### Abstract

The Kramers-Kronig relations between the real and imaginary parts of a response function are widely used in solid-state physics to evaluate the corresponding quantity if only one component is measured. They are among the most fundamental statements since only based on the analytical behavior and causal nature of the material response [Phys. Rev. 104, 1760-1770 (1956)]. Optical losses, for instance, can be obtained from the dispersion of the dielectric constant at all wavelengths, and vice versa [Handbook of optical constants of solids, Vol. 1, p. 35]. Although the general validity was never casted into doubt, it is a longstanding problem that Kramers-Kronig relations cannot simply be applied to anisotropic crystalline materials because contributions from different directions mix in a frequency-dependent way. Here we present a general method to identify frequency-independent principal polarizability directions for which the Kramers-Kronig relations are obeyed even in materials with lowest symmetry. Using generalized spectroscopic ellipsometry on a single crystal surface of triclinic pentacene, as an example, enables us to evaluate the complex dielectric constant and to compare it with band-structure calculations along the crystallographic directions. A general recipe is provided how to proceed from a macroscopic measurement on a low symmetry crystal plane to the microscopic dielectric properties of the unit cell, along whose axes the Kramers-Kronig relations hold.

Original language | English (US) |
---|---|

Pages (from-to) | 19770-19778 |

Number of pages | 9 |

Journal | Optics Express |

Volume | 16 |

Issue number | 24 |

DOIs | |

State | Published - Nov 24 2008 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Optics Express*,

*16*(24), 19770-19778. https://doi.org/10.1364/OE.16.019770

**Kramers-Kronig-consistent optical functions of anisotropic crystals : Generalized spectroscopic ellipsometry on pentacene.** / Dressel, M.; Gompf, B.; Faltermeier, D.; Tripathi, A. K.; Pflaum, J.; Schubert, M.

Research output: Contribution to journal › Article

*Optics Express*, vol. 16, no. 24, pp. 19770-19778. https://doi.org/10.1364/OE.16.019770

}

TY - JOUR

T1 - Kramers-Kronig-consistent optical functions of anisotropic crystals

T2 - Generalized spectroscopic ellipsometry on pentacene

AU - Dressel, M.

AU - Gompf, B.

AU - Faltermeier, D.

AU - Tripathi, A. K.

AU - Pflaum, J.

AU - Schubert, M.

PY - 2008/11/24

Y1 - 2008/11/24

N2 - The Kramers-Kronig relations between the real and imaginary parts of a response function are widely used in solid-state physics to evaluate the corresponding quantity if only one component is measured. They are among the most fundamental statements since only based on the analytical behavior and causal nature of the material response [Phys. Rev. 104, 1760-1770 (1956)]. Optical losses, for instance, can be obtained from the dispersion of the dielectric constant at all wavelengths, and vice versa [Handbook of optical constants of solids, Vol. 1, p. 35]. Although the general validity was never casted into doubt, it is a longstanding problem that Kramers-Kronig relations cannot simply be applied to anisotropic crystalline materials because contributions from different directions mix in a frequency-dependent way. Here we present a general method to identify frequency-independent principal polarizability directions for which the Kramers-Kronig relations are obeyed even in materials with lowest symmetry. Using generalized spectroscopic ellipsometry on a single crystal surface of triclinic pentacene, as an example, enables us to evaluate the complex dielectric constant and to compare it with band-structure calculations along the crystallographic directions. A general recipe is provided how to proceed from a macroscopic measurement on a low symmetry crystal plane to the microscopic dielectric properties of the unit cell, along whose axes the Kramers-Kronig relations hold.

AB - The Kramers-Kronig relations between the real and imaginary parts of a response function are widely used in solid-state physics to evaluate the corresponding quantity if only one component is measured. They are among the most fundamental statements since only based on the analytical behavior and causal nature of the material response [Phys. Rev. 104, 1760-1770 (1956)]. Optical losses, for instance, can be obtained from the dispersion of the dielectric constant at all wavelengths, and vice versa [Handbook of optical constants of solids, Vol. 1, p. 35]. Although the general validity was never casted into doubt, it is a longstanding problem that Kramers-Kronig relations cannot simply be applied to anisotropic crystalline materials because contributions from different directions mix in a frequency-dependent way. Here we present a general method to identify frequency-independent principal polarizability directions for which the Kramers-Kronig relations are obeyed even in materials with lowest symmetry. Using generalized spectroscopic ellipsometry on a single crystal surface of triclinic pentacene, as an example, enables us to evaluate the complex dielectric constant and to compare it with band-structure calculations along the crystallographic directions. A general recipe is provided how to proceed from a macroscopic measurement on a low symmetry crystal plane to the microscopic dielectric properties of the unit cell, along whose axes the Kramers-Kronig relations hold.

UR - http://www.scopus.com/inward/record.url?scp=56749185784&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=56749185784&partnerID=8YFLogxK

U2 - 10.1364/OE.16.019770

DO - 10.1364/OE.16.019770

M3 - Article

C2 - 19030062

AN - SCOPUS:56749185784

VL - 16

SP - 19770

EP - 19778

JO - Optics Express

JF - Optics Express

SN - 1094-4087

IS - 24

ER -