Inverse design of a grating metasurface for enhancing spontaneous emission through hyperbolic metamaterials

Haoran Ma; Gang Bao; Jun Lai; Junshan Lin

doi:10.1364/JOSAB.497519

Journal of the Optical Society of America B
Vol. 41,
Issue 2,
pp. A79-A85
(2024)
•https://doi.org/10.1364/JOSAB.497519

Inverse design of a grating metasurface for enhancing spontaneous emission through hyperbolic metamaterials

Haoran Ma, Gang Bao, Jun Lai, and Junshan Lin

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Haoran Ma, Gang Bao, Jun Lai, and Junshan Lin, "Inverse design of a grating metasurface for enhancing spontaneous emission through hyperbolic metamaterials," J. Opt. Soc. Am. B 41, A79-A85 (2024)

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- Photonics
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About this Article
History
- Original Manuscript: June 9, 2023
- Revised Manuscript: December 22, 2023
- Manuscript Accepted: December 24, 2023
- Published: January 23, 2024
Virtual Issues
JOSA B Feature Issue: Inverse Design in Photonics (2024)

Abstract

This work is concerned with inverse design of the grating metasurface over hyperbolic metamaterials (HMMs) in order to enhance spontaneous emission (SE). We formulate the design problem as a PDE-constrained optimization problem and employ the gradient descent method to solve the underlying optimization problem. The adjoint-state method is applied to compute the gradient of the objective function efficiently. Computational results show that the SE efficiency of the optical structure with the optimized metasurface increases by 600% in the near field compared to the bare HMM layer. In particular, an optimized double-slot metasurface obtained by this design method enhances the SE intensity by a factor of over 100 in the observation region.

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The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Fig. 2	$L_{x}$ (µm)	$L_{y}$ (µm)	$D_{s}$ (µm)	$ϵ_{x}$		$ϵ_{y}$
Absorbing layer			2	$1 + 12 l_{x}^{2} i / k$		$1 + 12 l_{y}^{2} i / k$
HMM (hbN)^b	8	0.1	0.01	−8.2085 $+$ 0.4571i		2.7544 $+$ 0.0004i
Grating (Au)	8	$f$	0.11	−1637.4700 + 541.0360i		−1637.4700 $+$ 541.0360i
Region $D$	4	1	2	1		1
Region $Θ$	4	1	7	1		1
Algorithm 1	$I$	$L$ (µm)	$N$	$h_{M}$	$h_{ϵ}$	$h_{T}$	$c$
Section 3.B.1	40	8	400	0.1	1e-3	0.02	$\leq 0.5$
Sections 3.B.2 and 3.B.3	40	8	400	0.3	5e-5	0.02	$\leq 0.2$

	$J_{D} / J_{D}^{0}$	$J_{Θ} / J_{Θ}^{0}$	$h$
Initial value	5.4508	0.9370
Step 1	7.1902	2.3161	0.1000
Step 2	29.3840	10.5830	0.0650
Step 3	30.4933	11.1838	0.0050
Step 4	32.9589	11.1509	0.0030
Step 5	33.5276	11.3387	0.0020

	$J_{D} / J_{D}^{0}$	$J_{Θ} / J_{Θ}^{0}$	$h$
Initial value	0.1298	0.1056
Step 1	0.1443	0.0974	0.30000
Step 2	0.1677	0.0859	0.30000
Step 3	158.8009	44.5984	0.30000
Step 4	161.7653	50.7434	0.00037

$λ$ (µm)	$α$ (nm)	$β$ (nm)	$J_{D} / J_{D}^{0}$	$J_{Θ} / J_{Θ}^{0}$
5.88	270	30	64.5569	59.4256
6.17	280	20	81.1792	30.2575
6.49	270	30	97.5710	38.7869
6.85	230	45	139.5458	44.4297
7.25	230	45	175.8272	47.6854
7690	220	50	191.1147	60.6277
8.20	230	45	204.1575	67.5201

Fig. 2	$L_{x}$ (µm)	$L_{y}$ (µm)	$D_{s}$ (µm)	$ϵ_{x}$		$ϵ_{y}$
Absorbing layer			2	$1 + 12 l_{x}^{2} i / k$		$1 + 12 l_{y}^{2} i / k$
HMM (hbN)^b	8	0.1	0.01	−8.2085 $+$ 0.4571i		2.7544 $+$ 0.0004i
Grating (Au)	8	$f$	0.11	−1637.4700 + 541.0360i		−1637.4700 $+$ 541.0360i
Region $D$	4	1	2	1		1
Region $Θ$	4	1	7	1		1
Algorithm 1	$I$	$L$ (µm)	$N$	$h_{M}$	$h_{ϵ}$	$h_{T}$	$c$
Section 3.B.1	40	8	400	0.1	1e-3	0.02	$\leq 0.5$
Sections 3.B.2 and 3.B.3	40	8	400	0.3	5e-5	0.02	$\leq 0.2$

Abstract

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