Rotational Raman scattering in the Earth's atmosphere ... - SRON

8 Chapter 1
a)
hc ν
virtual energy level
hc ν
b) c)
hc ν
hc( ν− ∆ν)
hc ν hc( ν+ ∆ν)
Cabannes
∆J=0
i=f
Stokes
f
i
i
∆J=+2 ∆J =−2
f
Anti−Stokes
Figure 1.3: Molecular scattering involves an incident photon that brings a molecule with initial energy
state i to a virtual energy state (dashed line). Subsequently, the molecule falls back to a lower energy state
f by releasing a photon. If this final state f has the same energy as the initial state i the scattering process
is said to be elastic and corresponds to Cabannes scattering (a). When the released photon has a lower
energy than the incident photon (E f > E i ) the process is called Stokes rotational Raman scattering (b).
When the released photon gains energy (E f < E i ) the scattering process is called anti-Stokes rotational
Raman scattering (c). The net rotational energy transitions have to obey the quantum law ∆J = ±0, 2.
We restrict ourselves to pure rotational Raman scattering processes (∆v=0; ∆J = ±2).
Rotational Raman scattering by air molecules that involves a released photon with less energy than
the incident one (∆J = +2; Fig. 1.3b) is referred to as Stokes rotational Raman scattering and inelastic
scattering that involves an energy gain of the released photons (∆J = −2 ; Fig. 1.3c) is called anti-
Stokes rotational Raman scattering [Young, 1982]. The energies of the anti-Stokes rotational Raman
photons are given by
hcν = hcν in + (4hcB 0 − 6hcD 0 )(J − 1 2 ) − 8hcD 0(J − 1 2 )3 , J = 2, 3,... , (1.4)
and the energy of the Stokes rotational Raman photons are given by
hcν = hcν in − (4hcB 0 − 6hcD 0 )(J + 3 2 ) + 8hcD 0(J + 3 2 )3 , J = 0, 1,... , (1.5)
where hcν in is the energy of the incident light (see e.g. Fish and Jones [1995].) The energy shifts,
and thus the wavenumber shifts ν−ν in , only adopt discrete values. It is important to realize that these
fixed shifts in energy lead to wavelength shifts λ−λ in that are not fixed with respect to the wavelength
of the incident light λ in . At shorter wavelengths the shifts in terms of wavelength are smaller than
at longer wavelengths. This makes the use of wavenumbers more elegant and simple to describe the
Raman effect. Nevertheless, both descriptions are used throughout this thesis.
The line-strengths of the individual rotational Raman lines can be measured in the laboratory or
can be calculated from theory (e.g. [Chance and Spurr, 1997, Burrows et al., 1996, Penney et al.,
scattering process involves much larger energy shifts than pure rotational Raman scattering, i.e. -2331 cm −1 and -1555
cm −1 for N 2 and O 2 , respectively. For incident light at 400 nm, this corresponds to wavelength shifts of +41.1 nm
and +26.5 nm for N 2 and O 2 , respectively. Burrows et al. [1996] estimated that the largest spectral features caused by
vibrational Raman scattering are expected to be maximally 0.27% in GOME reflectivity spectra.