A 2×2 Matrix Algebra for Electromagnetic Wave Propagation in Stratified Biaxial Media

Jovanović, Nenad; Papousek, W.

doi:10.1078/1434-8411-00017

Cited by 7 publications

(5 citation statements)

References 18 publications

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“…If we multiply (24) and (31) by β| [here, only the exponential of the bra-vector should be complex conjugated, for example, s| = (−q y q x )e −ik x x−ik y y ] and taking into account that β|β = δ β,β , we get the following system of equations corresponding to the boundary condition at the interface z = 0:…”

Section: A General Form Of the Dispersion Relationmentioning

confidence: 99%

“…As a result, the understanding and analytical treatment of electromagnetic phenomena in biaxial media is significantly more complex than in the uniaxial case. In this context, a very recent study has reported on a rigorous analytical solution for the dispersion of surface waves on the boundaries of biaxial crystals [21]; however, up to now, studies on the electromagnetic modes in biaxial slabs have been mainly the subject of a numerical analysis [22][23][24] or some particular configurations, such as grounded crystal slabs with mode fixed propagation directions [25].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Analytical approximations for the dispersion of electromagnetic modes in slabs of biaxial crystals

Álvarez‐Pérez¹,

Воронин²,

Volkov³

et al. 2019

Phys. Rev. B

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Anisotropic crystals have recently attracted considerable attention because of their ability to support polaritons with a variety of unique properties, such as hyperbolic dispersion, negative phase velocity, or extreme confinement. Particularly, the biaxial crystal α-MoO 3 has been demonstrated to support phonon polaritons, light coupled to lattice vibrations, with in-plane anisotropic propagation and unusually long lifetime. However, the lack of theoretical studies on electromagnetic modes in biaxial crystal slabs impedes a complete interpretation of the experimental data, as well as an efficient design of nanostructures supporting such highly anisotropic polaritons. Here, we derive the dispersion relation of electromagnetic modes in biaxial slabs surrounded by semi-infinite isotropic dielectric half-spaces with arbitrary dielectric permittivities. Apart from a general dispersion relation, we provide very simple analytical expressions in typical experiments in nano-optics: the limits of short polaritonic wavelength and/or very thin slabs. The results of our study will allow for an in-depth analysis of anisotropic polaritons in novel biaxial van der Waals materials.

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Section: A General Form Of the Dispersion Relationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analytical approximations for the dispersion of electromagnetic modes in slabs of biaxial crystals

Álvarez‐Pérez¹,

Воронин²,

Volkov³

et al. 2019

Phys. Rev. B

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show abstract

“…A general result for transmittance and reflectance of anisotropic absorbing multilayer structure can be found in [22]. We note that a decrease in the transmittance of a multilayer structure can be due to absorption in the layers and/or to reflections at the interfaces.…”

Section: Mathematical Models and Methodsmentioning

confidence: 73%

Optical characterization of dyed liquid crystal cells

Addai1¹,

Xiao²,

Zheng³

et al. 2022

Preprint

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The guest-host liquid crystal display, first proposed in 1968, relies on controlling the orientation of dichroic dyes dissolved in a nematic liquid crystal host. Controlling the orientation of the liquid crystal and of the dissolved dye with an electric field allows control of the transmittance of the cell. Knowing the dielectric properties at optical frequencies of the dye and liquid crystal mixtures is crucial for the optimal design of guest-host liquid crystal devices. In this work, the dielectric functions of various layers in liquid crystal cells are described by models obeying the Kramers-Kronig relations: the Sellmeier equation for transparent layers and causal Gaussian oscillator model for absorbing layers. We propose a systematic way to accurately model the dielectric response of each layer by minimizing the sum of squared differences between the measured transmittance spectrum of a guest-host cell in the near-UV/vis range and the prediction of the transmittance of the modeled multilayer structure. By measuring the transmittance for incident light polarized parallel and perpendicular to the nematic director allows us to separately characterize the two principal dielectric functions of the uniaxial sample. Our results show that the causal Gaussian oscillator model can accurately characterize the dielectric functions of dyes in liquid crystals.

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“…The coupled boundary conditions can be formulated as a cascaded 4 × 4 matrix equation that can be solved for reflection, refraction, transmission, and polarization conversion for any incident polarization at any incidence angle (with corresponding transverse ⃗ k T ) onto an arbitrary anisotropic thin film stack [137,138,139]. Surprisingly this can be further reduced to a more compact 2 × 2 cascaded matrix equation [4,7,140] that can be used to solve this problem without any approximations found in earlier extended Jones matrix approximations [141,142] that only solved for the off-axis transmission and neglected multiple reflections [143]. The propagation of a superposition of plane waves in terms of a paraxial expansion of the wave vector in anisotropic media [62,119] has been extended to allow the computation of the propagation of Gaussian beams in such an anisotropic multilayer [144].…”

Section: Anisotropic Fresnel Coefficients and Multilayersmentioning

confidence: 99%

Vector Fourier optics of anisotropic materials

McLeod

Wagner

2014

Adv. Opt. Photon.

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The Fourier optics technique is founded on the transfer function derived from the scalar wave equation and thus has traditionally been applied to monochromatic scalar fields propagating paraxially in isotropic lossless materials. We review scalar and vector diffraction theory to show that the scalar Fourier optics technique can be seamlessly extended to the case of time-dependent nonparaxial and evanescent vector fields propagating in anisotropic and/or absorbing materials. The missing piece is shown to be the Fourier-domain vector boundary conditions that have recently been derived from the real-domain vector Rayleigh-Sommerfeld diffraction integral. These boundary conditions, complemented by the anisotropic transfer functions provided by the roots of the Booker quartic, combine the rigor of Green's function integrals with the intuitive simplicity and general applicability of Fourier optics. We illustrate the power of this technique via analytically simple solutions to traditionally complex problems such as Fresnel transmission between arbitrary media, uniaxial conoscopy, and biaxial conical refraction. The accuracy of vector near-field diffraction is validated via comparison with the finite-difference time-domain method.

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A 2×2 Matrix Algebra for Electromagnetic Wave Propagation in Stratified Biaxial Media

Cited by 7 publications

References 18 publications

Analytical approximations for the dispersion of electromagnetic modes in slabs of biaxial crystals

Analytical approximations for the dispersion of electromagnetic modes in slabs of biaxial crystals

Optical characterization of dyed liquid crystal cells

Vector Fourier optics of anisotropic materials

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