## Abstract

In this paper, we present the design, the fabrication and the characterization of an Arrayed Waveguide Grating (AWG) based on a SiGe graded index waveguide platform, operating at 4.5 µm. These devices were specifically designed to work together with an array of Distributed Feedback Bragg Quantum Cascade Lasers (DFB-QCL) emitting at different wavelengths. The AWG enables to combine the different light sources into a single output and the design adopted allows to maximize transmission over the entire spectral range defined by the array of DFB-QCLs.

© 2015 Optical Society of America

## 1. Introduction

Mid Infra-Red (mid IR) is particularly interesting in the field of spectroscopic gas sensing. Indeed, many gases present strong absorption lines in this spectral area. Moreover, the appearance of new mid IR laser sources such as Distributed Feedback Bragg Quantum Cascade Lasers (DFB-QCLs) and Interband Cascade Lasers (DFB-ICLs) permits the easy, and highly specific, detection of these gases by a simple absorption measurement. These sources present a high spectral purity (typically 10 MHz when used in continuous mode) and a high stability. However, their tunability is quite small (3 cm^{−1}), limiting the use of one laser for one gas. Given that, we propose, in order to tackle the issue of multi-gas sensing, to combine an array of DFB-QCLs [1], evenly spaced by steps of 3 cm^{−1}, with a wavelength multiplexer. The idea there is to obtain a tunable, monolithic, single output source. Wavelength tuning can be done either by changing the driving current of one DFB-QCL within its 3 cm^{−1} range of tunability, or by switching from one DFB-QCL to the next one. As an example, ideally, an array of 15 DFB-QCLs evenly spaced by 3 cm^{−1} steps when combined to an appropriately designed multiplexer, will yield a monochromatic light source, having the spectral purity of a single DFB-QCL but being tunable over a range of 15*3 cm^{−1}. We will now focus on the multiplexer, which is the topic of this article.

Various wavelength multiplexers have been thoroughly studied for telecom applications in the near IR range; among them is the Arrayed Waveguide Grating (AWG) [2,3]. Several technical solutions have been proposed to use those AWG in the mid IR range [4]. For instance, AWG based on Silicon-On-Insulator (SOI) waveguides have been proposed by Muneeb et al. [5] who demonstrated an AWG working at 3.8 µm. However, this technical solution is limited to wavelength below 4 µm, because of the absorption of the SiO_{2} buried layer. This SOI platform was more recently reviewed by Mashanovich et al. [6]. Another technical solution has been proposed by Malik and associates [7]: their AWG is based on Ge-On-Silicon waveguides with a demonstration at 5 µm. In a recent paper [8], we proposed a new waveguide platform based on SiGe graded index waveguides. This material presents an important transparency range from 3 µm to 8 µm and full compatibility with Complementary Metal Oxide Semiconductor (CMOS) processing. It allows the fabrication of single mode waveguides in the full transparency range. This wide spectral range is of particular interest for gas sensing applications. As a first proof of concept, we have thus fabricated an AWG working at 4.5 µm based on SiGe graded index waveguides. We present, in this paper, the design, process and characterization of the AWG. The final purpose of the AWG presented in this paper is to be used, in a multiplexing way, in conjunction with an array of DFB-QCLs. The spectral spacing of the DFB-QCLs array will then be matched with the spectral spacing of the AWG inputs. Thus, the DFB-QCLs array will be multiplexed by the AWG leading to an integrated multi-λsource with a single output. Please note that, in this paper, we focus only on the AWG, its design and optical properties when used in the de-multiplexing way.

## 2. AWG design

A detailed description of AWG working principle can be found in [3,9]. Nevertheless in our case, we wanted to explore the use of SiGe/Si waveguides to cover the whole 3-8 µm spectral band [8,10,11] for beam routing. Thus, we developed a software tool kit based on a Gaussian approximation of waveguide fundamental mode and Fourier diffraction optics in order to rapidly design AWG devices. A detailed description of the equation involved can be found in [12]. A synthetic description of the different calculation steps used by this design tool is provided thereafter. Figure 1(a) shows the basic principle of an AWG working in the de-multiplexing way.

