Basics

• velocity with which phase fronts propagated in a medium: v_ph

• more general term: velocity of light

• considered for: plane waves, where wavefronts are simply moving in a direction perpendicular to their orientation

• related to wavenumber k and (angular) optical frequency ω:

  

• in vacuum: phase velocity equals speed of light, c = 299,792,458 m/s, independent of optical frequency + equal to group velocity

• in medium: phase velocity smaller than c, by refractive index n.

• In visible spectral region: typical transparent crystals & optical glasses have n between 1.4 & 2.8, semicond. higher

• in X-ray region: refractive indices are slightly below 1

  -> corresponds to phase velocity slightly above vacuum velocity of light

  -> similar effects caused e.g. by optical resonances of atoms in visible spectral region

  -> this does not allow for superluminal transmission of information, or for violating causality

• can create: negative-index media

• this can cause: phase velocity can be directed in opposite to the direction of the energy flow

• due to Gouy phase shift, these move slightly faster near the focus

• phase delay per unit length, or that quantity devided by 2π:

  

  -> λ is the wavelength in the medium (not the vacuum wavelength)

• angular wavenumber: magnitude of wave vector

  = phase delay per unit length during propagation of plane wave

• in spectroscopy, wavenumber is:

  

  -> usually considered in vacuum

• Light in a medium: wavenumber = vacuum wavenumber * refractive index

• wavenumber related to phase change per unit length of a plane wave in homogeneous medium

  -> for focused beams: phase change per unit length is modified with respect to that for a plane wave

  -> for Gaussian beams: this modification is Gouy phase shift

  -> for propagation of guided waves in waveguides: imaginary part of propagation constant γ (called β) is the relevant quantity

= oscillation freq. of the corresponding electromagnetic wave

• calculated with: ν = c / λ

• visible light: 400 THz - 700 THz = 700 nm to 400 nm

• angular freq: ω = 2π ν

• optical power usually distributed over some freq. range, sometimes spends a whole octave (i.e. a factor of two in terms of freq.) or even substantially more

• highly freq.-stabilized lasers:

  -> can produce light with very small optical bandwidth, sometimes even below 1 Hz (= extremely small fraction of mean optical freq. of 100s of THz + very high stability of that freq.)

  -> also called “optical freq. standards“; required for optical clocks

• opt. freq. can be measured far more precisely than wavelengths: “freq. metrology“

  -> not directly detected like