Engineering wave localization in a fractal waveguide network

Pal, Biplab; Patra, Pinaki; Saha, Jyoti Prasad; Chakrabarti, Abhijit

doi:10.1103/physreva.87.023814

Cited by 15 publications

(11 citation statements)

References 59 publications

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“…As first introduced by Sheng et al [55,56], the wave propagation through any quasi-one dimensional network can be exactly mapped back onto the corresponding electronic case with the appropriate parametric substitution. The analogy [31,57] of the network equations with that of an electron propagating in a similar lattice helps us to study the localization of classical waves. Also, this mapping is entirely a mathematical construction and once this is done the RSRG recursion relations are insensitive to whether the input comes from a quantum case or a classical one.…”

Section: A Photonic Analoguementioning

confidence: 99%

Analytical Study of Quasi-One-Dimensional Flat Band Networks and Slow Light Analogue

Nandy¹

2019

Acta Phys. Pol. A

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Exact method of analytical solution of flat, non-dispersive eigenstates in a class of quasi-one dimensional structures is reported within the tight-binding framework. The states are localized over certain sublattice sites. One such finite size cluster of atomic sites is decoupled from the rest of the system by the special 'non-permissible' vertex having zero amplitude. This immediately leads to the self-trapping of the incoming excitation. We work out an analytical scheme to discern the localizing character of the diffraction free dispersionless modes using real space renormalization group technique. Supportive numerical calculations of spectral profile and transport are demonstrated to substantiate the essence of compact localized states. Possible experimental scope regarding the photonic analogue of the tight-binding electronic case is also discussed elaborately. This eventually unfolds the concepts of slow light and the related re-entrant mode switching from the study of optical dispersion.

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Section: A Photonic Analoguementioning

confidence: 99%

Analytical Study of Quasi-One-Dimensional Flat Band Networks and Slow Light Analogue

Nandy¹

2019

Acta Phys. Pol. A

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“…This leads to the concept of staggered localized modes, where one can have the liberty to delay the onset of localization in space using the RSRG index, and an appropriate frequency [23].…”

Section: Spatial Distribution Of the Flat Band States And The Stagger...mentioning

confidence: 99%

“…The other point of interest in the present work is to analyze the distribution of the amplitudes of such flat band states in real space. Recently, a class of localized eigenfunctions in deterministic fractal geometries has been revealed both in the context of electronic states and optical modes [22,23] which can in principle, be delayed in space by an appropriate choice of the energy of the electron or the frequency of the injected wave. Such states exhibit a fragmented distribution in the respective spectra, a consequence of the underlying lattice topology.…”

Section: Introductionmentioning

confidence: 99%

Engineering slow light and mode crossover in a fractal-kagome waveguide network

Nandy

Chakrabarti

2016

Phys. Rev. A

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We present an analytically exact scheme of unraveling a multitude of flat, dispersionless photonic bands in a kagomé waveguide strip where each elementary plaquette hosts a deterministic fractal geometry of arbitrary size. The number of non-dispersive eigenmodes grows as higher and higher order fractal geometry is embedded in the kagomé motif. Such eigenmodes are found to be localized with finite support in the kagomé strip and exhibit a hierarchy of localization areas. The onset of localization can, in principle, be delayed in space by an appropriate choice of frequency of the incident wave. The length scale at which the onset of localization for each mode occurs, can be tuned at will as prescribed here using a real space renormalization method. Conventional methods of extracting the non-dispersive modes in such geometrically frustrated lattices fail as a non-translationally invariant fractal decorates the unit cells in the transverse direction. The scheme presented here circumvents this difficulty, and thus may inspire the experimentalists to design similar fractal incorporated kagomé or Lieb class of lattices to observe a multifractal distribution of flat photonic bands.

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“…[3,4] Optical waveguide networks (OWNs) composed of 1D waveguides are another type of interesting PBG structures. [5][6][7][8][9][10][11][12] PBG and photonic localization are DOI: 10.1002/andp.202000584 the two main characteristics of PBG structures. Thereinto, PBG can inhibit spontaneous radiation, control and motivate medium radiation, and develop various optical emission devices, [13,14] optical waveguides, [15][16][17] optical filters, [18,19] high efficiency total reflection mirrors, [20,21] low threshold lasers, [22,23] and photon frequency converters.…”

Section: Introductionmentioning

confidence: 99%

Ultrawide Photonic Bandgap and Ultrastrong Photonic Localization Produced by Series of Periodic Networks

Yang

Deng

et al. 2021

Annalen der Physik

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A series of periodic networks is designed, in which all of the unit cells construct a series of fractal triangles, and their extraordinary optical characteristics for producing ultrawide photonic bandgap (PBG) and ultrastrong photonic localization are investigated. The results indicate that with increasing fractal generation, the number of equivalent triangular loops increases exponentially, and consequently the gap-midgap ratio of the PBG produced by the networks with the integer waveguide length ratio of 1:2 enlarges rapidly and tends to the limit at 200%. For the networks with the noninteger waveguide length ratio of 1:2 ± d (where 0 < d ≤ 10 −2 ), an extremely narrow passband occurs in the middle of the wide PBG. Furthermore, the ultrastrong photonic localization is generated when the electromagnetic wave with the frequency of the all-transmission peak in the ultranarrow passband propagates in the networks. This type of fractal triangular networks may have applications to design all-optical devices, such as highly sensitive optical filters, highly sensitive all-optical switches, and high-performance photonic energy-storage devices.

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Engineering wave localization in a fractal waveguide network

Cited by 15 publications

References 59 publications

Analytical Study of Quasi-One-Dimensional Flat Band Networks and Slow Light Analogue

Analytical Study of Quasi-One-Dimensional Flat Band Networks and Slow Light Analogue

Engineering slow light and mode crossover in a fractal-kagome waveguide network

Ultrawide Photonic Bandgap and Ultrastrong Photonic Localization Produced by Series of Periodic Networks

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