Book contents
- Frontmatter
- Contents
- Preface
- 1 Critical effects in semiclassical scattering
- 2 Diffraction and Coronae
- 3 The rainbow
- 4 The glory
- 5 Mie solution and resonances
- 6 Complex angular momentum
- 7 Scattering by an impenetrable sphere
- 8 Diffraction as tunneling
- 9 The Debye expansion
- 10 Theory of the rainbow
- 11 Theory of the glory
- 12 Near-critical scattering
- 13 Average cross sections
- 14 Orbiting and resonances
- 15 Macroscopic applications
- 16 Applications to atomic, nuclear and particle physics
- References
- Index
12 - Near-critical scattering
Published online by Cambridge University Press: 02 December 2009
- Frontmatter
- Contents
- Preface
- 1 Critical effects in semiclassical scattering
- 2 Diffraction and Coronae
- 3 The rainbow
- 4 The glory
- 5 Mie solution and resonances
- 6 Complex angular momentum
- 7 Scattering by an impenetrable sphere
- 8 Diffraction as tunneling
- 9 The Debye expansion
- 10 Theory of the rainbow
- 11 Theory of the glory
- 12 Near-critical scattering
- 13 Average cross sections
- 14 Orbiting and resonances
- 15 Macroscopic applications
- 16 Applications to atomic, nuclear and particle physics
- References
- Index
Summary
For the Light which falls upon the Farther Surface of the first Glass where the interval between the Glasses is not above the ten hundred thousandth part of an Inch will go through that Surface, and through the Air or Vacuum between the Glasses, and enter into the second Glass
(Newton 1704, Query 29)In Chapters 9 to 11, the discussion of Mie scattering was restricted to N > 1. We now consider a new type of semiclassical diffraction effect, not included in the classification given in Chapter 1, that takes place, for N < 1, near the critical angle for total reflection. It occurs, for example, in the scattering of light by air bubbles in water.
In the geometrical-optic limit, the new effect, near-critical scattering, does not correspond to a caustic singularity in the light intensity, which remains continuous: there is a limiting singularity, but only in the gradient of the intensity. We refer to it as a weak caustic.
The penetration of light incident beyond the critical angle into the optically rarer medium is the earliest example of tunneling in physics. It was discovered, amazingly enough, by Newton, who observed frustrated total reflection in his experiments on Newton's rings (see the above quotation).
According to Newton's ideas, a light ray would follow a parabolic path within the rarer medium before returning to the denser one. This would produce a lateral displacement of the reflected beam. Although our views about paths differ from Newton's, the displacement does exist: it is known as the Goos–Hänchen shift (Goos & Hänchen 1947). In near-critical scattering from a curved interface, it is modified by the dynamical effects of curvature.
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- Diffraction Effects in Semiclassical Scattering , pp. 143 - 163Publisher: Cambridge University PressPrint publication year: 1992