Unidirectional channel-drop filter by one-way gyromagnetic photonic crystal waveguides

Fu, Jinxin; Lian, Jin; Liu, Rongjuan; Gan, Lin; Li, Zhiyuan

doi:10.1063/1.3593027

Cited by 80 publications

(47 citation statements)

References 16 publications

(13 reference statements)

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“…They have enabled novel device designs for tunable delays and phase shifts with unity transmission [7], reflectionless waveguide bends and splitters [30], signal switches [31], directional filters [32,33], broadband circulators [34] and slowlight waveguides [35]. Very recently, multi-mode one-way waveguides of large bulk Chern numbers (|C| = 2, 3, 4) have been constructed by opening gaps of multiple point degeneracies simultaneously [13], providing even richer possibilities in device functionalities.…”

Section: Gyromagnetic Photonic Crystalsmentioning

confidence: 99%

Topological photonics

2014

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The application of topology, the mathematics studying conserved properties through continuous deformations, is creating new opportunities within photonics, bringing with it theoretical discoveries and a wealth of potential applications. This field was inspired by the discovery of topological insulators, in which interfacial electrons transport without dissipation even in the presence of impurities. Similarly, the use of carefully-designed wave-vector space topologies allows the creation of interfaces that support new states of light with useful and interesting properties. In particular, it suggests the realization of unidirectional waveguides that allow light to flow around large imperfections without back-reflection. The present review explains the underlying principles and highlights how topological effects can be realized in photonic crystals, coupled resonators, metamaterials and quasicrystals.Frequency, wavevector, polarization and phase are degrees of freedom that are often used to describe a photonic system. In the last few years, topology -a property of a photonic material that characterizes the quantized global behavior of the wavefunctions on its entire dispersion band-has been emerging as another indispensable ingredient, opening a path forward to the discovery of fundamentally new states of light and possibly revolutionary applications. Possible practical applications of topological photonics include photonic circuitry less dependent on isolators and slow light insensitive to disorder.Topological ideas in photonics branch from exciting developments in solid-state materials, along with the discovery of new phases of matter called topological insulators [1, 2]. Topological insulators, being insulating in their bulk, conduct electricity on their surfaces without dissipation or backscattering, even in the presence of large impurities. The first example was the integer quantum Hall effect, discovered in 1980. In quantum Hall states, two-dimensional (2D) electrons in a uniform magnetic field form quantized cyclotron orbits of discrete eigenvalues called Landau levels. When the electron energy sits within the energy gap between the Landau levels, the measured edge conductance remains constant within the accuracy of about one part in a billion, regardless of sample details like size, composition and impurity levels. In 1988, Haldane proposed a theoretical model to achieve the same phenomenon but in a periodic system without Landau levels [3], the so-called quantum anomalous Hall effect.Posted on arXiv in 2005, Haldane and Raghu transcribed the key feature of this electronic model into photonics [4,5]. They theoretically proposed the photonic analogue of the quantum (anomalous) Hall effect in photonic crystals [6], the periodic variation of optical materials, molding photons the same way as solids modulating electrons. Three years later, the idea was confirmed by Wang et al., who provided realistic material designs [7] and experimental observations [8]. Those studies spurred numerous subsequent theoretical [9...

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Section: Gyromagnetic Photonic Crystalsmentioning

confidence: 99%

Topological photonics

2014

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“…Negative Chern numbers represent the negative group velocities of the corresponding one-way edge states. We note that although the calculations here are done in 2D for TM modes, the designs can exactly be translated to 3D metallic waveguides in experiments [3,[21][22][23][24]. The material dispersion does not change the main features in the map, if the material operation frequency is placed at the center of the gap of interest.…”

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confidence: 99%

“…Using the discovered multimode one-way waveguides, we also predicted an adjustable power splitter with unity efficiency. Since the first demonstration of the quantum (anomalous) Hall phase in photonic crystals, there have been a wide range of theoretical [26][27][28][29][30][31][32] and experimental [21][22][23][24] efforts to investigate systems with single-mode one-way edge states. We expect our findings of large Chern numbers and multimode one-way waveguides to create even wider opportunities in topological photonics.…”

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confidence: 99%

Multimode One-Way Waveguides of Large Chern Numbers

2014

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“…Fundamentally, having band gaps with higher gap Chern numbers greatly expands the phases available for topological photonics. These results can potentially enable multimode one-way waveguides with high capacity and coupling efficiencies, as well as many other devices [22][23][24][25]. A topological photonic circuit can also be made …”

Section: Prl 115 253901 (2015) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 98%

High Chern Numbers in Photonic Crystals

Rechtsman

2015

Physics

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Despite great interest in the quantum anomalous Hall phase and its analogs, all experimental studies in electronic and bosonic systems have been limited to a Chern number of one. Here, we perform microwave transmission measurements in the bulk and at the edge of ferrimagnetic photonic crystals. Band gaps with large Chern numbers of 2, 3, and 4 are present in the experimental results, which show excellent agreement with theory. We measure the mode profiles and Fourier transform them to produce dispersion relations of the edge modes, whose number and direction match our Chern number calculations. DOI: 10.1103/PhysRevLett.115.253901 PACS numbers: 42.79.Ta, 42.70.Qs, 42.79.Fm, 42.79.Gn The Chern number [1] is an integer defining the topological phase in the quantum Hall effect (QHE) [2], which determines the number of topologically protected chiral edge modes. The quantum anomalous Hall effect (QAHE) possesses these same properties as an intrinsic property of the band structure with time reversal symmetry breaking [3,4]. Recent experiments have discovered the QAHE and its analogs in ferrimagnetic photonic crystals [5], magnetically doped thin films [6], and ultracold fermion lattices [7]. However, the Chern numbers observed in all of these systems were limited to AE1. Finding larger Chern numbers would fundamentally expand the known topological phases [8][9][10][11][12].Here, we provide the first explicit experimental observation of Chern numbers of magnitude 2, 3, and 4, by measuring bulk transmission, edge transmission, and the edge-mode dispersion relations in a ferrimagnetic photonic crystal. The excellent agreement between the experiment and the modeling allows us to identify various topological band gaps and map out the dispersion relations of one-way edge modes for the first time in any QHE or QAHE system in nature.In a 2D system one can realize bands with nonzero Chern numbers, and generate the QAHE, by applying a T-breaking perturbation [13][14][15]. The Chern number is defined as the integral of the Berry flux over the entire Brillioun zone. When connected bands are gapped by a T-breaking perturbation, the bands will exchange equal and opposite Berry flux at each degenerate point, with the total Berry flux exchanged determining the Chern number. For instance, two isolated bands connected by one pair of Dirac points gapped by T-breaking will acquire AE2π Berry flux (π from each Dirac point) and a Chern number associated with the band gap ("gap Chern number") of AE1. A general way to calculate the gap Chern number (C gap ¼ ΣC i ) is to sum the Chern numbers of all the bands below the band gap [16]. A band gap with C gap ¼ 0 is trivial, while a band gap with C gap ≠ 0 is topologically nontrivial.In our previous theoretical study, we found that the magnitude of the gap Chern number can be increased above one by simultaneously gapping multiple sets of Dirac and quadratic degeneracies. If Berry flux from the gapped degeneracies adds constructively, C gap can be large. In Fig. 1(a) we present a theoretical to...

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Unidirectional channel-drop filter by one-way gyromagnetic photonic crystal waveguides

Cited by 80 publications

References 16 publications

Topological photonics

Topological photonics

Multimode One-Way Waveguides of Large Chern Numbers

High Chern Numbers in Photonic Crystals

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