Higher-Order Singularity Based on Three-Dimensional Non-Hermitian System

Miaomiao Zhang; Yan Zhang; Jiale Zhang; Jing Chen

doi:10.3788/LOP242048

Laser & Optoelectronics Progress, Volume. 62, Issue 7, 0726001(2025)

Higher-Order Singularity Based on Three-Dimensional Non-Hermitian System

Miaomiao Zhang^*, Yan Zhang, Jiale Zhang, and Jing Chen

College of Electronic and Optical Engineering & College of Flexible Electronics (Future Technology), Nanjing University of Posts and Telecommunications, Nanjing 210023, Jiangsu , China

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Figures & Tables(8)

Fig. 1. Circuit system design drawing

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Fig. 2. Degenerate characteristics of phases under various conditions. (a) $E {P_{2}}^{(1)}$ and $E {P_{4}}^{(2)}$ under Case 1; (b) $E {P_{2}}^{(2)}$ and $E {P_{4}}^{(3)}$ under Case 2; (c) $E {P_{4}}^{(1)}$ and $E P_{8}$ under Case 3; (d) intersection line of two planes in Case 3

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Fig. 3. Parameter space phase diagram of $Δ C^{2} / 4 {K_{2}}^{2} — {K_{1}}^{2} / {K_{2}}^{2}$

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Fig. 4. Eigenvalue phase diagrams with variations in the real and imaginary parts. (a) P1 corresponds to parameter; (b) P2 corresponds to parameter; (c) P3 corresponds to parameter

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Fig. 5. Variation of real and imaginary parts at P4 with three different real parameters $C_{0}$ introduced.(a) $C_{0}$ =20 μF; (b) $C_{0}$ =10 μF;(c) $C_{0}$ =0 μF

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Fig. 6. Real and imaginary parts of eigenvalues at P5 and P6 in the class III region of parameter space phase diagram.(a) P5 with $C_{0} \neq 0 μ F$ ; (b) P5 with $C_{0} = 0 μ F$ ; (c) P6 with $C_{0} \neq 0 μ F$

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Fig. 7. Observing node energy changes based on LTspice simulation. (a) Based on $E {P_{2 -}}^{(1)}$ in Fig. 4(c); (b) based on Fig. 4(a) where the parameter $E {P_{4}}^{(2)}$ is produced after setting $C_{0}$ to 0; (c) based on the higher-order singularity point $E P_{8}$ that appears in Fig. 5(c)

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Table 1. Analyzing energy changes of infinitely repeating minimal unit cell structure unit: V

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Table 1. Analyzing energy changes of infinitely repeating minimal unit cell structure unit: V

Corresponding node	Number of repeated minimal unit cell structures N
Corresponding node	N=1	N=3	N=5	N=7
Node 1	8×10¹⁹（-4×10¹⁹）	9×10¹⁹（-6×10¹⁹）	2.1×10²⁰（-1.2×10²⁰）	5×10¹⁹（-1×10²⁰）
Node 2	8×10¹⁸（-1.4×10¹⁹）	1.2×10²⁰（-8×10¹⁹）	1.4×10²⁰（-8×10¹⁹）	1.6×10¹⁹（-3.2×10¹⁹）
Node 3 Node 4	3.6×10¹⁹（-6.3×10¹⁹） 3×10¹⁹（-2×10¹⁹）	8×10¹⁹（-5×10¹⁹） 4.9×10¹⁹（-2.8×10¹⁹）	8×10¹⁹（-1×10¹⁹） 4×10¹⁹（-8×10¹⁹）	8×10¹⁹（-1.2×10²⁰） 4×10¹⁹（-8×10¹⁹）

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Miaomiao Zhang, Yan Zhang, Jiale Zhang, Jing Chen. Higher-Order Singularity Based on Three-Dimensional Non-Hermitian System[J]. Laser & Optoelectronics Progress, 2025, 62(7): 0726001

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Paper Information

Category: Physical Optics

Received: Sep. 26, 2024

Accepted: Nov. 15, 2024

Published Online: Mar. 20, 2025

The Author Email:

DOI:10.3788/LOP242048

CSTR:32186.14.LOP242048

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology