Bragg-induced power oscillations in PT -symmetric periodic photonic structures

Abstract

We study Bragg-induced power oscillations in Fourier space between a pair of optical resonant transverse modes propagating through a periodic PT symmetric lattice, represented by a refractive index that includes gain and loss in a balanced way. Our results imply that the PT -symmetric system shows exceptionally rich phenomena absent in its Hermitian counterpart. It is demonstrated that the resonant modes exhibit unique characteristics such as Bragg power oscillations controlled via the PT symmetry, severe asymmetry in mode dynamics, and trapped enhanced transmission. We have also performed numerical simulations in (1+1) and (2+1) dimensions of propagating Gaussian beams to compare with analytical calculations developed under a two-waves model.

Nonparaxial electromagnetic Bragg scattering in periodic media with PT symmetry

“…and for three values of ε 0 while ε R is fixed at 1 . In contrast with the paraxial result for which W 1 = 1 constant [20], here at the symmetry breaking point we find no occurrence of mode trapping. Actually here, we find that W 1 oscillates harmonically transferring power to and from efficiently, while the amplitude of the W −1 oscillation increases with z 2 .…”

“…Furthermore, as ε 0 increases, the growth of the amplitude of the oscillations becomes slower. Thus, at the symmetry breaking point, we find a quite asymmetric dynamics comparing W −1 and W 1 and both dynamics are strikingly contrasting with the paraxial Bragg oscillations reported in [20].…”

“…First thing we note is that it is a conservative process, as the sum of the power contained in the the resonant Bragg modes is always equals to the input power. Compared to the paraxial case [20], the oscillations exhibit a richer structure. It is clear that two superposed oscillations occur: the envelope, with a much longer spatial period, modulating the phase-like oscillation.…”

“…Furthermore, experiments on the properties of microwave diffraction in periodic structures have been reported in 2D artificial dielectric media [18], and in the optical regime in volume holographic gratings [19]. Bragg oscillations have been reported in PT -symmetric photonic lattices [20].…”

Bragg-induced oscillations in non-PT complex photonic lattices

“…Bloch oscillations in an optical setup with PT symmetry was also considered [20]. Until now, attention to Bragg oscillations in optical beams propagating in periodic photonic structures was devoted to linear Hermitian [16], nonlinear Hermitian [22], linear PT -symmetric [21]. It should be noted here, that in this last reference within a two-mode approach, oscillations were retrieved below the symmetry breaking point while above it, depending on the initial condition, exponential growth or mode trapping.…”