Fully stable numerical calculations for finite one-dimensional structures: Mapping the transfer matrix method

Luque-Raigon, Jose Miguel; Halme, Janne; Míguez, Hernán

doi:10.1016/j.jqsrt.2013.10.007

Cited by 22 publications

(19 citation statements)

References 13 publications

(39 reference statements)

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“…Interestingly, the relations given in Eqs. (38), (B15), and (B18) are shown to be essentially independent of the assumption of lossless materials and thus can be used when the medium is absorbing.…”

Section: Discussionmentioning

confidence: 99%

“…[36][37][38]). Similarly, one of the important results of a rigorous analysis performed within such a framework in Ref.…”

Section: Discussionmentioning

confidence: 99%

“…Equation (B12) shows that the symmetry relations (37) remain valid even if the dielectric constants are complex valued and the medium is absorbing. Since identities (38) are derived from Eqs. (37) and (27) without recourse to the unitarity relations, they also hold for lossy materials.…”

Section: Symmetriesmentioning

confidence: 99%

“…As it can be seen from formulas (B12), the symmetry relations (37) are satisfied even if the dielectric constants ⊥ , , and z are complex valued. So, the applicability range of identities (38) includes lossy (absorbing) anisotropic materials described by the dielectric tensor of the form given in Eq. (B1).…”

Section: Appendix B: Uniformly Anisotropic Planar Structuresmentioning

confidence: 99%

“…An important point is that, similar to identities (38), the assumption of lossless (nonabsorbing) medium is not required to derive the symmetry relations (B15) and (B18).…”

mentioning

confidence: 99%

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Optics of short-pitch deformed-helix ferroelectric liquid crystals: Symmetries, exceptional points, and polarization-resolved angular patterns

Kiselev

Chigrinov

2014

Phys. Rev. E

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In order to explore electric-field-induced transformations of polarization singularities in the polarizationresolved angular (conoscopic) patterns emerging after deformed-helix ferroelectric liquid crystal (DHFLC) cells with subwavelength helix pitch, we combine the transfer matrix formalism with the results for the effective dielectric tensor of biaxial FLCs evaluated using an improved technique of averaging over distorted helical structures. Within the framework of the transfer matrix method, we deduce a number of symmetry relations and show that the symmetry axis of L lines (curves of linear polarization) is directed along the major in-plane optical axis which rotates under the action of the electric field. When the angle between this axis and the polarization plane of incident linearly polarized light is above its critical value, the C points (points of circular polarization) appear in the form of symmetrically arranged chains of densely packed star-monstar pairs. We also emphasize the role of phase singularities of a different kind and discuss the enhanced electro-optic response of DHFLCs near the exceptional point where the condition of zero-field isotropy is fulfilled.

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Section: Discussionmentioning

confidence: 99%

“…[36][37][38]). Similarly, one of the important results of a rigorous analysis performed within such a framework in Ref.…”

Section: Discussionmentioning

confidence: 99%

Section: Symmetriesmentioning

confidence: 99%

Section: Appendix B: Uniformly Anisotropic Planar Structuresmentioning

confidence: 99%

“…An important point is that, similar to identities (38), the assumption of lossless (nonabsorbing) medium is not required to derive the symmetry relations (B15) and (B18).…”

mentioning

confidence: 99%

See 3 more Smart Citations

Optics of short-pitch deformed-helix ferroelectric liquid crystals: Symmetries, exceptional points, and polarization-resolved angular patterns

Kiselev

Chigrinov

2014

Phys. Rev. E

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Adaptable Ultraviolet Reflecting Polymeric Multilayer Coatings of High Refractive Index Contrast

