In addition, the following relation which is called in general a dispersion relation of
waves is obtained:
ω
2
¼ c
2 k
2
ð2:2:15Þ
In Fig. 2.8, the schematics of a snapshot of the electromagnetic wave is plotted. It
is noted that the magnetic field is perpendicular to the electric field, and ExB should
be in the direction of k, the propagation direction. The wavenumber is a vector as
seen in (2.2.9) and given to be in a vector form, k.
H. Hertz who heard the prediction by Maxwell has carried out the experimental
proof of the electromagnetic wave in his laboratory with the use of high-voltage
discharge. As suggested in (2.2.10), Hertz generated the electromagnetic wave by
flowing discharge current in a high-voltage gap. Then, the electric field by the
electromagnetic wave was detected, although it is not monochromatic, but it consists
of a wide range of frequency.
Historically the electromagnetic waves have been called as a variety of names
depending on the frequency. Radio waves have the longest wavelength, and gamma
rays have the shortest. The visible region of light is very narrow in wavelength from
about 350 nm to 750 nm (0.35–0.75 μm).
2.2.3 Lasers as Coherent Electromagnetic Waves
Let us introduce the vector potential of electromagnetic field of a laser beam:
A ¼ A 0 ω
ð Þε cos k Á r À ωt
ð
Þ
ð 2:2:16Þ
In (2.2.16), ω ¼ kc and ε is a unit vector showing the direction of the electric field.
Then, the electric and magnetic fields of the wave are calculated with the use of the
relation for electromagnetic waves:
E ¼ À
∂
∂t
A
B ¼ ∇ Â A
ð2:2:17Þ
Equation (2.2.16) provides both fields as:
Magnetic field
Electric field
Wavelength λ
Fig. 2.8 Schematics of the
electric and magnetic fields
of plane electromagnetic
fields propagating from the
left to right
44
2 Laser Absorption by Coulomb Collision
waves is obtained:
ω
2
¼ c
2 k
2
ð2:2:15Þ
In Fig. 2.8, the schematics of a snapshot of the electromagnetic wave is plotted. It
is noted that the magnetic field is perpendicular to the electric field, and ExB should
be in the direction of k, the propagation direction. The wavenumber is a vector as
seen in (2.2.9) and given to be in a vector form, k.
H. Hertz who heard the prediction by Maxwell has carried out the experimental
proof of the electromagnetic wave in his laboratory with the use of high-voltage
discharge. As suggested in (2.2.10), Hertz generated the electromagnetic wave by
flowing discharge current in a high-voltage gap. Then, the electric field by the
electromagnetic wave was detected, although it is not monochromatic, but it consists
of a wide range of frequency.
Historically the electromagnetic waves have been called as a variety of names
depending on the frequency. Radio waves have the longest wavelength, and gamma
rays have the shortest. The visible region of light is very narrow in wavelength from
about 350 nm to 750 nm (0.35–0.75 μm).
2.2.3 Lasers as Coherent Electromagnetic Waves
Let us introduce the vector potential of electromagnetic field of a laser beam:
A ¼ A 0 ω
ð Þε cos k Á r À ωt
ð
Þ
ð 2:2:16Þ
In (2.2.16), ω ¼ kc and ε is a unit vector showing the direction of the electric field.
Then, the electric and magnetic fields of the wave are calculated with the use of the
relation for electromagnetic waves:
E ¼ À
∂
∂t
A
B ¼ ∇ Â A
ð2:2:17Þ
Equation (2.2.16) provides both fields as:
Magnetic field
Electric field
Wavelength λ
Fig. 2.8 Schematics of the
electric and magnetic fields
of plane electromagnetic
fields propagating from the
left to right
44
2 Laser Absorption by Coulomb Collision