranging from 4.42 to 5.12 µm, but intrinsically suffers from a low tuning speed due to the slow heat transfer process (resonance frequency of 62 Hz).
The challenge with MEMS-tunable gratings is to displace the grating over a large angular range at an appreciable speed to enable a fast and wide spectral acquisition. Furthermore, the spectral resolution is often limited by the small focal length required for compact systems. To address the limitations of existing technologies, this work presents the design of an innovative fully integrated wide spectrum MOEMS tunable grating-based spectrometer using thick silicon-on-insulator (SOI). The system enables real-time spectroscopy and operates with a single detector. In contrast with the previous demonstrations of MEMS tunable diffraction gratings described above, in our system, the concave grating is implemented inside a planar waveguide, which forms a micro-platform. This implementation controls the vertical expansion of the beam enabling a large optical mode size in the horizontal direction while ensuring minimal losses in the gap required for mechanical movement. The planar concave grating is angularly tuned by rotating the micro-platform, which is integrated in the same plane as a circular electrostatic comb drive actuator that provides a large bi-directional angular motion of more than 8° on each side at a resonant frequency of 1.76 kHz. The MEMS platform enables high-speed spectral acquisition over a wavelength range more than 2 times larger than the previous MOEMS spectrometers based on a tunable grating. More details about the MEMS actuator and its beam steering capabilities can be found in [5]. Moreover, to the authors knowledge, the MOEMS spectrometer design proposed herein is the first fully integrated MOEMS-grating based spectrometer. We present the concept and the proposed designs and simulation results demonstrating the wide spectrum that can be acquired over the grating rotation to show the potential of our approach along with a detailed analysis of the simulated spectra.
2. System overview
2.1 Micro-opto-electro-mechanical spectrometer
The MOEMS spectrometer is designed to operate over a wide wavelength range (>100 nm) with a resolution as low as 0.8 nm. As shown in Fig. 1, it is based on a tunable planar concave grating integrated with a MEMS rotational comb drive on the same chip and in the same plane using a novel fabrication technology. This co-integration is challenging because MEMS actuators incorporate suspended structures in order to move [15,50]. Thus, to control light in waveguide-based MOEMS, either the waveguide must have discontinuities, or the light is controlled by moving structures around the core of the waveguide to modify its effective refractive index. In the former case, careful design of the optical guiding layer is needed in order to minimize optical losses at the discontinuities. Unlike submicron waveguides used in standard silicon photonic processes that have a 220 nm thick device layer [52], with the 3 µm SOI platform it is possible to design a single mode rib waveguide with a large optical mode in both the lateral and transverse directions [53,54]. The large mode size is needed to minimize the divergence of the light beam in the gap required for mechanical movement. With this type of optical waveguide, 3D simulations show that it is possible to create gaps as large as 3 µm while still maintaining a transmission efficiency of 80%. Moreover, the grating can be fabricated at the same time as the MEMS actuators, which simplifies the fabrication process.
Fig. 1. Schematic of the MOEMS spectrometer: (a) top view (b) enlarged view of the back facet of the grating with metal reflectors (c) cross-section of the device.
Figure 1(a) illustrates the proposed design architecture along with the principle of operation of the MOEMS spectrometer. An enlarged schematic of the metallized grating facet is presented in Fig. 1(b), and a cross-sectional view of the design is provided in Fig. 1(c) depicting the material stack. As shown in Fig. 1(a), the chirped and blazed grating in the MOEMS spectrometer is designed based on the well-known Rowland geometry [55] and is defined on the back edge of the MEMS platform [5]. The light signal to be analyzed is brought to the planar waveguide through a single-mode input rib waveguide, expands, crosses the gap and illuminates the grating, where it is simultaneously reflected and diffracted, and then each wavelength is re-focused at different locations along the focal plane. Accordingly, only a narrow fraction of the spectrum will be coupled to the output waveguide. In previously reported integrated echelle grating spectrometers [36,56–59], the grating is fixed and the spectrum is acquired at once by a series of output waveguides arrayed along the Rowland circle. In contrast to these systems, our spectrometer has a single output waveguide and wavelength tuning is performed by varying the angular position of the grating with respect to the input/output waveguides. This is done by applying an actuation voltage of up to 150 V to the silicon comb-drive. The whole spectrum can be read by continuously measuring the output with a single detector and correlating the result with the position of the grating. By eliminating the array of output waveguides/photodetectors, the chip-size, price and insertion loss induced by the arrayed output waveguides are reduced significantly. Moreover, this implementation avoids the difference in loss induced by variations in length between the output waveguides and different photodetector couplings.
