A `dispersion relation´relates frequency and wavelength of a harmonic wave. That is, the wavelength of the wave due to a change in its frequency. For electromagnetic waves (e.g. light), the dispersion relation is k =", where n is the refractive index. Consider two wn harmonic electromagnetic waves of equal amplitude travelling in the same direction in vacuum with wavelengths, 500nm and 505nm.
A `dispersion relation´relates frequency and wavelength of a harmonic wave. That is, the wavelength of the wave due to a change in its frequency. For electromagnetic waves (e.g. light), the dispersion relation is k =", where n is the refractive index. Consider two wn harmonic electromagnetic waves of equal amplitude travelling in the same direction in vacuum with wavelengths, 500nm and 505nm.
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Transcribed Image Text:A 'dispersion relation' relates frequency and wavelength of a harmonic wave. That is, the
wavelength of the wave due to a change in its frequency. For electromagnetic waves (e.g.
light), the dispersion relation is k :
where n is the refractive index. Consider two
C
harmonic electromagnetic waves of equal amplitude travelling in the same direction in
vacuum with wavelengths, 500nm and 505nm.
a) Consider if both waves now travel through a material with index, n=1.5. Their
frequency remains the same but their wavelength changes due to the new material.
Calculate the beat frequency, beat wavenumber (i.e. k), carrier frequency, and carrier
wavenumber.
b) With the numbers in a), calculate the velocity of the envelope and the velocity of the
carrier.
c) Consider now if the index varies with the vacuum wavelength, n(500nmn)=1.5214
and n(505nm)=1.5211. (frequency never changes when entering a material). What is
the velocity of the carrier and envelope in this case?
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