Chiral Tensor Research Articles

Highly efficient all-dielectric optical tensor impedance metasurfaces for chiral polarization control.

We propose a highly efficient (nearly lossless and impedance-matched) all-dielectric optical tensor impedance metasurface that mimics chiral effects at optical wavelengths. By cascading an array of rotated crossed silicon nanoblocks, we realize chiral optical tensor impedance metasurfaces that operate as circular polarization selective surfaces. Their efficiencies are maximized through a nonlinear numerical optimization process in which the tensor impedance metasurfaces are modeled via multi-conductor transmission line theory. From rigorous full-wave simulations that include all material losses, we show field transmission efficiencies of 94% for right- and left-handed circular polarization selective surfaces at 800 nm.

Oscillating chiral tensor spectrum from axionic inflation

We study the axionic inflation with a modulated potential and examine if the primordial tensor power spectrum exhibits oscillatory feature, which is testable with future space-based gravitational wave experiments such as DECIGO and BBO. In the case of the single-field axion monodromy inflation, it turns out that it is difficult to detect the oscillation in the spectrum due to suppression of the sub-Planckian decay constant of axion. On the other hand, in the case of aligned chromo-natural inflation where the axion is coupled to a SU(2) gauge field, it turns out that the sizable oscillation in the tensor spectrum can occur due to the enhancement of chiral gravitational waves sourced by the gauge field. We expect that this feature will be a new probe to axion phenomenologies in early universe through the chiral gravitational waves.

Axion inflation with an SU(2) gauge field: detectable chiral gravity waves

We study a single field axion inflation model in the presence of an SU(2) gauge field with a small vev. In order to make the analysis as model-independent as possible, we consider an arbitrary potential for the axion that is able to support the slow-roll inflation. The gauge field is coupled to the axion with a Chern-Simons interaction $$ \frac{\lambda }{f}{F}_{\mu \nu}^a{\tilde{F}}_a^{\mu \nu } $$ where $$ \frac{\lambda }{f}\sim \frac{\mathcal{O}(10)}{M_{\mathrm{pl}}} $$ . It has a negligible effect on the background evolution, $$ \frac{\rho \mathrm{Y}\mathrm{M}}{M_{\mathrm{pl}}^2{H}^2}\lesssim {\upepsilon}^2 $$ . However, its quantum fluctuations make a significant contribution to the cosmic perturbation. In particular, the gauge field has a spin-2 fluctuation which explicitly breaks the parity between the left- and right-handed polarization states. The chiral tensor modes are linearly coupled to the gravitational waves and lead to a circularly polarized tensor power spectrum comparable to the unpolarized vacuum power spectrum. Moreover, the scalar sector is modified by the linear scalar fluctuations of the gauge field. Since the spin-0 and spin-2 fluctuations of the SU(2) gauge field are independent, the gauge field can, at the same time, generate a detectable chiral gravitational wave signal and have a negligible contribution to the scalar fluctuations, in agreement with the current CMB observations.

Multipolar Effects in the Optical Active Second Harmonic Generation from Sawtooth Chiral Metamaterials.

Based on the facts that chiral molecules response differently to left- and right-handed circular polarized light, chiroptical effects are widely employed for determining structure chirality, detecting enantiomeric excess, or controlling chemical reactions of molecules. Compared to those in natural materials, chiroptical behaviors can be significantly amplified in chiral plasmonic metamaterials due to the concentrated local fields in the structure. The on-going research towards giant chiroptical effects in metamaterial generally focus on optimizing the field-enhancement effects. However, the observed chiroptical effects in metamaterials rely on more complicated factors and various possibilities towards giant chiroptical effects remains unexplored. Here we study the optical-active second harmonic generation (SHG) behaviors in a pair of planar sawtooth gratings with mirror-imaged patterns. Significant multipolar effects were observed in the polarization-dependent SHG curves. We show that the chirality of the nanostructure not only give rise to nonzero chiral susceptibility tensor components within the electric-dipole approximation, but also lead to different levels of multipolar interactions for the two orthogonal circular polarizations that further enhance the nonlinear optical activity of the material. Our results thus indicate novel ways to optimize nonlinear plasmonic structures and achieve giant chiroptical response via multipolar interactions.

