TABLE I
Comparison of results for scattering by a sinusoidal interface, as described by Fig. 1 with ∊a = 1, ∊r = ∊f = ∊s = 4, θ = 45°, and d/λ = 1. Here
refers to power of propagating harmonics in air (u = a) or dielectric (u = s) while ΣP denotes the total scattered power.
P | Perpendicular (TE) polarization |
---|
tg/λ = 0.005 | tg/λ = 0.5 |
---|
van den Berg | Chang et al. | van den Berg | Chang et al. |
---|
| 0.203990 | 0.2037150 | 0.02418 | 0.0349913 |
| 0.000027 | 0.0000265 | 0.06367 | 0.0537149 |
| 0.795207 | 0.7961250 | 0.39340 | 0.3492882 |
| 0.000056 | 0.0000550 | 0.34700 | 0.3307839 |
| 0.000074 | 0.0000817 | 0.11222 | 0.1693248 |
| 0.000000 | 1.3 × 10−9 | 0.05563 | 0.0618147 |
ΣP | 0.999357 | 1.0000032 | 0.99610 | 0.9999178 |
P | Parallel (TM) polarization |
tg/λ = 0.005 | tg/λ = 0.5 |
van den Berg | Chang et al. | van den Berg | Chang et al. |
| 0.041490 | 0.0414955 | 0.00344 | 0.0035820 |
| 0.000027 | 0.0000410 | 0.01309 | 0.0111254 |
| 0.958225 | 0.9583494 | 0.42706 | 0.4887857 |
| 0.000049 | 0.0000403 | 0.38488 | 0.3241987 |
| 0.000099 | 0.0000732 | 0.15480 | 0.1361058 |
| 0.000000 | 9.3 × 10−9 | 0.02065 | 0.0361654 |
ΣP | 0.999890 | 0.9999994 | 1.00392 | 0.9999630 |
TABLE II
Comparison of results for guiding by a sinusoidal grating, as described by Fig. 1 with ∊a = 1,∊r = (1.62 + i10−3)2, ∊f = 2.465, ∊s = 2.295, tr = (0.48 − tg/2) μm, tf = 0.80 μm, d = 0.606 μm, and λ = 0.6328 μm. All β0 and α are in (μm)−1.
tg (μm) | TE0 mode |
---|
β0 | α |
---|
Nevière et al. | Chang et al. | Nevière et al. | Chang et al. |
---|
0.1 | 15.27145 | 15.27126 | 3.705 × 10−3 | 3.751 × 10−3 |
0.2 | 15.25515 | 15.25450 | 6.559 | 6.620 |
0.3 | 15.23249 | 15.23124 | 7.819 | 7.875 |
0.4 | 15.20492 | 15.20273 | 8.320 | 8.393 |
tg (μm) | TM0 mode |
β0 | α |
Nevière et al. | Chang et al. | Nevière et al. | Chang et al. |
0.1 | 15.23659 | 15.23653 | 3.350 × 10−3 | 3.335 × 10−3 |
0.2 | 15.21835 | 15.21816 | 5.454 | 5.395 |
0.3 | 15.19198 | 15.19161 | 6.310 | 6.184 |
0.4 | 15.16032 | 15.15965 | 6.376 | 6.161 |
TABLE III
Comparison of results for guiding by a rectangular grating, as described by Fig. 1 with ∊a = 1, ∊r = ∊f = 3, ∊s = 2.3, and d/λ = 0.5. The width of the rectangular corrugation (along x) is d1 = d/2 and tr = 0.
tg/λ | TE0 mode; tf/λ = 1/π |
---|
β0/k0 | αλ |
---|
Peng et al. | Chang et al. | Peng et al. | Chang et al. |
---|
0.2 | 1.5808 | 1.5809 | 1.8716 × 10−2 | 1.8743 × 10−2 |
0.4 | 1.5823 | 1.5823 | 2.3398 | 2.3520 |
0.6 | 1.5812 | 1.5813 | 1.5246 | 1.5248 |
0.8 | 1.5823 | 1.5827 | 2.104 | 2.185 |
1.0 | 1.5820 | 1.5827 | 1.417 | 1.395 |
tg/λ | TM0 mode; tf/λ = 0.5 |
β0/k0 | αλ |
Peng et al. | Chang et al. | Peng et al. | Chang et al. |
0.2 | 1.6069 | 1.6078 | 5.6875 × 10−3 | 5.4020 × 10−3 |
0.4 | 1.6086 | 1.6088 | 6.1578 | 6.1378 |
0.6 | 1.6090 | 1.6088 | 4.4800 | 4.6267 |
0.8 | 1.6089 | 1.6087 | 4.8822 | 5.2453 |
1.0 | 1.6092 | 1.6086 | 4.6137 | 4.6936 |