A universal method of extraction of the complex dielectric function ϵ(ω)=ϵ1(ω)+iϵ2(ω) from experimentally accessible optical quantities is developed. The central idea is that ϵ2(ω) is parameterized independently at each node of a properly chosen anchor frequency mesh, while ϵ1(ω) is dynamically coupled to ϵ2(ω) by the Kramers–Kronig (KK) transformation. This approach can be regarded as a limiting case of the multioscillator fitting of spectra, when the number of oscillators is on the order of the number of experimental points. In the case of the normal-incidence reflectivity from a semi-infinite isotropic sample the new method gives essentially the same result as the conventional KK transformation of reflectivity. In contrast to the conventional approaches, the proposed technique is applicable, without readaptation, to virtually all types of linear-response optical measurements, or arbitrary combinations of measurements, such as reflectivity, transmission, ellipsometry, etc., done on different types of sa...

Kramers–Kronig constrained variational analysis of optical spectra

The effects of intermolecular interactions on the optical spectra of oligothiophenes are examined. Absorption spectra of isolated molecules are calculated and experimentally recorded in a rigid host matrix whereby molecules are distributed randomly or organized unidirectionally. Absorption spectra of thin films in an ordered and disordered state are given. Ordered films have three principal spectral regions which are discussed in terms of classical exciton theory. Absorption spectra in transmission of single crystals of quinquethiophene and sexithiophene are analyzed. The lowest optically allowed transition in the crystal corresponds to the lowest Davydov component. It consists of a sharp peak that is observed for even-numbered oligothiophenes in b polarization, and absent for odd-numbered rings due to the perfect alignment of the transition dipole moment with the long molecular axis. The upper Davydov component is viewed in both thin film and single crystal spectra. In between the two principal Davydov c...

Experimental determination of excitonic levels in α-oligothiophenes

An aggregate photoconductive film with a broad spectral sensitivity which is useful for electrophotographic applications is described. It consists of an aryl‐substituted thiapyrylium salt (dye) and a dialkylamino‐substituted triphenylmethane (sensitizer‐carrier–transport component, ST) disperesed in poly(4,4′‐isopropylidenediphenyl carbonate). A crystalline complex of the polymer and the dye forms an aggregate as a separate phase. Its formation is accompanied by a red shift in the absorption spectrum and a greatly enhanced photoconductive response which is augmented by the ST component. The aggregate has been simulated by a 2 : 1 complex of dye and 4,4′‐isopropylidenediphenyl‐bis‐phenyl carbonate, a two‐unit model of the polymer. Single crystals of the model complex were grown and its structure was determined from x‐ray‐diffraction data. In the monoclinic (P21/a) crystals, the approximately planar dye cations are arranged 3.44 A apart in stacks along a and the stacks are arranged in (010) sheets. The carbonate molecules are extended head to tail in chains along a so that substitution of isopropylidene groups for the end hydrogen atoms would result in a polymer. The chains also form (010) sheets and the structure consists of alternating dye and carbonate layers along b. There is no evidence of any bonding interactions between or within the sheets. The model complex crystals are good photoconductors. The optical behavior of the aggregate can be explained as a symmetry‐allowed crystal transition derived from the lowest molecular singlet state of the dye. The photoconductive behavior of aggregate films is described in detail in the accompanying paper, hereafter referred to as Paper II.

An aggregate organic photoconductor. I. Chemical composition, preparation, physical structure, and optical properties.


 The lattice symmetry of a crystal is one of the most important factors in determining its physical properties. Particularly, low-symmetry crystals offer powerful opportunities to control light propagation, polarization and phase. Materials featuring extreme optical anisotropy can support a hyperbolic response, enabling coupled light-matter interactions, also known as polaritons, with highly directional propagation and compression of light to deeply sub-wavelength scales. Here we show that monoclinic crystals can support hyperbolic shear polaritons, a new polariton class arising in the mid- to far-infrared due to shear dissipation in the dielectric response. This feature emerges in materials where the dielectric tensor cannot be diagonalized, that is, in low-symmetry monoclinic and triclinic crystals where multiple oscillators with non-orthogonal relative orientations contribute to the optical response. Hyperbolic shear polaritons complement previous observations of hyperbolic phonon polaritons in orthorhombic and hexagonal crystal systems, unveiling new features, such as the continuous evolution of their propagation direction with frequency, tilted wavefronts and asymmetric responses. The interplay between diagonal loss and off-diagonal shear dissipation in the dielectric response of these materials has implications for new forms of non-Hermitian and topological photonic states. We anticipate that our results will motivate new directions for polariton physics in low-symmetry materials, which include geological minerals, many common oxides and organic crystals, significantly expanding the material base and extending design opportunities for compact photonic devices.

/pdf/hyperbolic-shear-polaritons-in-low-symmetry-crystals-31rsv50ceb.pdf

Hyperbolic Shear Polaritons in Low-Symmetry Crystals

The lattice symmetry of a crystal is one of the most important factors in determining its physical properties. Particularly, low-symmetry crystals offer powerful opportunities to control light propagation, polarization and phase1-4. Materials featuring extreme optical anisotropy can support a hyperbolic response, enabling coupled light-matter interactions, also known as polaritons, with highly directional propagation and compression of light to deeply sub-wavelength scales5. Here we show that monoclinic crystals can support hyperbolic shear polaritons, a new polariton class arising in the mid-infrared to far-infrared due to shear phenomena in the dielectric response. This feature emerges in materials in which the dielectric tensor cannot be diagonalized, that is, in low-symmetry monoclinic and triclinic crystals in which several oscillators with non-orthogonal relative orientations contribute to the optical response6,7. Hyperbolic shear polaritons complement previous observations of hyperbolic phonon polaritons in orthorhombic1,3,4 and hexagonal8,9 crystal systems, unveiling new features, such as the continuous evolution of their propagation direction with frequency, tilted wavefronts and asymmetric responses. The interplay between diagonal loss and off-diagonal shear phenomena in the dielectric response of these materials has implications for new forms of non-Hermitian and topological photonic states. We anticipate that our results will motivate new directions for polariton physics in low-symmetry materials, which include geological minerals10, many common oxides11 and organic crystals12, greatly expanding the material base and extending design opportunities for compact photonic devices. 

/pdf/hyperbolic-shear-polaritons-in-low-symmetry-crystals-9g51byb0.pdf

Hyperbolic shear polaritons in low-symmetry crystals

The properties of the dielectric tensor of a monoclinic crystal are reviewed and the nature of transverse excitations is pointed out. Reflection equations for normal incidence on the (010) plane and (001) plane are presented, by use of which full information on all tensor components may be obtained from reflection measurements and Kramers- Kronig analysis. A reflection equation for oblique incidence on faces ( h 1 , O, h 3 ) with plane of incidence (010) and transverse magnetic polarization allows the comparison of reflectance spectra calculated from the dielectric tensor components with respective experimental spectra. Simple model calculations related to exciton structures in molecular crystals and quasi one-dimensional materials are displayed.

K.L. Kliewwer

Papers

Reflection spectroscopy on monoclinic crystals