EM waves

Question 1

How does Maxwell’s equations look in vacuum?

Answer 1

Absence of sources, density of el. = 0, J = 0.

Question 2

What characterise EM waves?

Answer 2

Frequency and wavelength of their oscillation

Question 3

What carry EM waves?

Answer 3

Energy, momentum and angular momentum that can be imparted to matter with which they interact

Question 4

How is the relationship between E,B and k-vector?

Answer 4

k must be // E x B

Question 5

Which types of EM waves are there?

Answer 5

• Plane waves: infinite parallel wavefronts planes, normal to propagation direction
• Spherical waves: generated by point sources, their intensity is isotropic in space and decay i as 1/r
• Harmonic waves: superposition of them defines ANY arbitrary waveform

Question 6

What is the Poynting vector?

Answer 6

Vector with direction and amplitude of energy flow; it defines the average power density.

Question 7

What is the intensity of an EM wave?

Answer 7

I = Poynting/area

Question 8

EM waves in matter vs. in vacuum

Answer 8

E field in matter depends on the dielectric “constant” –> EM waves in matter travels at a different speed than c

Question 9

Index of refraction

Answer 9

n = c/v = √Epsilon_r

Question 10

n = n’ + n’’

Answer 10

n’: refractive index, it determines the speed of light inside the medium
n’’: extinction coefficient, it leads to exponential decay of EM field inside a medium

Question 11

Lambert-beer law

Answer 11

I = I(0)exp(-αz)
α = attenuation coefficient = -2n’‘ω/c

Question 12

Rayleigh scattering

Answer 12

Scattering due to small particle, smaller than the wavelength of light

Question 13

Classical Rayleigh scattering

Answer 13

electrons oscillate due to E-field –> each atom behaves as a tiny dipole antenna, emitting EM radiation with the same frequency ω as that of the primary wave (oscillating dipole generates a E-field itself)

Question 14

QM Rayleigh scattering

Answer 14

Elastic scattering (no absorption, same frequency and phase is absorbed and reemitted) is possible due to virtual absorption and emission of photons by electrons. The excited electron exists in an energy state ∆E only for a ∆t (∆E∆t = ℏ)

Question 15

Refraction

Answer 15

Change in direction of propagating EM wave due to change of the transmission medium –> change direction due to change of phase velocity –> change of phase velocity due to refractive index
* change of velocity v≠c of the transmitted wave as due to the phase shift accumulated by the light propagating inside the material

Question 16

Snell’s law

Answer 16

n_i sin(θ_i) = n_t sin(θ_t)

Question 17

Dispersion

Answer 17

Change of refactive index n depending on the wavelength –> Prisma “splits” the light

Question 18

Reflection

Answer 18

Change in direction of a wavefront at an interface between two media, and it returns into the incident medium.

Question 19

When n becomes less than 1 the phase velocity of the light is greater than c. This may seem to contradict the special theory of relativity.
This occurs when the charges in the medium oscillate slightly out of phase with respect to the driving electric field, which is equivalent to a negative electric polarization of the material (εr < 1). How do you explain that?

Answer 19

Remember that the phase velocity is defined as the rate at which the crests of the waveform propagate; that is, the rate at which the phase of the waveform is moving. The group velocity is the rate that the envelope of the waveform is propagating; that is, the rate of variation of the amplitude of the waveform. Provided the waveform is not distorted significantly during propagation, it is the group velocity that represents the rate at which information (and energy) may be transmitted by the wave

Question 20

How does an atom react to an EM wave?

Answer 20

In two ways:
1. If the photon energy matches a transition from an electronic state to another, the atom will ”absorb” light. Upon relaxation, light can then be reemitted at the same or different frequency, depending on the element and atomic density of the medium. In a dense medium, for example, it is likely that the atom will decay back to the lower state by a non-radiative process (e.g., by phonon or electron emission) leading to dissipative absorption (transfer of photon energy to heat).

2. If the energy of the photon does not match the difference between an occupied and an empty energy level of the atom, we can imagine that the atom remains in the ground state while the electronic cloud vibrates slightly at the frequency of the incident light (virtual electronic exctitations). These oscillations are equivalent to an oscillating dipole moment, which produces a radiation field at the same frequency as the exciting light. Thus photons are continuously absorbed and reemitted with the same frequency and direction relative to the incident EM wave, and we speak of non-resonant elastic scattering.

Question 21

Scattering by a rarefied medium

Answer 21

The scattered wavelets add constructively with each other in the forward direction. This condition is true for all such wavelets regardless of both how many scatterers there were and how they were distributed.

Question 22

Scattering by a dense medium

Answer 22

For every molecule there will always be another one at the distance ≈ λ2 from it, with a field that will cancel the field emitted by the former, the net E−field at a point in any transverse or backward direction will always be the sum of many out-of-phase fields, and therefore very small. Each atom becomes a source of spherical wavelets
* Only in the forward direction the fields add up in phase, leading to the propagation of the wave through the medium.
* The more dense, uniform, and ordered the medium is (as in liquids and solids) the more complete will be the lateral destructive interference.