FDTD Modeling of FID Signal in Chirped-Pulse Millimeter Wave Spectroscopy Alexander Heifetz1, Sasan Bakhtiari1, Hual-Teh Chien1, Stephen Gray1, Kirill Prozument1, and Richard M. Williams2 1Argonne National Laboratory 2Pacific Northwest National Laboratory 71st International Symposium on Molecular Spectroscopy

Outline Motivation Approach Preliminary conclusions Developing room temperature chemical sensor of trace gases using chirped-pulse millimeter wave (CPMMW) technique Exploring strategies to improve sensitivity of free induction decay (FID) signal Approach Developed computational electrodynamics model of CPMMW using finite-difference time-domain (FDTD) method Wrote 1-D MATLAB code and performed preliminary computer simulations on a small grid Studied electromagnetic power flow in gas cell Preliminary conclusions FID emission collinear with incident pulse Nuclear Engineering Division, Argonne National Laboratory

Gas Sensing Using CPMMW Rotational Spectroscopy Principles CPMMW technique based on measuring free induction decay (FID) signal following passage of broadband pulse Advantages High specificity because of narrow linewidth at low pressure and room temperature Enables background-free measurement FID and incident pulse time-resolved FID signal can be amplified with LNA independently of incident pulse Zero-mean noise removed by averaging Challenges Sensitivity of CPMMW should be improved Argonne National Laboratory

Motivation for Computational Electrodynamics Model Development Develop computational platform for signal sensitivity analysis Specific questions in this study Detection efficiency of FID measurement in forward direction Collect all emitted electromagnetic signals? Spatially resolve FID and incident pulse Detect FID in backscattering configuration? Conventional Transmission Geometry Design Hypothetical Backscattering Geometry Design Nuclear Engineering Division, Argonne National Laboatory

Computational Electrodynamics Approach Electromagnetic fields in gas cell modeled by solving Maxwell’s equations in 1-D grid using finite-difference time domain (FDTD) method Model interaction of molecules with electromagnetic field using density matrix (DM) formulation for two-level system Enters Maxwell’s equations through induced polarization term Concurrently solve Maxwell’s equations with auxiliary DM equations |a> |b> Argonne National Laboratory

Comparison to Past Work Previous Work Our Approach Model entire molecular ensemble in gas cell with one two level system No electromagnetic field phase information Analytical solution: J.C. McGurk, T.G. Schmalz, and W.H. Flygare, “Fast passage in rotational spectroscopy: Theory and experiment,” J. Chem. Phys. 60 (11), 4181 (1974). Numerical FDTD solution: R.W. Ziolkowski, J.M. Arnold, D.M. Gogny, “Ultrafast pulse interaction with two-level atoms,” Phys. Rev. A 52(4), 3082 (1995). Model gas cell as collection of independent two-level systems Introduce electromagnetic field phase information Equivalent to line of resonant dipoles |a> |b> |a> |b> Δx i i+1 i+2   x Argonne National Laboratory

Numerical Implementation Wrote 1-D FDTD code in MATLAB Each two-level system at every grid point solved independently by calling MATLAB ODE45 routine Discretization in space and time related as Δx=cΔt Performed numerical simulations on small grid Grid consists of approximately 100 points ( 1.5cm physical length) Open boundary conditions Δx i i+1 i+2   x Nuclear Engineering Division, Argonne National Laboatory

Preliminary FDD Simulation Results Incident linearly frequency-chirped pulse 100ns duration, 4GHz bandwidth Time domain Frequency domain. Argonne National Laboratory

Preliminary FDTD Simulation Results Calculated FID pulse Molecular resonant absorption/emission frequency of 50GHz Time domain Frequency domain. Argonne National Laboratory

Preliminary FDTD Simulation Results Electromagnetic field phasors inside the gas cell Electric field increases linearly inside gas cell Oscillations could be physical (standing waves) or unphysical (numerical errors) - TBD All FID signal power flows in forward direction Consistent with observation of no back-propagating FID signal in experiments Argonne National Laboratory

Analytical Explanation of FDTD Simulations Consider constructive/destructive interference of signals due to each resonant dipole In 1-D, each dipole radiates isotopically in +x (φ+=ωt – kx) and –x (φ-=ωt + kx) directions Example: FID signals due to dipoles i and i+1 In +x direction, Δφ =0, phase of each dipole is the same as the phase of the excitation pulse In –x direction, Δφ=ωΔt Δx i i+1 i+2   x Nuclear Engineering Division, Argonne National Laboatory

Conclusion Developed computational electrodynamics model of CPMMW using FDTD method Wrote 1-D MATLAB code and performed computer simulations on a small grid Results indicate all FID signal power flow is in forward direction Consistent with observation of no back-propagating FID signal in experiments Strategies for numerical optimization to expedite calculations and model larger geometries under investigation Argonne National Laboratory