The Dirac cone underlies many unique electronic properties of graphene 1 and topological insulators 2 , and its band structure-two conical bands touching at a single point-has also been realized for photons in waveguide arrays 3 , atoms in optical lattices 4 , and through accidental degeneracy 5,6 . Deformations of the Dirac cone often reveal intriguing properties; an example is the quantum Hall effect, where a constant magnetic field breaks the Dirac cone into isolated Landau levels 7 . A seemingly unrelated phenomenon is the exceptional point [8][9][10][11] , also known as the parity-time symmetry breaking point [12][13][14][15] , where two resonances coincide in both their positions and widths. Exceptional points lead to counter-intuitive phenomena such as loss-induced transparency 16 , unidirectional transmission or reflection [17][18][19][20][21][22][23] , and lasers with reversed pump dependence [24][25][26] or single-mode operation 27, 28 . These two fields of research are in fact connected: here we discover the ability of a Dirac cone to evolve into a ring of exceptional points, which we call an "exceptional ring." We experimentally demonstrate this concept in a photonic crystal slab. Angle-resolved reflection measurements of the photonic crystal slab reveal that the peaks of reflectivity follow the conical band structure of a Dirac cone from accidental degeneracy, whereas the complex eigenvalues of the system are deformed into a two-dimensional flat band enclosed by an exceptional ring. This deformation arises from the dissimilar radiation rates of dipole and quadrupole resonances, which play a role analogous to the loss and gain in parity-time symmetric systems. Our results indicate that the radiation that exists in any open system can fundamentally alter its physical properties in ways previously expected only in the presence of material loss and gain.Closed and lossless physical systems are described by Hermitian operators, which guarantee realness of the eigenvalues and a complete set of eigenfunctions that are orthogonal to each 2 other. On the other hand, systems with open boundaries 10, 29 or with material loss and gain [12][13][14][16][17][18][19][20][21][22][23][24][25][26][27][28] are non-Hermitian 8 and have non-orthogonal eigenfunctions with complex eigenvalues where the imaginary part corresponds to decay or growth. The most drastic difference between Hermitian and non-Hermitian systems is that the latter exhibit exceptional points (EPs) where both the real and the imaginary parts of the eigenvalues coalesce. At an EP, two (or more) eigenfunctions collapse into one so the eigenspace no longer forms a complete basis, and this eigenfunction becomes orthogonal to itself under the unconjugated inner product [8][9][10][11] . To date, most studies of EP and its intriguing consequences concern parity-time symmetric systems that rely on material loss and gain [12][13][14][16][17][18][19][20][21][22][23][24][25][26][27][28] , but EP is a general property that requires only non-Hermiticity. Here, we...

We present the spatially accelerating solutions of the Maxwell equations. Such nonparaxial beams accelerate in a circular trajectory, thus generalizing the concept of Airy beams.For both TE and TM polarizations, the beams exhibit shape-preserving bending with subwavelength features, and the Poynting vector of the main lobe displays a turn of more than 90°.We show that these accelerating beams are self-healing, analyze their properties, and compare to the paraxial Airy beams. Finally, we present the new family of periodic accelerating beams which can be constructed from our solutions.

The diversity of light-matter interactions accessible to a system is limited by the small size of an atom relative to the wavelength of the light it emits, as well as by the small value of the fine-structure constant. We developed a general theory of light-matter interactions with two-dimensional systems supporting plasmons. These plasmons effectively make the fine-structure constant larger and bridge the size gap between atom and light. This theory reveals that conventionally forbidden light-matter interactions--such as extremely high-order multipolar transitions, two-plasmon spontaneous emission, and singlet-triplet phosphorescence processes--can occur on very short time scales comparable to those of conventionally fast transitions. Our findings may lead to new platforms for spectroscopy, sensing, and broadband light generation, a potential testing ground for quantum electrodynamics (QED) in the ultrastrong coupling regime, and the ability to take advantage of the full electronic spectrum of an emitter.

Light–electron interaction is the seminal ingredient in free-electron lasers and dynamical investigation of matter. Pushing the coherent control of electrons by light to the attosecond timescale and below would enable unprecedented applications in quantum circuits and exploration of electronic motions and nuclear phenomena. Here we demonstrate attosecond coherent manipulation of a free-electron wave function, and show that it can be pushed down to the zeptosecond regime. We make a relativistic single-electron wavepacket interact in free-space with a semi-infinite light field generated by two light pulses reflected from a mirror and delayed by fractions of the optical cycle. The amplitude and phase of the resulting electron–state coherent oscillations are mapped in energy-momentum space via momentum-resolved ultrafast electron spectroscopy. The experimental results are in full agreement with our analytical theory, which predicts access to the zeptosecond timescale by adopting semi-infinite X-ray pulses.

We present self-accelerating self-trapped beams in nonlinear optical media, exhibiting self-focusing and self-defocusing Kerr and saturable nonlinearities, as well as a quadratic response. In Kerr and saturable media such beams are stable under self-defocusing and weak self-focusing, whereas for strong self-focusing the beams off-shoot solitons while their main lobe continues to accelerate. Self-accelerating self-trapped wave packets are universal, and can also be found in matter waves, plasma, etc.

