Optical crossover phenomenon due to a central 90°-twist defect in a chiral sculptured thin film or chiral liquid crystal

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Abstract

We present a theoretical analysis of a remarkable phenomenon evinced by a periodic structurally chiral material-for example, a chiral sculptured thin film (STF) or a chiral liquid crystal-with a central 90°-twist defect illuminated with normally incident, circularly polarized light. Based on the coupled-wave theory (CWT), an approximate but closed-form solution of the relevant boundary-value problem is obtained in terms of a 4×4 CWT transmission matrix. The CWT transmission matrix is decomposed into two terms. The first term favours total transmission in the central part of the Bragg regime of the axially excited, structurally chiral material, while the second term favours total reflection in the whole Bragg regime. When the thickness of the structurally chiral material is relatively small, the second term is dominated by the first, which gives rise to a co-handed transmittance peak in the centre of the Bragg regime. As the thickness increases, the second term becomes significant and interferes with the first term such that the transmission matrix is isomorphic to that of a defect-free structurally chiral material-except in a tiny wavelength-regime wherein the L∞-norms of the two terms become identical to engender the total-reflection feature. Hence, the co-handed transmittance peak diminishes (and eventually vanishes) as the thickness increases and is replaced by a cross-handed reflectance peak. The bandwidths of the two peaks depend, in different ways, on the local birefringence of the structurally chiral material.

Original languageEnglish (US)
Pages (from-to)2985-3004
Number of pages20
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume461
Issue number2061
DOIs
StatePublished - Aug 9 2005

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Twist
Liquid Crystal
Liquid crystals
Crossover
Thin Films
crossovers
Defects
liquid crystals
Thin films
Handed
defects
Term
thin films
Wave transmission
transmittance
matrices
Transmittance
norms
boundary value problems
polarized light

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

Cite this

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title = "Optical crossover phenomenon due to a central 90°-twist defect in a chiral sculptured thin film or chiral liquid crystal",
abstract = "We present a theoretical analysis of a remarkable phenomenon evinced by a periodic structurally chiral material-for example, a chiral sculptured thin film (STF) or a chiral liquid crystal-with a central 90°-twist defect illuminated with normally incident, circularly polarized light. Based on the coupled-wave theory (CWT), an approximate but closed-form solution of the relevant boundary-value problem is obtained in terms of a 4×4 CWT transmission matrix. The CWT transmission matrix is decomposed into two terms. The first term favours total transmission in the central part of the Bragg regime of the axially excited, structurally chiral material, while the second term favours total reflection in the whole Bragg regime. When the thickness of the structurally chiral material is relatively small, the second term is dominated by the first, which gives rise to a co-handed transmittance peak in the centre of the Bragg regime. As the thickness increases, the second term becomes significant and interferes with the first term such that the transmission matrix is isomorphic to that of a defect-free structurally chiral material-except in a tiny wavelength-regime wherein the L∞-norms of the two terms become identical to engender the total-reflection feature. Hence, the co-handed transmittance peak diminishes (and eventually vanishes) as the thickness increases and is replaced by a cross-handed reflectance peak. The bandwidths of the two peaks depend, in different ways, on the local birefringence of the structurally chiral material.",
author = "Fei Wang and Akhlesh Lakhtakia",
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T1 - Optical crossover phenomenon due to a central 90°-twist defect in a chiral sculptured thin film or chiral liquid crystal

AU - Wang, Fei

AU - Lakhtakia, Akhlesh

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N2 - We present a theoretical analysis of a remarkable phenomenon evinced by a periodic structurally chiral material-for example, a chiral sculptured thin film (STF) or a chiral liquid crystal-with a central 90°-twist defect illuminated with normally incident, circularly polarized light. Based on the coupled-wave theory (CWT), an approximate but closed-form solution of the relevant boundary-value problem is obtained in terms of a 4×4 CWT transmission matrix. The CWT transmission matrix is decomposed into two terms. The first term favours total transmission in the central part of the Bragg regime of the axially excited, structurally chiral material, while the second term favours total reflection in the whole Bragg regime. When the thickness of the structurally chiral material is relatively small, the second term is dominated by the first, which gives rise to a co-handed transmittance peak in the centre of the Bragg regime. As the thickness increases, the second term becomes significant and interferes with the first term such that the transmission matrix is isomorphic to that of a defect-free structurally chiral material-except in a tiny wavelength-regime wherein the L∞-norms of the two terms become identical to engender the total-reflection feature. Hence, the co-handed transmittance peak diminishes (and eventually vanishes) as the thickness increases and is replaced by a cross-handed reflectance peak. The bandwidths of the two peaks depend, in different ways, on the local birefringence of the structurally chiral material.

AB - We present a theoretical analysis of a remarkable phenomenon evinced by a periodic structurally chiral material-for example, a chiral sculptured thin film (STF) or a chiral liquid crystal-with a central 90°-twist defect illuminated with normally incident, circularly polarized light. Based on the coupled-wave theory (CWT), an approximate but closed-form solution of the relevant boundary-value problem is obtained in terms of a 4×4 CWT transmission matrix. The CWT transmission matrix is decomposed into two terms. The first term favours total transmission in the central part of the Bragg regime of the axially excited, structurally chiral material, while the second term favours total reflection in the whole Bragg regime. When the thickness of the structurally chiral material is relatively small, the second term is dominated by the first, which gives rise to a co-handed transmittance peak in the centre of the Bragg regime. As the thickness increases, the second term becomes significant and interferes with the first term such that the transmission matrix is isomorphic to that of a defect-free structurally chiral material-except in a tiny wavelength-regime wherein the L∞-norms of the two terms become identical to engender the total-reflection feature. Hence, the co-handed transmittance peak diminishes (and eventually vanishes) as the thickness increases and is replaced by a cross-handed reflectance peak. The bandwidths of the two peaks depend, in different ways, on the local birefringence of the structurally chiral material.

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