Wannier functions of a one-dimensional photonic crystal with inversion symmetry

Romano, Maria Cecilia; Nacbar, Denis Rafael; Bruno-Alfonso, Alexys

doi:10.1088/0953-4075/43/21/215403

Cited by 13 publications

(7 citation statements)

References 14 publications

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“…The dielectric function has the periodicity of the photonic crystal, such that (z + d) = (z), with d = a + b the period of the crystal. Considering normal incidence only, we write the magnetic field as [59]:…”

Section: A Derivation Of the Dispersion Equationmentioning

confidence: 99%

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Topological photonic Tamm states and the Su-Schrieffer-Heeger model

et al. 2020

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In this paper we study the formation of topological Tamm states at the interface between a semi-infinite one-dimensional photonic-crystal and a metal. We show that when the system is topologically non-trivial there is a single Tamm state in each of the band-gaps, whereas if it is topologically trivial the band-gaps host no Tamm states. We connect the disappearance of the Tamm states with a topological transition from a topologically non-trivial system to a topologically trivial one. This topological transition is driven by the modification of the dielectric functions in the unit cell. Our interpretation is further supported by an exact mapping between the solutions of Maxwell's equations and the existence of a tight-binding representation of those solutions. We show that the tight-binding representation of the 1D photonic crystal, based on Maxwell's equations, corresponds to a Su-Schrieffer-Heeger-type model (SSH-model) for each set of pairs of bands. Expanding this representation near the band edge we show that the system can be described by a Dirac-like Hamiltonian. It allows one to characterize the topology associated with the solution of Maxwell's equations via the winding number. In addition, for the infinite system, we provide an analytical expression for the photonic bands from which the band-gaps can be computed. arXiv:2001.10628v1 [cond-mat.mes-hall]

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Section: A Derivation Of the Dispersion Equationmentioning

confidence: 99%

“…(7) Now, we can make use the transfer matrix method [59,60] to obtain the fields at z + ∆z from their expressions at z, that is:…”

Section: A Derivation Of the Dispersion Equationmentioning

confidence: 99%

Topological photonic Tamm states and the Su-Schrieffer-Heeger model

et al. 2020

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“…As an application of these tools, let us construct the MLWFs for the "Photonic Kronig-Penney" (PhKP) model of a 1D photonic crystal [37]. The PhKP model can be realized by a periodic one dimensional array of slabs of width ab and dielectric constant ε separated by regions of vacuum of width a(1 − b), where 0 < b < 1.…”

Section: A Properties Of Maxwell's Equations In a Photonic Crystalmentioning

confidence: 99%

“…Although the symmetry properties of photonic band representations have proved useful, little attention has been paid thus far to the localized (hybrid) Wannier functions themselves. Photonic Wannier functions have been used to numerically study defect modes in photonic crystals [37][38][39][40][41][42][43][44][45][46][47]. Here we aim to connect this earlier work on photonic Wannier functions directly to topology, showing how the theory of band representations can be used to study photonic crystals in a new light.…”

Section: Introductionmentioning

confidence: 99%

Wannier Function Methods for Topological Modes in 1D Photonic Crystals

Gupta,

Bradlyn

2022

Preprint

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In this work, we use Wannier functions to analyze topological phase transitions in one dimensional photonic crystals. We first review the construction of exponentially localized Wannier functions in one dimension, and show how to numerically construct them for photonic systems. We then apply these tools to study a photonic analog of the Su-Schrieffer-Heeger model. We use photonic Wannier functions to construct a quantitatively accurate approximate model for the topological phase transition, and compute the localization of topological defect states. Finally, we discuss the implications of our work for the study of band representations for photonic crystals.

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“…More recently, the case of simple bands in 1D crystals without inversion symmetry () and the exact optimization of the localization of generalized WFs of a pair of bands () have been addressed. Furthermore, the ideas have been extended to deal with photonic structures () and persistent currents in quantum rings ().…”

Section: Introductionmentioning

confidence: 99%

Wannier functions of cumulene: A tight‐binding approach

Ribeiro

Nacbar

Bruno-Alfonso

2015

Physica Status Solidi (b)

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Exponentially localized Wannier functions of cumulene are calculated from the Bloch functions obtained through a tight‐binding approach. Numerical results and discussions are given for the π and σ bands. In the latter case, the single‐band Wannier functions are similar to the orbitals of a diatomic molecule, while the two‐band Wannier functions resemble hybrid atomic orbitals. Contour plot of an sp‐like Wannier function of cumulene.

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Wannier functions of a one-dimensional photonic crystal with inversion symmetry

Cited by 13 publications

References 14 publications

Topological photonic Tamm states and the Su-Schrieffer-Heeger model

Topological photonic Tamm states and the Su-Schrieffer-Heeger model

Wannier Function Methods for Topological Modes in 1D Photonic Crystals

Wannier functions of cumulene: A tight‐binding approach

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