40
2 Optical Fiber Structures and Light Guiding Principles
Example 2.2 (a) Consider an incoming photon that boosts an electron from a ground
state level E 1 to an excited level E 2 . If the incoming photon energy E = E 2 – E 1 =
1.512 eV, what is the wavelength of the incoming photon? (b) Now suppose this
excited electron loses some of its energy and moves to a slightly lower energy level
E 3 . If the electron then drops back to level E 1 thereby emitting a photon of energy
E 3 – E 1 = 1.450 eV, what is the wavelength of the emitted photon?
Solution (a) Referring back to Sect. 1.2, from Eqs. (1.2) and (1.3), λ incident =
1.2405/1.512 eV = 0.820 μm = 820 nm. (b) From Eqs. (1.2) and (1.3), λ emitted
= 1.2405/1.450 eV = 0.855 μm = 855 nm.
2.2 Basic Laws and Definitions of Optics
This section reviews some of the basic optics laws and definitions relevant to optical
fiber transmission technology [1, 3]. These include Snell’s law, the definition of
the refractive index of a material, and the concepts of reflection, refraction, and
polarization.
2.2.1 Concept of Refractive Index
A fundamental optical parameter of a material is the refractive index (or index of
refraction). In free space light travels at a speed c = 2.99793 × 10
8 m/s ≈ 3 × 10
8
m/s. The speed of light is related to the frequency ν and the wavelength λ by c =
νλ. Upon entering a dielectric or nonconducting medium the wave now travels at a
speed s, which is characteristic of the material and is less than c. The ratio of the
speed of light in a vacuum to that in matter is the index of refraction n of the material
and is given by Eq. (2.15). Representatives values are listed in Table 2.1
n =
c
s
(2.15)
2.2.2 Basis of Reflection and Refraction
The concepts of reflection and refraction can be interpreted by considering the
behavior of light rays associated with plane waves traveling in a dielectric material.
When a light ray encounters a boundary separating two different dielectric media,
part of the ray is reflected back into the first medium and the remainder is bent (or
refracted) as it enters the second material. This is shown in Fig. 2.6 for the interface
2 Optical Fiber Structures and Light Guiding Principles
Example 2.2 (a) Consider an incoming photon that boosts an electron from a ground
state level E 1 to an excited level E 2 . If the incoming photon energy E = E 2 – E 1 =
1.512 eV, what is the wavelength of the incoming photon? (b) Now suppose this
excited electron loses some of its energy and moves to a slightly lower energy level
E 3 . If the electron then drops back to level E 1 thereby emitting a photon of energy
E 3 – E 1 = 1.450 eV, what is the wavelength of the emitted photon?
Solution (a) Referring back to Sect. 1.2, from Eqs. (1.2) and (1.3), λ incident =
1.2405/1.512 eV = 0.820 μm = 820 nm. (b) From Eqs. (1.2) and (1.3), λ emitted
= 1.2405/1.450 eV = 0.855 μm = 855 nm.
2.2 Basic Laws and Definitions of Optics
This section reviews some of the basic optics laws and definitions relevant to optical
fiber transmission technology [1, 3]. These include Snell’s law, the definition of
the refractive index of a material, and the concepts of reflection, refraction, and
polarization.
2.2.1 Concept of Refractive Index
A fundamental optical parameter of a material is the refractive index (or index of
refraction). In free space light travels at a speed c = 2.99793 × 10
8 m/s ≈ 3 × 10
8
m/s. The speed of light is related to the frequency ν and the wavelength λ by c =
νλ. Upon entering a dielectric or nonconducting medium the wave now travels at a
speed s, which is characteristic of the material and is less than c. The ratio of the
speed of light in a vacuum to that in matter is the index of refraction n of the material
and is given by Eq. (2.15). Representatives values are listed in Table 2.1
n =
c
s
(2.15)
2.2.2 Basis of Reflection and Refraction
The concepts of reflection and refraction can be interpreted by considering the
behavior of light rays associated with plane waves traveling in a dielectric material.
When a light ray encounters a boundary separating two different dielectric media,
part of the ray is reflected back into the first medium and the remainder is bent (or
refracted) as it enters the second material. This is shown in Fig. 2.6 for the interface