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When Light is Scattered from an Atom or Molecule , most Photons are elastically scattered ( Rayleigh Scattering ). The scattered photons have the same energy ( Frequency ) and, therefore, Wavelength , as the incident photons. However, a small fraction of light (approximately 1 in 107 photons) is scattered at optical frequencies different from, and usually lower than, the frequency of the incident photons. In a gas, Raman scattering can occur with a change in vibrational, rotational or electronic energy of a molecule (see Energy Level ). Chemists are concerned primarily with the vibrational Raman effect.

In 1922, India n physicist Chandrasekhara Venkata Raman published his work on the "Molecular Diffraction of Light," the first of a series of investigations with his collaborators which ultimately led to his discovery on 28 February 1928 of the radiation effect which bears his name. The Raman effect was first reported by C.V. Raman and K.S. Krishnan , and independently by Grigory Landsberg and Leonid Mandelstam in 1928 . Raman received the Nobel Prize in 1930 for his work on the scattering of light.


RAMAN SCATTERING: STOKES AND ANTI-STOKES

The interaction of light with matter in a linear regime allows the absorption or simultaneous emission of light of energy precisely matching the difference in energy levels of the interacting electrons. The Raman effect is a Nonlinear (third order) effect.

The Raman effect corresponds, in ). There are three possibilities :
  • no energy exchange between the incident photons and the molecules (and hence no Raman effect)

  • energy exchanges occur between the incident photons and the molecules. The energy differences are equal to the differences of the vibrational and rotational energy-levels of the molecule. In crystals only specific Phonons are allowed (solutions of the wave equations which do not cancel themselves) by the periodic structure, so Raman scattering can only appear at certain frequencies. For amorphous materials like glasses, more phonons are allowed and thereby the discrete spectral lines become broad.

  • molecule absorbs energy: Stokes scattering. The resulting photon of lower energy generates a Stokes Line on the red side of the incident spectrum.

  • molecule loses energy: anti-Stokes scattering. Incident photons are shifted to the blue side of the spectrum, thus generating an anti-Stokes line.



These differences in energy are measured by subtracting the energy of the mono-energetic laser light from the energy of the scattered photons. The absolute value, however, doesn't depend on the process (Stokes or anti-Stokes scattering), because only the energy of the different vibrational levels is of importance. Therefore, the Raman spectrum is symmetric relative to the Rayleigh band. In addition, the intensities of the Raman bands are only dependent on the number of molecules occupying the different vibrational states, when the process began. The Boltzmann Distribution teaches us that more molecules occupy the lower energy levels in most cases:



with:

:N_0: amount of atoms in the lower vibrational state

:N_1: amount of atoms in the higher vibrational state

:g_0: Degeneration in the lower vibrational state (amount of Orbitals of the same energy)

:g_1: Degeneration in the higher vibrational state (amount of Orbitals of the same energy)

:\Delta E_v: energy difference between these two vibrational states

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