Download Interaction of Electromagnetic Radiation with Matter

Interaction of Electromagnetic
Radiation with Matter
Dielectric Constant and Atomic
Polarizability
• Under the action of the electric field, the
positive and negative charges inside each
atom are displaced from their equilibrium
positions.
• The induced dipole moment is
p = αE
Where α is atomic polarizability.
Dielectric Constant and Atomic
Polarizability
• The dielectric constant of a medium will
depend on the manner in which the atoms are
assembled. Let N be the number of atoms per
unit volume. The polarization can be written
approximately as
P=Np=NαE=ε0ΧE
Where Χ is susceptibility.
Dielectric Constant and Atomic
Polarizability
• The dielectric constant ε of the medium is
• If the medium is nonmagnetic (i.e., μ=μ0), the
index of refraction is given by
Classical Electron Model
• In classical physics, we assume that the
electrons are fastened elastically to the atoms
and obey the following equation of motion
• The electric field of the optical wave in the
atom can be written as
Classical Electron Model
• The equation has the following steady-state
solution
• The induced dipole moment is
• The atomic polarizability is
Classical Electron Model
• If there are N atoms per unit volume, the
index of refraction of such a medium is
• If the second term in this equation is small
compared to 1, the index of refraction can be
written as
Dispersion and Complex Refractive
Index
• From the equation
• We can get that the index of refraction is higher
for the waves with larger ω.
• The phenomenon that the refractive index
depends on frequency is called the phenomenon
of dispersion.
Dispersion and Complex Refractive
Index
• The imaginary term iϒω in the equation
accounts for the damping of electron motion
and gives rise to the phenomenon of optical
absorption.
Dispersion and Complex Refractive
Index
• The complex refractive index can be written as
Dispersion and Complex Refractive
Index
• For a wave written as
• In which
• Using the complex refractive index, the wave
number K becomes
Dispersion and Complex Refractive
Index
• The electric field of the wave becomes
Optical Pulse and Group Velocity
• In the pulsed mode, the pump energy can be
concentrated into extremely short time
durations, thereby increasing the peak power.
• The propagation of a pulse due to dispersion
can be described by representing the pulse as
a sum of many plane-wave solutions of
Maxwell’s equations.
Optical Pulse and Group Velocity
• The scalar amplitude ψ(z,t) can be thought of
as one of the components of electromagnetic
field vectors. If A(k) denotes the amplitude of
the plane-wave component with wave
number k, the pulse ψ(z,t) can be written as
Optical Pulse and Group Velocity
• A laser pulse is usually characterized by its
center frequency ω0 or wave number k0 and
the frequency spread Δ ω or spread in wave
number Δk. In other words, A(k) is sharply
peaked around k0. We expand ω(k) around the
value k0 in terms of a Taylor series:
Optical Pulse and Group Velocity
• The ψ(z,t) becomes
• The integral in above equation is a function of
the composite variable [z – (dω/dk)0t] only
and is called the envelope function
Optical Pulse and Group Velocity
• The amplitude of the pulse can be written as
• This shows that, apart from an overall phase,
the laser pulse travels along undistorted in
shape
Optical Pulse and Group Velocity
• The group velocity of the pulse is
• The group velocity represents the transport of
energy.