The Scattering Problem in <i>PT</i>‐Symmetric Periodic Structures of 1D Two‐Material Waveguide Networks

Wu, Huaming; Yang, Xiangbo; Tang, Ying; Tang, Xiaopeng; Deng, Dongmei; Liu, Hongzhan; Wei, Zhongchao

doi:10.1002/andp.201900120

Cited by 18 publications

(11 citation statements)

References 41 publications

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“…( 2), already proposed by Refs. [43,44]. We note that this condition would support the bidirectional reflectionless, because it results in (M N 1 ) 12 = 0 and (M N 1 ) 21 = 0 (r R,N = 0 and r L,N = 0).…”

Section: (A)mentioning

confidence: 85%

“…At each connecting interface, the wave function and its derivative are continuous. The latter condition is related to energy flux conservation, [43,44].…”

Section: Appendix Bmentioning

confidence: 99%

“…Although several works involving a finite periodic PT-symmetric structures in one dimension had been explored in Refs. [21,28,[42][43][44], the relationship of PT phases, Bloch phase, and propagating transmittance between the building unit cell and its integrated system still remains open. In this work, we investigate the scattering behavior occurred at a finite periodic optical waveguide network in which its unit cell has PT symmetry.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: (A)mentioning

confidence: 85%

“…At each connecting interface, the wave function and its derivative are continuous. The latter condition is related to energy flux conservation, [43,44].…”

Section: Appendix Bmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Lee

2022

Preprint

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“…In this section, we analyze the scattering properties of SOPTPC with N unit cells, in which case the frequency is considered to be real. As demonstrated by 24 , 26 , 27 , the transmittance for the incidences from both sides, the reflectance for the incidence from the left side, and the reflectance for the incidence from the right side can be expressed as …”

Section: Scattering Propertiesmentioning

confidence: 99%

Band structures and scattering properties of the simplest one-dimensional $${\mathscr {P}}{\mathscr {T}}$$-symmetric photonic crystal

Wang

Gou

2022

Sci Rep

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We elucidate the band structures and scattering properties of the simplest one-dimensional parity–time ($${\mathscr {P}}{\mathscr {T}}$$ P T )-symmetric photonic crystal. Its unit cell comprises one gain layer and one balanced loss layer. Herein, the analytic expressions of the band structures and scattering properties are derived, and based on these relations, we reveal and explain the following phenomena: Exceptional point pairs appear from Brillouin boundaries at a nonzero non-Hermiticity. With an increase in non-Hermiticity, each of these pairs moves toward the Brillouin center, finally coalescing into a single point at the Brillouin center at a critical non-Hermiticity value. Near the exceptional point, singular scattering is observed and explained. This refers to the phenomenon whereby transmittances and reflectances for left and right incidences reach exceptionally large values simultaneously. Moreover, these are infinite at some discrete points at which poles and zeros of the scattering matrix are attained. In forbidden gaps, unidirectional weak visibility, where transmittances are zero, is disclosed and analyzed: specifically, the reflectance for incidence from one side is very large, whereas that for incidence from the other side is very small. In this phenomenon, the eigenstates of the scattering matrix are the incident waves from the left and right sides, and their eigenvalues are the corresponding reflectances. Our results are important as new functional optical devices can potentially be developed by utilizing these novel phenomena.

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“…In 2007, El-Ganainy et al [5] constructed PT-symmetric optical systems with complex refractive index materials under paraxial approximation condition, which followed n(x) = n * (x) distribution. Subsequently, the special optical characteristics of PT-symmetric optical systems, such as unidirectional invisibility, [10][11][12][13][14][15][16]20,22] ultrastrong transmission and reflection, [11,15,19] and coherent perfect absorption, [8,16,21] have attracted widespread attention. In, 2017, our research group [18] DOI: 10.1002/andp.202200207 combined the concept of PT-symmetry with optical waveguide networks to construct PT-symmetric optical waveguide networks.…”

Section: Introductionmentioning

confidence: 99%

Quasi‐Blackbody, Bidirectional Super Reflection, and New Total Reflection Produced by Periodic Optical Waveguide Networks Based on Three‐Order PT‐Symmetric Substructures

et al. 2022

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In this paper, six kinds of periodic optical waveguide networks are designed to study the influence of three-order parity-time-symmetric (PT-symmetric) substructures on the singular optical characteristics. It is found that different characteristics correspond to different PT-symmetric substructures, and new singular optical characteristics are produced by adjusting the PT-symmetric substructures. This work demonstrates that these six kinds of systems can create novel quasi-blackbody, super reflection, and new total reflection, which are significantly different from the corresponding traditional properties and have not been reported yet. These findings may deepen the understanding of PT-symmetric optical systems and optical waveguide networks, and these new characteristics may possess potential applications in the design of multifunctional optical structures with efficient information processing.

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The Scattering Problem in PT‐Symmetric Periodic Structures of 1D Two‐Material Waveguide Networks

Cited by 18 publications

References 41 publications

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

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

Band structures and scattering properties of the simplest one-dimensional $${\mathscr {P}}{\mathscr {T}}$$-symmetric photonic crystal

Quasi‐Blackbody, Bidirectional Super Reflection, and New Total Reflection Produced by Periodic Optical Waveguide Networks Based on Three‐Order PT‐Symmetric Substructures

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