Topologically Protected Complete Polarization Conversion

Guo, Yu; Xiao, Meng

doi:10.1103/physrevlett.119.167401

Cited by 105 publications

(86 citation statements)

References 33 publications

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“…The slab is placed on a mirror. In a recent paper, we showed that such a structure can achieve complete conversion between linear polarizations. And moreover such complete conversion is topological in nature, and hence can occur over a wide range of frequencies .…”

Section: Introductionmentioning

confidence: 99%

“…In a recent paper, we showed that such a structure can achieve complete conversion between linear polarizations. And moreover such complete conversion is topological in nature, and hence can occur over a wide range of frequencies . Building upon our previous works, here we show that this structure can achieve arbitrary polarization conversion: For an incident light with any given polarization, arbitrary output polarization can be achieved over a wide range of frequencies, provided that we simply vary the direction of the incident light with respect to the structure, without any modification of the structure.…”

Section: Introductionmentioning

confidence: 99%

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Arbitrary Polarization Conversion with a Photonic Crystal Slab

Guo

Xiao

Zhou

et al. 2019

Advanced Optical Materials

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Our structure consists of a photonic crystal slab patterned with a square array of air holes introduced into the dielectric slab and a mirror underneath, as illustrated in Figure 1. We choose the periodicity of the structure such that within the wavelength It is shown that a simple photonic crystal slab structure provides a powerful mechanism for the control of the polarization properties of light. For a lossless system, for a given incident light with any fixed polarization, one can generate arbitrary polarization in the reflected light, as one varies the direction of the incident light. In the lossy system, the capability for arbitrary polarization generation is still preserved for s-or p-polarized incident light. This capability for arbitrary polarization generation closely relates to the nontrivial topological properties of the reflection matrix of the structure and exists over a wide range of frequencies.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Arbitrary Polarization Conversion with a Photonic Crystal Slab

Guo

Xiao

Zhou

et al. 2019

Advanced Optical Materials

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“…These are artificial materials composed of two or more different constituents which form a macroscopic crystalline structure. A few important examples are gyrotropic photonic crystals [31][32][33], Floquet topological insulators [39][40][41] and bianisotropic metamaterials [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56]. Instead, we focus on the microscopic domain and utilize the periodicity of the atomic lattice itself.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal topological electromagnetic phases of matter

Mechelen

Jacob

2019

Phys. Rev. B

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In 2+1D, nonlocal topological electromagnetic phases are defined as atomic-scale media which host photonic monopoles in the bulk band structure and respect bosonic symmetries (e.g. time-reversal T 2 = +1). Additionally, they support topologically protected spin-1 edge states, which are fundamentally different than spin-1 ⁄2 and pseudo-spin-1 ⁄2 edge states arising in fermionic and pseudo-fermionic systems. The striking feature of the edge state is that all electric and magnetic field components vanish at the boundary -in stark contrast to analogs of Jackiw-Rebbi domain wall states. This surprising open boundary solution of Maxwell's equations, dubbed the quantum gyroelectric effect [Phys. Rev. A 98, 023842 (2018)], is the supersymmetric partner of the topological Dirac edge state where the spinor wave function completely vanishes at the boundary. The defining feature of such phases is the presence of temporal and spatial dispersion in conductivity (the linear response function). In this paper, we generalize these topological electromagnetic phases beyond the continuum approximation to the exact lattice field theory of a periodic atomic crystal. To accomplish this, we put forth the concept of microscopic photonic band structure of solids -analogous to the traditional theory of electronic band structure. Our definition of topological invariants utilizes optical Bloch modes and can be applied to naturally occurring crystalline materials. For the photon propagating within a periodic atomic crystal, our theory shows that besides the Chern invariant C ∈ Z, there are also symmetry-protected topological (SPT) invariants ν ∈ ZN which are related to the cyclic point group CN of the crystal ν = C mod N . Due to the rotational symmetries of light R(2π) = +1, these SPT phases are manifestly bosonic and behave very differently from their fermionic counterparts R(2π) = −1 encountered in conventional condensed matter systems. Remarkably, the nontrivial bosonic phases ν = 0 are determined entirely from rotational (spin-1) eigenvalues of the photon at high-symmetry points in the Brillouin zone. Our work accelerates progress towards the discovery of bosonic phases of matter where the electromagnetic field within an atomic crystal exhibits topological properties. * zjacob@purdue.edu long wavelength approximation to the exact lattice field theory of optical Bloch waves. In this regime, we must consider not only the first spatial component σ xy (ω, k) = σ xy (ω, k, 0) but all spatial harmonics of the crystal g = 0, to infinite order, J Hall x (ω, k) = g σ xy (ω, k, g)E y (ω, k + g).(1) arXiv:1812.01183v2 [cond-mat.str-el]

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“…The topological field theory of light has surfaced in knotted solutions of Maxwell's equations [10,11], as well as the uncertainty relations for photons [12]. Along side this, there have been important recent developments to formulate topological properties for photons utilizing photonic crystals and metamaterials [13][14][15][16][17][18][19][20][21][22][23][24][25]. The pioneering work in topological photonic crystals has shown the existence of edge states robust to disorder.…”

Section: Introductionmentioning

confidence: 99%

Photonic Dirac monopoles and skyrmions: spin-1 quantization [Invited]

Mechelen¹,

Jacob²

2018

Opt. Mater. Express

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We introduce the concept of a photonic Dirac monopole, appropriate for photonic crystals, metamaterials and 2D materials, by utilizing the Dirac-Maxwell correspondence. We start by exploring vacuum where the reciprocal momentum space of both Maxwell's equations and the massless Dirac equation (Weyl equation) possess a magnetic monopole. The critical distinction is the nature of magnetic monopole charges, which are integer valued for photons but half-integer for electrons. This inherent difference is directly tied to the spin and ultimately connects to the bosonic or fermionic behavior. We also show the presence of photonic Dirac strings, which are line singularities in the underlying Berry gauge potential. While the results in vacuum are intuitively expected, our central result is the application of this topological Dirac-Maxwell correspondence to 2D photonic (bosonic) materials, as opposed to conventional electronic (fermionic) materials. Intriguingly, within dispersive matter, the presence of photonic Dirac monopoles is captured by nonlocal quantum Hall conductivity -i.e. a spatiotemporally dispersive gyroelectric constant. For both 2D photonic and electronic media, the nontrivial topological phases emerge in the context of massive particles with broken time-reversal symmetry. However, the bulk dynamics of these bosonic and fermionic Chern insulators are characterized by spin-1 and spin-1 ⁄2 skyrmions in momentum space, which have fundamentally different interpretations. This is exemplified by their contrasting spin-1 and spin-1 ⁄2 helically quantized edge states. Our work sheds light on the recently proposed quantum gyroelectric phase of matter and the essential role of photon spin quantization in topological bosonic phases. * zjacob@purdue.edu arXiv:1806.09879v3 [physics.optics]

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Topologically Protected Complete Polarization Conversion

Cited by 105 publications

References 33 publications

Arbitrary Polarization Conversion with a Photonic Crystal Slab

Arbitrary Polarization Conversion with a Photonic Crystal Slab

Nonlocal topological electromagnetic phases of matter

Photonic Dirac monopoles and skyrmions: spin-1 quantization [Invited]

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