L2

Question 1

Artificial Crystals

Answer 1

• Artificial crystals for optical frequencies behave like natural crystals at X-ray frequencies.
• Key approximation: light at optical frequencies has a much longer wavelength than the inter-atomic spacing.

Question 2

Bound / Free Charges / Currents

Answer 2

• Bound charges: immobile (core electrons and localized valence electrons).
• Free charges: charges that can move.
• Bound currents: small current loops (intrinsic spin, orbital angular momentum).
• Free currents: macroscopic currents (current in a copper wire).

Question 3

Polarization Density

context? meaning?

Answer 3

• Introduce electric flux density D (displacement field)
• define polarization density P

Question 4

Magnetization Density

change / add context

Answer 4

New magnetic field vector H and definition of magnetization density. Rewritten curl equation, removing explicit dependence on bound currents.

Question 5

Macroscopic Approximation

what does it approximate and how?

Answer 5

• Approximate free charge/current as average over the cube volume.
• Bound charge/current approximated as boundary effects.

Question 6

Assumption 1

Context!

Answer 6

• P depends on E
• M depends on B
• Good in most cases, but not when magnetoelectric coupling is significant.

Question 7

Assumption 2

Answer 7

• P and M depend on local values of E and B.
• Equivalent to the long wavelength assumption.

Question 8

Assumption 3

add to combined card

Answer 8

• Dependence of P and M on E and B is not location-dependent (homogeneity).
• Easily corrected with boundary conditions.

Question 9

Assumption 4

add to list of assumptions, then delete

Answer 9

• P and M depend on immediate values of E and B (dispersionless).
• Often invalid, but repaired using dispersion.

Question 10

Assumption 5

add to combined card

Answer 10

• P and M are linear in E and B (linearity)

Question 11

Assumption 6

make a card with a list of all the names of assumptions

Answer 11

P and M are in the same or opposite direction as E and B (isotropy).

Question 12

Laser in sugar solution

Answer 12

Laser light passes through a sugar solution. The gradient in refractive index causes curvature of the light beam.

Question 13

Refractive Indices

Answer 13

Representative refractive indices (@20℃):
- Vacuum: 1
- Air: 1.00027
- Water: 1.33
- Silicon: 3.48 (1550nm)

Question 14

Plane Waves

Answer 14

Wave equation is linear. Linear combination of plane wave solutions is also a solution. E and B lie in a plane normal to the direction of propagation k (TEM).

Question 15

Optical Impedance

Answer 15

In vacuum, Z₀ = 377 Ω. This gives the amplitude ratio between electric and magnetic fields in an EM wave.

Question 16

Linear Polarization

Answer 16

Electric field points either parallel or antiparallel to a fixed direction.

Question 17

Polarization Effects

Answer 17

Polarization affects reflection, absorption, and scattering of light. Optically active materials rotate the polarization plane of linearly polarized light.

Question 18

Light Absorption

Answer 18

Green light is absorbed more strongly by a red balloon than by a transparent or green balloon.

Question 19

Energy Transport by Light

Answer 19

Light transports energy. Examples include laser machining and two-photon polymerization.