The input (area “1” in Fig. 1(a)) is a single mode waveguide. This waveguide, as well as all waveguides in areas “3” and “6” has the following structure: the cladding is Si, the core is Si_{1-x}Ge_{x} with a triangular index profile in the direction perpendicular to the substrate (as illustrated in Fig. 1(b)); The Ge ratio increases from 0% up to 40% and decreases back to 0% in a triangular and symmetrical shape, with an overall thickness of 3 µm. The width of the waveguide is 3.3 µm. A detailed description of these waveguides can be found in [8]. We present in Fig. 1(c) a simulation of the mode profile (normalized field vector |Ey|/|Ey(0,0)|) calculated using the Phoenix/Field Designer software at a wavelength of 2235 cm^{−1}. The triangular profile was approximated by a 30 steps pyramidal profile. In Fig. 1(d), we present the X and Y cross sections of the field together with Gaussian fits. According to the theory of optical waveguides, the field distribution of the vertically polarized fundamental mode (TM mode) presents no discontinuities and can be approximated by the product of two Gaussian functions (both transverse directions). We define the “vertical” direction as the one perpendicular to the substrate's plan. The field presents a “horizontal” and a “vertical” dependence.

We will first focus on the “horizontal” dependence of the field. This waveguide feeds a planar waveguide (area “2” in Fig. 1) in which the optical beam is not guided anymore in the horizontal direction; the Gaussian wave propagates from its beam waist to the far field (end of area “2”) following a classical Gaussian beam diffraction equation [13]. At the end of area “2”, the optical field is injected in an array of waveguides (area “3” in Fig. 1). The intensity coupled in each waveguide can be calculated analytically as a Gaussian-Gaussian overlap integral [14]. At the end of area “3”, because each waveguide of the array has a different length, each mode has a different phase. Hence, in each waveguide, the field can still be expressed as a Gaussian function with a phase shift. These waveguides recombine at the beginning of area “4”; the total field being the sum of each waveguide field.

Area “5” is a planar waveguide and a recombination area where the fields coming from each waveguide interfere and focus at the end of area “5”. In this image plane, the lateral position of the focal point will shift with respect to the wavelength. By placing output waveguides at proper positions along the image plane, a spatial separation of the different wavelength channels is obtained. As explained by Zhou et al. [12], the field at the end of the recombination area “5” is the Fourier Transform of the field at the beginning of area “5”.

Let us now switch to the field in the vertical direction. It remains guided in the different areas of the AWG. Thus, the field can be modeled by a Gaussian function. Nevertheless, a transmission coefficient must be used at each waveguide/planar waveguide interface in order to take into account the slight width difference between the planar area and the waveguide mode fields. Again, this transmission coefficient can be calculated analytically as a Gaussian-Gaussian overlap integral [14].

Based on this analytical calculation method, we developed a design tool which calculates very quickly the spectral response of our AWGs. Input parameters are the minimum and maximum wavenumbers, the number of channels, the flatness of the overall spectral response [9], the waveguide opto-geometrical parameters (width, effective index at relevant wavelengths) and the gaussian fit parameters of the fundamental mode of the waveguide. It is also possible to introduce a distance between waveguides at the input and output of the array. From there and using the method described in [9], our tool calculates the diffraction order, the path difference between array waveguides and the number of array waveguides (which can be adjusted). The array waveguide routing is implemented using the method described in [15]. Taking the angle of the central input waveguide as a parameter, the array waveguides geometries are calculated automatically. Finally, once satisfied with the results, a Graphic Data System (GDS) file of the device is automatically generated. The results presented here were calculated without random phase noise. An improved version of this tool which includes phase noise simulation is now available and may be the subject of a future publication.

