Efficient and Stable Implementation of RCWA for Ultrathin Multilayer Gratings: <i>T</i>-Matrix Approach Without Solving Eigenvalues

Li, Jie; Shi, Lihua; Ma, Yao; Ran, Yuzhou; Liu, Yicheng; Wang, Jianbao

doi:10.1109/lawp.2020.3041299

Cited by 8 publications

(13 citation statements)

References 14 publications

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“…It is also possible to subdivide non-uniformly, according to the local cross-sectional shape of the structure. Moreover, our implementation uses the first-order expansion that we derived, although we can easily extend it to use even higher order expansion by recursively substituting a lower-order expansion into (10) and (11). In practice, our method based on the first-order expansion already outperforms the conventional RCWA.…”

Section: Discussionmentioning

confidence: 99%

“…Numerical evaluation of ( 14), however, is rather challenging. Prior works use a low-order Taylor expansion of the matrix exponentials to evaluate (14) [10,20]. But to use this expansion, section length must be excessively short (i.e., z i − z i−1 ≤ 0.1λ where λ is the wavelength), and a large number of sections are needed.…”

Section: High-order Semi-analytical Methodsmentioning

confidence: 99%

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VarRCWA: An Adaptive High-Order Rigorous Coupled Wave Analysis Method

Zhu¹,

Zheng²

2022

Preprint

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Semi-analytical methods, such as rigorous coupled wave analysis, have been pivotal for numerical analysis of photonic structures. In comparison to other methods, they offer much faster computation, especially for structures with constant cross-sectional shapes (such as metasurface units). However, when the cross-sectional shape varies even mildly (such as a taper), existing semi-analytical methods suffer from high computational cost. We show that the existing methods can be viewed as a zeroth-order approximation with respect to the structure's cross-sectional variation. We instead derive a high-order perturbative expansion with respect to the cross-sectional variation. Based on this expansion, we propose a new semi-analytical method that is fast to compute even in presence of large cross-sectional shape variation. Furthermore, we design an algorithm that automatically discretizes the structure in a way that achieves a user specified accuracy level while at the same time reducing the computational cost.

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Section: Discussionmentioning

confidence: 99%

Section: High-order Semi-analytical Methodsmentioning

confidence: 99%

VarRCWA: An Adaptive High-Order Rigorous Coupled Wave Analysis Method

Zhu¹,

Zheng²

2022

Preprint

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“…Our following work will discuss twodimensional ultrathin periodic structures such as crossed gratings, frequency selective surface, and metasurface. Algorithm 1 [12] This paper Algorithm 1 [12] This paper ×10 9 (b) Fig. 5.…”

Section: Discussionmentioning

confidence: 99%

“…Fig. 5 shows the condition number of the conventional method [12] and the proposed method under different truncation orders. Highly consistent results are obtained for the different simulation methods as shown in Fig.…”

Section: Numerical Example and Comparisonmentioning

confidence: 99%

Efficient and Explicit Fourier Modal Method for Ultrathin Metallic Gratings

Li¹,

Shi²,

Jin

et al. 2022

Chinese J of Electronics

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The solution of large matrix eigenvalues and complex linear equations limits the Fourier modal method (FMM) application in ultrathin metallic gratings (UMG) analysis. This paper proposes an efficient and explicit FMM method for analyzing UMG. The proposed method avoids solving complex linear equations and eigenvalues of eigenmatrix in the conventional method by simplifying the implementation equations. Two numerical examples then verify the reliability of the proposed method compared with CST simulations and the conventional method. The proposed method is proven efficient in decreasing the CPU time by over 80% and demanding significantly less memory.

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“…Solution to Maxwell’s equations (eq ) can also be expressed as a product integral that involves matrix exponentials: , Numerical evaluation of eq , however, is rather challenging. Prior works use a low-order Taylor expansion of the matrix exponentials to evaluate eq . , But to use this expansion, section length must be excessively short (i.e., z i – z i –1 ≤ 0.1λ, where λ is the wavelength), and a large number of sections are needed. Another approach is to convert the product of matrix exponential into the exponential of matrix summation, similar to ∏ i exp( x i ) = exp(∑ i x i ) for scalar values x i .…”

Section: Solving Maxwell’s Equationsmentioning

confidence: 99%

VarRCWA: An Adaptive High-Order Rigorous Coupled Wave Analysis Method

Zhu

Zheng

2022

ACS Photonics

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Semianalytical methods, such as rigorous coupled wave analysis, have been pivotal in the numerical analysis of photonic structures. In comparison to other numerical methods, they have a much lower computational cost, especially for structures with constant cross-sectional shapes (such as metasurface units). However, when the cross-sectional shape varies even mildly (such as a taper), existing semianalytical methods suffer from high computational costs. We show that the existing methods can be viewed as a zeroth-order approximation with respect to the structure’s cross-sectional variation. We derive a high-order perturbative expansion with respect to the cross-sectional variation. Based on this expansion, we propose a new semianalytical method that is fast to compute even in the presence of large cross-sectional shape variation. Furthermore, we design an algorithm that automatically discretizes the structure in a way that achieves a user-specified accuracy level while at the same time reducing the computational cost.

show abstract

Efficient and Stable Implementation of RCWA for Ultrathin Multilayer Gratings: T-Matrix Approach Without Solving Eigenvalues

Cited by 8 publications

References 14 publications

VarRCWA: An Adaptive High-Order Rigorous Coupled Wave Analysis Method

VarRCWA: An Adaptive High-Order Rigorous Coupled Wave Analysis Method

Efficient and Explicit Fourier Modal Method for Ultrathin Metallic Gratings

VarRCWA: An Adaptive High-Order Rigorous Coupled Wave Analysis Method

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