Table I
Design of Equivalent Period in Oblique Incidence (45°/Air) by Parallel Demands: Pairs (Yep, Yes) Compatible by the Equality Hp = Hs = ℋ; nH = 2.35, nL = 1.38
HLH | LHL |
---|
|
|
---|
Yep | Yes | ℋ | Yes | ℋ |
---|
1.0 | 0.646 | 2.330 | 0.587 | −1.117 |
1.5 | 1.077 | 1.173 | 1.065 | −0.156 |
2.0 | 1.628 | 0.477 | 1.656 | 0.504 |
2.5 | 2.290 | −0.033 | 2.286 | 1.036 |
2.94 | 2.940 | −0.403 | — | — |
3.0 | 3.030 | −0.449 | 2.920 | 1.511 |
3.316 | — | — | 3.316 | 1.789 |
3.5 | 3.802 | −0.813 | 3.544 | 1.950 |
4.0 | 4.585 | −1.143 | 4.161 | 2.368 |
Table II
Design of Depolarized Periods with Refractive Indices 2.0–1.38–2.0, at 45° from the Air, with Intersectional Level 2.659; Postulated ϕe: (a) 45°, (b) −45°; Two Solutions A and B in ϕ2 for Each Case with ϕ1 Split and Partially Spurious
| ϕ2 |
| |
|
| |
|
---|
(a) ϕe = 45° |
A | −32.47° | 40.94° | | 39.60° | −5.79° | | −6.07° |
| Ye/ϕe | | 2.659/45° | | 1.316 | | 1.719/−45° |
B | 212.47° | −84.21° | | −83.93° | −130.94° | | −129.60° |
| Ye/ϕe | | 2.659/45° | | 1.316 | | 1.719/−45° |
(b)ϕc = −45° |
A | 32.47° | 5.79° | | 6.07° | −40.94° | | −39.60° |
| Ye/ϕe | 1.316 | | 1.719/45° | | 2.659/−45° | |
B | 147.5° | −49.06° | | −50.4° | −95.79° | | −96.07° |
| Ye/ϕe | 1.316 | | 1.719/45° | | 2.659/−45° | |
Table III
Checking the
Compromise on Selected Index Combinations and Various ϕe
Index combination | Nominal Ye/ϕe |
| (Ye/ϕe)p | (Ye/ϕe)s |
---|
(a) HLH |
2.0–1.38–2.0 | 2.659/90° | 71.7/70.3 | 2.659/90.8° | 2.657/89.1° |
| 2.659/45° | 40.9/39.6 | 2.659/45.4° | 2.683/43.6° |
2.6–1.49–2.6 | 3.246/90° | 58.3/57.3 | 3.246/91.0° | 3.246/88.9° |
2.6–1.87–2.6 | 3.605/90° | 86.4/86.3 | 3.605/90.1° | 3.605/89.9° |
(b) LHL | | | | |
1.38–2.35–1.38 | 3.316/30° | −12.7/−14.6 | 3.177/32.4° | 3.593/26.8° |
1.38–4.50–1.38 | 6.050/45° | −9.1/−11.6 | 5.650/37.8° | 6.910/50.0° |
Table IV
Reduced Form of Table II After Elimination of Spurious Results,
Compromise, and Conversion to Positive Thicknesses
| ϕ1 | ϕ2 | 2ϕ1 +ϕ2 | (2ϕ1 +ϕ2)/45° |
---|
Ye = 2.659 |
| A | 40.27° | 147.53° | 228.07° | 5.06 |
ϕe =45° |
| B | 95.93° | 202.47° | 394.33° | 8.76 |
Ye = 2.659 |
| A | 139.73° | 32.47° | 311.93° | 6.93 |
ϕe =−45° |
| B | 84.07° | 147.5° | 315.64° | 7.01 |
Table V
Reduced Form of Results for 2.0–1.38–2.0 When ϕe = ±90°
| | | ϕ2 | ϕ1 |
---|
Ye = 2.659; | ϕe = 90° | A | −49.41° | 70.7° |