An example of spectral response is provided in Fig. 2(a). Figure 2(b) is a copy of Fig. 2(a) but, for the sake of clarity, several channels were removed and the transmission scale was changed. We now define and present in Fig. 2(b) a set of parameters that will be useful in the following. Let us first recall that, by combining an array of DFB-QCLs with the AWG, we want to build a single output, mono-mode light source with the spectral purity of a DFB-QCL, which can be tuned over the whole wavelength range of the DFB-QCLs array. Our goal is to obtain a source with an intensity output as flat as possible over the entire spectral range targeted. To help us describe this property, we introduce three parameters. First, the “inter-band flatness”, see Fig. 2(b), which is the difference between the maximal transmission of a channel and the intersection point with the adjacent channel. Second, the “broadband flatness” which is the difference of maximal transmission between the central channel (ν = 2235 cm^{−1}) and the lower of the two external ones (ν = 2185 cm^{−1} and ν = 2285 cm^{−1}). Third, the “central transmission” which is the transmission of the central channel. In Fig. 2(b), the broadband flatness is small (1 dB) and the central transmission high (−1 dB), which is satisfactory. On the other hand, the inter-band flatness is very high (13 dB). This last point should definitely be improved in order to obtain a source with an intensity output as constant as possible.

This is why we decided to introduce Multi Mode Interference (MMI) couplers at the exit port of our AWGs.

#### 2.1 Implementation of MMI couplers

Using MMIs [3,16] enables to flatten the spectral response of each AWG channel, privileging flat intensity output over the entire spectral range, while degrading the maximum peak transmission, however. In order to implement MMIs in our simulation, we model them as the sum of two Gaussian curves. This approximation permits to keep an analytical calculation method. In Fig. 3, we present a vertical cross section of the MMI output Electrical field (calculated with a Beam Propagation Method (BPM) RSoft) and the fit obtained with two Gaussians functions.

From this point we were able to simulate the influence of the MMI on the spectral response of the AWG. The result is presented in Fig. 4.

As one can see in Fig. 4(b), the influence of the MMI coupler is twofold. First it reduces the central transmission by 3 dB. Second, it considerably reduces the inter-band flatness from 13 dB to 5 dB, which was the result expected. As a conclusion, we can say that even if we have lost some overall transmission, the MMI seems to be a clear improvement regarding our application.

#### 2.2 Implementation of taper and dispersion compensation

At the interface between the planar waveguide and the array (e.g. between zones “2” and “3” and in zone “4” of Fig. 1) it is preferable to have the waveguides close to each other in order to optimize transmission at this interface. As a consequence, waveguides will couple some light thus inducing a phase error in the array. To overcome this difficulty, it is possible to use tapers on these waveguides. At the beginning of the array, waveguide will be larger and the fundamental mode will be more confined, with therefore less coupling. After the taper, the distance between the waveguides will be larger which also minimizes coupling. This phenomenon is well described in [17]. In that case, the taper shape and angle can be optimized in order to avoid coupling between the fundamental mode and higher order or cladding modes using the adiabatic criterion: α(z) << w/2λ (n_{eff} –n_{max}) where z is the propagation axis, w the local width of the waveguide, α is the local angle of the taper and n_{max} is the max refractive index of higher order modes or cladding index if the waveguide is single mode [18]. Both AWGs with and without standard linear tapers were implemented in the design for further investigations.

With the software presented above, we designed different types of AWGs some with tapers or MMIs or both. Dispersion compensation was taken into account during the design. This compensation concerns the dispersion of the waveguides and planar waveguide fundamental mode's effective index. We also designed an AWG without dispersion compensation for test purposes. This particular AWG was useful because at the time of design, we did not have a measurement of the dispersion of SiGe at around 4.5 µm. These dispersions were measured (with the Mlines technique) after the fabrication of the AWGs; the results of the Mlines measurements will be presented in a coming paper [10]. As a summary, we present in Table 1 the parameters corresponding to the different versions of the AWGs.

