Optical Bit Error Rate

Chapter 2.10.1 - Background

2.10   PARADOXES

2.10.1   Background


In this section, we make certain observations that appear to be paradoxes, which, if
proven feasible, may open a new chapter in optical and photonic technology and
optical propagation.

In the most general solution, the electric field of a monochromatic traveling
plane harmonic wave in free space is of the form E(z, t):

 E(z, t) = Re{F exp[–iω(trn/c)]}

Where Re is the real part of { }, F is a complex vector (of the form α + ), ω is
the wave frequency, n is a unit vector along the axis of propagation z, such as z =
rn, and k = ωn/c is the wave vector such that k = 2πn/λ, λ = 2π/k, and λ =
c/ω.

When light propagates in matter, then

 dH/dz = – i(ω/c) (εE), and dE/dz = –i (ω/c) (χH)

where ε and χ are the dielectric constant and susceptibility of the material.

From the last relationship we obtained

 d2E/dz2 = –(w2/c2)(εχE)

The solution of this is

 

In this case, the wave vector is k = (ω/c) , or k = (w/v)z, where v is the speed
of light in the medium.

In this analysis, we consider monochromatic light. Realistically, the frequency
of a photonic signal consists of a band of frequencies distributed within Δω, ω0
Δω/2 < ω < ω0 + Δω/2. Introducing a new variable, ξ = ω ω0, this yields a term E0
exp[–i (ω0tk0z)] that represents a traveling wave with a mean carrier frequency
ω0 but with an amplitude that is no longer constant but has a maximum value propagating
with group velocity ug = /dk.

 

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