Conservation relations and anisotropic transmission resonances in one-dimensionalPT-symmetric photonic heterostructures

Abstract

We analyze the optical properties of one-dimensional (1D) PT -symmetric structures of arbitrary complexity. These structures violate normal unitarity (photon flux conservation) but are shown to satisfy generalized unitarity relations, which relate the elements of the scattering matrix and lead to a conservation relation in terms of the transmittance and (left and right) reflectances. One implication of this relation is that there exist anisotropic transmission resonances in PT -symmetric systems, frequencies at which there is unit transmission and zero reflection, but only for waves incident from a single side. The spatial profile of these transmission resonances is symmetric, and they can occur even at PT -symmetry breaking points. The general conservation relations can be utilized as an experimental signature of the presence of PT -symmetry and of PT -symmetry breaking transitions. The uniqueness of PT -symmetry breaking transitions of the scattering matrix is briefly discussed by comparing to the corresponding non-Hermitian Hamiltonians.

PT-Symmetric Acoustics

“…[41,43]. In this respect, we shall demonstrate the frequency at which the transmission becomes unitary and is related to an exceptional point by investigating the spectral properties of the scattering matrix.…”

“…In the broken phase (red curve), the second components of the eigenvectors are purely imaginary, and under conjugation, one of the components transforms into the other. It should be pointed out that the unusual scattering properties of the PT -symmetric medium have also been demonstrated in optics and electronics, both in theories and experiments [41,42,44,45].…”

Systematic pathway toPT-symmetry breaking in scattering systems

“…An interesting development in the context of PT -symmetric optical devices has been recently achieved [11] showing that a general PTsymmetric scattering system can undergo a multitude of spontaneous symmetry breaking transitions. A benchmark of these transitions is the parametric change of the magnitude |λ S | of the eigenvalues of the S-matrix leading to a phase diagram separating the PT -symmetric, norm preserving eigenstates characterized by a pair of complex eigenvalues with |λ S | = 1 from the broken, amplified and lossy eigenstates of an inverse-conjugate pair of eigenvalues with |λ S | = 1 [12]. Nevertheless, the scattering states which are eigenstates of the S-matrix comprise only a small subspace of all possible scattering states, demanding specific efforts for the preparation of the appropriate conditions of the scattering system.…”

“…However, recently the study of light scattering in unbounded domains, where a PTsymmetric device resides, has been addressed [11,12] and followed by an investigation of the link between the breaking of PT -symmetry in bounded and unbounded systems [13]. One-dimensional PT -symmetric photonic heterostructures have been associated with appealing phenomena such as the existence of anisotropic transmission resonances [12], double refraction [3] and power oscillations [7,14].…”

Eigenvalue dynamics in the presence of nonuniform gain and loss

“…The conditions presented here vastly expand the design space for observing these effects. We also show that a similarly broad class of systems exhibit a loss-induced narrowing of the density of states.Recently, the study of parity-time (PT ) symmetric optical systems has highlighted the importance of exploring non-Hermitian systems with patterned gain and loss [1][2][3][4][5][6][7][8][9][10][11], and has led to the discovery of a remarkable array of phenomena, such as loss-induced transmission in waveguides [12], unidirectional transport behavior [13][14][15][16][17], reversed pump dependence in lasers [18][19][20], and band flattening in periodic structures [4,[21][22][23][24]. These effects are leading to new possibilities for constructing on-chip integrated photonic circuits for the manipulation of light.…”