Chirality refers to a geometric phenomenon in which objects are not superimposable on their mirror image. 1 Structures made of nano-scale chiral elements can display chiroptical effects, such as dichroism for left-and right-handed circularly polarized light, which makes them of high interest for applications ranging from quantum information processing and quantum optics 2,3 to circular dichroism spectroscopy and molecular recognition. 4 At the same time, strong chiroptical effects have been challenging to achieve even in synthetic optical media and chiroptical effects for light with normal incidence has been speculated to be prohibited in lossless, thin, quasi-twodimensional structures. 5-8 Here, we report on our experimental realization of a giant chiroptical effect in a thin monolithic photonic crystal mirror. Unlike conventional mirrors, our structure selectively reflects only one spin state of light, while preserving its handedness, with a near unity level of circular dichroism. The operational principle of the photonic-crystal mirror relies on Guided Mode Resonance (GMR) with 1 arXiv:1911.09227v1 [physics.optics] 21 Nov 2019 simultaneous excitation of leaky TE and TM Bloch modes in the photonic crystal slab.Such modes are not reliant on the suppression of their radiative losses through the long-range destructive interference and even small areas of the photonic-crystal exhibit robust circular dichroism. Despite its simplicity, the mirror strongly surpasses the performance of earlier reported structures and, contrary to a prevailed notion, demonstrates that near unity reflectivity contrast for the opposite helicities is achievable in a quasi-two-dimensional structure.

We present a semiclassical theory of the linear and nonlinear optical response of graphene. The emphasis is placed on the nonlinear optical response of graphene from the standpoint of the underlying chiral symmetry. The Bloch quasiparticles in the low-energy limit around the degeneracy points are dominantly chiral. It is shown that this chiral behavior in conjunction with scale invariance in graphene around the Dirac points results in the strong nonlinear optical response. Explicit expressions for the linear and nonlinear conductivity tensors are derived based on semiconductor Bloch equations (SBEs). The linear terms agree with the result of Kubo formulation. The three main additive mechanisms contribute in the nonlinear optical response of graphene: pure intraband, pure interband and the interplay between them. For each contribution, an explicit response function is derived. The Kerr-type nonlinearity of graphene is then numerically studied and it is demonstrated that the nonlinear refractive index of graphene can be tuned and enhanced by applying a gate voltage. It is also discussed that a strong Kerr nonlinearity can be achieved in a gated graphene monolayer. However, this nonlinearity is accompanied with a significant amount of absorption loss.

Graphene’s giant nonlinear optical response along with its integrability has made it a vaunted material for on-chip photonics. Despite a multitude of studies confirming its strong nonlinearity, there is a lack of reports examining the fundamental processes that govern the response. Addressing this gap in knowledge we analyse the role of experimental parameters by systematically measuring the near-infrared spectral dependence, the sub-picosecond temporal evolution and pulse-width dependence of the effective Kerr coefficient ( n 2 , eff ) of graphene in hundreds of femtosecond regime. The spectral dependence measured using the Z-scan technique is corroborated by a density matrix quantum theory formulation to extract a n 2 , eff ∝ λ 2 dependence. The temporal evolution obtained using the time-resolved Z-scan measurement shows the nonlinearity peaking at zero delay time and relaxing on a time-scale of carrier relaxation. The dependence of the n 2 , eff on pulse duration is obtained by expanding the input pulse using a prism-pair set-up. Our results provide an avenue for controllable tunability of the nonlinear response in graphene, which is limited in silicon photonics.

We reveal that optical saturation of the low-energy states takes place in graphene for arbitrarily weak electromagnetic fields. This effect originates from the diverging field-induced interband coupling at the Dirac point. Using semiconductor Bloch equations to model the electronic dynamics of graphene, we argue that the charge carriers undergo ultrafast Rabi oscillations leading to the anomalous saturation effect. The theory is complemented by a many-body study of the carrier relaxations dynamics in graphene. It will be demonstrated that the carrier relaxation dynamics is slow around the Dirac point, which in turn leads to a more pronounced saturation. The implications of this effect for the nonlinear optics of graphene are then discussed. Our analysis shows that the conventional perturbative treatment of the nonlinear optics, i.e., expanding the polarization field in a Taylor series of the electric field, is problematic for graphene, in particular at small Fermi levels and large field amplitudes.Graphene is a two-dimensional material made of carbon atoms in a honeycomb structure. Its reduced dimensionality and the symmetries of its crystalline structure render graphene a gapless semiconductor [1]. Graphene exhibits a wealth of exceptional properties, including a remarkably high mobility at room temperature [2], Klein tunneling and Zitterbewegung [3,4], existence of a nonzero Berry phase, anomalous quantum Hall effect [5-7], quantum-limited intrinsic conductivity [8], and a unique Landau level structure [9,10]. Underlying these peculiar electronic properties are its pseudo-relativistic quasiparticles that obey the massless Dirac equation [1]. As a direct consequence of their massless nature, the Dirac fermions have definite chiralities [11,12]. Owing to the specific symmetries of the crystalline structure of graphene, the dynamics of the massless Dirac quasiparticles and their chiral character are topologically preserved-i.e., many-body induced band renormalizations as well as any moderate perturbations of the lattice will not open a gap in graphene's band structure [13]. A large number of the unusual properties of graphene are associated with the topologically protected band-crossing and the chiral dynamics of the charge carriers [3].One major consequence of the topologically protected chirality of the charge carriers is the anomalous structure of the interband coupling mediated by an electromagnetic field. Its dipole matrix element obtained in the length gauge [14] exhibits a singularity at the degeneracy points, in contrast to ordinary (and even other gapless) semiconductors [15,16]. This has raised some controversy regarding the treatment of the optical response of graphene [15,17,18]. Specifically, the perturbative treatment of the nonlinear optical response has been questioned [17,19]. The nonlinear optical coeffi-cients of graphene obtained by means of perturbation theory suffer from a nonresolvable singularity [15,17]. Although substantial effort has been spent on developing comprehensive models for the ...

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