Photonic Floquet media with a complex time-periodic permittivity

Article

关键词: TOPOLOGICAL INSULATORS;    LINEAR CIRCUITS;    MODULATION;    PLASMA;    LIGHT;   

DOI  :  10.1103/PhysRevB.98.085142

来源: SCIE

【 摘 要 】

We study the formation of exceptional points (EPs) in a photonic medium with a complex time-periodic permittivity, i.e., epsilon(t) = epsilon(o) + epsilon(r), sin(Omega t). We formulate Maxwell's equations in the form of a first-order non-Hermitian Floquet Hamiltonian matrix and solve it analytically for the Floquet band structures. In the case when E r is real, to the first order in epsilon(r), the band structures show a phase transition from an exact phase with real quasienergies to a broken phase with complex quasienergies inside a region of wave-vector space, the so-called k gap. We show that the two EPs at the upper and lower edges of the k gap have opposite chiralities in the stroboscopic sense. By picking up the mode with a positive imaginary quasienergy, the wave propagation inside the k gap can grow exponentially. In three dimensions, such pairs of EPs span two concentric spherical surfaces in the (k)over-right-arrow space and repeat themselves periodically in the quasienergy space with Omega as the period. However, in the case when epsilon(r )is purely imaginary, the k gap disappears and gaps in the quasienergy space are opened. Our analytical results agree well with finite-difference time domain simulations. To second order in epsilon(r), additional EP pairs are found for both the cases of real and imaginary epsilon(r) . We also extend our theory to the case where the permittivity is simultaneously modulated in both space and time, i.e., epsilon(x, t) = epsilon(o) + epsilon(r )sin(Omega t - beta x + phi). For a real epsilon(r), we find that EPs also exist when the modulation speed c(m) = Omega/beta is faster than the speed of the wave travelling inside the medium.

【 授权许可】

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