The normal of the grating that passes through its center is matched with the pivot point of the MEMS platform to enable a constant angular rotation with minimal translational offsets. The grating is allowed to rotate by a gap inside the slab waveguide, as shown in Fig. 1(c). The gap size is determined by the minimum feature size that can be created by contact lithography and can be as small as 1 µm. Since the silicon device layer is used to implement optical waveguides, it should not be doped to minimize optical losses. Therefore, the MEMS comb drive must be coated with a thin layer of aluminum to increase its conductivity. The aluminum layer will also cover the backside of the grating in order to increase its reflectivity. The overall size of the spectrometer is 1.4 mm × 4.0 mm.
Two grating designs, D1 and D2, both in Eagle mount configuration, are proposed targeting different resolutions and spectra. This configuration was chosen to maximize diffraction efficiency over the angular range of the MEMS platform and to minimize the impact of its translational offset. The goal with D1 was to maximize the free spectral range (FSR) of the grating to measure the widest spectrum possible. This first design integrates a planar concave grating (PCG) that can achieve a 3-dB resolution as low as 2.7 nm and covers a bandwidth of 250 nm (1439–1689 nm) over a total angular displacement of 10°, whereas the second design is tailored to maximize resolution for the same overall device dimensions. It has a 3-dB bandwidth of at least 1.6 nm at the price of a smaller FSR and consequently a narrower operational bandwidth of 212.9 nm (1441.6–1654.5 nm) for a 12° rotation span. Both designs have a single input/output rib waveguide. All rib waveguides are 2.4 µm wide and shallowly etched (1.75 µm deep) to be single mode. The waveguide effective refractive index for TE and TM are 3.4554 and 3.4551, respectively. The mode profiles for both polarizations are shown in Fig. 2. They will be covered with a quarter wavelength (at 1550 nm) layer of parylene to reduce reflections at the interface forming the gap in the slab region and to increase the reflectivity of the metal reflector covering the back facet of the grating [60,61].
Fig. 2. Intensity distribution of the (left) TE mode and (right) TM mode for the channel waveguides in the MOEMS spectrometer.
2.2 MOEMS spectrometer echelle grating design
Echelle gratings, or PCGs, are diffractive-based devices with a folded beam path architecture in which phase-delays are induced. On the other hand, AWGs are analogous in terms of operational principle but differs in their implementation. In AWG phase-delay occurs in the individual array waveguides connecting the two free propagation region (FPR) [31]. While coupling losses are the main source of losses for both devices, PCGs use of space more efficiently and hence are more compact, which makes them less vulnerable to local fabrication variations and processing window stability (i.e., sidewall roughness and micro-cracks). Thus, PCGs are advantageous and favored for applications where small size, high spectral finesse, high resolution, scalability, low loss, and fabrication tolerance are an asset [45]. However, this comes at a price: the deeply etched facets have stringent fabrication requirements. Grating teeth that are not etched vertically can be a significant source of loss. Various approaches have been proposed and adopted to mitigate this problem and improve the reflectivity of the grating facets as reported in [55,60]. One successful technique is based on the deposition of a quarter wavelength layer of SiO2 covered by a layer of metal and by blazing and chirping the facets [55]. The efficiency of this approach in thick SOI platforms has been proved by the work done in [61], in which they designed an echelle grating fabricated on the platform provided by VTT Finland [53]. They reported a minimum experimental insertion loss of 1 dB, loss non-uniformity as low as 1 dB, a polarization dependent loss (PDL) and polarization dependent shift (PDWS) as low as 0.58 dB and 0.32 dB, respectively. Accordingly, in this work, we adopt the same technique, but we propose to replace SiO2 with parylene to work as a cladding for the slab waveguide and to enhance the reflectivity of the facets (see Supplement 1, section 3). Parylene has a similar refractive index as silica and offers many advantages including high conformity and high adherence to silicon.
