Nonlinear Metamaterials in HPM Applications

Transcription

1 Nonlinear Metamaterials in HPM Applications Hamide Seidfaraji, Mehmet Fatih Su, Christos Christodoulou University of New Mexico 1 MURI TELECON August 2nd, 2013

2 What is this about? Our consortium members are studying the use of passive metamaterial structures to engineer dispersion relations useful for traveling wave tube (TWT) and other beam- wave interactions. We are investigating the use of nonlinear elements, varactors in particular, in order to make such passive structures more frequency agile. This presentation discusses the challenges of simulating such active structures and suggests applications in high power microwave sources where such structures might be used in the future. 2

3 What is this about? There are many good ideas for mi ga ng shortcomings of metamaterials and improving their u lity: Increase bandwidth of opera on (metamaterials normally operate within narrow- band resonances) Make structure recon igurable, tunable Develop methods to approximate metamaterials as homogenized media HPM environments are different: Electric ield, mechanical, and heat stresses might become an issue; the structure might break down partially or resonant frequencies might shift Wideband designs might not work as intended for the same reason Recon igurable systems might not work as intended for slightly different reasons Must be careful with models: underlying approximations, small- signal models, series expansions, etc. might become invalid 3

4 Wideband, Recon igurable Metamaterials The good: 50% bandwidth improvement with fractal SRR pattern The bad: Will this work in a HPM environment? [T. M. De la Mata Luque, N. R. Devarapalli, C. G. Christodoulou, PIER, vol. 131, pp , 2012] 4

5 Wideband, Recon igurable Metamaterials [T. M. De la Mata Luque, N. R. Devarapalli, C. G. Christodoulou, PIER, vol. 131, pp , 2012] The good: Reconfigurable system via switches The bad: Will this work in a HPM environment? 5

6 Tunable Metamaterials [B. Arritt, B. Adomanis, T. Khraishi, and D. Smith, Appl. Phys. Lett., 97, , 2010] 6 The good: System is reconfigurable via mechanical strain The bad: Can change resonance frequency arbitrarily in a HPM environment

7 What is this about? There are many good ideas for mi ga ng shortcomings of metamaterials and improving their u lity: Increase bandwidth of opera on (metamaterials normally operate within narrow- band resonances) Make structure recon igurable, tunable Develop methods to approximate metamaterials as homogenized media HPM environments are different: Electric ield, mechanical, and heat stresses might become an issue; the structure might break down partially or resonant frequencies might shift Wideband designs might not work as intended for the same reason Recon igurable systems might not work as intended for slightly different reasons Must be careful with models: underlying approximations, small- signal models, series expansions, etc. might become invalid 7

8 What is this about? We need to ü understand better how to simulate HPM environments (dielectric breakdown, etc.) ü develop a better design and optimization work low to produce metamaterials suitable for HPM environments We will start with the basics and simpler proof of concept works We will use a two- prong approach Study nonlinear metamaterials that can respond to various stimuli (improve frequency agility) Study simulation of HPM environments (both full- wave and approximate) 8

9 Metamaterial Example: Split Ring Resonator Structural parameters, d=t=0.2 mm, w=0.9 mm, R=3.6 mm. 9

10 Varactor- Loaded Split- Ring Resonator Inserting a varactor onto a ring gap or between two SRR rings provides for nonlinear behavior Normally one would put the varactor as a lumped element CST MWS does not support varactors natively as lumped elements Must use equivalent circuit model shown on the right Then we change power, see how varactor changes things The circuit can be barely simulated with CST lumped elements. CST diode model is oversimpli ied and might not provide a useful approximation. 10

11 Where do I put them? Loaded waveguides (inside or on the wall) Phase shifters, antennas Varactor/nonlinear element stays outside if possible TWTs loaded on the inside or outside of permanent magnets Varactor /nonlinear element stays outside if possible 11

