Stable computations of the spherically layered media theory with high lossy media by using scaled Bessel functions

Table 1. High loss medium.
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Table 1. High loss medium.
Layer 1 2 3 4 5
a (m) 1 11 15 20 $ \infty $
$ \varepsilon_r $ 2 $ 1+x^{\prime \prime} $ 8 2.9 2
$ \mu_r $ 8 $ 1+x^{\prime \prime} $ 2 3 2

Table 2. Large radius.
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Table 2. Large radius.
Layer 1 2 3 4 5
a (m) 100 $ a_2 $ 1000 1200 $ \infty $
$ \varepsilon_r $ 2 $ 1+2i $ 8 2.9 2
$ \mu_r $ 8 $ 1+2i $ 2 3 2

Table 3. Plane wave incidence.
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Table 3. Plane wave incidence.
Layer 1 2 3 4 5
a (m) 1 2 $ a_3 $ 50 $ \infty $
$ \varepsilon_r $ 1 1 $ 3+x^{\prime\prime}i $ 1 2
$ \mu_r $ 1 3 $ 1+x^{\prime\prime}i $ 1 2

Table 4. Computational efficiency comparison.

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Table 4. Computational efficiency comparison.

Cases	Proposed (s)	Traditional (s)
$ x^{\prime \prime} = 55 $ in Fig. 5(a)	0.038594	0.030055
$ x^{\prime \prime} = 57 $ in Fig. 5(a)	0.036000	0.026603
$ x^{\prime \prime} = 60 $ in Fig. 5(a)	0.039843	0.029271
$ a_2=350.6 $ in Fig. 5(b)	0.291736	0.182420
$ a_2=350.7 $ in Fig. 5(b)	0.290019	0.184975
$ a_2=350.8 $ in Fig. 5(b)	0.308167	0.182530
$ x^{\prime \prime} = 2.90 $ in Fig. 7(a)	0.341995	0.231653
$ x^{\prime \prime} = 2.95 $ in Fig. 7(a)	0.389680	0.238650
$ x^{\prime \prime} = 3.00 $ in Fig. 7(a)	0.341986	0.238495
$ a_2=200 $ in Fig. 7(b)	0.441799	0.314423
$ a_2=300 $ in Fig. 7(b)	0.450923	0.354294
$ a_2=350 $ in Fig. 7(b)	0.278002	0.182116
$ x^{\prime \prime}=7.00 $ in Fig. 8(a)	0.089817	0.075163
$ x^{\prime \prime}=8.00 $ in Fig. 8(a)	0.093355	0.075676
$ x^{\prime \prime}=8.50 $ in Fig. 8(a)	0.085650	0.067904
$ a_3=4.151 $ in Fig. 8(b)	0.086647	0.071480
$ a_3=4.152 $ in Fig. 8(b)	0.085975	0.067385
$ a_3=4.153 $ in Fig. 8(b)	0.091902	0.073083

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Jia-Hui Wang, Bo O. Zhu. Stable computations of the spherically layered media theory with high lossy media by using scaled Bessel functions[J]. Journal of Electronic Science and Technology, 2025, 23(1): 100291

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