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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 66, Iss. 6 — Jun. 1, 1976
  • pp: 547–554

Dispersion relations and sum rules for magnetoreflectivity

David Y. Smith  »View Author Affiliations


JOSA, Vol. 66, Issue 6, pp. 547-554 (1976)
http://dx.doi.org/10.1364/JOSA.66.000547


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Abstract

Dispersion relations and sum rules for the dichroic reflectivity and phase shifts of circularly polarized modes are developed for the magneto-optical case. The reduction in crossing-relation symmetry arising from the presence of a magnetic field and the consequent non-Kramers-Kronig form of the dichroism dispersion relations are discussed in terms of the analyticity of the amplitude reflectivity. Sum rules are derived from the low- and high-frequency limits of the dichroism dispersion relations. These rules include the general results that ∫<sup>∞</sup><sub>0</sub> ω<sup>-1</sup> ln[r+(ω)/r<sub>-</sub>(ω)]dω = 0 and ∫<sup>∞</sup><sub>0</sub>[θ+(ω)-θ<sub>-</sub>(ω)]dω = πω<sub>c</sub>, where r<sub>±</sub>(ω) and θ±(ω) are the amplitude and phase of the amplitude reflectivity for the circular modes and ω<sub>c</sub> is the cyclotron frequency. Approximate finite-energy dispersion relations and sum rules are developed and their range of validity examined.

© 1976 Optical Society of America

Citation
David Y. Smith, "Dispersion relations and sum rules for magnetoreflectivity," J. Opt. Soc. Am. 66, 547-554 (1976)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-66-6-547

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