Towards 2+4 formulation of M5-brane

We present an attempt to formulate an action for the worldvolume theory of a single M5-brane, based on the splitting of the six worldvolume directions into 2+4, which breaks manifest Lorentz invariance from $SO(1,5)$ to $SO(1,1)\times SO(4)$. To this end, an action for the free six--dimensional (2,0) chiral tensor multiplet, and separately, a nonlinearly interacting chiral 2-form action are constructed. By studying the Lagrangian formulation for the chiral 2-form with 2+4 splitting, it is suggested that, if exists, the modified diffeomorphism of the theory on curved six--dimensional space--time is less trivial than its 1+5 and 3+3 counterpart, thus hindering the coupling of the chiral 2-form to the induced metric on the worldvolume of the M5-brane. We discuss difficulties of further generalisation of the theory. Finally, in terms of Hamiltonian analysis, we show that the naively gauge-fixed failed-PST-covariantised Lagrangian has the correct number of degrees of freedom, and satisfies the hyper--surface deformation algebra.

One-Dimensional Chirality: Strong Optical Activity in Epsilon-Near-Zero Metamaterials.

We suggest that electromagnetic chirality, generally displayed by 3D or 2D complex chiral structures, can occur in 1D patterned composites whose components are achiral. This feature is highly unexpected in a 1D system which is geometrically achiral since its mirror image can always be superposed onto it by a 180 deg rotation. We analytically evaluate from first principles the bianisotropic response of multilayered metamaterials and we show that the chiral tensor is not vanishing if the system is geometrically one-dimensional chiral; i.e., its mirror image cannot be superposed onto it by using translations without resorting to rotations. As a signature of 1D chirality, we show that 1D chiral metamaterials support optical activity and we prove that this phenomenon undergoes a dramatic nonresonant enhancement in the epsilon-near-zero regime where the magnetoelectric coupling can become dominant in the constitutive relations.

Nonlocal homogenization theory in metamaterials: Effective electromagnetic spatial dispersion and artificial chirality

We develop, from first principles, a general and compact formalism for predicting the electromagnetic response of a metamaterial with nonmagnetic inclusions in the long-wavelength limit, including spatial dispersion up to the second order. Specifically, by resorting to a suitable multiscale technique, we show that the effective medium permittivity tensor and the first- and second-order tensors describing spatial dispersion can be evaluated by averaging suitable spatially rapidly varying fields, each satisfying electrostatic-like equations within the metamaterial unit cell. For metamaterials with negligible second-order spatial dispersion, we exploit the equivalence of first-order spatial dispersion and reciprocal bianisotropic electromagnetic response to deduce a simple expression for the metamaterial chirality tensor. Such an expression allows us to systematically analyze the effect of the composite spatial symmetry properties on electromagnetic chirality. We find that even if a metamaterial is geometrically achiral, i.e., it is indistinguishable from its mirror image, it shows pseudo-chiral-omega electromagnetic chirality if the rotation needed to restore the dielectric profile after the reflection is either a ${0}^{\ensuremath{\circ}}$ or ${90}^{\ensuremath{\circ}}$ rotation around an axis orthogonal to the reflection plane. These two symmetric situations encompass two-dimensional and one-dimensional metamaterials with chiral response. As an example admitting full analytical description, we discuss one-dimensional metamaterials whose single chirality parameter is shown to be directly related to the metamaterial dielectric profile by quadratures.

A supersymmetric reduction on the three-sphere

We present the embedding of three-dimensional SO(4)⋉R6 gauged N=4 supergravity with quaternionic target space SO(4,4)/(SO(4)×SO(4)) into D=6, N=(1,0) supergravity coupled to a single chiral tensor multiplet through a consistent reduction on AdS3×S3.

A Kaluza–Klein inspired action for chiral p-forms and their anomalies

The dynamics of chiral p-forms can be captured by a lower-dimensional parity-violating action motivated by a Kaluza–Klein reduction on a circle. The massless modes are (p−1)-forms with standard kinetic terms and Chern–Simons couplings to the Kaluza–Klein vector of the background metric. The massive modes are p-forms charged under the Kaluza–Klein vector and admit parity-odd first-order kinetic terms. Gauge invariance is implemented by a Stückelberg-like mechanism using (p−1)-forms. A Chern–Simons term for the Kaluza–Klein vector is generated at one loop by massive p-form modes. These findings are shown to be consistent with anomalies and supersymmetry for six-dimensional supergravity theories with chiral tensor multiplets.

The Yang-Mills and chiral fields in six dimensions

In previous work (Singh, 2011), we constructed an action in six dimensions using Yang-Mills fields and an auxiliary Abelian field. Here we first write down all the equations of motion and the constraints which arise from such an action. From these equations we reproduce all dynamical equations and the constraints required for self-dual tensor field theory constructed by Lambert-Papageorgakis, which describes (2,0) supersymmetric CFT in 6D. This is an indication of the fact that our 6D gauge theory contains all the same information as the on-shall theory of chiral tensor fields.

