1. June 21st 2011 66 OSU Mol. Spect. Symp.TB01 8:30 a.m Model Calculations of Molecular Rapid Passage and Infrared Free Induction Decay Signals Using a Voltage Modulated Quantum Cascade Laser Geoffrey Duxbury, and Nigel Langford Department of Physics, University of Strathclyde, John Anderson Building, 107 Rottenrow, Glasgow, G4 0NG, UK g.duxbury@strath.ac.uk 1

2. June 21st 2011 Maxwell Bloch Parameters Calculation of polarization of a two level system or systems Step length 1 m, total pathlength 100 m Chirp rate and power through the cell switched at a preset offset from line centre Laser frequency scanned to higher wavenumber/cm -1 followed by a reverse scan to original starting conditions Switch S can be different for forward and reverse scan, limits S=0 FID, S=1 rapid passage, f-forward, r- reverse 66 OSU Mol. Spect. Symp.TB01 8:30 a.m 2

3. June 21st 2011 Parameters Used in Rapid Passage Calculations Scan range in units of Doppler width, D, (ubar ) Step length 1 m Cumulative polarization evaluated at each step Chirp rate and power switched at specific frequency offset from line centre Rapid sweep phase, scanned to higher frequency, followed by reverse scan to original starting conditions Power pasing through cell following switch may be varied from that in slow scan to zero. S=1 rapid passage, S=0 free induction decay 66 OSU Mol. Spect. Symp.TB01 8:30 a.m 3

4. Calculated cumulative polarization of N2O. N2O press. 1 mTorr, N2 0.5 Torr, June 21st 2011 66 OSU Mol. Spect. Symp. TB01 8:30 a.m. (a) 20 m(b) 20 m(c) 100 m 6 D below line centre (a) FID Sf=Sr=0 (b) (ii) Sf=0.2,Sr=0.1 (iii) Sf=0.2,Sr=0.0 3D below line centre The other values as (a) 3D below line centre The other values as (a ) 4

5. Calculated cumulative population change in N2O using 100 m path length. N2O press. 1 mTorr, N2 0.5 Torr, June 21st 2011 66 OSU Mol. Spect. Symp. TB01 8:30 a.m. (a)FID only (i) Sf=Sr=0 (ii) Sf=0.2, Sr=0.1 (b)FID only (i) Sf=Sr=0,(iii) Sf=0.2, Sr=0 3D below line centre The other values as earlier figures 5

6. Rapid Passage structure plotted as a function of frequency scan during the forward and reverse scans June 21st 2011 66 OSU Mol. Spect. Symp. TB01 8:30 a.m. 100 m 3D below line centre (a)FID only (i) Sf=Sr=0 (ii) Sf=0.2, Sr=0.1 (b)FID only (i) Sf=Sr=0,(iii) Sf=0.2, Sr=0 6

7. One Doppler width below line centre June 21st 2011 66 OSU Mol. Spect. Symp. TB01 8:30 a.m. 100 m (a)FID only (i) Sf=Sr=0, (ii) Sf=0.2, Sr=0.1 (b) (ii) Sf=0.2 Sr=0.1, (iii) Sf=0.2, Sr=0 7

8. Typical oscillatory structure on blue side with an initial blue scan, 100 m path length. N2O press. 1 mTorr, N2 0.5 Torr, June 21st 2011 66 OSU Mol. Spect. Symp. TB01 8:30 a.m. 1 D above line centre (a)FID (i) Sf=Sr=0 (b)(ii) Sf=0.2,Sr=0.1 (iii) Sf=0.2. Sr=0.0 (c)Central sections of (i) and (iii) enlarged, very small rapid passage signal seen in (iii) 8

9. June 21st 2011 Conclusions Two types of oscillatory structure associated with free precession can occur Free induction decay (FID) instigated by rapid turn on or turn off of the pulse Rapid passage induced signals which follow the rapid sweep through an absorption line Direction of the original chirp is away from line centre FID signals are dominant. 9

10. June 21st 2011 Acknowledgements Part of this research was performed at the W.R. Wiley Environmental Molecular Sciences Laboratory, a national user facility sponsored by the Department of Energy’s Office of Biological and Environmental Research located at the Pacific Northwest National Laboratory. Pacific Northwest National Laboratory is operated for the United States Department of Energy by Battelle under Contract DE-AC06-76RLO 1830. G. Duxbury is grateful to J.F. Kelly and T.A. Blake of the W.R. Wiley Environmental Molecular Sciences Laboratory for their initial suggestions about a joint research project, and for their help in measuring and analysing the experimental spectra of Nitrous Oxide and Nitric Oxide. This analysis led to the development of the model described in this paper. G. Duxbury would also like to thank the Leverhulme trust for the award of an Emeritus Fellowship, and the Royal Society of Edinburgh for the award of a travel grant. 1010