Table I
Coefficients Appearing in Eq. (19)
Number of layers | Which layer | κ1 | κ2 | P(C0) | Q(C0) |
---|
2 | 1 | 4 | 3 | 1 |
|
3 | 1 | 8 | 7 | 3 |
|
4 | 1 | 16 | 15 |
|
|
4 | 2 | 16 | 11 |
| same |
5 | 1 | 32 | 31 |
|
|
5 | 2 | 16 | 13 |
| same |
6 | 1 | 64 | 63 |
|
|
6 | 2 | 64 | 57 |
| same |
6 | 3 | 32 | 21 |
| same |
Approximate refractive indices for AR coatings with Chebyshev AR coatings according to
Eq. (19). Layer 1 is adjacent to the incident medium of index
n0 and the last layer is contiguous to the substrate of index
ns.
Table II
Comparison of Approximate and Exact Index Values
| | Cosine of the relative bandwidth C0 |
---|
| |
|
---|
ns | Layer | 0.309 | 0.707 | 0.951 |
---|
2.0 | 1 | 1.0492 | 1.0490 | 1.0856 | 1.0850 | 1.247 | 1.245 |
| 2 | 1.2475 | 1.2472 | 1.2776 | 1.2772 | 1.354 | 1.354 |
5.0 | 1 | 1.1203 | 1.1175 | 1.2172 | 1.2085 | 1.703 | 1.663 |
| 2 | 1.6742 | 1.6702 | 1.7729 | 1.7648 | 2.037 | 2.020 |
10 | 1 | 1.1806 | 1.1722 | 1.3392 | 1.3111 | 2.213 | 2.070 |
| 2 | 2.0976 | 2.0830 | 2.2840 | 2.2539 | 2.798 | 2.734 |
A comparison of the refractive indices of a four-layer Chebyshev AR coating, as obtained from exact theory (roman) and the approximation (italic) in
Eqs. (19) and
(20) vs the cosine of the bandwidth in
Eq. (7). The exact results are from Tables 6.04-3 and 6.04-4 of Ref.
10 and correspond to
Wq of 0.4, 1.0, and 1.6 for
C0 of 0.309, 0.707, and 0.951, respectively.
Table III
Approximate Indices for Maximally Flat AR Coatings
Number of layers | ith Layer | ni | ni+1 |
---|
2 | 1,2 | (n0)3/4 | (ns)1/4 | (n0)1/4 | (ns)3/4 |
3 | 1,2 | (n0)7/8 | (ns)1/8 | (n0)1/2 | (ns)1/2 |
| 3 | (n0)1/8 | (ns)7/8 | | |
4 | 1,2 | (n0)15/16 | (ns)1/16 | (n0)11/16 | (ns)5/16 |
| 3,4 | (n0)5/16 | (ns)11/16 | (n0)1/16 | (ns)15/16 |
5 | 1,2 | (n0)31/32 | (ns)1/32 | (n0)13/16 | (ns)3/16 |
| 3 | (n0)1/2 | (ns)1/2 | | |
| 4,5 | (n0)3/16 | (ns)13/16 | (n0)1/32 | (ns)31/32 |
6 | 1,2 | (n0)63/64 | (ns)1/64 | (n0)57/64 | (ns)7/64 |
| 3,4 | (n0)21/32 | (ns)11/32 | (n0)11/32 | (ns)21/32 |
| 5,6 | (n0)7/64 | (ns)57/64 | (n0)1/64 | (ns)63/64 |
Approximate values for the refractive indices of maximally flat AR coatings. Layer 1 is adjacent to the incident medium of index
n0 and the last layer is contiguous to the substrate of index
ns.