1. ONR AppEl @ 1 A Wave Chaos Approach to Understanding and Mitigating Directed Energy Effects Steven Anlage, Thomas Antonsen, Edward Ott

2. ONR AppEl @ 2 The Maryland Wave Chaos Group Tom AntonsenSteve Anlage Ed Ott Jen-Hao Yeh James Hart Now at Lincoln Labs Biniyam Taddese Graduate Students Ming-Jer Lee Harita Tenneti Trystan Koch Undergraduate Student Christopher Bennett Post-Doc Dr. Gabriele Gradoni 2010 URSI Young Scientist Award NRL Collaborators: Tim Andreadis, Lou Pecora, Hai Tran, Sun Hong, Zach Drikas, Jesus Gil Gil Funding: AFOSR MURI 2001; AFOSR; ONR MURI 2007; ONR AppEl

3. ONR AppEl @ 3 A Wave Chaos approach to understanding / quantifying DE Effects in electronics The model works for ‘ray-chaotic’ enclosures Two incident rays with slightly different initial directions have rapidly diverging trajectories Embrace CHAOS as the central organizing principle! Many electronic enclosures display ray chaos Computer enclosures Aircraft cockpits Ship compartments Offices etc.

4. ONR AppEl @ 4 The Random Coupling Model A quantitative model of statistical and systematic aspects of HPM effects in enclosures Statistical aspects: The underlying classical chaos means that the wave properties are ‘universal’ and governed by Random Matrix Theory (RMT) ► The statistics of all wave properties (resonant freqs., standing wave patterns, Z, Y, S, etc.) are UNIVERSAL and governed by a single loss parameter: The non-universal aspects are captured by the radiation impedance Z rad of the coupling ‘ports’ Z rad of the ports can be determined by a number of techniques, both experimental and theoretical RCM Web Site: http://www.cnam.umd.edu/anlage/RCM/index.htm

5. ONR AppEl @ 5 Effect of Direct Ray Paths Original Random Coupling Model (RCM) - RF energy is randomized on entering cavity - Only radiation impedance of ports, cavity volume and average Q are important In some geometries, or in narrow frequency bands specifics of internal geometry are important Modified Random Coupling Model - J. Hart et al., PHYSICAL REVIEW E 80, 041109 (2009) - Allows for systematic improvement by inclusion of geometric details if known - Can be used in conjunction with measured data Systematic aspects of HPM Effects Inclusion of ‘Short Orbits’ in the RCM

6. ONR AppEl @ 6 Extensions of The Random Coupling Model Systematic aspects of HPM Effects Inclusion of ‘Short Orbits’ in the RCM James Hart, T. Antonsen, E. Ott, Phys. Rev. E 80, 041109 (2009)  is a complex matrix with universal fluctuations governed by the loss parameter  f 3dB /  f ↔ ↔ ↔ ↔ ↔ ↔ ↔↔ ↔ ↔ ↔ ↔ ↔ ↔ Survival probability in the ensemble Uniform attenuation Theory work funded by AFOSR

7. ONR AppEl @ 7 Data and Theory smoothed with the same 125-cm (240 MHz window) low-pass filter Nonuniversal Properties Captured by the Extended RCM Empty Cavity Data Theory includes all orbits to 200 cm length J.-H. Yeh, et al., Phys. Rev. E 81, 025201(R) (2010); J.-H. Yeh, et al., arXiv:1006.3040 Experimental work funded by AFOSR, and now ONR/AppEl

8. ONR AppEl @ 8 Extensions of The Random Coupling Model Realistic systems consist of many coupled enclosures Can the RCM be extended to handle these situations? J. P. Parmentier (ONERA)

9. ONR AppEl @ 9 Extending the RCM to the case of Coupled Cavities The statistics of coupling are dominated by the statistics of transmission through the first cavity, scaled by the mean impedance of the next cavity Generalize to an arbitrary cascade of enclosures and treat junction topology Fluctuations in transmission through cavity 1 Mean properties of cavity 2 Cavity 1 Cavity 2 Approximations: high loss, weak transmission

10. ONR AppEl @ 10 Extending the RCM to the case of Coupled Cavities Future Work: Consider networks of coupled cavities Graph topology

11. ONR AppEl @ 11 The Statistics of Tunneling between Enclosures In some cases, two enclosures will be coupled by structures beyond cutoff Examples include metal ducts at frequencies below cutoff, intermediate rooms/compartments that are below resonance Can we use what we know about chaotic eigenfunctions to solve this problem? Does it make a difference if the enclosures are regular or chaotic? Enclosure 1Enclosure 2 Barrier Work in collaboration with Lou Pecora @ NRL Enclosure 1 Enclosure 2 Barrier Regular Enclosure case Ray Chaotic Enclosure case

12. ONR AppEl @ 12 The Statistics of Tunneling between Enclosures: The 1D Case Energy splitting  k 2 is proportional to the tunneling rate through the barrier

13. ONR AppEl @ 13 Splitting Fluctuations versus Energy These splittings, and their fluctuations, are predictable in the chaotic case Numerical simulations by Lou Pecora (NRL)

14. ONR AppEl @ 14 Results of Wave Chaos Theory The theory uses the random plane wave hypothesis to calculate the tunneling rate Sliding average of mean splittingSliding average of splitting fluctuations Black lines (Data) – simulations by Lou Pecora (NRL) Surprisingly, all three agree quite closely… Wave chaos theory in agreement with simulations

15. ONR AppEl @ 15 Ray-Chaotic Enclosure Barrier Infinite Waveguide The tunneling escape rate will vary from mode to mode, giving fluctuations in the quality factor of the modes. The mean and fluctuations of the 1/Q with k 2 should follow the wave chaos theory predictions An Experiment to Test the Wave Chaos Tunneling Theory

16. ONR AppEl @ 16 New Research and Transfer of RCM Knowledge Base to Naval Research Lab We are collaborating with the group of Tim Andreadis to test the RCM is more realistic scenarios, and to transfer our knowledge / know-how to DoD Experimental tests of the RCM in 3D enclosures Hai Tran and Zach Drikas Radiation Impedance Measurement New Antenna Configuration

17. ONR AppEl @ 17 Anlage et al. Acta Physica Polonica A 112, 569 (2007) The Electromagnetic Chaotic Time-Reversal Sensor 60ns pulse with 7GHz (λ~4cm) center frequency. Transmitted Sona Work funded by ONR MURI 2007

18. ONR AppEl @ 18 ELECTROMAGNETIC Chaotic Time-Reversal Sensor:- Injection of time reversed Sona Sensors based on time-reversed pulse reconstruction: B. T. Taddese, et al., Appl. Phys. Lett. 95, 114103 (2009) B. T. Taddese, et al., arXiv:1008.2409

19. ONR AppEl @ 19 Short Monopole Inside Electromagnetic Time-Reversal of Enclosure with Aperture Sun Hong, Zach Drikas, Hai Tran, Jesus Gil Gil, Tim Andreadis, NRL Step 1: Step 2: Port 1 Port 2 5ns

20. ONR AppEl @ 20 Conclusions The Random Coupling Model is being extended and generalized in new ways Short Orbits Connected Enclosures Electrically Large Antennas Theory and Experiment work in parallel, and stimulate each other NRL Collaboration has resulted in: New experiments and new applications for the RCM and time-reversed EM Extension of the RCM Transfer of know-how to DoD IC Post-Doc grant: Nonlinear time-reversed electromagnetics DURIP proposal: System for Investigation of Terahertz Wave Chaos Future Work: Experimental test of tunneling fluctuations Theory of multiple connected and networked enclosures Modeling and experiments of fading statistics