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Newton held the view that light has corpuscular nature, even though he was the firstone to use the superposition effects of light, known as Newton’s rings ), which he used to accurately measure the curvature of his handpolished plano-convex lens to construct his telescope. Huygens was Newton’s contemporary but steadfastly held the view that light is a wave phenomenon. Huygens
hypothesized that waves travel while generating secondary wavelets, which can be paraphrased as follows: Each displaced field point on a propagating wave front acts as if it is a new point source for a new spherical wave in an attempt to hand over the quickest way possible the state of its own displacement to all possible next contiguous points so that the displaced tension field points can return back to their original state of equilibrium. A displaced point on a medium under tension is naturally a new source point. It does return to its original state of equilibrium, but only after the
entire wave packet passes through the point under consideration. For material-based tensions fields—such as string waves due to mechanical tension on a wire, sound waves due to pressure tension of the air, water waves due to surface, and gravitational tensions of the water surface, etc.—the wave propagation can be observed as a physically moving group of wave crests and troughs. In each one of theses cases, the tension field is held by a material substrate, which is directly measurable and/or observable.
Note also that the propagating waves are simply states of excitation of
the respective tension fields. The energy is still held by the substrate. The waves are
propagating while making the energy of the local dormant tension field available
for exchange through interactions with other entities that can be stimulated by the
waves. For EM waves, we have not yet succeeded in making the substrate; which
sustains the electromagnetic tension field, directly visible with any instrumentation.
Hence, the state of our knowledge about the nature of photons or photon wave packets
is still in a state of evolution, along with the consequent confusion. In this chapter,
we will only discuss the aspects of the NIW property that are already embedded in
the diffraction integral.
The world of optical science and engineering revolves around generating, manipulating, propagating, and detecting optical radiation. This chapter discusses the deeper physical significance of the Huygens–Fresnel’s diffraction integral, which remains as the mathematical workhorse for propagating light through free space, material media, and engineered boundary between media. The mathematical strength of HF integral lies with the fact that it obeys Helmholtz’s wave equation,
which again obeys Maxwell’s wave equation. In spite of the real successes of quantum mechanics (QM) to explain
(1) the emission of light through transition frequency, Ehmnmn, and
(2) Dirac’s quantization of light into Einstein’s indivisible photons, no optical engineer propagates indivisible photons through the optical system they design. Even in the rapidly expanding fields of nanophotonics and plasmonic photonics, where microscopic properties of materials are critical, people use Maxwell’s wave equation. Only lip service is given to the concept of the indivisible photon.
Accordingly, it is worth looking deeper into the physical significance of the HF integral and its limitations. Almost all precision instrumental and measurement-oriented modeling of the propagation of EM waves, from radio frequencies to soft x-ray frequencies, are accurately carried out using the HF diffraction integral. Examples are simply numerous, including
(1) the evolution of laser modes and pulses
(2) image processing and Fourier optics ,
(3) complex lens and mirror designs for cameras, telescopes, and microscopes,
(4) optical fibers and components essential for optical communication systems , the key enabler
of the global Internet system, and
(5) rapidly progressing nanophotonic and plasmonic photonics, along with
optical antennatechnologies.
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