Stokes shift

This article refers to the Stokes Displacement, sometimes referred to as Stokes' Law. For further regularities, rules and theorems established by the physicist and mathematician Sir George Gabriel Stokes, see Stokes' laws .

Simplified representation of the Stokes shift in the spectrum

The Stokes shift ( English Stokes shift ) - also called Stokes rule or Stokes law - is the shift of the wavelength or the frequency of light ( electromagnetic radiation ) between absorption and emission . It occurs, for example, with fluorescence and the Raman effect .

discovery

The name Stokes shift goes back to the mathematician and physicist Sir George Gabriel Stokes . In 1852 he recognized the law that the light emitted again by fluorescent substances has a longer wavelength than the previously absorbed light. In the case of substances that fluoresce due to incident light, the re-emitted light is therefore always longer-wave.

description

In the experiment carried out by Stokes, the shift can be described by two effects. After absorption or emission, electrons are only rarely in the vibronic ground state of the electronically excited state or the electronic ground state, which leads to a non-radiative relaxation in the respective vibronic ground state. In most cases, however, the stronger effect is solvent relaxation.

Fluorescent dyes are generally considered to be dipoles . The non-excited system is mostly in equilibrium. As a result, the electronic ground state is energetically preferred. After absorption, the system is no longer in equilibrium because the dipole of the dye has changed. As soon as the system is in equilibrium again, the electronically excited state is preferred, its energy level is consequently lower than before, but that of the electronic ground state is higher. As a result, the energy difference between the states in the excited system is smaller than in the non-excited system, so that less energy is emitted during emission than was absorbed during absorption.

In some cases, deviating from this basic rule, the wavelength of the re-emitted light may not have been changed. In these cases, one speaks of the occurrence of resonance fluorescence .

In the case of laser transitions, the quotient of the energy difference between the upper and lower laser level and the excitation and ground state is also referred to as the Stokes efficiency of a laser. In this case, this corresponds to the quantum defect or the quotient of the pump wavelength and the laser wavelength of the laser used.

Mathematical description

The Stokes shift is the difference in energy between incoming and outgoing photons :

${\displaystyle {\begin{aligned}\Delta E_{\mathrm {photon} }&=E_{\mathrm {out} }-E_{\mathrm {in} }\\&=h\left(\nu _{\mathrm {out} }-\nu _{\mathrm {in} }\right)\\&=hc\left({\frac {1}{\lambda _{\mathrm {out} }}}-{\frac {1}{\lambda _{\mathrm {in} }}}\right)\end{aligned}}}$

${\displaystyle \nu }$ ... frequency

h ... Planck's quantum of action

c ... the speed of light

${\displaystyle \lambda }$ ... wavelength

If only one photon is absorbed per molecule, the wavelength of the outgoing photons is greater than that of the incoming:

${\displaystyle \lambda _{\mathrm {out} }>\lambda _{\mathrm {in} }.}$

The energy loss of the photon is converted into heat or vibration energy of the absorbing particle:

${\displaystyle {\begin{aligned}\Leftrightarrow {\frac {1}{\lambda _{\mathrm {out} }}}&<{\frac {1}{\lambda _{\mathrm {in} }}}\\\Leftrightarrow c\left({\frac {1}{\lambda _{\mathrm {out} }}}-{\frac {1}{\lambda _{\mathrm {in} }}}\right)&<0\\\Leftrightarrow \nu _{\mathrm {out} }-\nu _{\mathrm {in} }&<0\\\Leftrightarrow \Delta E_{\mathrm {photon} }&<0\\\Leftrightarrow \Delta E_{\mathrm {teilchen} }&>0.\end{aligned}}}$

In the optical wavelength range, the Stokes shift is often given as the difference between the wavelengths, in units of nanometers (nm) or as a wave number in units of cm ⁻¹ :

${\displaystyle \lambda _{s}=\left|\lambda _{\mathrm {out} }-\lambda _{\mathrm {in} }\right|.}$

Anti-Stokes shift

If, on the other hand, an excitation already present in the material ( e.g. a phonon in solids ) is destroyed when the photon is emitted, this is known as an anti-Stokes shift . The wavelength of the outgoing photons is shorter than that of the incoming photons . This is for example in the non-linear Raman spectroscopy (engl., In the form of coherent anti-Stokes Raman scattering coherent anti-Stokes Raman scattering CARS) utilized for material investigation.

See also

• Quantum yield
• Franck-Condon principle

Individual evidence

1. ^ T. Graf: Laser. Basics of laser beam sources 1st edition. Vieweg + Teubner, 2009, p. 182ff.