## On the Lorentz-Lorenz formula and the Lorentz model of dielectric dispersion: addendum

Optics Express, Vol. 11, Issue 21, pp. 2791-2792 (2003)

http://dx.doi.org/10.1364/OE.11.002791

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### Abstract

The approximate equivalence relation equating the frequency dispersion of the Lorentz model alone with that modified by the Lorentz-Lorenz formula is shown to also equate the branch points appearing in each of these two descriptions.

© 2003 Optical Society of America

1. K. E. Oughstun and N. A. Cartwright, “On the Lorentz-Lorenz formula and the Lorentz model of dielectric dispersion,” Opt. Express **11**, 1541–1546 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-13-1541. [CrossRef] [PubMed]

*ε*(

*ω*) in terms of the mean molecular polarizability

*α*(

*ω*) as

*ω*

_{0}is the undamped resonance frequency of the harmonically bound electron of charge magnitude

*q*

_{e}and mass

*m*

_{e}with number density

*N*, phenomenological damping constant

*δ*and plasma frequency

*b*

^{2}/(6

*δω*

_{0})≪1 is satisfied. The Lorentz-Lorenz relation (1) with the Lorentz model (2) of the molecular polarizability gives the relative dielectric permittivity as

*ω*

_{*}. The value of this resonance frequency

*ω*

_{*}that will yield the same value for

*ε*(0) as given by Eq. (3) is given by [1

1. K. E. Oughstun and N. A. Cartwright, “On the Lorentz-Lorenz formula and the Lorentz model of dielectric dispersion,” Opt. Express **11**, 1541–1546 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-13-1541. [CrossRef] [PubMed]

1. K. E. Oughstun and N. A. Cartwright, “On the Lorentz-Lorenz formula and the Lorentz model of dielectric dispersion,” Opt. Express **11**, 1541–1546 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-13-1541. [CrossRef] [PubMed]

*ω*

_{*}=

*ω*

_{0}, then the branch points of

*n*(

*ω*) for the Lorentz-Lorenz modified Lorentz model are shifted inward toward the imaginary axis from the branch point locations for the Lorentz model alone provided that the inequality

*b*

^{2}/3-

*δ*

^{2}≥0 is satisfied. If the opposite inequality

*b*

^{2}/3-

*δ*

^{2}<0 is satisfied, then the branch points

*ω*

_{*}is given by the equivalence relation (5), then the locations of the branch points of the complex index of refraction

*n*(

*ω*) for the Lorentz-Lorenz modified Lorentz model and the Lorentz model alone are exactly the same. The branch cuts for these two models are then also the same (or can be chosen so). It then follows that the analyticity properties for these two causal models of the dielectric permittivity are the same. This important result is central to the asymptotic description of both ultrawideband signal and ultrashort pulse propagation in Lorentz model dielectrics, particularly when the number density of molecules is large.

## References and links

1. | K. E. Oughstun and N. A. Cartwright, “On the Lorentz-Lorenz formula and the Lorentz model of dielectric dispersion,” Opt. Express |

**OCIS Codes**

(260.2030) Physical optics : Dispersion

(320.5550) Ultrafast optics : Pulses

**ToC Category:**

Research Papers

**History**

Original Manuscript: July 17, 2003

Revised Manuscript: October 13, 2003

Published: October 20, 2003

**Citation**

Kurt Oughstun and Natalie Cartwright, "On the Lorentz-Lorenz formula and the Lorentz model of dielectric dispersion: addendum," Opt. Express **11**, 2791-2792 (2003)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-21-2791

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### References

- K. E. Oughstun and N. A. Cartwright, "On the Lorentz-Lorenz formula and the Lorentz model of dielectric dispersion," Opt. Express 11, 1541-1546 (2003), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-13-1541">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-13-1541</a>. [CrossRef] [PubMed]

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