Smirnov

Ito

Calvo

et al. 2015

Advanced Optical Materials

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a series of undesirable photoreactions promoted by the absorption of UV photons, which lead to the deterioration of their mechanical and optical properties. Polymers are usually transparent to part of the UV spectrum, so a commonly employed synthetic strategy to attain UV blocking fi lms is based on embedding inorganic [3][4][5][6][7] or organic [8][9][10] UV absorbers within a polymeric matrix. The main drawback of this approximation is the short term durability of the shielding effect as a result of the photodegradation of either host, guest, or both, caused by the absorption of the same radiation from which protection is sought after. [11][12][13] Approaches based on fl exible inorganic nano structured multilayers that effi ciently refl ect radiation in an arbitrary spectral range as a result of interference effects, rather than by absorption, present a promising alternative route worth to be explored. [14][15][16][17] Unfortunately, a similar approach based on the alternation of polymeric fi lms exclusively is not feasible since the refractive index contrast typically achieved is so small that a large number of layers is required to reach a signifi cant refl ectance, and only in a narrow spectral range. [ 18,19 ] The use of all-polymeric materials of high refractive index contrast to build multilayer back refl ectors or UV shields will also be an advantage in the fi eld of fl exible and polymeric solar cells, in which some approaches based on inorganic materials have already been developed. [ 20,21 ] Very recently, some of us proved that a porous stratifi ed structure displaying strong refl ection peaks in the UV range can be attained from a block copolymer (BCP) fi lm. [ 22 ] In particular, it was demonstrated that a fi lm made of a diblock copolymer containing polystyrene (PS) and polymethyl methacrylate (PMMA), in brief [poly(styreneblock -methyl methacrylate) PS-b -PMMA)], can be used as starting material to attain ordered porous multilayers through a process that involves collective osmotic shock (COS). The fi nal structure shows alternate dense and porous layers, with signifi cant refractive index contrast, which endow it with photonic crystal properties in the UV range. At that moment, the appearance of the layered structure was hypothetically attributed to dynamic effects during the COS process occurring over ordered arrangements of isolated PMMA spheres embedded in a cross-linked PS matrix in the starting slab, which had previously been subjected to thermal and UV annealing processes. Further studies, herein reported, have demonstrated that the mechanism of formation of the porous layered structure is different to that originally A synthetic route is demonstrated to build purely polymeric nanostructured multilayer coatings, adaptable to arbitrary surfaces, and capable of effi ciently blocking by refl ection a targeted and tunable ultraviolet (UV) range. Refl ection properties are determined by optical interference between UV light beams refl ected at the interfaces between polystyrene layers of diff...

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Broadband circular dichroism in chiral plasmonic woodpiles

et al. 2023

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The circular dichroism (CD) of a material is the difference in optical absorption under left- and right-circularly polarized illumination. It is crucial for a number of applications, from molecular sensing to the design of circularly polarized thermal light sources. The CD in natural materials is typically weak, leading to the exploitation of artificial chiral materials. Layered chiral woodpile structures are well known to boost chiro-optical effects when realized as a photonic crystal or an optical metamaterial. We here demonstrate that light scattering at a chiral plasmonic woodpile, which is structured on the order of the wavelength of the light, can be well understood by considering the fundamental evanescent Floquet states within the structure. In particular, we report a broadband circular polarization bandgap in the complex band structure of various plasmonic woodpiles that spans the optical transparency window of the atmosphere between 3 and 4 $$\upmu$$ μ m and leads to an average CD of up to 90% within this spectral range. Our findings could pave the way for an ultra-broadband circularly polarized thermal source.

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Fully stable numerical calculations for finite one-dimensional structures: Mapping the transfer matrix method

Cited by 22 publications

References 13 publications

Optics of short-pitch deformed-helix ferroelectric liquid crystals: Symmetries, exceptional points, and polarization-resolved angular patterns

Optics of short-pitch deformed-helix ferroelectric liquid crystals: Symmetries, exceptional points, and polarization-resolved angular patterns

Adaptable Ultraviolet Reflecting Polymeric Multilayer Coatings of High Refractive Index Contrast

Broadband circular dichroism in chiral plasmonic woodpiles

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