## 1 Introduction  
The mid-infrared (MIDIR) spectral region (2-20 \(\upmu\)m) became a field of major applicative interest over the past decade. Sharp and strong molecular absorption bands of various chemical compounds in that region make the use of MIDIR radiation well-adapted for a large number of applications, including biosensing and medical diagnosis [1; 2; 3], security and defense [4; 5; 6; 7], and astronomy, among others [8; 9]. Such a wide range of applications led to the development of a plethora of photonic components, including sources [10; 11; 12], waveguides, spectrometers [13; 14], and modulators for lock-in detection [15; 16]. Moreover, in order to reach higher MIDIR wavelengths, various photonic platforms were developed, such as III-V materials [17; 18; 19], chalcogenide [20; 21; 22; 23], and silicon and silicon-compatible materials [24; 25; 26; 27; 28; 29; 30; 31; 32; 33]. MIDIR photonic integrated circuits leveraging the mature Si technology have great potential for low-power consumption and low-cost systems that are meant to outperform existing technologies. Among the available group IV-compatible MIDIR platforms, silicon germanium (SiGe), and more specifically, Ge-rich SiGe alloys exhibit a compelling combination of flexible material tunability [34], large transparency, wideband operation [35; 36; 37], and remarkable nonlinear properties [40]. Here, we study the use of the Ge-rich SiGe platform to develop wideband and polarization-independent MIDIR components for free-space communications.  
Earth atmosphere's absorption spectrum contains two transparency windows in the MIDIR region that are very interesting for free-space communications. These two MIDIR windows, which lie within the 3-5 \(\upmu\)m (mid-wavelength IR, MWIR) and 8-14 \(\upmu\)m (long-wavelength IR, LWIR) wavelength ranges, present two major advantages compared to their near-infrared (NIR) counterparts, namely (i) reduced Rayleigh and Mie scattering [41; 42], and (ii) improved robustness against spectral radiance from the main sources of background noise in free-space optical communications (moon, sun, earth, and city lights) [41; 42]. As light arrives at the receiver point with an unknown polarization state [43; 44], we propose the development of polarization-insensitive photonic circuits for information processing. Main geometric parameters of Ge-rich SiGe waveguides were optimized to yield wideband polarization-independent behavior within both atmospheric transparency windows. The difference between the effective indexes of the fundamental transverse electric (TE) mode and the fundamental transverse magnetic (TM) mode was kept below 2 \(\times\) 10\({}^{-4}\), which enabled the implementation of polarization-insensitive devices and circuits. Moreover, this wideband operation allows, for example, transmitting a large number of communication channels, each carrying information from a directly modulated MIDIR quantum cascade laser (QCL) [45]. In addition, a wideband and polarization-insensitive Ge-rich SiGe multimode interference structure (MMI) was optimized to operate in the second atmospheric transparency window. The operational \(-\)1 dB bandwidth for the designed MMI extends across a wavelength of 7.5 \(\upmu\)m to 12.65 \(\upmu\)m. These basic building blocks pave the way for the development of polarization-insensitive MIDIR photonic components in on-chip transceivers for free-space communications.