Analytical Mode Matching in Stacked Subwavelength Gratings

$Cross section diagram of double layers grating and calculation errors of diffraction efficiency. (a) Section diagram (Λ=780 nm, s/Λ=0.72,z1=440 nm,z2=370 nm); (b) comparison of diffraction efficiency calculated by rigorous coupled wave analysis and mode analytical method$

Fig. 3. Cross section diagram of double layers grating and calculation errors of diffraction efficiency. (a) Section diagram (Λ=780 nm, s/Λ=0.72,z₁=440 nm,z₂=370 nm); (b) comparison of diffraction efficiency calculated by rigorous coupled wave analysis and mode analytical method

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Fig. 4. Comparison of the amplitude distribution of magnetic field calculated by two methods in the double layers grating. (a) Rigorous coupled wave analysis; (b) mode analytical method

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Fig. 5. Amplitude distribution of magnetic field of the first four modes in the double layers grating. (a) Mode 1; (d)mode 2; (c)mode 3; (d)mode 4

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$Sectional diagram of three-layer stacked grating and calculation error of diffraction efficiency. (a) Section diagram (Λ=690 nm, s/Λ=0.76, z1=405 nm, z2=662 nm, z3=284 nm); (b) comparison of diffraction efficiency calculated by rigorous coupled wave analysis and mode analytical method$

Fig. 6. Sectional diagram of three-layer stacked grating and calculation error of diffraction efficiency. (a) Section diagram (Λ=690 nm, s/Λ=0.76, z₁=405 nm, z₂=662 nm, z₃=284 nm); (b) comparison of diffraction efficiency calculated by rigorous coupled wave analysis and mode analytical method

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Fig. 7. Calculation results of three-layer stacked grating. (a) Amplitude distribution of magnetic field of the first four modes in the grating; (b) perfect cancellation of two modes at the output plane(z=0) leading to high reflectivity

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Table 1. Running time of different algorithms for the double layers grating calculation
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Table 1. Running time of different algorithms for the double layers grating calculation
Diffraction orders 2 3 4 10 101
Running time of AMM(100 times) /s 4.13 4.97 5.52 17.21 —
Running time of RCWA(once) /s — — — — 11.87

Table 2. Running time of different algorithms for three-layers stacked grating calculation
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Table 2. Running time of different algorithms for three-layers stacked grating calculation
Diffraction orders 2 3 4 101
Running time of AMM(100 times) /s 7.91 9.88 19.27 —
Running time of RCWA(once) /s — — — 22.62

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Jinlong Zhang, Shuaikai Shi, Hongfei Jiao, Xinbin Cheng. Analytical Mode Matching in Stacked Subwavelength Gratings[J]. Acta Optica Sinica, 2020, 40(12): 1205001

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Paper Information

Category: Diffraction and Gratings

Received: Feb. 17, 2020

Accepted: Mar. 23, 2020

Published Online: Jun. 3, 2020

The Author Email: Zhang Jinlong (jinlong@tongji.edu.cn)

DOI:10.3788/AOS202040.1205001

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Running time of different algorithms for the double layers grating calculation

Table 1. Running time of different algorithms for the double layers grating calculation

Table 2. Running time of different algorithms for three-layers stacked grating calculation

Table 2. Running time of different algorithms for three-layers stacked grating calculation