Quantum theory of line shapes in coherent Raman spectroscopy of gases and liquids

Jón Örn Bjarnason, Bruce S Hudson, Hans C. Andersen

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

The fully quantum mechanical theory of coherent Raman scattering in gases and liquids is developed. In this theory, the electromagnetic radiation is described as a quantized field, and the quantum mechanical transition amplitude for the scattering process is calculated. This is formally different from the usual semiclassical theory in which the radiation field is characterized as a classical electromagnetic wave and nonlinear susceptibilities are used to describe the interaction of radiation and matter. The Doppler broadened line shape for the ideal gas is calculated and found to be non-Gaussian with a width that is 1.2 times larger than the Doppler width for spontaneous Raman scattering in the forward direction. This differs from a previously published result. The rotational-vibrational band shape is shown to be related to a correlation function for rotational-vibrational motion. This correlation function is the same as that describing spontaneous Raman scattering, but the relationship of the correlation function to the spectrum is different. In the absence of correlations between rotation and vibration the spectrum can be related to a Laplace transform (with an imaginary argument) of a rotational correlation function. The line shape is calculated for two special cases, free rotational motion and Brownian rotational motion.

Original languageEnglish (US)
Pages (from-to)4130-4148
Number of pages19
JournalThe Journal of Chemical Physics
Volume70
Issue number9
StatePublished - 1979
Externally publishedYes

Fingerprint

Quantum theory
quantum theory
line shape
Raman spectroscopy
Gases
Raman scattering
Liquids
liquids
gases
Electromagnetic waves
Raman spectra
Coherent scattering
electromagnetic radiation
Radiation
Laplace transforms
coherent scattering
ideal gas
radiation distribution
Scattering
magnetic permeability

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

Bjarnason, J. Ö., Hudson, B. S., & Andersen, H. C. (1979). Quantum theory of line shapes in coherent Raman spectroscopy of gases and liquids. The Journal of Chemical Physics, 70(9), 4130-4148.

Quantum theory of line shapes in coherent Raman spectroscopy of gases and liquids. / Bjarnason, Jón Örn; Hudson, Bruce S; Andersen, Hans C.

In: The Journal of Chemical Physics, Vol. 70, No. 9, 1979, p. 4130-4148.

Research output: Contribution to journalArticle

Bjarnason, JÖ, Hudson, BS & Andersen, HC 1979, 'Quantum theory of line shapes in coherent Raman spectroscopy of gases and liquids', The Journal of Chemical Physics, vol. 70, no. 9, pp. 4130-4148.
Bjarnason, Jón Örn ; Hudson, Bruce S ; Andersen, Hans C. / Quantum theory of line shapes in coherent Raman spectroscopy of gases and liquids. In: The Journal of Chemical Physics. 1979 ; Vol. 70, No. 9. pp. 4130-4148.
@article{3a2942d1915048909d6be55202f9ab7a,
title = "Quantum theory of line shapes in coherent Raman spectroscopy of gases and liquids",
abstract = "The fully quantum mechanical theory of coherent Raman scattering in gases and liquids is developed. In this theory, the electromagnetic radiation is described as a quantized field, and the quantum mechanical transition amplitude for the scattering process is calculated. This is formally different from the usual semiclassical theory in which the radiation field is characterized as a classical electromagnetic wave and nonlinear susceptibilities are used to describe the interaction of radiation and matter. The Doppler broadened line shape for the ideal gas is calculated and found to be non-Gaussian with a width that is 1.2 times larger than the Doppler width for spontaneous Raman scattering in the forward direction. This differs from a previously published result. The rotational-vibrational band shape is shown to be related to a correlation function for rotational-vibrational motion. This correlation function is the same as that describing spontaneous Raman scattering, but the relationship of the correlation function to the spectrum is different. In the absence of correlations between rotation and vibration the spectrum can be related to a Laplace transform (with an imaginary argument) of a rotational correlation function. The line shape is calculated for two special cases, free rotational motion and Brownian rotational motion.",
author = "Bjarnason, {J{\'o}n {\"O}rn} and Hudson, {Bruce S} and Andersen, {Hans C.}",
year = "1979",
language = "English (US)",
volume = "70",
pages = "4130--4148",
journal = "Journal of Chemical Physics",
issn = "0021-9606",
publisher = "American Institute of Physics Publising LLC",
number = "9",

}

TY - JOUR

T1 - Quantum theory of line shapes in coherent Raman spectroscopy of gases and liquids

AU - Bjarnason, Jón Örn

AU - Hudson, Bruce S

AU - Andersen, Hans C.

PY - 1979

Y1 - 1979

N2 - The fully quantum mechanical theory of coherent Raman scattering in gases and liquids is developed. In this theory, the electromagnetic radiation is described as a quantized field, and the quantum mechanical transition amplitude for the scattering process is calculated. This is formally different from the usual semiclassical theory in which the radiation field is characterized as a classical electromagnetic wave and nonlinear susceptibilities are used to describe the interaction of radiation and matter. The Doppler broadened line shape for the ideal gas is calculated and found to be non-Gaussian with a width that is 1.2 times larger than the Doppler width for spontaneous Raman scattering in the forward direction. This differs from a previously published result. The rotational-vibrational band shape is shown to be related to a correlation function for rotational-vibrational motion. This correlation function is the same as that describing spontaneous Raman scattering, but the relationship of the correlation function to the spectrum is different. In the absence of correlations between rotation and vibration the spectrum can be related to a Laplace transform (with an imaginary argument) of a rotational correlation function. The line shape is calculated for two special cases, free rotational motion and Brownian rotational motion.

AB - The fully quantum mechanical theory of coherent Raman scattering in gases and liquids is developed. In this theory, the electromagnetic radiation is described as a quantized field, and the quantum mechanical transition amplitude for the scattering process is calculated. This is formally different from the usual semiclassical theory in which the radiation field is characterized as a classical electromagnetic wave and nonlinear susceptibilities are used to describe the interaction of radiation and matter. The Doppler broadened line shape for the ideal gas is calculated and found to be non-Gaussian with a width that is 1.2 times larger than the Doppler width for spontaneous Raman scattering in the forward direction. This differs from a previously published result. The rotational-vibrational band shape is shown to be related to a correlation function for rotational-vibrational motion. This correlation function is the same as that describing spontaneous Raman scattering, but the relationship of the correlation function to the spectrum is different. In the absence of correlations between rotation and vibration the spectrum can be related to a Laplace transform (with an imaginary argument) of a rotational correlation function. The line shape is calculated for two special cases, free rotational motion and Brownian rotational motion.

UR - http://www.scopus.com/inward/record.url?scp=0001304466&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001304466&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0001304466

VL - 70

SP - 4130

EP - 4148

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 9

ER -