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

Weimin Wang; Junlong Kou; Yanqing Lu

doi:10.3788/AOS240428

Journals >Acta Optica Sinica >Volume 44 >Issue 10 >Page 1026003 > Article

Acta Optica Sinica
Vol. 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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DOI: 10.3788/AOS240428 Cite this Article Set citation alerts

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 Copy Citation Text

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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

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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Relationship between symmetry and topological charges. (a) PhCS with C4v symmetry and the corresponding Brillouin zone; (b) relationship between parity under mirror symmetry and topological charge

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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$C_{4 v}$	$E$	$2 C_{4}$	$C_{2}$	$2 σ_{v}$	$2 σ_{d}$
$A_{1}$	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 1. Character table for

C_{4 v}

point group

Symmetry	Representation	Charge
$C_{2 v}$	$A_{1}$ , $A_{2}$	$2 n \pm 1$
$C_{2 v}$	$B_{1}$ , $B_{2}$	$2 n$
$C_{3 v}$	$A_{1}$ , $A_{2}$	$3 n + 1$
$C_{3 v}$	$E$	$3 n + 1$
$C_{4 v}$	$A_{1}$ , $A_{2}$	$4 n + 1$
	$B_{1}$ , $B_{2}$	$4 n - 1$
	$E$	$4 n \pm 1$
$C_{6 v}$	$A_{1}$ , $A_{2}$	$6 n + 1$
	$B_{1}$ , $B_{2}$	$6 n - 2$
	$E_{1}$	$6 n + 1$
	$E_{2}$	$6 n - 2$

Table 2. Irreducible representation of point group and corresponding topological charge

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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