In this section, we present the main results that allowed us to define the grating parameters for the D1 and D2 designs. A detailed discussion of the methodology used to select the optimum value of the different parameters is provided in Supplement 1, section 1. The Rowland radius is set to 750 µm for both designs. Low orders of diffraction were considered to obtain a large FSR. As explained in Supplement 1, the choice of $\textrm{m,}\;{\mathrm{\theta}_{\textrm{in}}},\; \mathrm{\beta}$ and LD involves a trade-off between the device performance and its operational wavelength range. Thus, we designed PCGs with two different input/output angular position. The grating designs make use of input/output waveguides with their center located at $50^\circ{/}55^\circ $ and $70^\circ{/}75^\circ $ from the grating normal for D1 and D2, respectively. A large angle of incidence in D2 is used to acquire higher resolution, while D1 is used to provide lower side lobes and higher uniformity across the filtered spectra.
In static PCGs that require an array of output waveguides, it is challenging to take advantage of the finer resolution obtained with large angles of incidence and diffraction. This is because the effective waveguide spacing for a fixed waveguide pitch decreases by a factor of cos$(\beta )$ along the Rowland circle for larger angular output positions. Thus, in order to avoid coupling between the output waveguides, the waveguide pitch should be increased [37]. Therefore, this limits the number of output signals in a conventional PCG design. However, in the MOEMS spectrometer, this limitation is alleviated since a single output waveguide is used. In order to avoid truncation of the input wavefronts arriving on the grating during rotation, we performed simulations based on the Huygen-Fresnel principle using the software EPIPPROP to study beam propagation in the slab area and the profile of the beam incident on the grating as a function of the angle of incidence, which is controlled by rotating the MEMS. The grating length (L) required to capture the entirety of the incident light is then estimated.
Finally, to increase reflectivity and compensate for the Fresnel reflection loss both PCG designs are based on perfectly chirped and blazed reflectors as reported in [55] and are designed to be fabricated on a 6” SOI wafer with a 3 µm thick silicon layer and 2 µm buried oxide layer. Since the fundamental slab modes for both polarizations are very well confined into the silicon layer their effective and group indices are the same (to the third decimal place) and at 1550 nm they are ${n_{eff}}\textrm{ = 3}\textrm{.47}$ and ${n_g}\textrm{ = 3}\textrm{.59}$, respectively. The fabrication process developed to realize the proposed devices is described in Supplement 1, section 3. The thickness of the layers in the optical stack were chosen to provide high confinement and low optical losses, small polarization dependence and relaxed fabrication tolerance [53]. Also, it allows for monolithic integration with MEMS actuators. The theoretical analysis of the wavelength coupled to the output waveguide as a function of the angle of the grating is presented in Supplement 1, section 2. The parameters defining each of the designs are summarized in Table 1.
Table 1. Summary of the parameters of the gratings for designs D1 and D2.
2.3 Micro-platform
The MEMS platform was modelled and optimized through a combination of finite element analysis (FEM) simulations and experimental validation with the SOIMUMPs fabrication process from MEMSCAP [5]. The FEM simulations were done using the software ANSYS (version 18.0, ANSYS, Inc., Canonsburg, PA, USA). The electrostatic actuator configuration that will be used for the tunable MOEMS spectrometer is shown in Fig. 2. It was fabricated for mechanical testing only on a SOI wafer with a 25 µm silicon layer and thus does not include an echelle grating. However, simulations show that the actuation voltage for thinner silicon layers (i.e. 3 µm and 10 µm) remains approximately the same since the reduction in vertical area of the electrostatic actuator is compensated by a decrease in the stiffness of the anchor. The maximum actuation voltage required rotate the platform by 6° in one direction is 150 V [5]. The area where the grating would be etched is shown in Fig. 3. To achieve a large bi-directional angular rotation (±9°) with a circular motion (i.e., how close it can trace a perfect circular path), the virtual pivot point was optimized to be at $\textrm{2/3}$ of the length of the anchor. The grating will be etched with a radius of 750 µm covering an arc of 135° on the back of the micro-platform. The device exhibits a resonant frequency of 1.76 kHz. More details about the MEMS actuator optimization can be found in [5].
