G. Millot

Study of collisional effects on band shapes of the ν1/2ν2 Fermi dyad in CO2 gas with stimulated Raman spectroscopy. I. Rotational and vibrational relaxation in the 2ν2 band

The 2ν2 component of the Fermi dyad ν1/2ν2 of CO2 has been studied with high‐resolution stimulated Raman spectroscopy (SRS). The behavior of the band shape has been explored in a large density range: 0.2 to 50 amagat at a temperature of 295 K and 0.5 to 20 amagat at 500 K. Energy corrected sudden (ECS) and modified energy gap (MEG) laws are used to model the relaxation matrix in order to account for the collisional narrowing induced by rotational energy transfers. ECS model allows us to accurately determine the vibrational shift and width as a function of density by fitting the experimental spectra, leading to the determination of the vibrational relaxation coefficients for the 2ν2 mode. Connection is established between the present calculations of the collisionally narrowed SRS spectra based on the diagonalization of the relaxation matrix, which applies for any line overlap, and the usual spectral line shape for weak line coupling. Particular emphasis is put on the situation of strong collapse and on the...

Collisional effects in the stimulated Raman Q branch of O2 and O2–N2

The fundamental isotropic Raman Q branch of oxygen at pressures up to 2 atm and for temperatures between 295 and 1350 K has been recorded using stimulated Raman gain spectroscopy (SRGS) for collisions with oxygen and nitrogen. The line broadening and line shifting coefficients have been determined for several rotational quantum numbers (up to N=55 at 1350 K). The temperature dependence of these coefficients has also been studied for most of the rotational lines. The line parameters (widths and shifts) have been then calculated a priori through a semiclassical model. A good agreement between experimental and theoretical data has been observed. Another theoretical approach based on fitting and scaling law has been used to calculate the line broadening coefficients. It is shown that a modified exponential energy gap model (MEG) and an energy corrected sudden law (ECS) for the state‐to‐state rotationally inelastic rates, account for the rotational and temperature dependences of the observed linewidths. With r...

High-resolution stimulated Raman spectroscopy of O2

Abstract The S S and O O branches of the fundamental vibrational band of molecular oxygen in its electronic ground state have been resolved for the first time in Raman spectroscopy. The spectra have been observed, at room temperature and low pressure, with a stimulated Raman scattering (S.R.S.) spectrometer including a multipass cell. From these accurate Raman data combined with microwave data, we have improved the values of the vibrational, rotational, spin-spin, and spin-rotation interactions constants in the v = 1 vibrational state. Moreover, Raman Q branches of the first and second hot-bands have been recorded, allowing us to determine a set of molecular parameters for the v = 2 and v = 3 states, useful for Coherent Anti-Stokes Raman Spectroscopy (C.A.R.S.) diagnostics in combustion media.

Study of rotational relaxation fitting laws from calculations of SRS N2 Q-branch

Abstract Modified polynomial energy gap law (PEGL) and exponential energy gap law (EGL) have been fitted on a set of line broadening coefficients. This set of values has been recently obtained by high-resolution inverse Raman spectroscopy and covers a wide temperature range and a great number of Q( J ) rotational lines. A consistent description of the J and temperature dependences of linewidth is obtained from the two considered laws. These laws together with the general expression of the SRS profile permit a predictive synthetization of the collisionally narrowed Q-branch for pressures up to 35 atm. An excellent reproduction of the observed spectra is evidenced by using the EGL model if the collisional lineshifts of the Q( J ) components are accounted for. This model is applicable to high temperature, the simulation of SRS or CARS spectra requiring only the knowledge of the lineshifts temperature dependence.

A rotational thermalization model for the calculation of collisionally narrowed isotropic raman scattering spectra - application to the SRS N2 Q-branch

Abstract A model for the calculation of collisionally narrowed isotropic. Raman scattering spectra is proposed. In this model, the rotational transition probabilities are calculated within the strong collision approximation, allowing the rotational energy transfer rates to be expressed in terms of the sole individual Q( J ) line broadening coefficients. These transfer rates satisfy both detailed balance principle and unitarity of the scattering matrix in contrast with most of the previous approaches. Under further approximation concerning the rotational distribution of the collisional frequency, simpler expressions for transfer rates are deduced, which do not satisfy necessarily both unitarily and detailed balance. A simple analytical expression for the Q-branch profile is then obtained. An experimental study of the isotropic Q-branch for N 2 as a function of pressure has been conducted at room temperature by stimulated Raman spectroscopy (SRS). The Q-branch profiles calculated from the present model show a good agreement with SRS experiments, in particular when the lines overlap and when collisional narrowing takes place. This agreement is quite similar to that obtained by using a polynomial inverse energy gap law to describe the rotational energy transfer rates, and the results of these two models are closer for higher temperatures. The simple analytical expression mentioned above for the Q-branch profile, which is inaccurate at room temperature, becomes reliable at high temperature.

