PT-Symmetry Breraking in Double-Slab Surface-Plasmon Polaritons Waveguides

Youngsun Choi Department of Physics, Hanyang University, Seoul, South Korea Jong-Kyun Hong Department of Electronic Engineering, Hanyang University, Seoul, South Korea Jin-Ho Cho Department of Physics, Hanyang University, Seoul, South Korea Kwang-Geol Lee Department of Physics, Hanyang University, Seoul, South Korea Seok Ho Song Department of Physics, Hanyang University, Seoul, South Korea

In optics, PT-symmetric structures can be realized by symmetric index guiding and an antisymmetric gain/loss profile, that is, n(x) = n*(-x) [1]. In a coupled-waveguide the real values of the refractive index should be same in both channels, and the imaginary values have opposite sign.

We suggest double-slab (DS) surface plasmon polaritons (SPP) waveguides as a test-bench of PT-symmetry. DS-SPP system is a stacked multi-layers of metal (M) and insulator (I) in a sequence of IMIMI. For the symmetrically-coupled long-range SPP mode, field profile inside a DS-SPP waveguide shows a flat-top mode at a critical wavelength λc [2]. Especially when the core index of the waveguide is bigger than that of cladding, the effective imaginary index (Im{neff}) changes with the core thickness while the effective real index (Re{neff}) remains constant. Figure (a) shows the schematic of a single DS-SPP waveguide (inset) and its effective refractive index of a SPP mode. System parameters of nc =1.47, nd =1.45, metal(Au) thickness t =20 nm are assumed. At the critical wavelength λc =925.7 nm, the real-refractive index of a SPP mode remains constant while the imaginary-refractive index decreases monotonously as D increases as shown below. By coupling two DS-SPP waveguides as shown in Fig. (b) a passive PT-symmetric system can be made. Two DS-SPP waveguides have same system parameters except the core diameter D, to have same Re{neff} in both channels, but different Im{neff} from each other. The core diameter of the channel 2 (Fig. (b)) is larger than that of the channel 1 by ΔD. With increasing ΔD, difference in the Im{neff} between two channels gradually increases (Fig. (a)), having a similar meaning of controlling the gain and the loss in two channels.

effective index, structure

[1] C. M. Bender and S. Boettcher, "Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry," Phys. Rev. Lett. 80, 5243–5246 (1998).

[2] J. Yoon, S. H. Song, and S. Park, "Flat-top surface plasmon-polariton modes guided by double-electrode structures," Opt. Express 15, 17151 (2007).

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