Fig. 3. A scanning electron micrograph of the rotary MEMS platform showing the virtual pivot point and the location where the grating will be etched [5].
3. Simulation results
To demonstrate the potential of the MOEMS spectrometer, we adopted a hybrid approach combining ray tracing and 3-D full vectorial simulations. In the first stage, the optical design software Zemax was used to model and evaluate light propagation inside the MOEMS spectrometer. Raytracing simulations were done in non-sequential mode to evaluate the effect of rotation and translation on the image plane, which represents the beam in the tangential plane projected onto the output waveguide. A gaussian beam with a waist size equal to the waveguide beam width calculated from the software Mode Solution from Lumerical for the TE polarization was used in the simulation as the input beam. We studied the wavelength coupled at the output by continuously changing the input and output positions to mimic the grating rotation and then compared the results with theoretical calculations, which we found to be closely matching. The beam at the output port during tuning is found to have a gaussian shape with a waist size equal the input beam.
After validating the optomechanical designs proposed herein, accurate and precise simulations to study the diffraction efficiency and the filtered spectra were performed. Three-dimensional full vectorial simulations based on the Huygen-Fresnel principle were conducted to model the grating and simulate the filtered spectra with the software EPIPPROP from Photon Design. Two-dimensional finite difference eigenmode simulations with MODE Solution were used to design the single mode rib waveguide and to determine the minimum bending radius for the layout of the devices. The simulated optical spectra obtained for both grating designs are presented in the following sections. The performance of the MOEMS spectrometer is characterized by different metrics, which are illustrated in Fig. 4.
Fig. 4. Schematic representation showing the performance metrics used to characterize the response of the spectrometer.
3.1 Resolving power
The most critical criterion that defines the performance of a grating is its resolving power (RP). The theoretical resolution is determined based on the Rayleigh criterion [62], which can be calculated from the resolving power expressed as $\textrm{RP = mN = }\frac{\lambda }{{\Delta \lambda }}$. This yields a theoretical RP of 1185 and 2010, and a theoretical upper bound of the smallest resolvable wavelength difference, which is defined as the 1-dB bandwidth, for a central wavelength ${\lambda _0}$ of 1550 nm of 1.4 nm and 0.7 nm for design 1 and 2, respectively. The simulated 3-dB bandwidth (BW) for ${\lambda _0}$ is 3.01 nm for D1 vs. 1.62 nm for D2 (see Fig. 5). Moreover, the variation in the 3-dB BW for the acquired spectra as the grating is rotating is plotted in Fig. 5. The maximum variation across the scanning range is only 0.3 nm for D1 and 0.1 nm for D2. This discrepancy in the resolution during tuning is mainly attributed to the shift from the original Rowland configuration. Compared to other diffractive-based spectrometer designs reported previously [3,55,61,63], the resolution variation across the acquired spectrum is negligible for such a high resolution, large FSR and wide angular span.
Fig. 5. Simulated performance metrics variation as a function of angular tuning for (a) design D1, and (b) design D2. The graphs show the variation of the 1-dB (red), 3-dB (black) and 10-dB (green) bandwidth along with the insertion loss (pink) and crosstalk (blue) values. The arrows indicate to which vertical scale the curves are associated.
