Absorption, dispersion, and Kramers-Kronig

What is dispersion in materials?

• The absorption of light by materials

• The function of wavelength in materials

• The phase shifts among different frequencies in materials

• The spread of frequencies in materials

How can we model light absorption in materials?

• By using indices of refraction with imaginary terms

• By subtracting pure sine waves from the original signal

• By phase-shifting different frequencies in the pulse

• By delaying frequencies with respect to each other

What is the relationship between temporal and spectral widths in a pulse of light?

• Fourier transform relationship

• Inverse relationship

• Direct proportionality

• No relationship

What happens to a pulse of light when a highly absorbent material removes a specific frequency from its spectrum?

• The pulse extends out forever

• The pulse becomes narrower

• The pulse disappears completely

• The pulse remains unchanged

Why is it important to have a frequency-dependent index of refraction in order to preserve causality?

• To ensure absorption and dispersion go hand in hand

• To prevent the pulse from reaching back in time

• To maintain a causal theory of electromagnetism

• To avoid phase shifts among different frequencies

What is the relationship between the real and imaginary parts of a frequency-domain linear causal response function?

• They are unrelated

• They are inversely proportional

• They are related by the Kramer-Kronig relations

• They are equal

What do the Kramer-Kronig relations express?

• The relationship between dispersion and absorption

• The relationship between the real and imaginary parts of the susceptibility

• The relationship between the index of refraction and the permittivity

• The relationship between the temporal and spectral widths of a pulse

How can the real part of the susceptibility be determined if the absorption spectrum is known?

• By measuring the index of refraction

• By using the Fourier transform

• By applying the Kramer-Kronig relations

• By analyzing the dispersion behavior

What is the purpose of Kramer-Kronig relations in measuring the index of refraction?

• To determine the dispersion behavior of a material

• To calculate the absorption spectrum of a material

• To find the relationship between the real and imaginary parts of the susceptibility

• To back out the real part of the susceptibility from the absorption spectrum

Why is a causal behavior important in electromagnetism?

• To ensure physical theories are realistic

• To make movies more enjoyable

• To simplify mathematical calculations

• To avoid complex analysis