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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 49, Iss. 6 — Jun. 1, 1959
  • pp: 609–614

Intensity and Damping Dependence of Various Parameters Describing Spectral-Line Shapes

R. D. WALDRON  »View Author Affiliations

JOSA, Vol. 49, Issue 6, pp. 609-614 (1959)

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Analytical expressions are presented for the frequency dependence of loss factor, conductivity, loss tangent, amplitude attenuation per radian (absorption index), imaginary refractive index, amplitude and power attenuation per unit length (absorption coefficient), and reflectivity for a damped harmonic oscillator system. Equations are given for the displacement of maxima of these parameters as a function of line strength and width (intensity and damping). Some limiting value relations are given, and the functional dependences of the parameters illustrated graphically. Applications to physical problems are discussed briefly.

R. D. WALDRON, "Intensity and Damping Dependence of Various Parameters Describing Spectral-Line Shapes," J. Opt. Soc. Am. 49, 609-614 (1959)

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  1. W. Heitler, The Quantum Theory of Radiation (Clarendon Press, Oxford, 1954).
  2. E. P. Gross, Phys. Rev. 97, 395 (1955).
  3. M. Born and K. Huang, Dynamical Theory of Crystal Lattices (Clarendon Press, Oxford, 1954).
  4. A. von Hippel, Dielectrics and Waves (John Wiley & Sons, Inc., New York, 1954).
  5. T. H. Havelock, Proc. Roy. Soc. (London) A86, 1 (1911); A105, 488 (1924).
  6. I. Simon, J. Opt. Soc. Am. 41, 336 (1951).
  7. The rationalized mks system is employed in this presentation.
  8. The velocity of light ν=∂x/∂t at constant phase. From the equation for Ey, for constant phase, xt/β+const, then ν=ω/β=1/real part of ((∊*µ*)½=√2/{[(∊′µ′-∊″µ″)2+(∊′µ″+∊″µ′)2]½+(∊′µ′-∊″µ″)})½.
  9. The appropriate field E in this expression is discussed later.
  10. For real media with additional susceptibility terms, we may write [Equation] where Eq is the local electric field associated with xq*, [Equation] and X=X0/a.
  11. n* has been multiplied by the scale factor a=1.5 for proper reflectivity.
  12. The theory of impedance-circle diagrams is important in electric transmission-line engineering, and is discussed in several texts, e.g., J. C. Slater, Microwave Transmission (McGraw-Hill Book Company, Inc., New York, 1942).
  13. In Havelock's notation q1′, g, k, and y are equivalent to a, X, l, and f2-1 = -s, respectively.
  14. In his notation the coefficient of the term q1k2y should be 32 instead of 16.
  15. gi is 1/∊0 times an anisotropy factor h, depending on the detailed structure of the oscillator system. For an isotropic array of dipoles with large interoscillator distance, h=-⅔ and gi=-2/(3∊0).

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