Usually a light beam pushes a particle when the photons act upon it. We investigate the optical forces by nonparaxial gradientless beams and find that the forces can drag suitable particles all the way towards the light source. The major criterion of realizing the backward dragging force is the strong nonparaxiality of the light beam, which contributes to the pulling force owing to momentum conservation. The nonparaxiality of the Bessel beam can be manipulated to possess a dragging force along both the radial longitudinal directions, i.e., a ``tractor beam'' with stable trajectories is achieved.

Energy characteristics of the superposition of TE- and TM-polarized electromagnetic Bessel beams are studied. For some phase differences between TE and TM waves the components of the Poynting vector vary in sign. We call this situation “negative propagation,” because locally the beam may behave like a wave propagating in the direction opposite to the conventional one. We predict the following phenomena, which should confirm negative beam propagation: reflection of the beam from a circular aperture and unusual movement of microparticles in the beam.

A Bessel beam without an axial gradient can exert a pulling force on an object [A. Novitsky, C.\,W. Qiu, and H. Wang, Phys. Rev. Lett. 107, 203601 (2011)]. However, it cannot be called a ``tractor beam'' per se, as long as the light pulling effect is ultrasensitive to the object's material and size, a perturbation of which will make the optical traction go away. In this Letter, we investigate and report on the universality for a Bessel beam to be either a material-independent or size-independent optical tractor beam within the dipolar regime. Moreover, a general condition for a nonparaxial laser to be simultaneously a material- and size-independent tractor beam is proposed. These universal pulling effects and conditions are discussed in association with insight on modified far-field scattering, scattering resonances, and induced polarizabilities. Interestingly, we find that the acoustic pulling force exhibits only size independence, owing to the acoustic scattering theory in contrast to the light scattering counterpart. The findings pave the way for the realistic engineering and application of universal tractor beams pulling a wide variety of objects.

We employ a homogenization technique based on the Lorentz electronic theory to show that planar chiral structures (PCSs) can be described by an effective dielectric tensor similar to that of biaxial elliptically dichroic crystals. Such a crystal is shown to behave like a PCS insofar as it exhibits its characteristic optical properties, namely, corotating elliptical polarization eigenstates and asymmetric, direction-dependent transmission for left- or right-handed incident wave polarization.

$\mathcal{PT}$ symmetry is a unique platform for light manipulation and versatile use in unidirectional invisibility, lasing, sensing, etc. Broken and unbroken $\mathcal{PT}$-symmetric states in non-Hermitian open systems are described by scattering matrices. A multilayer structure, as a simplest example of the open system, has no certain definition of the scattering matrix, since the output ports can be permuted. The uncertainty in definition of the exceptional points bordering $\mathcal{PT}$-symmetric and $\mathcal{PT}$-symmetry-broken states poses an important problem, because the exceptional points are indispensable in applications such as sensing and mode discrimination. Here we derive the proper scattering matrix from the unambiguous relation between the $\mathcal{PT}$-symmetric Hamiltonian and scattering matrix. We reveal that the exceptional points of the scattering matrix with permuted output ports are not related to the $\mathcal{PT}$ symmetry breaking. Nevertheless, they can be employed for finding a lasing onset as demonstrated in our time-domain calculations and scattering-matrix pole analysis. Our results are important for various applications of the non-Hermitian systems including encircling exceptional points, coherent perfect absorption, $\mathcal{PT}$-symmetric plasmonics, etc.

Using the Maxwell-Bloch equations for resonantly absorbing and amplifying media, we study the temporal dynamics of light propagation through the $\mathcal{PT}$-symmetric structures with alternating loss and gain layers. This approach allows us to precisely describe the response of the structure near the exceptional points of $\mathcal{PT}$ symmetry breaking phase transition and, in particular, take into account the nonlinear effect of loss and gain saturation in the $\mathcal{PT}$ symmetry broken state. We reveal that in this latter state the multilayer system possesses a lasinglike behavior, releasing the pumped energy in the form of powerful pulses. We predict locking of pulse direction due to the $\mathcal{PT}$ symmetry breaking, as well as saturation-induced irreversibility of phase transition and nonreciprocal transmission.