Polarization Field in Momentum Space of Two-Dimensional Photonic Crystal Slabs (Invited)

Weimin Wang; Junlong Kou; Yanqing Lu

doi:10.3788/AOS240428

Acta Optica Sinica, Volume. 44, Issue 10, 1026003(2024)

Polarization Field in Momentum Space of Two-Dimensional Photonic Crystal Slabs (Invited)

Weimin Wang¹, Junlong Kou^1,2,4、**, and Yanqing Lu^1,3,4、*

Author Affiliations

¹School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, Jiangsu , China

²School of Integrated Circuit, Nanjing University, Suzhou 215163, Jiangsu , China

³College of Engineering and Applied Sciences, Nanjing University, Nanjing 210023, Jiangsu , China

⁴Wujin-NJU Institute of Future Technology, Changzhou 213153, Jiangsu , China

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Figures & Tables(11)

Fig. 1. Definition of polarization field and schematics of polarization states. (a) Schematic of radiative states and traditional bound states; (b) illustration of C points, L lines, and V points in parameter space; (c) schematic of the Poincaré sphere

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Fig. 2. Relationship between symmetry and topological charges. (a) PhCS with $C_{4 v}$ symmetry and the corresponding Brillouin zone; (b) relationship between parity under mirror symmetry and topological charge

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Fig. 3. Polarization graph in momentum space^[77]. (a) Schematic of a polarization graph and its dual graph; (b) total topological charge of a bounded face in the polarization graph is zero; (c) charge of a bounded face in the dual graph is exactly the charge of corresponding vertex in the original graph

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Fig. 4. Results related to polarization singularities in non-degenerate bands. (a) Correspondence between BICs and V points^[43]; (b) generation of C points by breaking $C_{2}$ symmetry and disrupting V points^[46]

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Fig. 5. Evolution of polarization singularities in non-degenerate bands. (a) Evolution of V points under structural parameter changes^[43]; polarization fields and polarization singularities in systems with (b) $C_{6 v}$ , (c) $C_{2 v}$ , (d) $C_{3 v}$ , and (e) $C_{1 h}$ symmetries^[35]

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Fig. 6. Evolution of polarization singularities in degenerate bands. (a) $C_{4 v}$ system degenerates to $C_{2 v}$ ^[80]; (b) $C_{6 v}$ system degenerates to $C_{2 v}$ ^[80]; (c) merging of C points and half-integer V points^[39]; (d) Fermi arc^[82]

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Fig. 7. Applications of polarization fields. (a) Merging BICs^[42]; (b) generation of vortex beams^[85]; (c) beam shift^[86]

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Fig. 8. Schematic of the structure achieving UGR and relationship between polarization singularities and $δ$ in the downward radiation channel^[55]

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Fig. 9. Principles of edge detection and schematic of the experimental setup^[60]. Transmission curves near the LHC point for (a) RCP and (b) LCP incident light, respectively; (c) integration of PhCS into a conventional 4f imaging system, enabling bright-field imaging and edge detection

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Table 1. Character table for $C_{4 v}$ point group
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Table 1. Character table for $C_{4 v}$ point group
$C_{4 v}$ $E$ $2 C_{4}$ $C_{2}$ $2 σ_{v}$ $2 σ_{d}$
$A_{1}$ 1 1 1 1 1
$A_{2}$ 1 1 1 -1 -1
$B_{1}$ 1 -1 1 1 -1
$B_{2}$ 1 -1 1 -1 1
$E$ 2 0 -2 0 0

Table 2. Irreducible representation of point group and corresponding topological charge
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Table 2. Irreducible representation of point group and corresponding topological charge
Symmetry Representation Charge
$C_{2 v}$ $A_{1}$ , $A_{2}$ $2 n \pm 1$
$B_{1}$ , $B_{2}$ $2 n$
$C_{3 v}$ $A_{1}$ , $A_{2}$ $3 n + 1$
$E$ $3 n + 1$
$C_{4 v}$ $A_{1}$ , $A_{2}$ $4 n + 1$
$B_{1}$ , $B_{2}$ $4 n - 1$
$E$ $4 n \pm 1$
$C_{6 v}$ $A_{1}$ , $A_{2}$ $6 n + 1$
$B_{1}$ , $B_{2}$ $6 n - 2$
$E_{1}$ $6 n + 1$
$E_{2}$ $6 n - 2$

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Weimin Wang, Junlong Kou, Yanqing Lu. Polarization Field in Momentum Space of Two-Dimensional Photonic Crystal Slabs (Invited)[J]. Acta Optica Sinica, 2024, 44(10): 1026003

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