3.2 Grating efficiency
Most planar waveguide grating-based spectrometers suffer from birefringence [64,65], which leads to an undesirable polarization-dependent wavelength shift (PDWS) and polarization-dependent loss (PDL). However, these impairments have a very small impact when the spectrometer is implemented on a thick SOI platform. The birefringence in thick SOI waveguides is less than $\textrm{1}{\textrm{0}^{\textrm{ - 3}}}$ refractive index unit, which is on the order of the numerical precision of the simulations. Figure 6(a) shows the small difference in the simulated spectrum obtained at the end of the output waveguide between the transverse electric (TE) and transverse magnetic (TM) light for an angle of incidence of 50°. Figure 6(b) shows overlaid of the central wavelength at the output for the TE and TM polarizations when the angle of incidence varies by ±5° in design 1. These results are in accordance with the theoretical calculated $\Delta \textrm{n} = n_{TE} - n_{TM}$, and the PDL and PDWS are as low as 0.1 dB and 0.1 nm, respectively, for both designs. These results are on average close to the results reported in [63,66,67] and slightly better than [61]. Since the PDWS is significantly lower than the resolutions of both spectrometers, they are effectively polarization independent.
Fig. 6. Overlaid of the simulated spectra of the TE and TM polarizations (left) and central channel (right) acquired over 10° of rotation.
Both spectrometer designs achieve a high diffraction efficiency, which is defined as the power of the diffracted light collected by the output waveguide with respect to power of the incident light launched in the input waveguide in the operating order m. The grating incorporated in D1 delivers an efficiency of about 82% whereas the grating in design 2 provides an efficiency of 90%.
3.3 Wavelength scanning range, resolution and spectral acquisition
The range of wavelengths that can be scanned by the MOEMS spectrometers is limited by the FSR (calculated from Supplement 1, Eq. (S2)) of the gratings and not by the range of motion of the MEMS actuator. Thus, the angular rotation span induced by the MEMS comb-drive is tailored accordingly for D1 and D2. The optimum angular tuning range for D1 and D2 are respectively 9.5° and 12° to fully scan the FSR. D1 covers the wavelength range from 1.41 µm to 1.68 µm whereas D2 operates from 1.44 µm to 1.65 µm. The simulated operational range for both designs is broad enough to cover the bandwidth required for most applications in near-infrared (NIR) spectroscopy, lab-on-chip and chemical sensing applications [68,69]. Figures 7(a) and 8(a) show the simulated filtered spectral response for a complete wavelength swept in 1° angular step for both designs, and Figs. 7(b) and 8(b) shows the operational wavelength range over the full angular span. These results for ${\lambda _c}^{\prime}$ from the simulations are in agreement with the theoretical values ${\lambda _t}$ derived from Supplement 1, Eq. (S6) for both designs as shown in Figs. 7(b) and 8(b).
Fig. 7. (a) Simulated spectral response for a full angular span in 1°step, and (b) spectral range covered with a full angular scan (${\lambda _s}:$ wavelength acquired from simulation) for Design1 compared to the theoretical calculations (calculated ${\lambda _t}$ from the theoretical analysis).
Fig. 8. (a) Simulated spectral response for a full angular span in 1°step, and (b) spectral range covered with a full angular scan for Design 2.
The maximum insertion loss (IL) calculated along the filtered spectra for D1 is about −1.8 dB versus −1.9 dB for the second design. The insertion loss is calculated as the difference between the peak transmission of the coupled wavelength at the output waveguide with the input power. The mean deviation values for the IL are 0.05 and 0.007 dB for D1 and D2, respectively. The loss non-uniformity is calculated as the difference of the peak amplitude of the given filtered BW with respect to the peak of the filtered output with minimum IL (see Fig. 4). D1 exhibits an average deviation of 0.002 dB compared to 0.09 dB for D2. These losses are mainly attributed to the excitation of higher order vertical modes in the slab waveguide which create “ghost-peaks”. However, the higher losses obtained for D2 are mainly due to the large incident angle that illuminates grating facets further away from the pole where the higher order terms in the optical path length difference (OPDL) expression become more significant so that they cannot be neglected, and they will be considered as path length errors which will eventually degrade the image quality (OPDL is the difference in path length for a ray incident on the grating at an arbitrary point on the grating compared to a ray incident on the pole [37]). This is in addition to the fact that larger parts of the shaded facets are illuminated during tuning.
