Resonance phenomena in finite-periodic multilayer sequence of identical gratings of rectangular bars

Kazanskiy, V.B.; Podlozny, V.

doi:10.1002/(sici)1098-2760(19990520)21:4<299::aid-mop20>3.0.co;2-n

Cited by 6 publications

(3 citation statements)

References 1 publication

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“…Within the diffractive optics community, [67][68][69] there's a contention that producing a multilevel diffractive lens [70] characterized by a surface profile comprising several discrete surface heights-presents a more straightforward task compared to crafting a binary ML, which consists of only two-level surface heights. [71] This argument hinges on the notion that the feature size of the diffractive lens is generally larger.…”

Section: Mls Versus Sdlsmentioning

confidence: 99%

A Review on Reconfigurable Metalenses Revolutionizing Flat Optics

Khonina,

Butt,

Kazanskiy

2023

Advanced Optical Materials

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Metalenses (MLs), representing a groundbreaking paradigm shift within the realm of optics, have ushered in a transformative era in the ability to manipulate and harness the power of light. Diverging from the conventional approach reliant on curved surfaces to bend light, MLs harness intricate arrays of minuscule nanostructures to exert precise control over the phase and amplitude of incident light waves. This revolutionary technology bestows a plethora of advantages, including the creation of ultra‐compact optical systems, the enhancement of focusing capabilities to unprecedented levels, and the capability to rectify optical aberrations in a significantly thinner and more lightweight form factor. MLs have discovered a multitude of applications spanning diverse fields, from imaging and photography to augmenting reality and refining medical devices. They stand as a beacon of hope for reshaping the landscape of optical systems, courtesy of their remarkable adaptability and exceptional performance. As the evolution of MLs forges ahead, they hold immense potential to transcend the boundaries of what can be accomplished in the domain of light‐based technologies. This review presents the recent advances in reconfigurable MLs and their applicability to imaging systems.

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Section: Mls Versus Sdlsmentioning

confidence: 99%

A Review on Reconfigurable Metalenses Revolutionizing Flat Optics

Khonina,

Butt,

Kazanskiy

2023

Advanced Optical Materials

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“…Fortunately, the finite periodic case, involving 2 × 2 matrices, can be solved analytically for an arbitrary number of unit cells, N, first demonstrated in the optical case by Abèles [3] in 1950 and extended to the quantum context [4] in 1981 and later by others [5,6]. Thus, for one-dimensional (1D) waves in locally periodic (finite periodic) media [7][8][9][10][11][12][13], analytical expressions for quantities like the transmittance are available in terms of the Chebyshev polynomials of the second kind [14].…”

Section: Introductionmentioning

confidence: 99%

Exact closed forms for the transmittance of electromagnetic waves in one-dimensional anisotropic periodic media

Torres-Guzmán,

Díaz-de-Anda,

Arriaga

2024

J. Phys. A: Math. Theor.

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In this work, we obtain closed expressions for the transfer matrix and the transmittance of electromagnetic waves propagating in ﬁnite 1D anisotropic periodic stratiﬁed media with an arbitrary number of cells. By invoking the Cayley-Hamilton theorem on the transfer matrix for the electromagnetic ﬁeld in a periodic stratiﬁed media formed by N cells, we obtain a fourth-order recursive relation for the matrix coefﬁcients that deﬁnes the so-called Tetranacci Polynomials. In the symmetric case, corresponding to a unit-cell transfer matrix with a characteristic polynomial where the coefﬁcients of the linear and cubic terms are equal, closed expressions for the solutions to the recursive relation, known as symmetric Tetranacci Polynomials, have recently been derived, allowing us to write the transfer matrix and transmittance in a closed form. We show as sufﬁcient conditions that the 4 × 4 differential propagation matrix of each layer in the binary unit cell, ∆, a) has eigenvalues of the form ± p1, ± p2, with p1 ≠ p2, and b) its off-diagonal 2 × 2 block matrices possess the same symmetric structure in both layers. Otherwise, the recursive relations are still solvable for any 4×4-matrix and provide an algorithm to compute the N-th power of the transfer matrix without carrying out explicitly the matrix multiplication of N matrices. We obtain analytical expressions for the dispersion relation and transmittance, in closed form, for two ﬁnite periodic systems: the first one consists of two birefringent uniaxial media with their optical axis perpendicular to the z-axis, and the second consists of two isotropic media subject to an external magnetic field oriented along the z-axis and exhibiting the Faraday effect. Our formalism applies also to lossy media, magnetic anisotropy or optical activity.

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“…It has been extensively studied in different fields of physics involving wave propagation [1,2]. The resonant transmission is present in mechanical waves analyzed in acoustic [3,4], in electromagnetic waves studied in optics [5,6,7], and in quantum mechanics [8,9,10,11,12]. From Esaki seminal papers [13,14,15], electronic perfect tunnelling in a double barrier system has been explained in terms of the quasi-bound states (QBS) between the barriers [16].…”

Section: Introductionmentioning

confidence: 99%

Recurrence in Resonant Transmission of One-Dimensional Array of Delta Potentials

2014

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The resonant transmission of a moving particle which interacts with an one-dimensional array of N δ-function potentials is investigated. A suitable transfer matrix formulation is used to obtain the particle transmission. We give the parameters for perfect tunnelling and the transcendental equation for the quasi-bound state energies for N = 2, 3 and 4. Conditions for perfect tunnelling and resonant transmission are discussed for arrays with arbitrary N . A model to explain how the tunnelling energy filter works in these systems is proposed here.

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Resonance phenomena in finite-periodic multilayer sequence of identical gratings of rectangular bars

Cited by 6 publications

References 1 publication

A Review on Reconfigurable Metalenses Revolutionizing Flat Optics

A Review on Reconfigurable Metalenses Revolutionizing Flat Optics

Exact closed forms for the transmittance of electromagnetic waves in one-dimensional anisotropic periodic media

Recurrence in Resonant Transmission of One-Dimensional Array of Delta Potentials

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