1. 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

2. 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

3. 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

4. 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

5. 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
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Argonne National Laboratory

6. 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
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i+1
i+2 x
Argonne National Laboratory

7. 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

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

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

10. 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

11. 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

12. 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