Unidirectional reflectionless transmission for two-dimensional 
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-symmetric periodic structures

Yuan, Lijun; Lu, Ya Yan

doi:10.1103/physreva.100.053805

Cited by 24 publications

(13 citation statements)

References 34 publications

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“…Figure 7 shows the transmittance T ± = |t ± | 2 and reflectance R ± = |r ± | 2 as functions of the frequency. As is well known (see, for example, [26]) for PT -symmetric structures, the two transmission coefficients t + and t − coincide. The figure clearly shows the shift of the zeros of the reflectance close to the critical point.…”

Section: Scattering Matrix and Unidirectional Reflectionless Transmis...supporting

confidence: 58%

“…Moreover, as the gain and loss increases, there is a shift in the zeros: the zero of one of the reflection coefficients will be shifted upwards and one will be shifted downwards. We emphasize that, unlike previous work based on coupled-mode approximations (for example [15,23]) or perturbation theory [26], the methods presented here provide a rigorous explanation for unidirectional reflectionless transmission and are valid even in regimes with large gain and loss.…”

Section: Introductionmentioning

confidence: 92%

“…For example, the scattered wave can now depend on which side the incident wave is impinging from. While being impossible in structures without gain and loss, PT -symmetric structures can have frequencies at which the reflection is zero when the wave is impinging from one side, and non-zero when the wave is impinging from the opposite side [15,18,26]. We will refer to such case as unidirectional reflectionless transmission.…”

Section: Introductionmentioning

confidence: 99%

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Exceptional points in parity-time-symmetric subwavelength metamaterials

Ammari¹,

Davies²,

Hiltunen³

et al. 2020

Preprint

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When sources of energy gain and loss are introduced to a wave scattering system, the underlying mathematical formulation will be non-Hermitian. This paves the way for the existence of exceptional points, whereby eigenmodes are linearly dependent. The main goal of this work is to study the existence and consequences of exceptional points in the setting of high-contrast subwavelength metamaterials. We begin by studying a system of two paritytime-symmetric subwavelength resonators and prove that this system supports exceptional points. Using homogenization theory, we study a large ensemble of resonators and show that this behaviour can be replicated at the macroscale. Finally, we study a metascreen of subwavelength resonators and prove that there are frequencies at which this system exhibits unidirectional reflectionless transmission.

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Section: Scattering Matrix and Unidirectional Reflectionless Transmis...supporting

confidence: 58%

Section: Introductionmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Exceptional points in parity-time-symmetric subwavelength metamaterials

Ammari¹,

Davies²,

Hiltunen³

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…where S 11 , S 21 , S 22 and S 12 are the reflection and transmission coefficients associated with the left and right incident waves, respectively, and they are the entries of a 2 × 2 scattering matrix S. Due to the reciprocity and energy conservation, S is a symmetric and unitary matrix [49]. For Eq.…”

Section: Structural Perturbationmentioning

confidence: 99%

Perturbation theories for symmetry-protected bound states in the continuum on two-dimensional periodic structures

Yuan

2020

Phys. Rev. A

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On dielectric periodic structures with a reflection symmetry in a periodic direction, there can be antisymmetric standing waves (ASWs) that are symmetry-protected bound states in the continuum (BICs). The BICs have found many applications, mainly because they give rise to resonant modes of extremely large quality-factors (Q-factors). The ASWs are robust to symmetric perturbations of the structure, but they become resonant modes if the perturbation is non-symmetric. The Q-factor of a resonant mode on a perturbed structure is typically O(1/δ 2 ) where δ is the amplitude of the perturbation, but special perturbations can produce resonant modes with larger Q-factors. For twodimensional (2D) periodic structures with a 1D periodicity, we derive conditions on the perturbation profile such that the Q-factors are O(1/δ 4 ) or O(1/δ 6 ). For the unperturbed structure, an ASW is surrounded by resonant modes with a nonzero Bloch wave vector. For 2D periodic structures, the Q-factors of nearby resonant modes are typically O(1/β 2 ), where β is the Bloch wavenumber. We show that the Q-factors can be O(1/β 6 ) if the ASW satisfies a simple condition.

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“…These distinctive PT phases can serve as exotic functionalities, for example, uni-directional invisibility [21,[27][28][29], subdiffraction imaging [30,31], coherent perfect absorber-laser [19,20], PT-symmetric whispering gallery mode resonators [32,33], uni-directional optical pulling force [34][35][36], superior sensing capability [7,8,37,38], single-mode microrings lasing [39,40], and Bloch oscilla-tions [41].…”

Section: Introductionmentioning

confidence: 99%

Propagating waves, bi-directional reflectionless, and coherent perfect absorber-laser in finite periodic PT-symmetric waveguide networks

Lee

2022

Preprint

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We investigate the scattering behavior between a unit cell with PT-symmetry and its integrated system composed of the N-cells. In particular, we discuss the formations of propagating transmittance, bi-directional reflectionless, and coherent perfect absorber-laser (CPAL) occurred at a finite periodic optical waveguide network. Through the use of parametric space obtained from considerations of PT-symmetric transfer matrix and Lorentz reciprocity theorem, our outcome is regardless of operating frequency, system configurations, and materials embedded, also valid for any two-port wave systems. Hence, we can interpret the relationship among the Bloch phase and the consequent propagating transmitted wave. We observe that when its building unit cell is operated at PT broken symmetric phase or an exceptional point, the integrated system would always have a propagating transmitted wave, independent of the number and transmission phase of the unit cell. On the other hand, when the unit cell is operated at PT-symmetric phase, the formation of propagating transmitted waves would depend on the transmission phase of that. We find that even though the unit cell is not operated at the exceptional point, with a proper number of unit cells and operation of specific PT-phase, it can eventually achieve the reflectionless with bi-directionality. To implement CPAL in an integrated system, there are two approaches. One is by unit cells having CPAL, while its construction number has to be odd. Another one is through operation of specific broken symmetric phases and a proper number of unit cells, while the transmission phase is required to be null. We believe this work could offer an alternative means to observe extraordinary wave phenomena of PT-symmetric photonics by a replacement of a finite periodic structure.

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Unidirectional reflectionless transmission for two-dimensional PT -symmetric periodic structures

Cited by 24 publications

References 34 publications

Exceptional points in parity-time-symmetric subwavelength metamaterials

Exceptional points in parity-time-symmetric subwavelength metamaterials

Perturbation theories for symmetry-protected bound states in the continuum on two-dimensional periodic structures

Propagating waves, bi-directional reflectionless, and coherent perfect absorber-laser in finite periodic PT-symmetric waveguide networks

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