| | B | 229.41° | 109.3° |
| ϕe = −90° | A | 49.41° | −70.7° |
| | B | 130.58° | −109.3° |
Table VI
Final Tunings of Selected Depolarized Periods of the λ/4 Type; Each Value ϕ° Also Expressed as a Multiple of 90°
Index combination | | ϕ1 | ϕ2 |
---|
2.0–1.38–2.0 |
| (a) | 70.7° | 130.6° |
Ye = 2.659 | | 0.7855 | 1.4511 |
h = −0.759 | (b) | 109.3° | 49.4° |
| | 1.2144 | 0.5488 |
2.6–1.49–216 |
| (a) | 57.8° | 157.6° |
Ye = 3.245 | | 0.6422 | 1.7511 |
h = −0.380 | (b) | 122.2° | 22.4° |
| | 1.3577 | 0.2488 |
2.6–1.87–2.6 |
| (a) | 86.4° | 97.6° |
Ye = 3.606 | | 0.9600 | 1.0844 |
h = −0.991 | (b) | 93.6° | 82.4° |
| | 1.0400 | 0.9155 |
Table VII
Complete Schematic Designs for an Array of Depolarized Partial Reflectors with Outer Matchings from the Appendix
Code | Representative admittance scheme | Number of real layers | Depolarized reflection level (%) |
---|
S-21 | 1.69/3.605/2.85 | 5 | 21 |
S-30 | 1.077/3.245/2.85 | 9 | 30 |
S-33 | 1.204/3.245/2.33 | 9 | 33.5 |
S-38 | 1.077/3.605/2.85 | 9 | 38 |
S-47 | 0.856/3.605/2.85 | 9 | 46.7 |
S-44 | 1.69/3.605–2.659–3.605/2.85 | 11 | 44 |
S-48 | 1.204/3.245–2.659–3.245/ 2.33 | 15 | 48.5 |
S-53 | 0.856/3.245–2.659–3.245/ 2.85 | 15 | 53.8 |
S-62 | 1.204/3.605–2.659–3.605/ 2.33 | 15 | 62.3 |
Table VIII
Refractive Indices for Three-Layer Depolarizing Outer-Left (Upper Lines) and Outer-Right (Lower Lines) λ/4 Extensions (Unless Specified, the Refractive Indices are Copied from Preceding Lines)
nA | nB | nC | Y′ or Y″ |
---|
1.49 | 1.614 | 1.38 | 1.623 |
| 1.187 | | 1.972 |
1.49 | 1.820 | 1.49 | 1.489 |
| 1.246 | | 2.087 |
1.49 | 2.308 | 1.7 | 1.204 |
| 1.345 | | 2.331 |
1.49 | 3.481 | 2.0 | 0.733 |
| 1.461 | | 2.375 |
1.7 | 1.906 | 1.38 | 1.513 |
| 1.267 | | 2.252 |
1.7 | 2.308 | 1.49 | 1.204 |
| 1.345 | | 2.331 |
1.7 | 3.904 | 1.7 | 0.547 |
| 1.482 | | 2.5 |
2.22 | 2.819 | 1.38 | 1.181 |
| 1.410 | | 3.105 |
Table IX
Refractive Indices for Five-Layer Depolarizing Outer-Left (Upper Lines) and Outer-Right (Lower Lines) λ/4 Extensions (Unless Specified, the Refractive Indices are Copied from Preceding Lines)
(nA | nB)2 | nC | Y′ or Y″ |
---|
1.49 | 1.902 | 2.0 | 1.304 |
| 1.476 | | 2.737 |
1.49 | 2.030 | 2.35 | 1.602 |
| 1.526 | | 3.301 |
1.7 | 2.175 | 1.7 | 1.077 |
| 1.578 | | 2.558 |
1.7 | 2.500 | 2.0 | 0.856 |
| 1.677 | | 2.770 |
1.7 | 2.716 | 2.22 | 0.756 |
| 1.731 | | 3.014 |