Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies

Feng, Liang; Xu, Yin; Fegadolli, William S.; Lu, M.; Oliveira, J.E.B.; Almeida, Vilson R.; Chen, Yanfeng; Scherer, Axel

doi:10.1038/nmat3495

Cited by 1,342 publications

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“…We expect that our predictions can be verified by combining recent advances in shaping complex wave fronts 3 with new techniques to fabricate non-Hermitian scattering structures with gain and loss [7][8][9][10] . As the precise combination of gain and loss in the same device is challenging, we suggest using passive structures with only loss in the first place.…”

Section: Discussionmentioning

confidence: 66%

“…They also remain valid for any sign of Kerr nonlinearity and thus allow us to perform a modulational stability analysis for non-homogeneous potentials. The most appropriate context to study the MI of such solutions is that of PT -symmetric optics [6][7][8][9][10][11]14,[19][20][21][22]24 . We find that in the selffocusing regime, the waves are always unstable, whereas in the defocusing regime the instability appears for specific values of Bloch momenta.…”

Section: Discussionmentioning

confidence: 99%

“…Such non-Hermitian potential regions 4,5 , which serve as sources and sinks for waves, respectively, can give rise to novel wave effects that are impossible to realize with conventional, Hermitian potentials. Examples of this kind, which were meanwhile also realized in the experiment [6][7][8][9][10] , are the unidirectional invisibility of a gain-loss potential 11 , devices that can simultaneously act as laser and as a perfect absorber [12][13][14] and resonant structures with unusual features like non-reciprocal light transmission 10 or loss-induced lasing [15][16][17] . In particular, systems with a so-called parity-time (PT ) symmetry 18 , where gain and loss are carefully balanced, have recently attracted enormous interest in the context of nonHermitian photonics [19][20][21][22][23][24] .…”

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confidence: 99%

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Constant-intensity waves and their modulation instability in non-Hermitian potentials

et al. 2015

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In all of the diverse areas of science where waves play an important role, one of the most fundamental solutions of the corresponding wave equation is a stationary wave with constant intensity. The most familiar example is that of a plane wave propagating in free space. In the presence of any Hermitian potential, a wave's constant intensity is, however, immediately destroyed due to scattering. Here we show that this fundamental restriction is conveniently lifted when working with non-Hermitian potentials. In particular, we present a whole class of waves that have constant intensity in the presence of linear as well as of nonlinear inhomogeneous media with gain and loss. These solutions allow us to study the fundamental phenomenon of modulation instability in an inhomogeneous environment. Our results pose a new challenge for the experiments on non-Hermitian scattering that have recently been put forward.

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Section: Discussionmentioning

confidence: 66%

Section: Discussionmentioning

confidence: 99%

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confidence: 99%

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Constant-intensity waves and their modulation instability in non-Hermitian potentials

et al. 2015

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“…Since it is not easy to achieve PT symmetry experimentally, several ways have been proposed to avoid the use of gain in a system. For example, a system with asymmetric loss is equivalent to a PT -symmetric system with a background of uniform loss, and so no gain is required to achieve an EP [3,[21][22][23][24]. In a system with many coupled modes, the emergence of multiple EPs and their interactions can occur under system parameter variation [25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Coalescence of exceptional points and phase diagrams for one-dimensionalPT-symmetric photonic crystals

2015

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Non-Hermitian systems with parity-time-(PT )-symmetric complex potentials can exhibit a phase transition when the degree of non-Hermiticity is increased. Two eigenstates coalesce at a transition point, which is known as the exceptional point (EP) for a discrete spectrum and spectral singularity for a continuous spectrum. The existence of an EP is known to give rise to a great variety of novel behaviors in various fields of physics. In this work, we study the complex band structures of one-dimensional photonic crystals with PT -symmetric complex potentials by setting up a Hamiltonian using the Bloch states of the photonic crystal without loss or gain as a basis. As a function of the degree of non-Hermiticity, two types of PT symmetry transitions are found. One is that a PT -broken phase can reenter into a PT -exact phase at a higher degree of non-Hermiticity. The other is that two EPs, one originating from the Brillouin zone center and the other from the Brillouin zone boundary, can coalesce at some k point in the interior of the Brillouin zone and create a singularity of higher order. Furthermore, we can induce a band inversion by tuning the filling ratio of the photonic crystal, and we find that the geometric phases of the bands before and after the inversion are independent of the amount of non-Hermiticity as long as the PT -exact phase is not broken. The standard concept of topological transition can hence be extended to non-Hermitian systems.