Study of collisional effects on band shapes of the ν1/2ν2 Fermi dyad in CO2 gas with stimulated Raman spectroscopy. II. Simultaneous line mixing and Dicke narrowing in the ν1 band

An experimental (SRS) and theoretical analysis for the ν1 component of the ν1/2ν2 Fermi dyad of CO2 has been performed for densities lying from 0.01 to 50 amagat at 295 K, and from 0.01 to 20 amagat at 500 K. At subatmospheric pressure, both line mixing and Dicke narrowing take place for this component due to the very weak Q line spacings. A simple method to account for both diffusional narrowing (due to velocity changing collisions) and collisional narrowing (due to energy transfers) on isotropic Raman Q‐branch profile is proposed. This method is based on the transformation of the collapsed Q‐branch profile as a sum of individual Lorentzian plus dispersive components whose parameters are density‐dependent. Such an exact transformation permits to easily introduce the averaging effect of velocity changing collisions on each component, and then on the collapsed Q‐branch itself. In the present study, the Galatry soft collision model is used to define a generalized complete profile for each Lorentzian plus di...

Collisional line broadening and line shifting in N2-CO2 mixture studied by inverse Raman spectroscopy

Abstract Collisional effects in the Raman Q-branch of N 2 perturbed by CO 2 have been studied by high-resolution stimulated Raman spectroscopy. The Raman spectra recorded in the 0.3–1.0 atm and 295–1000 K pressure and temperature ranges are fitted with a theoretical profile taking into account line broadening, frequency shift and line mixing due to rotational energy transfers. The data at low density are used as basic data for the modeling of rotationally inelastic rates through sets of adjustable parameters. We have used in this study the two main models developed in the last decade and known as modified exponential gap (MEG) and energy corrected sudden (ECS) laws. Experimental spectra recorded at density up to 32 amagat are compared with simulated spectra derived from both models. This constitutes a test for these models which give similar results at low density.

Rotational relaxation of nitrogen in ternary mixtures N2–CO2–H2O: Consequences in coherent anti‐Stokes Raman spectroscopy thermometry

The influence of CO2 and H2O on the rotational relaxation processes of N2 in ternary mixtures N2–CO2–H2O is investigated. The efficiency of these perturbers is responsible for significant modifications of the state‐to‐state relaxation rates and broadening coefficients. Flame data are well reproduced by taking into account these modifications. The role of these minor species in the determination of temperatures in premixed flames is analyzed. The present relaxation model allows us to understand why the discrepancy between observed and calculated coherent anti‐Stokes Raman spectroscopy (CARS) spectra in flames is sometimes resolved by empirically adding a dephasing component to pure nitrogen linewidths. Moreover, this model improves the accuracy of CARS temperature measurements.

Rotational and vibrational relaxation of the ν1/2ν2 Fermi dyad in CO2 gas from Raman‐infrared double resonance experiments

Time‐resolved Raman‐infrared double resonance experiments have been conducted on CO2 gas in order to determine collisional relaxation rates of energy levels. These total depopulation constants are measured in a three‐level double resonance scheme. A pulsed Raman excitation populates the studied state over a brief time interval (7 ns). The ensuing collisional depopulation of this level is monitored by a continuous probe CO2 laser whose transition originates in the same level. The transient absorption on the probe laser gives the time dependent population behavior. The high selectivity of the lasers allows the study of vibrational and rotational levels. The relaxation rates, of the (1000) vibrational state and, for the first time, of the J=14–34 rotational levels of the (0200) vibrational state, have been measured. The derived broadening coefficients have been compared to those calculated by a semiclassical model.

Coherent anti‐Stokes Raman spectroscopy study of collisional broadening in the O2–H2O Q branch

The fundamental isotropic Raman Q branch of oxygen perturbed by collisions with water vapor has been studied at pressures up to 1.5 atm and for temperatures between 446 and 990 K. The spectra have been recorded by using coherent anti‐Stokes Raman spectroscopy (CARS) which has been preferred to stimulated Raman spectroscopy (SRS) in order to obtain more signal and higher sensitivity as the mixture has a small percentage of oxygen. The high resolution CARS spectrometer uses a seeded Nd:YAG laser actively stabilized on an external Fabry–Perot interferometer to prevent any frequency drift during the course of the experiment. The line broadening coefficients have been determined for several rotational quantum numbers (up to N=31 at 990 K). The effect of the splitting into triplets at lower pressure and the effect of interferences between neighboring lines at higher pressure have been taken into account. The influence of Dicke narrowing has also been considered and special care has been taken to avoid Stark bro...