Optical Bit Error Rate

Chapter 2.1.1 - The Wave Nature of Light

2.1.1   The Wave Nature of Light

Monochromatic light consists of waves all of exactly the same “single” frequency
and it propagates in space with a spherical front. However, to simplify the mathe-
matical wave analysis, electromagnetic waves are considered planar. Thus, light is
described by the Maxwell’s electromagnetic plane wave equations:

 


Table 2.1


where Ñ2 is the Laplacian operator; v is the speed of the wave in a medium; θ is the
partial derivative; E and H are the electric and magnetic fields, respectively; D is
the electric displacement vector (its gradient is the charge density ρ); and B is the
magnetic induction vector.

When an electromagnetic wave propagates in a linear medium (e.g., noncrystalline),
these four vectors are inter-related by

 

where ε0 and μ0 are the dielectric permitivity and permeability, respectively, both
constants of free space, and P and M are the electric and magnetic polarization of
the wave, respectively. Then, the electric polarization is expressed as

 

where χ is the electric susceptibility of the medium. In a nonlinear medium, this is
expressed as a tensor and the latter relation includes higher-order terms. Moreover,
the dielectric constant of the material, ε, is connected with the susceptibility as

 

The propagation of a plane wave is described by the two relationships

 

and

 

where ω is the angular frequency, r is the directional vector, and k is the wave vector,
which is connected with the dielectric constant by the relationship

 

The aforementioned two wave relationships are complex numbers and they consist
of a real term, cos(x), and an imaginary term, sin(x). However, the real part of them
is simplified to

 

and

 

When the (monochromatic) plane wave travels in free space, it travels at a maximum
and constant speed (since μ0 and ε0 for free space are constant quantities):

 

where c = 2.99792458 × 1010 cm/sec, or ~30 cm/nsec.

When light travels in a medium (other than free space), then its velocity u is expressed
by

 

The speed of light, u, in a medium is always smaller than c, since μ > μ0 and ε < ε0.

UNLIMITED FREE
ACCESS
TO THE WORLD'S BEST IDEAS

SUBMIT
Already a GlobalSpec user? Log in.

This is embarrasing...

An error occurred while processing the form. Please try again in a few minutes.

Customize Your GlobalSpec Experience

Category: Fiber Optic Transceivers
Finish!
Privacy Policy

This is embarrasing...

An error occurred while processing the form. Please try again in a few minutes.