Bloch impedance in negative index photonic crystals

Croënne, Charles; Fabre, Nathalie; Gaillot, Davy P.; Vanbésien, O.; Lippens, D.

doi:10.1103/physrevb.77.125333

Cited by 43 publications

(16 citation statements)

References 41 publications

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“…Simovski et al [122] give a good overview of this method, which is followed by many authors to define and calculate impedances for PCs [62,65,141,142], and for metamaterials [138,139,[143][144][145][146]. If a well-defined PC impedance can exist, satisfy Eq.…”

Section: Scattering-based Definitionsmentioning

confidence: 99%

Photonic-crystal surface modes found from impedances

et al. 2010

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We present a rigorous definition of a wave impedance for 2D rectangular and triangular lattice photonic crystals (PCs), in the form of a matrix. Reflection and transmission at an interface between PCs can be represented by matrices that relate the Bloch mode (eigenmode) amplitudes in the two PCs; we show that these matrices, which are multi-mode generalisations of reflection and transmission coefficients, may be calculated from the PCs' impedances that we define.Given the impedances and Bloch factors (propagation constants) of a collection of PCs, the reflection and transmission properties of arbitrary stacks of these PCs may be calculated efficiently using a few matrix operations. Therefore our definition enables PC-based antireflection coatings to be designed efficiently: some computationally expensive simulations are required in an initial step to find a range of PCs' impedances, but then the reflectances of every coating that consists of a stack of these PCs can be calculated without any further simulations.We first define the PC impedance from the transfer matrix of a single PC layer (i.e., a grating). Since transfer matrix methods are not especially widespread, we also present a method and associated source code to extract a PC's propagating and evanescent Bloch modes from a scattering calculation that can be performed by any off-the-shelf field solver, and to calculate impedances from the extracted modal fields.Finally, we put our method to use. We apply it to design antireflection coatings, nearly eliminating reflection at a single frequency for one or both polarisations, or lowering it across a larger bandwidth. We use it to find surface modes at interfaces between PCs and air, and their projected band structures. We use the impedance to define effective parameters for PC homogenisation, and we briefly describe how our definition has been used to dispersion engineer a PC waveguide. Statement of contribution for joint author publicationsLawrence, F. J. et al. "Antireflection coatings for two-dimensional photonic crystals using a rigorous impedance definition". Appl. Phys. Lett. 93, 1114Lett. 93, (2008 This Letter is partially based on work done in FL's Honours year, and partially on work done during his PhD. Most of the software used was provided by KD and LB, and FL extended it in collaboration with them. In FL's PhD he extended the software implementation of the method (with help from KD and LB) to support non-normal incidence and frequencies above the first Wood anomaly. FL wrote the letter, which was heavily edited and proofread by MdS, KD, and LB.Lawrence, F. J. et al. "Impedance of square and triangular lattice photonic crystals". Phys. Rev. A 80, 23826 (2009) The suggestion of generalising the method to triangular lattices was made by FL's supervisors. LB supplied the orthogonality relations, which as noted in the paper are from previous work, and FL worked out how to use these to define the impedance for these structures. LB suggested the final notation used in the paper. Taking the Ma...

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Section: Scattering-based Definitionsmentioning

confidence: 99%

Photonic-crystal surface modes found from impedances

et al. 2010

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“…Because of the appearance of FMR, the unit cell exhibits a Lorentz type dispersion for the permeability with negative values around the FMR frequency. 24,25 On account of the stopband will appear in transmission spectrum when the permeability is negative, the ferrite rod can be used to fabricate filters. In addition, the FMR frequency decreases as l increases from 1 mm to 2.5 mm, which is consistent with that predicted by Eq.…”

Section: Resultsmentioning

confidence: 99%

Tunable metamaterial bandstop filter based on ferromagnetic resonance

et al. 2015

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Tunable wideband microwave bandstop filters have been investigated by experiments and simulations. The negative permeability is realized around the ferromagnetic resonance frequency which can be influenced by the demagnetization factor of the ferrite rods. For the filter composed of two ferrite rods with different size, it exhibits a -3 db stop bandwidth as large as 500 MHz, peak absorption of -40 db and an out-of-stopband insertion loss of -1.5 db. This work provides a new way to fabricate the microwave bandstop filters.

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“…Up to now, most of present metamaterial configuration are constructed by using artificial microstructures such as split ring resonator (SRR) or wire [7][8][9][10][11][12][13], whose size and periodicity are far smaller than the operating wavelengths so that the response of metamaterial to electromagnetic/optics wave can be interpreted by using effective parameters [14][15][16]. Generally, the macroscopic behaviours of metamaterial structure derived from effective electromagnetic parameters are engineered by the basic microstructure element, i.e., metamolecule.…”

Section: Introductionmentioning

confidence: 99%

Coupling Effect for Dielectric Metamaterial Dimer

Zhang¹,

Sadaune²,

Kang³

et al. 2012

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Abstract-In this paper, we report experimentally and numerically on coupling effects of dielectric metamaterial dimer (metadimer) which composed of two identical ceramic cubes with high permittivity. The distance dependence of Mie resonance for metadimer is investigated under various polarizations of external wave. By changing the configurations and alignment of dimer resonator, it is revealed that magnetic and electric resonances of metadimer exhibits a red/blue shift, resulting from longitudinal or transverse coupling effects of dipoles. Besides, quasi bound states between tightly stacked dielectric cubes are also been pointed out for electric Mie resonance, which is responsible for an unexpected frequency shift with a reverse variation.

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Bloch impedance in negative index photonic crystals

Cited by 43 publications

References 41 publications

Photonic-crystal surface modes found from impedances

Photonic-crystal surface modes found from impedances

Tunable metamaterial bandstop filter based on ferromagnetic resonance

Coupling Effect for Dielectric Metamaterial Dimer

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