# Evanescent waves

Two different evanescent wave theories have been proposed at NSF, one for evanescent waves leaking to the exterior of the EM Drive and one for evanescent waves strictly confined to its interior:

@Aero first proposed that evanescent waves *leaked* from the interior of the EM Drive through small gaps and produced an *external* evanescent wave near-field. @Aero studied (with a MEEP 2-D model) the interaction of these evanescent waves with the environment around the EM Drive, for example the stainless steel vacuum chamber at NASA Eagleworks. Shortly after this, Paul March reported at NSF conducting a test at NASA Eagleworks with the EM Drive outside the stainless steel vacuum chamber that exhibited measured thrust and thus may have nullified this hypothesis (several tests conducted by R. Shawyer and by Prof. Juan Yang may have also been conducted in environments were such interaction may have been nullified). @Aero also proposed another hypothesis involving evanescent waves and tachyons (hypothetical particles travelling faster than photons).

Later Desiato (@WarpTech) and Rodal proposed at the NSF forum that the EmDrive's tapered conical design causes a gradient in the electromagnetic field such that travelling waves (from the RF source) propagating towards the small end of the truncated cone are attenuated by the tapering geometry, producing evanescent waves that carry momentum. The EM Drive must then accelerate to satisfy conservation of momentum. The standing waves inside the EM Drive (responsible for the high Q resonance) are comprised of travelling waves propagating in opposite directions. (How the evanescent waves travelling toward the small end may benefit from the high Q stored energy density from the standing waves remains to be analyzed.) ^{[1]}

## Status

## Numerical Analysis

@Aero performed calculations for evanescent waves leaking from the EM Drive and producing an external near-field. He used a two-dimensional MEEP Finite Difference model that modeled the EM Drive truncated cone as a flat trapezium. Maxwell's equations were solved in the 2-D domain, thus the transverse electromagnetic vector could only be represented as a scalar. The 2-D model was due to the enormous amount of memory and computer time required by the Finite Difference method, which made a 3-D model in a home PC impractical. The results from the 2-D analysis showed a thrust force/input-power multiple of 2-3 times that of a perfectly collimated photon drive, which is significantly beneath the reported measurements of EM Drive by NASA Eagleworks, Shawyer's SPR and Prof. Juan Yang's team at NWPU.^{[2]}

Utilizing MEEP 2-D model, the conclusion was that due to rapid dropoff at the frustum surface, evanescent waves were of insufficient magnitude to explain the observed thrust.^{[3]}. See details about @aero's MEEP control file.

## Relevant Papers

- "Electromagnetic fields and transmission properties in tapered hollow metallic waveguides" by Xiahui Zeng and Dianyuan Fan. Optics Express Vol. 17, Issue 1, pp. 34-45 (2009) •doi: 10.1364/OE.17.000034
- "Extraordinary momentum and spin in evanescent waves" by Konstantin Y. Bliokh, Aleksandr Y. Bekshaev, and Franco Nori - See Supplementary Table 1.
- https://en.wikipedia.org/wiki/Mie_scattering
- http://thermopedia.com/content/137/
- http://www.orc.soton.ac.uk/publications/theses/1460T_lnn/1460T_lnn_03.pdf
- "Superluminal propagation of evanescent modes as a quantum effect" by Zhi-Yong Wang, Cai-Dong Xiong, Bing He.
- http://wwwsis.lnf.infn.it/pub/INFN-FM-00-04.pdf - I like Appendix B
- http://arxiv.org/pdf/1211.0530v2.pdf - This one just hints at our situation.
- http://bit.ly/1Ja6QLV - Again, hints
- http://tuttle.merc.iastate.edu/ee439/topics/tunneling.pdf - Tunneling and evanescent wave math are very similar.
- http://en.wikipedia.org/wiki/Maxwell_stress_tensor - Not quite sure why this is here, maybe the stress-energy tensor derivation?