## 3. AWG process

A SiGe/Si waveguide technology has been used to fabricate the AWG devices. This technology, developed on 200 mm wafers within the CEA-LETI pilot line facilities, is fully compatible with standard CMOS processing and allows the fabrication of low-loss large-bandwidth mid IR waveguides specifically designed for integrated gas sensing applications. A complete description of the waveguide structure is detailed in [8]. The core layer of the waveguide consists in a graded index SiGe layer grown by reduced pressure epitaxy where the Ge content is linearly increased from 0% to 42% and then decreased down to 0% in a quasi-triangular profile which is 3 µm thick [8]. To define all the passive functions, the waveguides core is patterned in this layer by conventional photolithography and deep reactive ion etching processes. Figure 5 shows 3D and cross-sectional Scanning Electron Microscopy (SEM) images of an AWG Multiplexer just after this step. Entrances waveguides are shown in Fig. 5(a). The initial spacing of 100 µm between adjacent waveguides, i.e. compatible with DFB-QCL arrays geometry, is progressively decreased down to a few microns (as required by design) at the entrance of the first diffractive area of the AWG. From the technology point of view, the minimum spacing between adjacent waveguides is limited by the subsequent gap filling with the Si epitaxial cladding layer, which imposes trenches larger than 2 µm. One can also see, in Fig. 5(a), that the 15 inputs are not bunched together. Indeed, they are divided into two groups of 10 and 5 waveguides covering the 2185-2212 cm^{−1} and the 2267-2280 cm^{−1} spectral ranges, respectively. This is due to the targeted application of this AWG, which is the detection of three gases (CO, N_{2}O and CO_{2}). The first group of 10 waveguides will address CO and N_{2}O and the second group CO_{2}. Let us add that we did not choose to fabricate an AWG continuously covering the 2185-2280 cm^{−1} range. It would have been technically possible. However, since our application did not require the central wavelengths, we decided not to add them; this means a reduced number of DFB-QCLs and a smaller AWG.

Figure 5(b) shows a SEM picture of the exit port of the AWG structure, where the nominal exit waveguide is the central one. Eight additional exit waveguides shifted by ± 5.9 cm^{−1}, ± 11.8 cm^{−1}, ± 29.4 cm^{−1} and ± 50 cm^{−1}, respectively, have been added to compensate eventual refractive index discrepancies due to technological uncertainties. Note that in this type of AWG, MMI structures have been added at the waveguide exit junction.

To complete the technological processing, the SiGe AWG is embedded in a 10 µm thick epitaxial Si layer deposited by reduced pressure epitaxy (Fig. 5(c) and Fig. 5(d)). This cladding layer is thick enough to ensure a complete optical isolation of the SiGe AWG from ambient atmosphere. This is of primary importance as those devices are specially developed for gas sensing applications. At the end of the process, a flat Si surface is recovered using chemical mechanical polishing process. This last step opens the way to the further integration of other devices on top of the waveguide passive functions (if necessary).

## 4. AWG characterization

As explained in the introduction, the final purpose of the AWG presented in this paper is to be used, in a multiplexing way, together with an array of 15 DFB-QCLs sources. Moreover, as explained in paragraph “3. AWG process”, eight additional exit waveguides have been added to compensate eventual refractive index discrepancies due to technological fluctuations and inaccuracies. Unfortunately, at the time of characterization, we had no DFB-QCLs array available to conduct the experiment. Therefore, we chose a different strategy in order to characterize the AWG. We used the AWG as a de-multiplexer in conjunction with a broadband source, e.g. a Fabry Perot QCL (FP-QCL). From this point of view, the AWG has 9 inputs and 15 outputs. The broadband FP-QCL was injected in one of the 9 inputs and the light coming out of the 15 output waveguides was spectrally analyzed. Then we repeated the experiment with injections in each of the 8 other inputs to get a full characterization of the AWG.

#### 4.1 Experimental setup and measurement

The goals of these characterizations were threefold: first, to measure the transmission range of each AWG entrance waveguide and compare it with the transmission range targeted by design. Second, to measure the absolute transmission of the AWGs and the cross-talk between adjacent input channels. Third, to evaluate the effectiveness of the MMI and taper structures as detailed in paragraph “2.1 Implementation of MMI couplers” and paragraph “2.2 Implementation of tapers and dispersion compensation”. A schema of the experimental setup is presented in Fig. 6.

