## 2 CLaDS Basic Operation Principles  
When the frequency of an electromagnetic wave coincides with a resonance of the irradiated medium (e.g., rotational, vibrational or electronic) absorption and dispersion of the transmitted light wave occurs. The amount of dispersion (measured as a change in refractive index per unit frequency) is proportional to the concentration of the absorbing species, thus it can be used for quantitative concentration measurements. Attempts to use refractive index measurements for molecular detection had already been made in 1902 [10], but only a few techniques have been implemented to-date for trace gas detection [11, 12, 13], and none of them is suitable for remote sensing. In contrast, the ClaDS technique is a promising dispersion-based method that can be used in a remote-sensing configuration and may become an attractive alternative to absorption-based techniques that rely on the Beer-Lambert law. The theory of CLaDS has been discussed in detail in Refs. [9, 14]. Here we provide only the necessary details needed for a self-contained description. A schematic diagram of the mid-IR CLaDS setup based on a distributed feedback (DFB) quantum cascade laser (QCL) is shown in Figure 1. In general, the output radiation from a frequency-chirped single-mode laser is directed through an optical frequency shifter (e.g., acousto-optical modulator-AOM). Electrically pumped semiconductor laser sources, especially QCLs operating in the mid-IR, are particularly suitable for this application due to their flexibility and convenience in terms of laser frequency modulation and control. However, any other single-mode laser source that allows for controlled frequency chirping can be used in CLaDS. Both the fundamental and the frequency shifted wave are combined into a single dual-frequency laser beam (in case of the AOM shifter the Mach-Zehnder interferometer arrangement is used). The dual-frequency beam is sent through a gas sample and is focused onto a fast photodetector that extracts the heterodyne beat-note between both frequency components. When the dual-frequency beam interacts with a molecular transition both wavelengths experience slightly different refractive indices. As the laser is frequency-chirped, the difference in propagation velocities impacts the instantaneous frequency difference between the two optical waves, and this effect (that is proportional to the chirp rate) can be directly measured as an instantaneous frequency of the heterodyne beat-note signal. This signal enhancement due to the frequency chirp rate is central to the concept of CLaDS signal generation [9]. The dispersion spectrum is obtained through frequency demodulation of the heterodyne beat-note and the molecular concentration can be retrieved through spectroscopic modeling based on parameters available from spectral databases or by using prior calibration of the system with reference gases. In this basic arrangement (as shown in Figure 1) by applying appropriate modulation to the laser injection current a linear chirp across the target molecular transition can be obtained and the dispersion spectrum is directly recorded using FM-demodulation of the heterodyne signal [9]. Such a configuration and data processing is defined as direct CLaDS. The most significant advantage of the CLaDS technique over a conventional absorption based measurement is the immunity of the molecular dispersion measurement (performed in the frequency domain) to fluctuations of the received optical power. As a consequence, the large baseline that is typically observed in DLAS is not present in CLaDS. Due to exponential character of the Beer-Lambert law, the non-linear dependence of the absorption on sample concentration represents another important drawback of DLAS, especially for samples with absorption larger than 10%. In contrast, the dispersion signal increases linearly withconcentration, resulting in an extended dynamic range for concentration measurements [15] that also allows for longer optical distances to be used in path-integrated molecular studies.