Structural Origins of Chiral Second-Order Optical Nonlinearity in Collagen: Amide I Band

The molecular basis of nonlinear optical (NLO) chiral effects in the amide I region of type I collagen was investigated using sum-frequency generation vibrational spectroscopy; chiral and achiral tensor elements were separated using different input/output beam polarization conditions. Spectra were obtained from native rat tail tendon (RTT) collagen and from cholesteric liquid crystal-like (LC) type I collagen films. Although RTT and LC collagen both possess long-range order, LC collagen lacks the complex hierarchical organization of RTT collagen. Their spectra were compared to assess the role of such organization in NLO chirality. No significant differences were observed between RTT and LC with respect to chiral or achiral spectra. These findings suggest that amide I NLO chiral effects in type I collagen assemblies arise predominantly from the chiral organization of amide chromophores within individual collagen molecules, rather than from supramolecular structures. The study suggests that sum-frequency generation vibrational spectroscopy may be uniquely valuable in exploring fundamental aspects of chiral nonlinearity in complex macromolecular structures.

Discrete gauge symmetries in discrete MSSM-like orientifolds

Motivated by the necessity of discrete ZN symmetries in the MSSM to insure baryon stability, we study the origin of discrete gauge symmetries from open string sector U(1)ʼs in orientifolds based on rational conformal field theory. By means of an explicit construction, we find an integral basis for the couplings of axions and U(1) factors for all simple current MIPFs and orientifolds of all 168 Gepner models, a total of 32 990 distinct cases. We discuss how the presence of discrete symmetries surviving as a subgroup of broken U(1)ʼs can be derived using this basis. We apply this procedure to models with MSSM chiral spectrum, concretely to all known U(3)×U(2)×U(1)×U(1) and U(3)×Sp(2)×U(1)×U(1) configurations with chiral bi-fundamentals, but no chiral tensors, as well as some SU(5) GUT models. We find examples of models with Z2 (R-parity) and Z3 symmetries that forbid certain B and/or L violating MSSM couplings. Their presence is however relatively rare, at the level of a few percent of all cases.

Puzzle of Bulk Conformal Field Theories at Central Chargec=0

Nontrivial critical models in 2D with a central charge c=0 are described by logarithmic conformal field theories (LCFTs), and exhibit, in particular, mixing of the stress-energy tensor with a "logarithmic" partner under a conformal transformation. This mixing is quantified by a parameter (usually denoted b), introduced in Gurarie [Nucl. Phys. B546, 765 (1999)]. The value of b has been determined over the last few years for the boundary versions of these models: b(perco)=-5/8 for percolation and b(poly)=5/6 for dilute polymers. Meanwhile, the existence and value of b for the bulk theory has remained an open problem. Using lattice regularization techniques we provide here an "experimental study" of this question. We show that, while the chiral stress tensor has indeed a single logarithmic partner in the chiral sector of the theory, the value of b is not the expected one; instead, b=-5 for both theories. We suggest a theoretical explanation of this result using operator product expansions and Coulomb gas arguments, and discuss the physical consequences on correlation functions. Our results imply that the relation between bulk LCFTs of physical interest and their boundary counterparts is considerably more involved than in the nonlogarithmic case.

Study on the dispersion relations of a relativistic annular electron beam guided by a finite axial magnetic field

The relativistic annular electron beam guided by a finite axial magnetic field is studied in this paper, in which the electron beam is considered as a special media. Making use of the constitutive transformation and the Lorentz transformation in the four-dimensional space, the permittivity tensor of the stationary magnetized plasma, the permittivity tensor, the permeability tensor and the chiral tensor of the electron beam in the rest (laboratory) frame are acquired. And the boundary conditions, including the surface current density due to the ripple of the beam, have been obtained. As an example of the applications of this approach, the dispersion relations of a relativistic annular electron beam guided by a finite axial magnetic field in a waveguide has been studied. The results of numerical calculation show that the present approach is more accurate and can provide clearer mode information for the electron beam. In addition, the results also show the axial magnetic field can affect the dispersion curves of space charge wave via the surface current density of an electron beam. Thus this approach can be exploited in a number of electron beam-wave interaction systems, including some kinds of free electron devices, plasma filled Cherenkov radiated free electron lasers and masers.

