FIG. 6. Chiral geometric phase in non-Hermitian potentials. (a,b) Chiral encircling around the EP [83]: (a) Evolution of two eigenmodes with starting points on different Riemann sheets for a CCW loop and (b) the same as that for a CW loop. (c) Asymmetric mode switching based on the dynamical encircling [83]. (d) Silicon photonics platform for the encircling of the EP in the on-chip photonic device [86]. Figure adapted from (a-c), ref. [83], Springer Nature; and (d), ref. [86], Springer Nature, with permission.
FIG. 1. Chirality in different physical domains of non-Hermitian photonics. For the optical field, E = eA(r,R)exp (iωt - ik(R) · r), where R is the system parameter vector and r is the position vector, the extended definition of optical chirality in non-Hermitian photonics can be classified according to each physical quantity: polarization e for SAM, wavefront A(r,R) for OAM, canonical momentum k(R) for wave propagation, and the geometry of state evolution in the system parameter space R. The system parameter R represents the complex optical potential that determines the condition of PT symmetry, including on-site and hopping constants defined by structural and material parameters.
FIG. 2. Chiral polarizations in non-Hermitian potentials. (a-e) Evolution of eigenpolarizations according to the phase of PT symmetry [36]: (a) Hermitian, (b) unbroken, (c) EP, and (d,e) non-Hermitian states. (f) The convergence of polarizations to the LCP state, showing spin black hole [36]. (g,h) The experimental platform for PT-symmetry-protected chirality: (g) lattice structures [36] and (h) photonic molecules [35]. Figure adapted from (a-g), ref. [36], OSA; and (h), ref. [35], APS, with permission.
FIG. 3. Chiral wavefronts in non-Hermitian potentials. (a-c) OAM microlaser [52]: (a) schematic, (b) OAM wavefront, and (c) fabricated device. (d,e) Broadband OAM laser using a tapered structure [53]: (d) schematic and (e) fabricated device. Figure adapted from (a-c), ref. [52], AAAS; and (d,e), ref. [53], with permission.
FIG. 4. Chiral propagations in non-Hermitian potentials. (a) A schematic of a WGM resonator for observing the chiral wave propagation [56]. (b,c) Asymmetric wave propagation for chiral absorption: (b) CCW and (c) CW wave propagation [57]. (d,e) Operation principle of the EP sensor: (d) square root response and (e) the physical origin from the large backscattering induced by the unperturbed system [67]. Figure adapted from (a), ref. [56], NAS; (b,c), ref. [57], APS; and (d,e), ref. [67], Springer Nature, with permission.
FIG. 5. Roles of degeneracy and disorders in chirality in non-Hermitian potentials. (a) The absence of PT-symmetric transitions: (b) modal profiles [69]. (c) The emergence of PT-symmetric transitions with discrete spatial symmetry: (d) modal profiles [69]. (e-g) Realizations of the chiral wave evolution in disordered photonic networks with different topological charges [70]. Figure adapted from (a-d), ref. [69], APS; and (e-g), ref. [70], AAAS, with permission.
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