Transcript Document
Frontiers in Spectroscopy. Ohio State University, March 2004 From quantum mechanics to auto-mechanics Oxford Institute for Laser Science Combustion Physics and Nonlinear Optics Group Paul Ewart Phase Matching: Conservation of momentum Physics: Grating formation + Readout Calculation of the Signal intensity: ~ Field effects + Atom effects The nonlinear wave equation Phase matching geometries Counter propagating pump (Phase Conjugate) pump k1 probe k4 k3 signal k2 pump Forward Folded Boxcars Geometry Esignal Epump Eprobe Epump We need to find the Polarization induced by the incoming 3 fields The polarization induced by 2 pump and 1 probe photon is given by r21 Susceptibility for saturated absorption Note: Signal proportional To phase conjugate of probe } Solve coupled equations Note reduced sensitivity to collisions of saturated signal Calculable on PC Full spectrum in <1 minute DFWM Spectra of C2: Saturation and spectral modelling 100 80 psc = 0.2 psc = 0.4 psc = 0.5 psc = 0.2 60 40 20 Unsaturated 0 psc = 1.8 psc = 2.1 psc = 2.5 psc = 2 Saturated psc = 5.5 psc = 6.25 psc = 7 psc = 8 Strongly saturated Experiment BLE Theory Abrams & Lind DFWM Lineshapes: power broadening with pump and probe saturation Laser Induced Thermal Gratings Laser Induced Thermal Gratings •Energy per pulse •Einstein B-coefficient •Grating “wavelength” •Laser pulse shape in time •Laser pulse profile in space •Einstein A-coefficient •Quenching rate •Diffusion rate Thermal Grating evolution (Bulk gas dynamics) Density Perturbation in LITGS Non-Statonary, Acoustic Components Density Variation (1) Acoustic gratings interfering… Speed of sound Temperature 0 50 100 150 Time (ns) Acoustic Thermal Grating (2) Temperature Acoustic Envelope 200 250 300 Density Variation Stationary Component - Thermal Diffusion grating… Decay by diffusion Pressure 0 50 100 150 200 250 300 Laser Induced Thermal Grating Scattering: simulation LITGS from OH in high pressure methane/air flame Analysis of LIGS signals The LIGS signal is a convolution of several functions: Excitation by pump laser pulse l (t) Quenching rates q(t) Evolution of the stationary and acoustic gratings r(s) t is the normalized time s is the Laplace transform variable density perturbation. r(s) Fourier transformed to R(w) l (t) Fourier transformed to L(w) q(t) Fourier transformed to Q(w) LIGS signal Z(w) = product of the Fourier transforms: Z(w) = R(w) . Q(w) . L(w) … Rapid fitting of simulated LIGS signals to data using T, P as fitting variables with calculated gas dynamic parameters.