Hawking radiation, covariant boundary conditions, and vacuum states

The basic characteristics of the covariant chiral current $⟨{J}_{\ensuremath{\mu}}⟩$ and the covariant chiral energy-momentum tensor $⟨{T}_{\ensuremath{\mu}\ensuremath{\nu}}⟩$ are obtained from a chiral effective action. These results are used to justify the covariant boundary condition used in recent approaches of computing the Hawking flux from chiral gauge and gravitational anomalies. We also discuss a connection of our results with the conventional calculation of nonchiral currents and stress tensors in different (Unruh, Hartle-Hawking and Boulware) states.

SPEEDING THE FRIEDMANN EXPANSION BY CHIRAL TENSOR PARTICLES

The status of the chiral tensor particles in the extended electroweak model, their experimental constraints, signatures and the possibilities for their detection at the new colliders are shortly reviewed. The cosmological effects of the additional particles are discussed. Namely, their characteristic interactions with the other components of the early Universe plasma and the corresponding cosmic times and temperatures are determined. The dynamical cosmological effect, namely the speeding of the Friedmann expansion due to the density increase caused by the chiral tensor particles and the additional Higgs doublet is discussed. The presence of the chiral tensor particles is allowed from cosmological considerations and welcomed by the particle physics phenomenology.

CHIRAL TENSOR FIELDS AND SPONTANEOUS BREAKING OF LORENTZ SYMMETRY

Antisymmetric tensor fields interacting with quarks and leptons have been proposed as a possible solution to the gauge hierarchy problem. We compute the one-loop beta function for a quartic self-interaction of the chiral antisymmetric tensor fields. Fluctuations of the top quark drive the corresponding running coupling to a negative value as the renormalization scale is lowered. This may indicate a nonvanishing expectation value of the tensor field, and thus a spontaneous breaking of Lorentz invariance. Settling this issue will need the inclusion of tensor loops.

Chiral Specificity of Doubly Resonant Sum-Frequency Generation in An Anisotropic Thin Film

The chiral specificity of infrared-visible sum-frequency generation (SFG) is investigated under doubly resonant (DR) conditions. An anisotropic thin film made of stacks of chiral supramolecular assemblies is investigated as a function of incoming and outgoing light polarizations. SFG experiments, crossed with in situ polarized absorption measurements, show that the double resonance process leads to a selection of the nonvanishing components of the chiral second-order susceptibility tensor. Specifically, it is demonstrated that a chiral component overcomes the achiral ones. This result is linked to the model for DR-SFG and to the selection rules of the vibration modes and electronic transition involved in the process.

QUANTIZATION OF CHIRAL ANTISYMMETRIC TENSOR FIELDS

Chiral antisymmetric tensor fields can have chiral couplings to quarks and leptons. Their kinetic terms do not mix different representations of the Lorentz symmetry and a local mass term can be forbidden by symmetry. The chiral couplings to the fermions are asymptotically free, opening interesting perspectives for a possible solution to the gauge hierarchy problem. We argue that the interacting theory for such fields can be consistently quantized, in contrast to the free theory which is plagued by unstable solutions. We suggest that at the scale where the chiral couplings grow large the electroweak symmetry is spontaneously broken and a mass term for the chiral tensors is generated nonperturbatively. Massive chiral tensors correspond to massive spin-one particles that do not have problems of stability. We also propose an equivalent formulation in terms of gauge fields.

Linear theory of the electron beam-wave-plasma interactions in a magnetized plasma waveguide

The theoretical study on the electron beam-wave interactions in a plasma waveguide immersed in a finite magnetic field is given in the article, in which both the plasma and the electron beam are considered as special media. Making use of the constitutive transformation and the Lorentz transformation in the four-dimensional space, the permittivity tensor of the stationary magnetized plasma, the permittivity tensor, the permeability tensor, and the chiral tensor of the electron beam in the rest (laboratory) frame are acquired. Therefore, two coupled wave equations for the magnetized plasma and electron beam have been obtained and the dispersion relations are then achieved by solving these coupled equations together with the boundary conditions including the surface current density due to the ripple of the plasma/beam. As an example of the applications of this approach, the beam-wave interactions in a practical plasma Cherenkov maser have been studied and the numerical calculations have been carried out in detail. It has been found that the present approach is more accurate and can provide clearer mode information for the electron beam-wave interactions in a magnetized plasma waveguide. This approach can be exploited in a number of electron beam-wave interaction systems including some kinds of free electron devices, plasma filled Cherenkov radiated free electron lasers and masers.