A fundamental building block for nanophotonics is the ability to achieve negative refraction of polaritons, because this could enable the demonstration of many unique nanoscale applications such as deep-subwavelength imaging, superlens, and novel guiding. However, to achieve negative refraction of highly squeezed polaritons, such as plasmon polaritons in graphene and phonon polaritons in boron nitride (BN) with their wavelengths squeezed by a factor over 100, requires the ability to flip the sign of their group velocity at will, which is challenging. Here we reveal that the strong coupling between plasmon and phonon polaritons in graphene-BN heterostructures can be used to flip the sign of the group velocity of the resulting hybrid (plasmon-phonon-polariton) modes. We predict allangle negative refraction between plasmon and phonon polaritons and, even more surprisingly, between hybrid graphene plasmons and between hybrid phonon polaritons. Graphene-BN heterostructures thus provide a versatile platform for the design of nanometasurfaces and nanoimaging elements.negative refraction | plasmon polariton | phonon polariton | graphene-boron nitride heterostructure P olaritons with high spatial confinement, such as plasmon polaritons in graphene (1-5) and phonon polaritons in a thin hexagonal boron nitride (BN) slab (6-15), enable control over the propagation of light at the extreme nanoscale, due to their in-plane polaritonic wavelength that can be squeezed by a factor over 100. Henceforth we use the term squeezing factor (or confinement factor) to define the ratio between the wavelength in free space and the in-plane polaritonic wavelength. The combination of tunability, low losses, and ultraconfinement (1,2,8,10,11,15) makes them superior alternatives to conventional metal plasmons and highly appealing for nanophotonic applications (3-5, 10-13, 15). Their extreme spatial confinement, however, also limits our ability to tailor their dispersion relations.Unlike the case of 2D plasmons, the coupling between metal plasmons in a metal-dielectric-metal structure dramatically changes their dispersion relation and can even flip the sign of their group velocities (16,17). This has led to exciting applications by tailoring the in-plane plasmonic refraction, giving flexibility in controlling the energy flow of light. Specifically, by flipping the sign of the group velocity of metal plasmons, plasmonic negative refraction has been predicted (16) and demonstrated (17). The negative refraction has also been extensively explored in metamaterials, metasurfaces, and photonic crystals (18-26), but they become experimentally very challenging to realize when dealing with polaritons with high squeezing factors. In contrast to metal plasmons, the group velocity of graphene plasmons (2,11,27) and all other 2D plasmons (28-32) is always positive, including that in graphene-based multilayer structures (33). This has made the in-plane negative refraction for highly squeezed 2D plasmon polaritons seem impossible to achieve.Contrary to 2D plas...

The Dirac cone underlies many unique electronic properties of graphene 1 and topological insulators 2 , and its band structure-two conical bands touching at a single point-has also been realized for photons in waveguide arrays 3 , atoms in optical lattices 4 , and through accidental degeneracy 5, 6 . Deformations of the Dirac cone often reveal intriguing properties; an example is the quantum Hall effect, where a constant magnetic field breaks the Dirac cone into isolated Landau levels 7 . A seemingly unrelated phenomenon is the exceptional point 8-11 , also known as the parity-time symmetry breaking point [12][13][14][15] , where two resonances coincide in both their positions and widths. Exceptional points lead to counter-intuitive phenomena such as loss-induced transparency 16 , unidirectional transmission or reflection 17-23 , and lasers with reversed pump dependence [24][25][26] or single-mode operation 27, 28 . These two fields of research are in fact connected: here we discover the ability of a Dirac cone to evolve into a ring of exceptional points, which we call an "exceptional ring." We experimentally demonstrate this concept in a photonic crystal slab. Angle-resolved reflection measurements of the photonic crystal slab reveal that the peaks of reflectivity follow the conical band structure of a Dirac cone from accidental degeneracy, whereas the complex eigenvalues of the system are deformed into a two-dimensional flat band enclosed by an exceptional ring. This deformation arises from the dissimilar radiation rates of dipole and quadrupole resonances, which play a role analogous to the loss and gain in parity-time symmetric systems. Our results indicate that the radiation that exists in any open system can fundamentally alter its physical properties in ways previously expected only in the presence of material loss and gain.Closed and lossless physical systems are described by Hermitian operators, which guarantee realness of the eigenvalues and a complete set of eigenfunctions that are orthogonal to each other. On the other hand, systems with open boundaries 10, 29 or with material loss and gain [12][13][14][16][17][18][19][20][21][22][23][24][25][26][27][28] are non-Hermitian 8 and have non-orthogonal eigenfunctions with complex eigenvalues where the imaginary part corresponds to decay or growth. The most drastic difference between Hermitian and non-Hermitian systems is that the latter exhibit exceptional points (EPs) where both the real and the imaginary parts of the eigenvalues coalesce. At an EP, two (or more) eigenfunctions collapse into one so the eigenspace no longer forms a complete basis, and this eigenfunction becomes orthogonal to itself under the unconjugated inner product 8-11 . To date, most studies of EP and its intriguing consequences concern parity-time symmetric systems that rely on material loss and gain [12][13][14][16][17][18][19][20][21][22][23][24][25][26][27][28] , but EP is a general property that requires only non-Hermiticity. Here, we show the existence of EPs in a photonic cryst...

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