<p dir="ltr">The objective of this research is to advance the development and application of laser diagnostics in gas phase medium, which ranges from atmospheric non-reacting flows to turbulent reacting flows in high-pressure, high-temperature environments. Laser diagnostic techniques are powerful tools for non-intrusive and in-situ measurements of important chemical parameters, such as temperature, pressure, and species mole fractions, in harsh environments. These measurements significantly advance the knowledge across various research disciplines, such as combustion dynamics, chemical kinetics, and molecular spectroscopy. In this thesis, detailed theoretical models and experimental analysis are presented for three different techniques: 1. Chirped-probe-pulse femtosecond coherent anti-Stokes Raman scattering (CPP fs CARS); 2. Two-color polarization spectroscopy (TCPS); 3. Ultrafast-laser-absorption-spectroscopy (ULAS). The first chapter provides a brief survey of laser diagnostics, including both linear and nonlinear methods. The motivations behind the three studies covered in this dissertation are also discussed. </p><p dir="ltr">In the second chapter, single-shot CPP fs CARS thermometry is developed for the hydrogen molecule at 5 kHz. The results are divided into two parts. The first part concentrates on the development of H₂ CPP fs CARS thermometry for high-pressure and high-temperature conditions. The second part demonstrates the application of H₂ CPP fs CARS in a model rocket combustor at pressures up to 70 bar. In the first part, H₂ fs CARS thermometry was performed in Hencken burner flames up to 2300 K, as well as in a heated gas-cell at temperatures up to 1000 K. It was observed that the H₂ fs CARS spectra are highly sensitive to the pump and Stokes chirp. Chirp typically originates from optical components such as windows and polarizers. As a result, the pump delay is modeled to provide a shift to the Raman excitation efficiency curve. With the updated theoretical model, excellent agreement was found between the simulated and experimental spectra. The averaged error and precision are 2.8% and 2.3%, respectively. In addition, the spectral phase and pump delay determined from the experimental spectra closely align with the theoretical predictions. It is also found that pressure does not have significant effects on the H₂ fs CARS spectra up to 50 bar at 1000 K. The collision model provides excellent agreement with the experiment. This allows the use of low-pressure laser parameters for high-pressure thermometry measurements. In the second part, spatially resolved H₂ temperature was measured in a rocket chamber at pressures up to 70 bar. This is the first demonstration of fs CARS thermometry inside a high-pressure rocket combustor. These results highlight the potential of using H₂ CPP fs CARS thermometry to provide quantitative data in high-pressure experiments for the study of combustion dynamics and model validation efforts at application relevant operating conditions.</p><p dir="ltr">The third chapter presents the development of a TCPS system for the study of the NO (<i>A</i>²Σ⁺-<i>X</i>²Π) state-to-state collision dynamics with He, Ar, and N₂. Two sets of TCPS spectra for 1% NO, diluted in different buffer gases at 295 K and 1 atm, were obtained with the pump beam tuned to the R₁₁(11.5) and ^OP₁₂(1.5) transitions. The probe was scanned while the pump beam was tuned to the line center. Collision induced transitions were observed in the spectra as the probe scanned over transitions that were not coupled with the pump frequency. The strength and structure of the collision induced transitions in the TCPS spectra were compared between the three colliding partners. Theoretical TCPS spectra, calculated by solving the density matrix formulation of the time-dependent Schrödinger wave equation, were compared with the experimental spectra. A collision model based on the modified exponential-gap law was used to model the rotational level-to-rotational level collision dynamics. An unique aspect of this work is that the collisional transfer from an initial to a final Zeeman state was modeled based on the difference in the cosine of the rotational quantum number <i>J</i> projection angle with the z-axis for the two Zeeman states. Rotational energy transfer rates and Zeeman state collisional dynamics were varied to obtain good agreement between theory and experiment for the two different TCPS pump transitions and for the three different buffer gases. One key finding, in agreement with quasi-classical trajectory calculations, is that the spin-rotation changing transition rate in the <i>A</i>²Σ⁺ level of NO is almost zero for rotational quantum numbers ≥ 8. It was necessary to set this rate to near zero to obtain agreement with the TCPS spectra. </p><p dir="ltr">The fourth chapter presents the development and application of a broadband ULAS technique operating in the mid-infrared for simultaneous measurements of temperature, methane (CH₄), and propane (C₃H₈) mole fractions. Single-shot measurements targeting the C-H stretch fundamental vibration bands of CH₄ and C₃H₈ near 3.3 μm were acquired in both a heated gas cell up to ~650 K and laminar diffusion flames at 5 kHz. The average temperature error is 0.6%. The average species mole fraction error are 5.4% for CH₄, and 9.9% for C₃H₈. This demonstrates that ULAS is capable of providing high-fidelity hydrocarbon-based thermometry and simultaneous measurements of both large and small hydrocarbons in combustion gases. </p>