Chapter 2 - Optical Propagation

2.1 INTRODUCTION

The study of optical signals propagating in matter requires a good understanding of
the physics of light and the properties of matter. How is light generated? What are its
nature and its properties? How does light interact with matter? How is the optical signal
affected by this interaction? In this chapter, we address these questions to help in
the understanding of light–matter interaction and how this affects signal quality.

Over the years, the nature of light has been explained based on the semiclassical
theory of the atom. Excited electrons rotate around the nucleus of the atom in
a higher-energy elliptical orbit, E_i, similar to how planets revolve around the sun.
Being at a higher energy, the electron rotates at a high rpm. Now, when the electron
is suddenly forced to a lower rpm, and thus to a lower rotational energy, an
amount of energy is released. That is, when the electron transits from a high-energy
orbit to a lower one, energy equal to the difference between the two energy
levels is released, E_released = E_i – E_j. However, since electron orbits are quantized
(they are not continuously distributed around the nucleus), so the amount of energy
released is quantized. As a consequence, specific atoms release specific
amounts of energy, as electrons transit from specific high-energy levels to specific
low-energy levels, which are characteristic for each element of the periodic
table. These energy quanta manifest themselves as photons if their energy is a
multiple of Planck’s constant, h.

Up to this point, this description neither tells us much about the characteristics of
the released photon, namely frequency, nor its dual electromagnetic and particle-
like nature. To further explore the nature of the photon, consider that an excited
electron moves in some elliptical orbit around the nucleus at some angular frequency
or rpm. Thus, the energy of the electron may be expressed as a function of its angular
frequency ω₁, E(ω₁). Since the electron has a charge and it is in continuous
motion, it represents a current creating a magnetic field around its elliptical orbit.
This magnetic field may be viewed (for simplicity) as an evolving toroidal and an
electric field perpendicular to it and the orbit of the electron (Figure 2.1).

Now, as the electron “moves” from an electromagnetic field rotating at ω₁ to another
with lower energy and angular frequency ω₂, the difference between the two
energies E(ω₁) – E(ω₂) corresponds to the released energy. If each magnetic and
electric field of each level is expressed as a complex function of ω, such as F(cos ω

Figure 2.1. An electron (dot) moves on an elliptical trajectory (dotted line) and generates an evolving magnetic field (circles) in a toroidal shape and at a frequency commensurate with its angular velocity _. The direction of the magnetic field depends on the direction of motion of the electron. If clockwise, the magnetic field is also clockwise.

+ j sin ω), then the difference of the two levels provides a cosine term, the argument
of which is ω₁– ω₂ = ω₃. Thus, the released energy is an electromagnetic wavelet at
frequency ω₃, which at the moment of its release is perpendicular to the orbital
plane of the electron. However, the released wavelet is no longer constrained to
move on a toroidal-shaped orbit, but escapes the atom’s influence, unraveling the
toroidal shape and propagating unbounded in a straight path in a corkscrew-like
manner (Figure 2.2). In this way, the magnetic and electric fields still remain orthogonal
and revolve around each other. Thus, this model explains the quantum-mechanical
electromagnetic nature of light, its frequency and unique “color,” and
its propagation characteristics in free space.

It turns out that the energy of the released electromagnetic wavelet, the photon,
is directly proportional to its frequency, with a constant of proportionality, Planck’s
constant, E = hv. Thus, one would be tempted to say that created photons move like
tiny electromagnetic “fuzzy” balls with total energy given by E = hv and moving in
free space at the speed of light defined in Einstein’s energy relationship E = mc². In
short, photons have particle properties and thus momentum that exerts pressure on a
target, which has been verified by many experiments (Figure 2.3), and it is routinely
experienced by satellites when they enter the path of solar light. However, the
philosophical search for the essence of light is intriguing, and still continues. A theory
that attempts to bridge the classical with quantum mechanics has been in active
development for the last 20 years and is known as the string theory (or “the theory
of everything”). According to it, everything consists of subquantum-mechanical,
multidimensional, oscillating strings, a bunch of which may define gravitons, nuclear
particles, electrons, photons, and so on. However, although this theory (or theories,
as there are many) is plausible, it remains unverified and experimentally unproven,
as it is the ancient philosophical “ether” that fills the universe and through
which light propagates. In this book and for all practical reasons, we adapt the clas-

Figure 2.2. A photon is born. As the electron “transits” to a lower-energy orbit, the energy difference E = E1 – E2 = h_ is emitted in the form of a photon with a magnetic field (H) remaining orthogonal to electric field (E) and moving in a clockwise direction in a corkscrew-like manner.

sical theory of the dual nature of light, waves, and particles, as this has been proven
in the lab of nature and explains most of the phenomena that involve light.

Based on the prevailing theory, if we could “see” what these unimaginable tiny
“fuzzy” balls look like, we would discover that all photons are not equal. Some are
red, some green, some blue, some have exotic colors, and some are even “invisible.”
Being different, photons have their own idiosyncratic moods and as they cross
fields of forces within matter, each type of photon travels at its own pace and on its
own individual path. And as they transverse matter, they also interact differently
with it and among themselves. This has been managed and specific devices have
been developed that are applicable in telecommunications and other applications.

In optical communications, a relatively good medium for photons to propagate
through is glass, especially when it is in the form of a very thin, uniform, ultrapure
fiber. In fact, glass fiber is the chosen transmission medium for high-speed, high-reliability,
and long-distance communications, both terrestrial and submarine. With
Dense Wavelength Division Multiplexing (DWDM) technology, 160 wavelengths
have been commercially used in a single fiber, resulting to an aggregate bandwidth

Figure 2.3. An old and simple but convincing experiment: when exposed to light, pressure (due to absorption) is exerted on the blackened surface of the paddles and the wheel rotates according to action–reaction, proving that photons behave like particles.

that exceeds one terabit per second. DWDM systems are currently on a trend toward
not only increasing both the density of wavelengths per fiber and thus the aggregate
bit rate, but also the fiber span without signal amplification.

Certain numbers mentioned in this book may seem very small or very large.
Table 2.1 puts in perspective what these numbers mean, such as a picosecond (ps) or
a terabit per second (Tbps).

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