12 Varactor Capacitance vs. Voltage 12

13 CST Simulation Issues We are interested in an in initely periodic array of loaded SRR elements. At irst we are willing to try steady state continuous or pulse excitations. Steady state continuous excitation is easy to do with CST MWS ü Use periodic (unit cell) boundaries, frequency domain solver ü Fast calculation, excellent convergence BUT frequency- domain solver cannot be used with nonlinear elements in play MUST use time- domain solver to accommodate varactor (in the form of an equivalent circuit lumped element) Periodic boundaries cannot be used Slow (or no) convergence MUST use supercell of SRRs to approximate in initely periodic structure with time- domain solver 13

14 More CST Simulation Issues The easiest way to igure out how the loaded SRR behaves is to check out the S- parameters Designate two waveguide ports, simulate (that was easy!) BUT S- parameter calculations with the default excitation source are normalized to 1 watt Can change source wave power by switching to a plane wave source Waveguide ports become useless MUST calculate re lection/transmission coef icients on our own Makes for tedious process How about changing the source pulse? One of the CST MWS pulse types has an amplitude term in the formula Otherwise, one can just write a custom function with the VBA editor Be careful, now the simulation ends at the end of source excitation duration 14

15 Double Exponential Excitation Simulate a 10x9 2- D SRR in time domain and compare the results with frequency domain solver (after de ining new excitation signal which is not normalized in either case) 15

16 Time- Domain vs. Frequency- Domain 10 0 (SRR loaded with 2.12 pf capacitance) Not in agreement SRR Resonance Frequency (Not in agreement) in the same senario Frequency Solver Time Domain Solver -10 S 11 (db) Frequency (GHz) 16

17 Resonant Frequency Changes with loaded SRRs in Outer Ring S 11 (db) C=0.63pF C=0.95pF C=1.25pF C=1.44pF C=1.70pF C=2.12pF C=2.67pF No Load No Load Frequency (GHz) 17

18 Inner Ring Loaded SRRs S C=0.63pF C=0.95pF C=1.25pF C=1.44pF C=1.70pF C=2.12pF C=2.67pF No Load Frequency (GHz) 18

19 It is clear that the effect of the capacitance in the inner split region is less than that of the outer split region Frequency (GHz) Inner Split Outer Split Capacitance (pf) 19

20 EMTL In this project we are interested in: Inves ga ng how to simulate various HPM- related phenomena (dielectric breakdown, large- signal modeling of lumped elements) Modeling nonlinear effects that change loaded metamaterial behavior Validate effective medium methods for HPM Validate metamaterials designed for HPM applications Need a more sophisticated tool to model all these aspects We have considered CST MWS, HFSS, MEEP, Angora FDTD, OpenEMS before settling on EMTL. 20

21 EMTL EMTL is a С++ library for programming Finite- Difference Time- Domain (FDTD) simula ons. Applica ons Photonic crystals, op cal filters, an reflec ve coa ngs; Waveguides and resonant cavi es; Design of electronic devices, including nanosized devices; Antennas and mobile phone design, etc. EMTL is in the process of becoming open source so ware. All contribu ons we provide will be published. 21

22 Conclusions and Next Steps We have discussed metamaterials with nonlinear elements and the challenges of simula ng such metamaterials. Next steps: Implement variable mesh size in EMTL (for more efficient simula on) Implement varactor model in EMTL or integrate with SPICE Validate effec ve medium approxima on in literature with full- wave nonlinear metamaterial models More to come 22

23 Thank You! Questions? 23

24 Backup Slides 24

25 Varactor Need to provide a model of the varactor in FDTD simula on. A Varactor diode is a P- N junc on diode that changes its capacitance and the series resistance as the bias applied to the diode is varied. diode is represented by a parallel nonlinear conductance G(V )and nonlinear capacitance C(V). where the charge accumulated by the varactor capacitance is And diode current is from Shockley ideal diode equa on or the diode law: VT is the thermal voltage, I S is the reverse bias satura on current and η is quality factor of the diode. where M (The slope of the log C vs. log V curve), C0(capacitance with no applied voltage) and Vf (built- in poten al) are available from the diode specifica on, 25