The FP-QCL was fabricated by the III-V Lab. It can deliver an average power of 5 mW when driven by a pulse generator (HP 8114 from Hewlett Packard) with a pulse width of 300 ns at a repetition rate of 100 kHz. The pulse is naturally chirped, which creates a continuous spectrum centered at ν_{0} = 2270 cm^{−1} with a Full Width at Half Maximum (FWHM) of 40 cm^{−1}. It is noteworthy that the spectrum can be considered as continuous because the detector used in the spectrometer (see below) is very slow compared to the pulse width. The FP-QCL is collimated and focused (using two LightPath BD2 390037 lenses) on one AWG input. The light coming out of each AWG output is collimated and directed towards a Fourier Transform Infra Red (FTIR) spectrometer (Brucker Vertex 80) equipped with a DTGS detector. In order to see the effect of the MMI structures, a high spectral resolution of 0.1 cm^{−1} was chosen. By carefully adjusting the positions of both illumination and mirror stages, one could select the input and output to be analyzed. In order to obtain absolute transmission values, we also measured the spectrum through a reference waveguide which is located just beside the AWG. This reference spectrum was used to normalize the spectrum measured through the AWG. As an example, we present in Fig. 7 the raw transmission spectra obtained for five adjacent outputs of an AWG, the FP-QCL being injected in the central input. We also plot the spectrum obtained when the FP-QCL is injected in the reference mono-mode waveguide.

The FP-QCL bandwidth (FWHM = 40 cm^{−1}) is not large enough to cover the AWG bandwidth (95 cm^{−1}). It is thus not possible to get a spectrum (with reasonable Signal to Noise Ratio) out of the 15 outputs while the FP-QCL is injected in a single input. Hence, this measurement has been repeated for each input of the AWG. We extracted, from the collected data, the central wavenumber corresponding to each output as well as the normalized transmission (output spectrum divided by reference spectrum).

#### 4.2 Experimental results: spectral analysis of AWGs

As explained above, 4 AWGs were designed and fabricated, each being more complex than the previous one: AWG1 is the nominal version. In AWG2, chromatic dispersion is taken into account in the design. Taper structures were added in AWG3. Finally, AWG4 has also MMI structures.

In this subsection we will focus on the spectral analysis of AWG2 and draw a comparison with AWG1, which will prove the necessity of correcting the chromatic dispersion.

When the FP-QCL is injected in one input, light comes out of several outputs and the FTIR measurements give the corresponding wavenumbers ν_{measured}. On the other hand, each output has been designed to transmit a specific wavenumber ν_{target}. In Fig. 8, we compared ν_{measured} and ν_{target} by plotting the difference (ν_{measured}-ν_{target}) versus the target wavenumber for a FP-QCL injection in each of the nine inputs of AWG2. The nine inputs are named Δν_{input} as they correspond to a deviation from the nominal input Δν_{input} = 0 cm^{−1}, as designed by modeling. Injecting the FP-QCL into the different inputs has allowed us to, first, measure each of the output channels and, second, verify that the shift between adjacent channels and the transmitted bandwidth fits the typical tunability of each source in DFB-QCL arrays. Furthermore, it has allowed measuring shifts of the overall AWG transmission band related to eventual discrepancies between the geometrical dimensions of the device, the refractive index of the different materials used and the parameters used for the design.

In Fig. 8 each line corresponds to an injection in one input and each point of the line corresponds to the central wavenumber of an illuminated output. The nine lines are parallel to the x axis. According to design, for each input, the shift measured should be equal to the nominal shift of the input, i.e. if the FP-QCL is injected in the central input, then for each output, ν_{measured} should be equal to ν_{target}. If the FP-QCL is injected in input Δν_{input} = 5.9 cm^{−1}, then for each output, ν_{measured} should be equal to ν_{target} + 5.9 cm^{−1} and so on. Figure 8 shows that the measured lines are all shifted by around 11 cm^{−1} compared to theoretical values from design. To quantify more precisely this shift and see if it is constant over the entire AWG operating range, we plotted, for each of the nine inputs, the mean value of Δν_{measured}: <ν_{measured}-ν_{target}> as a function of the design input shift Δν_{input}. This curve is presented in Fig. 9(a) together with a linear fit.