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“…The conditions presented here vastly expand the design space for observing these effects. We also show that a similarly broad class of systems exhibit a loss-induced narrowing of the density of states.Recently, the study of parity-time (PT ) symmetric optical systems has highlighted the importance of exploring non-Hermitian systems with patterned gain and loss [1][2][3][4][5][6][7][8][9][10][11], and has led to the discovery of a remarkable array of phenomena, such as loss-induced transmission in waveguides [12], unidirectional transport behavior [13][14][15][16][17], reversed pump dependence in lasers [18][19][20], and band flattening in periodic structures [4,[21][22][23][24]. These effects are leading to new possibilities for constructing on-chip integrated photonic circuits for the manipulation of light.…”

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confidence: 99%

Eigenvalue dynamics in the presence of nonuniform gain and loss

Cerjan¹,

Fan²

2016

Phys. Rev. A

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Loss-induced transmission in waveguides, and reversed pump dependence in lasers, are two prominent examples of counter-intuitive effects in non-Hermitian systems with patterned gain and loss. By analyzing the eigenvalue dynamics of complex symmetric matrices when a system parameter is varied, we introduce a general set of theoretical conditions for these two effects. We show that these effects arise in any irreducible system where the gain or loss is added to a subset of the elements of the system, without the need for parity-time symmetry or for the system to be near an exceptional point. These results are confirmed using full-wave numerical simulations. The conditions presented here vastly expand the design space for observing these effects. We also show that a similarly broad class of systems exhibit a loss-induced narrowing of the density of states.Recently, the study of parity-time (PT ) symmetric optical systems has highlighted the importance of exploring non-Hermitian systems with patterned gain and loss [1][2][3][4][5][6][7][8][9][10][11], and has led to the discovery of a remarkable array of phenomena, such as loss-induced transmission in waveguides [12], unidirectional transport behavior [13][14][15][16][17], reversed pump dependence in lasers [18][19][20], and band flattening in periodic structures [4,[21][22][23][24]. These effects are leading to new possibilities for constructing on-chip integrated photonic circuits for the manipulation of light.Here, we focus on two of these effects: loss-induced transmission in waveguides, and reversed pump dependence in lasers. Both of these effects are fascinating since they are quite counter-intuitive. They are also of potential practical importance in providing novel mechanisms for optical switching based on gain or loss modulation. In loss-induced transmission, loss is added to one of two otherwise identical, parallel coupled waveguides [12]. After a critical amount of loss is added, further increases in the absorption also increases the total transmission through the waveguide pair. Likewise, reversed pump dependence can be observed in laser systems consisting of two coupled cavities [18][19][20]25]. First, one of these cavities is pumped such that the total system begins to lase. However, if the pump in the first cavity is then held constant and the gain in the second cavity is increased, the total output lasing power can be seen to decrease until the total gain distribution becomes relatively uniform, so long as the added gain is sufficiently greater than the losses of the unpumped system. If the laser is close to threshold after gain is added to the first cavity, this mechanism can drive the laser below threshold.Initially, these types of counter-intuitive effects were found in PT symmetric systems in their broken phase, and thus the onset of these behaviors was associated with the occurrence of an exceptional point [12]. Subsequent analyses demonstrated that loss-induced transmission in waveguides and reverse pump dependence in lasers could be found in s...

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Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies

Cited by 1,342 publications

References 32 publications

Constant-intensity waves and their modulation instability in non-Hermitian potentials

Constant-intensity waves and their modulation instability in non-Hermitian potentials

Coalescence of exceptional points and phase diagrams for one-dimensionalPT-symmetric photonic crystals

Eigenvalue dynamics in the presence of nonuniform gain and loss

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