Symmetrical periods in antireflective coatings for plastic optics

Ulrike Schulz; Uwe B. Schallenberg; Norbert Kaiser

doi:10.1364/AO.42.001346

Applied Optics
Vol. 42,
Issue 7,
pp. 1346-1351
(2003)
•https://doi.org/10.1364/AO.42.001346

Symmetrical periods in antireflective coatings for plastic optics

Ulrike Schulz, Uwe B. Schallenberg, and Norbert Kaiser

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Ulrike Schulz, Uwe B. Schallenberg, and Norbert Kaiser, "Symmetrical periods in antireflective coatings for plastic optics," Appl. Opt. 42, 1346-1351 (2003)

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Abstract

Plastic optical parts require antireflective as well as hard coatings. A novel design concept for coating plastics combines both functions. Symmetrical three-layer periods with a phase thickness of 3/2π are arranged in a multilayer to achieve a step-down refractive-index profile. It is shown mathematically that the equivalent index of symmetrical periods can be lower than the lowest refractive index of a material used in the design, if the phase thickness of the symmetrical period is set equal to 3/2π instead of the usual π/2. The straightforward application of the concept to the design of antireflection coatings in general is demonstrated by example.

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Layer	Material	Design AR-hard-9 (QWOT)	AR-hard-9 Rearranged (QWOT)	Material or Equivalent Layer	Optical Thickness (QWOT)	Equivalent Index N′ at 516 nm	Equivalent Phase Thickness (Units of π/2)
1	L	2.443	1.000	L	1		1
			1.443	A′	3.00	1.3666	3.118
2	H	0.114	0.114
3	L	2.830	1.443
			1.387	B′	3.00	1.2835	3.081
4	H	0.226	0.226
5	L	2.704	1.387
			1.317	C′	3.00	1.1944	3.098
6	H	0.366	0.366
7	L	2.550	1.317
			1.233	D′	3.00	1.1111	3.075
8	H	0.534	0.534
9	L	1.233	1.233

Layer	Material or Equivalent Layer	Equivalent Phase Thickness (Units of π/2)	Equivalent Index N at 516 nm	Material	Optical Thickness by Herpin Replacement (QWOT)	Material	AR-hard-9a Obtained by Herpin Replacement (QWOT)
1	L	1.000		L	2	L	2.439
				L	0.439
2	A	1.000	1.5598	H	0.114	H	0.114
				L	0.439
3	L	2.000		L	2	L	2.819
				L	0.380
4	B	1.000	1.6607	H	0.226	H	0.226
				L	0.380
5	L	2.000		L	2	L	2.687
				L	0.307
6	C	1.000	1.7846	H	0.366	H	0.366
				L	0.307
7	L	2.000		L	2	L	2.529
				L	0.222
8	D	1.000	1.9185	H	0.534	H	0.534
				L	0.222
9	L	1.000	1.46	L	1	L	1.222

Material or Equivalent Layer	Equivalent Phase Thickness (Units of π/2)	Equivalent Index N′	Equivalent Index N	Material	Optical Thickness by Herpin Replacement (QWOT)	Material	AR-hard-9b Max. Flat Design (QWOT)
L	1	1.46		L	1.000
				L	1.000	L	2.450
				L	0.450
F′	3.00	1.3830	1.5413	H	0.093	H	0.093
				L	0.450
				L	1.000	L	2.780
				L	1.000
				L	0.330
G′	3.00	1.2210	1.7458	H	0.321	H	0.321
				L	0.330
				L	1.000	L	2.509
				L	1.000
				L	0.179
J′	3.00	1.0780	1.9774	H	0.622	H	0.622
				L	0.179
				L	1.000	L	2.179
				L	1.000
				L	0.000
K′	3.00	1.0151	2.1000	H	1.000	H	1.000
				L	0.000
				L	1.000	L	1.000

Layer	Material	Design AR-hard-9 (QWOT)	AR-hard-9 Rearranged (QWOT)	Material or Equivalent Layer	Optical Thickness (QWOT)	Equivalent Index N′ at 516 nm	Equivalent Phase Thickness (Units of π/2)
1	L	2.443	1.000	L	1		1
			1.443	A′	3.00	1.3666	3.118
2	H	0.114	0.114
3	L	2.830	1.443
			1.387	B′	3.00	1.2835	3.081
4	H	0.226	0.226
5	L	2.704	1.387
			1.317	C′	3.00	1.1944	3.098
6	H	0.366	0.366
7	L	2.550	1.317
			1.233	D′	3.00	1.1111	3.075
8	H	0.534	0.534
9	L	1.233	1.233

Layer	Material or Equivalent Layer	Equivalent Phase Thickness (Units of π/2)	Equivalent Index N at 516 nm	Material	Optical Thickness by Herpin Replacement (QWOT)	Material	AR-hard-9a Obtained by Herpin Replacement (QWOT)
1	L	1.000		L	2	L	2.439
				L	0.439
2	A	1.000	1.5598	H	0.114	H	0.114
				L	0.439
3	L	2.000		L	2	L	2.819
				L	0.380
4	B	1.000	1.6607	H	0.226	H	0.226
				L	0.380
5	L	2.000		L	2	L	2.687
				L	0.307
6	C	1.000	1.7846	H	0.366	H	0.366
				L	0.307
7	L	2.000		L	2	L	2.529
				L	0.222
8	D	1.000	1.9185	H	0.534	H	0.534
				L	0.222
9	L	1.000	1.46	L	1	L	1.222

Abstract

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Tables (3)

Equations (16)

Applied Optics