The measured curve is precisely fitted (R^{2} = 0.9995) by the equation: <Δν_{measured}> = 1.005<Δν_{target}> + 10.68. This result proves that the AWG has a spectral shift of 10.68 cm^{−1} from the initial design. The slope value of 1 proves that this shift is constant over the entire AWG. This last point reveals that the dispersion that was taken into account during the design of AWG2 was efficient. To further assess this point, we compare in Fig. 9(b) the results obtained for an injection in the inputs Δν_{input} = 11.8 cm^{−1} of both AWG1 (dispersion not corrected) and AWG2 (dispersion corrected); the curves are obtained in the same way as in Fig. 8. One can clearly see, in Fig. 9(b), the differences between AWG1 and AWG2. For AWG2, the residual error remains close to a constant value of 23 cm^{−1} over the measurement range. Meanwhile it increases for AWG1 by 8 cm^{−1} over the same range. This difference comes from the chromatic dispersion which was included in the design of AWG2 but not that of AWG1. This result is reproducible for an injection in the other 8 inputs of AWG1 and AWG2.

Finally, we decided to evaluate the influence of process inhomogeneities over the spectral behavior of AWG2s. Here, we only evaluate chip to chip stability (on a single wafer) and not wafer to wafer stability. To do so, we conducted the same experiment, as explained above, on the AWG2 of 4 chips taken from center to edge of a 200 mm wafer. We evaluated the residual error on all the outputs measured; it remained in the +/−0.5 cm^{−1} range. No additional drift due to process inhomogeneities were observed. Although this measurements were only made on a few AWGs (4 AWG2 over the 75 AWG2 included in a quarter of a wafer), this result gives us confidence that the design is robust.

As a conclusion, we can say that the spectral characteristics of AWG2 are in good agreement with the design except for a shift of 10.68 cm^{−1}. This shift remains constant over the entire AWG range for all the outputs and inputs measured. The chip to chip repeatability is also very good since no additional error or drift were observed. It is noteworthy that the 10.68 cm^{−1} shift is small compared to the wavenumber (2240 cm^{−1}): Δν/ν = 5‰; it is most likely due to an error in the evaluation of the effective index of the waveguide, which is determined from the absolute refractive index profile of the waveguide. This point will be further investigated in a coming paper [10]. After this spectral analysis, we will now study the effects of taper and MMI structures on the normalized transmissions.

#### 4.3 Characterization of taper (AWG3) and MMI (AWG4) structures

Following the same experimental procedure detailed above, we characterized the two others variations of AWG: AWG3 includes taper structures; AWG4 includes taper and MMI structures. We have plotted in Fig. 10 the normalized spectra measured at 3 outputs of AWG2 and AWG3 when light coming out of the FP-QCL is injected in input Δν_{input} = −11.8 cm^{−1}. The 2 subplots correspond to the 2 AWGs.

One can see in Fig. 10 the beneficial impact of tapers, which drastically improve crosstalk, which drops below 20 dB for AWG3 compared to 6 dB for AWG2. This result is in good agreement with simulations which forecasted a drop of −15 dB due to tapers. Tapers have otherwise almost no impact on the value of the central transmission; this point is also in good agreement with simulations.

Finally, we present in Fig. 11, the impact of MMI structures. In Fig. 11(a), AWG3 has some dispersion corrections and tapers; in Fig. 11(b), AWG4 has also MMI structures.

