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Electromagnetic and Optical Pulse Propagation

Part of the book series: Springer Series in Optical Sciences ((SSOS,volume 225))

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Abstract

Although the complete mathematical description of ultra-wideband dispersive pulse propagation can be rather involved, its physical interpretation is really rather straightforward.

“When you present a result that is new and unique, your critics first tell you that you must be wrong. When you persist and prove them wrong, they tell you that they knew the result all along. And finally, they tell you that the result is trivial”, as related to me by Emil Wolf.

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Notes

  1. 1.

    This is a variation of the following quote attributed to Schopenhauer: “Every problem passes through three stages on the way to acceptance: First, it appears laughable; second, it is fought against; third, it is considered self-evident.”

  2. 2.

    Being involved with both panels in the role of explaining the origin and physical properties of precursor fields, it was surprising to be called upon to defend both electromagnetic and linear system theory at a meeting with the second review panel.

  3. 3.

    The angle brackets 〈∗〉 denote a spatial average of the quantity ∗ over a macroscopically small but microscopically large region of space (see Sect. 4.1.1).

  4. 4.

    The group velocity v g(ω c) at this angular frequency value is, to a very good approximation, equal to the speed of light c (see Fig. 15.9), whereas both the energy velocity v E(ω c) and signal velocity v c(ω c) are both near to their respective minimum values (see Fig. 15.3).

  5. 5.

    The decibel equivalent net heat density is given by \(10\log _{10}\left (\mathcal {W}_{3D}(z)\right )\) with units of dBJ/m3.

  6. 6.

    There isn’t any pole contribution for a gaussian envelope pulse whose dynamical evolution is described completely by the precursor fields.

  7. 7.

    Here a t = 0 because incidence is on the optically denser medium (\(n_2^{\prime }(\omega ) > 1\)) for below resonance carrier frequencies when medium 2 is a single resonance Lorentz model dielectric as considered here. Special care must be taken for frequencies above resonance because \( 0 < n_2^{\prime }(\omega ) < 1\) so that, even though incidence is from vacuum (\(n_1^{\prime } = 1\)), medium 2 appears to be optically rarer.

  8. 8.

    The classic textbook analysis presented in Sect. 9.10 of Stratton [13] erroneously includes this \(e^{ik_2\varDelta z}\) propagation factor. Quite unfortunately, this error has been propagated through the published literature. As stated by Canning [58] “This is not done to single out Stratton. The error that we point out is ubiquitous in the Electromagnetic and Acoustics literature.” Nevertheless, the remainder of the analysis presented in Sect. 9.10 of Stratton is correct with the omission of this factor.

  9. 9.

    Notice that all equations and units of measurement in this section are in the MKSA system of units.

  10. 10.

    By a panel convened by the National Institute of Environmental Health Sciences’ (NIEHS) National Technology Program (NTP) of the US National Institutes of Health (NIH).

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  1. College of Engineering and Mathematical Sciences, University of Vermont, Burlington, VT, USA

    Kurt E. Oughstun

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Oughstun, K.E. (2019). Applications. In: Electromagnetic and Optical Pulse Propagation . Springer Series in Optical Sciences, vol 225. Springer, Cham. https://doi.org/10.1007/978-3-030-20692-5_8

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