The simulated 3-dB BW has a mean value of 3 nm for D1 vs 1.62 nm for D2. The 3-dB BW for both designs deviates from the mean value over the scanning range by 0.04 nm and 0.16 nm for D1 and D2, respectively. Whereas the 10-dB bandwidth computed from the maximum of each coupled wavelengths across the filtered spectrum exhibit a variation from the minimal value of less than 0.5 nm for D1 and of 0.1 nm for D2 (Fig. 5). These results shows an enhancement by a factor of 4 from the results obtained in [61]. This high uniformity across the simulated spectrum despite the large angular tuning was achieved by choosing a small diffraction order for both designs and a large number of grating teeth (N) to effectively diffract the majority of the input optical power. Moreover, most of the work reported in the field focused on the grating or the actuator structure itself and the acquired range during tuning. Also, some of them tuned their design to have a flat band pass channel [63,66]. Few of them addressed the issue of the uniformity of the filtered spectra. The minimum simulated phase-error crosstalk level increases from −91 dB to −74 dB for D1 and from −98 dB to −81 dB for D2 as the output wavelength increases. This variation in crosstalk is expected because as the angle of incidence increases stronger side lobes appears due to aberration resulting from the illumination of grating facets further away from the grating pole. The simulated level of cross-talk is 2 times better than the values obtained with previous integrated grating spectrometers fabricated in similar technologies and for such a wide wavelength tuning [61,63,66]. Both spectrometers are designed to have a Gaussian passband. The average and standard deviation characteristics of the filtered spectrum are summarized in Table 2.
Table 2. The average and standard deviation of the performance metrics of D1 and D2.
3.4 Grating dispersion
As stated in Supplement 1, Eqs. (S3) and (S4), the linear dispersion (LD) is a function of the input and output angular positions. Thus, the grating angular position will influence these metrics. The LD as function of the angular rotation for D1 and D2 is plotted in Fig. 9. This parameter increases when the angles of incidences increase. This explains the variation in the tuning response, where the wavelength shift is not constant during the angular tuning (i.e., the wavelength shift as function of 1° angular rotation for D1 and D2 plotted in Fig. 7 and Fig. 8 becomes smaller as the incident angle increases). Nevertheless, this nonlinear response can be characterized and used to calibrate the output wavelength measured as a function of the angular position of the grating. The displacement of the electrostatic actuator can be accurately monitored by measuring the capacitance of the comb drive [70].
Fig. 9. Variation in angular and linear dispersion as a function of angular tuning for (a) D1 and (b) D2.
4. Conclusion
We presented the design and simulation of tunable MOEMS spectrometers to be fabricated on a thick silicon photonic platform. Unlike other integrated micro-spectrometers, the proposed devices necessitate only a single detector and acquire spectra in time by rotating a curved diffraction grating around its axis with a MEMS platform integrated on the same die and in the same plane. To tackle the challenges encountered with such integration a custom fabrication process was developed. Two designs are proposed with different resolution that can find potential applications for lab-on-chip for biomedical and chemical analysis. Both devices provide a resolution higher than 1.62 nm, phase-error crosstalk level better than −74 dB, and low insertion loss $(\le -1.79\; \textrm{dB})$. The simulated spectra show good uniformity across the wavelength range. The results demonstrate the potential of the device as a low-cost compact solution for fully-integrated high-resolution on-chip spectral analysis over a wide band in the near infrared at wavelengths where affordable silicon photodetectors cannot be used.
Funding
Fonds de recherche du Québec – Nature et technologies; Centre for Optics, Photonics and Lasers; Regroupement Stratégique en Microsystèmes du Québec.
Acknowledgments
The authors would like to thank CMC Microsystems for providing the software tools.
Disclosures
The authors declare no conflicts of interest.
See Supplement 1 for supporting content.
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