By comparing Fig. 11(a) and Fig. 11(b), one can clearly see that the spectral transmission of each channel has been modified by the MMI structure. There is indeed a diminution of the inter-band flatness from 4 dB for AWG3 (without MMI) down to 2 dB for AWG4 (with MMI). The central transmission seems to be unaffected by the MMI structures. It should be noted that these two experimental results are at odds with simulations. Indeed, as explained in paragraph “2 AWG design”, simulations predict an inter-band flatness value of 13 dB and 5 dB for AWG without and with MMI respectively; the central transmission values are −1 dB and −4 dB, respectively. At the moment, we have no clear explanation for this discrepancy. Yet, we believe that the characteristics, in terms of transmission, of our AWG are interesting for DFB-QCLs array wavelength multiplexing.

Then, in order to get the full normalized transmission of AWG4 (i.e. over the 15 outputs), we tried to complete Fig. 11(b) with the normalized spectra coming from the 10 other outputs. Thus we injected the FP-QCL in the 8 other possible outputs. But although we were able to collect spectra from the 15 outputs, which enabled us to build Fig. 8, the Signal to Noise Ratio (SNR) was too poor to present them as in Fig. 11(b). To circumvent this SNR issue, one possibility would have been to use a detector with a higher detectivity (such as liquid Nitrogen cooled InSb or MCT) and a lock-in amplifier. But we did not have these types of detectors when the measurements were conducted. Another solution would have been to characterize the AWG with an array of DFB-QCL; we will try this solution when we have the corresponding array ready. Nevertheless, with the present experimental setup, we were able to collect the normalized spectra presented in Fig. 11(c). The plots correspond to the 5 outputs (2267 – 2280 cm^{−1}) when the FP-QCL is injected in inputs Δν_{input} = 0 cm^{−1} (green), −11.8 cm^{−1} (red) and −29.4 cm^{−1} (blue). In Fig. 11(c), one can see that the AWG transmission is quiet stable over the analyzed spectral range with a normalized transmission of −5 dB +/− 2 dB.

As far as the normalized transmission of the different AWGs is concerned, we can thus say that the addition of taper and MMI structures improves the AWG performances. We indeed want to obtain a source with an intensity output as constant as possible over the entire spectral range defined by the array of DFB-QCLs.

It is interesting to compare the AWG presented here with the one proposed by Malik et al. [7] who used a Germanium-on-Silicon (Ge-on-Si) platform. Indeed, both solutions target the same application: wavelength multiplexing of DFB-QCL's arrays in the mid IR range. In terms of technology, the Ge-on-Si platform leads to more compact AWGs (footprint: 1mm*1mm) than the SiGe one (footprint: 2cm*1cm). The Ge-on-Si platform technology is also simpler but propagation losses are higher: 4 dB/cm, as compared to 1 dB/cm for SiGe waveguides. However, if we take into account the propagation length in both solutions (0.5 cm and 2 cm, respectively), propagation losses in both types of AWGs are equal. Finally, the comparison of the performances of both types of AWGs is difficult since the approaches chosen by the two teams were different. Malik et al. indeed chose to separate the channels by 6 cm^{−1}; they thus obtained a good crosstalk (16-20 dB). Meanwhile, we chose to bring the channels closer to each other and add MMIs in order to obtain a continuous and flat transmission over the whole spectrum. The Ge-on-Si AWG central transmission (−3.1 dB) is higher than the SiGe one (−5 dB). Both platforms thus offer interesting and promising solutions, the best one depending on the application and the approach chosen.

## 7. Conclusion

In this paper, we have presented the design, process and characterization of SiGe AWGs working in the 4.5 µm range. The normalized transmission of those AWGs is around −5 dB. The broadband flatness and inter-band flatness are on the order of 2 dB. We thus obtained an AWG with a transmission of −5 dB +/− 2 dB over the entire measured spectrum. Coupled to an array of DFB-QCL, this AWG can multiplex 15 wavelengths in a single diffraction limited output waveguide. Finally, it should be emphasized that the design tool developed here, and the SiGe graded index waveguide platform used enables an easy transposition of this AWG to any wavelength in the spectral range from 3 µm up to 8 µm.

## Acknowledgments

This work was partially funded by the Clarity (Grant agreement No 288304) European Project. The Silicon Technology Departement from CEA-Leti MINATEC is gratefully acknowledged for the fabrication devices.

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