Five-port beam splitter of a single-groove grating

$Unified profiles of all of the propagating modes of a grating under a normal incidence with five transmitted orders. The shaded region is meant to be the ridge of the grating region. The parameters of the grating are f=0.5, Λ=3800 nm, wavelength of incidence is λ=1550 nm, the refractive indices of the groove and ridge are ng=1, nc=1.5007. Modes 0, 1, 4 are odd symmetric, while modes 2, 3, 5 are even symmetric.$

Fig. 2. Unified profiles of all of the propagating modes of a grating under a normal incidence with five transmitted orders. The shaded region is meant to be the ridge of the grating region. The parameters of the grating are $f = 0.5$ , $Λ = 3800 nm$ , wavelength of incidence is $λ = 1550 nm$ , the refractive indices of the groove and ridge are $n_{g} = 1$ , $n_{c} = 1.5007$ . Modes 0, 1, 4 are odd symmetric, while modes 2, 3, 5 are even symmetric.

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Fig. 3. Contour plot of uniformity (%) calculated by SMM. The grating material is BK-7 glass, and its duty cycle is $f = 0.5$ .

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$(a) Total transmitted diffraction efficiency and (b) uniformity of 1×5 beam splitting gratings with some fabrication errors.$

Fig. 4. (a) Total transmitted diffraction efficiency and (b) uniformity of $1 \times 5$ beam splitting gratings with some fabrication errors.

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Table 1. Coupling Coefficients and Effective Indices
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Table 1. Coupling Coefficients and Effective Indices
Mode 0 1 2 3 4 5
$n_{eff}$ 2.1431 1.8245 1.3393 0.8252 0.7955 0.1228
${| J_{q 0} |}^{2}$ 0 0 0.5454 0.1792 0 0.2689

Table 2. Diffraction Efficiency and Uniformity Before and After Optimization
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Table 2. Diffraction Efficiency and Uniformity Before and After Optimization
Diffraction efficiency (%)
Parameter $+ 2 nd$ $+ 1 st$ 0th $- 1 st$ −2nd Total Uniformity (%)
Before 18.37 18.69 19.43 18.69 18.37 93.5 2.83
After 18.96 18.98 18.96 18.98 18.96 94.8 0.39