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Selecting mode by the complex Berry phase in non-Hermitian waveguide lattices
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Figures (5) .
Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 1. (a) Schematic of the PT-symmetric SSH chain, with A and B sublattices indicated in red and blue, respectively. The intracell and intercell couplings are denoted by v and w . The gain and loss are balanced and denoted by γ . The equivalent DC field is represented by F . (b) Schematic of the equivalent waveguide array.
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Fig. 2. Dispersion relation and trajectory of q ( k )?=? w exp(? ik )?+? v in the complex plane. The parameters are (a) and (b) w ?=?0.6, v ?=?0.3, and γ ?=?0.2 for the topological nontrivial lattice and (c) and (d) w ?=?0.3, v ?=?0.6, and γ ?=?0.2 for the topological trivial lattice. The insets in (a) and (c) represent the corresponding structure of the waveguide array.
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Fig. 3. Evolution of the real part of the optical field undergoing amplified and damped BOs for the (a) and (b) nontrivial and (c) and (d) trivial lattice. The calculated parameters are (a) w ?=?0.6, v ?=?0.3, and γ ?=?0.2; (b) w ?=?0.6, v ?=?0.3, and γ ?=??0.2; (c) w ?=?0.3, v ?=?0.6, and γ ?=?0.2; and (d) w ?=?0.3, v ?=?0.6, and γ ?=??0.2. The equivalent DC field is F ?=?2π/100. Right insets represent the distributions of the real part of the output optical field with Ψ ?=?[ A ?15 B ?15 … A 15 B 15 ]. The excitation is a Bloch wave packet with Gaussian distribution in the B waveguides as B n? =?exp(? n 2 / D 2 ) with D ?=?4. (e)–(h) Proportion of the output optical field on eigenstates from the upper (red) and lower (blue) bands corresponding to (a)–(d).
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Fig. 4. (a) Imaginary part of the complex Berry phase versus γ . (b) Proportion of the Bloch mode of the upper band after a BO period versus γ . The state at the output port can be expanded as ψ ( z B )?>?=? a ? + R? >?+? b ? - R? >?with the Bloch wave vector k ?=?0 and the proportion in (b) is defined as a 2 /( a 2 ?+? b 2 ). The calculated parameters are w ?=?0.6 and v ?=?0.3 for the topological nontrivial lattice and w ?=?0.3 and v ?=?0.6 for the topological trivial lattice. The equivalent DC field is set as F ?=?2π/400. The excitation is the superposition of the Bloch mode of the upper and lower bands with equal proportion at k ?=?0.
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Fig. 5. Equivalent amplified and damped BOs and mode selection in the bent waveguide array. (a) Structure of the non-Hermitian bent waveguide array. (b) Cross-sectional profile of the waveguide array. The chrome (Cr) stripes with thickness of 4?nm and width of 80?nm are deposited on top of every A or B waveguide. The widths of the A and B waveguides are denoted by w A and w B , and the thickness is 100?nm. The intracell and intercell spacings between the adjacent waveguides are denoted by g 1 and g 2 . (c) Zoom-in of the input port of the waveguide array. The input port consists of five extended straight B waveguides to excite the superposition of the Bloch modes of the upper and lower bands. (d)–(i) Simulated distribution of the electric field amplitude E of the bent waveguide array and the real part of the magnetic field Hz in the output straight waveguide array. The insets represent the proportion of the output light from the upper (red) and lower (blue) bands. The structure parameters are (d)–(g) g 1 ?=?300?nm, g 2 ?=?170?nm, w A ?=?500?nm, and w B ?=?515?nm for the topological nontrivial lattice and (h)–(i) g 1 ?=?170?nm, g 2 ?=?300?nm, w A ?=?495?nm, and w B ?=?500?nm for the trivial case. The Cr strips are deposited on the B waveguides in (d) and (e) and on the A waveguides in (f)–(i). The bending radius is R ?=?150??m.
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