Self-Formation of Parity-Time Symmery in Lossy Media

Choloong Hahn Department of Physics, Hanyang University, Seoul, South Korea Youngsun Choi Department of Physics, Hanyang University, Seoul, South Korea Jong-Kyun Hong Department of Physics, Hanyang University, Seoul, South Korea Cha Hwan Oh Department of Physics, Hanyang University, Seoul, South Korea Seok Ho Song Department of Physics, Hanyang University, Seoul, South Korea

In optics, parity-time (PT) symmetry on light propagation occurs only when the refractive index distribution of loss/gain media obeys a relation of n(x) = n*(-x) [1]. The real index should be an even function of position whereas the imaginary be odd, therefore a π/2 phase-shift between the real and imaginary indices is crucial for PT symmetry [2].

We propose a mechanism for self-formation of an exact π/2-shift in complex media by employing a polarization interference on azo-chromophore films. When an azo-polymer film is illuminated by interference of two polarized beams, a surface-relief grating structure formed by the gradient force F(x) of polarization [3] contributes to the real-index distribution while the intensity distribution I(x) to the imaginary-index one. If we define α and β for the phases of F(x) and I(x), Δ ≡ α – β, the phase difference between F(x) and I(x). Δ is a function of ai and ψi (i = 1, 2), where ai is ellipticity and ψi polarization angle of the two interference beams as represented in inset of Fig. (a). Δ should be 0 or π for PT symmetry. Figure (a) shows parameter combinations for Δ = 0 or π with a1 = 0 and 0 < a2 < 1. This means that if one makes an interference with the parameters (ai and ψi) which make Δ = 0, then an exact π/2 shift in real and imaginary index distributions can be generated automatically. It is also worthy of noting that a special case when a1 = 0, a2 = 1, and θ = 45°, PT-symmetry in a complex media with Δ = 0 or π can always be achieved regardless of ψ with F(x) and I(x) as shown in Fig. (b).

[1] C. M. Bender, S. Boettcher, "Real spectra in non-Hermitian Hamiltonians having PT symmetry," Phys. Rev. Lett. Vol. 80, 5243 (1998).

[2] H. Hodaei, M. Miri, M. Heinrich, D. Christodoulides, M. Khajavikhan, "Parity-time-symmetric microring lasers," Science, Vol. 346, 975 (2014).

[3] W. Joo, C. Oh, Y. Han, “Influence of the Backbone on Photoinduced Birefringence in a Poly ( malonic ester ) Containing p -Cyanoazobenzene,” J. Phys. Chem. B, Vol. 106, 5378 (2002).

choloong.hahn@gmail.com









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