Number of optical axes in absorbing triclinic crystals

Golovina, T. G.; Константинова, А. Ф.; Konstantinov, Konstantin; Evdishchenko, E. A.

doi:10.1134/s1063774513060126

Cited by 3 publications

(11 citation statements)

References 4 publications

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“…[28] Note, in the case that the dielectric tensor is not symmetric anymore, e.g., due to the presence of an external magnetic field, the eigenstates for the propagation along the singular optic axis are elliptically and no longer circularly polarized. [28] Then, the directions of the singular optic axis cannot be described by a quartic polynomial as given by Equation (12). The corresponding equation can be found in ref.…”

Section: Wave Equationmentioning

confidence: 99%

Electromagnetic Waves in Crystals: The Presence of Exceptional Points

Sturm

2024

Advanced Photonics Research

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Although the investigation of the propagation of electromagnetic waves in crystals dates back to the 19th century, the presence of singular optic axes in optically anisotropic materials has not been fully explored until now. Along such an axis, either a left or a right circular polarized wave can propagate without changing its polarization state. More generally, these singular optic axes belong to exceptional points (EPs) in the momentum space and correspond to a simultaneous degeneration of the eigenmodes and their propagation properties. Herein, a comprehensive discussion on EPs in optically anisotropic materials, their occurrence, and properties as well as the properties of the electromagnetic waves propagating along such EPs is presented. The presence of such EPs, their spatial and spectral distribution in bulk, and semi‐infinite and finite crystals are discussed. It is shown that the presence of interfaces has a strong impact on the presence of the EPs and their spatial distribution. At an EP, the propagation of an arbitrarily polarized wave cannot be described by a superposition of two eigenmodes, as typically described in textbooks. This leads to singularities if the reflection and transmission coefficients have to be calculated. Here, two approaches are presented to overcome these limitations.

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Section: Wave Equationmentioning

confidence: 99%

Electromagnetic Waves in Crystals: The Presence of Exceptional Points

Sturm

2024

Advanced Photonics Research

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“…Further work on singular axes has been reported e.g. in [30][31][32][33][34][35][36][37][38][39][40][41], but we feel that parts of the optics community have largely forgotten about singular axes. A recent analysis provided an in depth view of the spectral dispersion and possible degeneracies of the singular axes [42] for monoclinic gallia as model system.…”

Section: @ Rrlmentioning

confidence: 99%

“…xz ε = The white dots indicate the angular position of the singular axes. axes degenerates, forming a "normal" (but absorptive) optic axis, rendering the material triaxial [42], a case also considered in [41]. A more detailed discussion can be found in [42].…”

Section: Singular Axes 31 Spectral Dispersionmentioning

confidence: 99%

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Optically anisotropic media: New approaches to the dielectric function, singular axes, microcavity modes and Raman scattering intensities

Grundmann

Sturm

Kranert

et al. 2016

Physica Rapid Research Ltrs

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Six out of seven crystal systems are optically anisotropic and birefringent. We review recent insight that biaxial crystals generally exhibit four singular axes (or exceptional points) which can pairwise degenerate for special cases. Planar anisotropic microcavities are discussed as effectively biaxial systems and we predict exceptional points and demonstrate experimentally partially coalesced eigenstates. Also the general form of the dielectric function of anisotropic crystals based on individual dipole oscillators for phonon and electronic resonance is discussed. The impact of birefringence on Raman scattering intensities has been historically either ignored or modeled incorrectly. A recent theory for uniaxial and biaxial crystals explains experimental Raman scattering intensities for excitation off the principal directions without free parameters, allowing the unambiguous determination of the Raman tensor components. The above points are demonstrated and relevant in particular for the currently technologically important materials GaN, ZnO (uniaxial) and β‐Ga2O3 (biaxial).

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“…The plane wave corresponding to non-semisimple degeneracy of P is called a Voigt wave. 1,2,10 Voigt waves propagate along singular optical axes, 11,12 which arise for isolated values of ψ, depending on the orientation of the x and y axes. [13][14][15][16][17] Certain biaxial 18 dielectric mediums and gyrotropic 19 dielectric mediums, for examples, support the propagation of Voigt waves, provided that the mediums are either dissipative or active.…”

Section: Introductionmentioning

confidence: 99%

Exceptional surface and compound waves

2022

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Guided by the planar interface of two dissimilar partnering mediums, a surface wave can be exceptional if at least one of the partnering mediums is anisotropic. Exceptional surface waves propagate in isolated directions parallel to the interfacial plane, whereas unexceptional (i.e., garden-variety) surface waves propagate for a non-degenerate angular interval of directions parallel to the interfacial plane. Also, exceptional surface waves have localization characteristics different from those of unexceptional surface waves: the decay of fields for an exceptional surface wave has a combined linear-exponential dependency on distance from the interface in an anisotropic partnering medium, whereas the decay is purely exponential for an unexceptional surface wave. In order for exceptional surface waves to exist, the constitutive parameters of that anisotropic partnering medium must satisfy certain constraints. Exceptional surface waves of different types have been reported: (a) If both partnering mediums are dielectric, at least one of the two is anisotropic, then exceptional surface waves classified as Dyakonov-Voigt surface waves can exist, whether or not the partnering mediums are dissipative. Whereas the planar interface of an isotropic dielectric medium and a uniaxial dielectric medium can guide one exceptional surface wave in each quadrant of the interface plane, the planar interface of an isotropic dielectric medium and a biaxial dielectric medium can guide two exceptional surface waves in each quadrant of the interface plane. Furthermore, doubly exceptional Dyakonov-Voigt surface waves, which exhibit a combined linear-exponential dependency on distance from the interface on both sides of the interface, have been reported on for the planar interface of a biaxial dielectric medium and a uniaxial dielectric medium. (b) If one of the partnering mediums is metallic and the other is dielectric, and at least one of them is anisotropic, then exceptional surface waves classified as surfaceplasmon-polariton-Voigt waves can exist. The notion of exceptional surface waves guided by a single planar interface has been extended to compound waves that are guided by a pair of parallel planar interfaces, provided that the distance between the two interfaces is not too great. For example, if a thin film of metal is embedded within an anisotropic dielectric medium, the two planar interfaces can guide exceptional compound-plasmonpolariton waves.

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Number of optical axes in absorbing triclinic crystals

Cited by 3 publications

References 4 publications

Electromagnetic Waves in Crystals: The Presence of Exceptional Points

Electromagnetic Waves in Crystals: The Presence of Exceptional Points

Optically anisotropic media: New approaches to the dielectric function, singular axes, microcavity modes and Raman scattering intensities

Exceptional surface and compound waves

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