Discrete thin-film layer thickness modulation

Bruce E. Perilloux

doi:10.1364/AO.37.003527

Applied Optics
Vol. 37,
Issue 16,
pp. 3527-3532
(1998)
•https://doi.org/10.1364/AO.37.003527

Discrete thin-film layer thickness modulation

Bruce E. Perilloux

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Bruce E. Perilloux, "Discrete thin-film layer thickness modulation," Appl. Opt. 37, 3527-3532 (1998)

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Abstract

A novel analytical thin-film design method is presented that is based on electrical engineering communication theory. The proposed thickness modulation describes the thickness modulation of discrete, homogeneous thin-film layers of a multilayer coating. One modulation scheme, amplitude modulation, is presented in which analytical equations determine individual layer thicknesses for a given modulation amplitude, carrier frequency (f _c), direct-current bias, as well as several layers and refractive indices. The spectral performance (especially stop bands) of multilayer coatings with alternating layers of two refractive indices is presented for different carrier frequencies and modulation amplitudes. For f _c ≤ 1, the ratio of the center frequencies of the first-order (f ₁) and the next present stop band (f ₂) is determined analytically from the modulation frequency for which f ₂/f ₁ = 2f _c + 1. Particular cases of the carrier frequency produce virtual stop bands below the spectral frequency of the first-order stop band as well as high-frequency harmonics. Degenerate and other cases of thickness-modulated designs are presented, along with other modulation methods.

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Layer	Film Material	Actual Period (T _actual)
Layer	Film Material	1	2	3	4	5	6	7	8	9	10
1	H	1.50	0.50	0.75	1.00	1.1545	1.25	1.3117	1.3536	1.383	1.4045
2	L	1.50	1.50	0.75	0.50	0.5955	0.75	0.8887	1.0000	1.0868	1.1545
3	H			1.50	1.00	0.5955	0.50	0.5495	0.6464	0.7500	0.8455
4	L			0.75	1.50	1.1545	0.75	0.5495	0.5000	0.5302	0.5955
5	H			0.75		1.5000	1.25	0.8887	0.6464	0.5302	0.5000
6	L			1.50		1.1545	1.50	1.3117	1.0000	0.7500	0.5955
7	H					0.5955		1.5000	1.3536	1.0868	0.8455
8	L					0.5955		1.3117	1.5000	1.3830	1.1545
9	H					1.1545		0.8887		1.5000	1.4045
10	L					1.5000		0.5495		1.3830	1.5000
11	H							0.5495		1.0868
12	L							0.8887		0.7500
13	H							1.3117		0.5302
14	L							1.5000		0.5302
15	H									0.7500
16	L									1.0868
17	H									1.3830
18	L									1.5000
No. layers		20	20	18	20	20	24	28	24	36	30
No. periods		10	10	3	5	2	4	2	3	2	3
Trans. Fig. No.		2(a)	2(b)	2(c)	2(d)	2(e)	2(f)	2(g)	2(h)	2(i)	2(j)

T _base	Stop-band Positions [wave number (μm^-1)]	Comments on TMD
1	0.67, 2.0	Degenerate, quarter-wave stack
2	1.0, 2.0	Degenerate, detuned, high-order stack
3	1.0, 1.66	First TMD, nonharmonic stop band
4	0.5, 1.0, 1.5, 2.5	TMD, virtual stopband at 0.5 and harmonics
5	0.57, 1.0, 1.4, 1.8, 2.25	TMD, virtual and nonharmonic stop bands
6	0.66, 1.0, 1.33, 1.65, 2.0	Same as T _base = 5
7	0.7, 1.0, 1.3, 1.6, 1.85, 2.45, 2.75	Same as T _base = 5
8	0.75, 1.0, 1.25, 1.5, 1.75, 2.25	TMD, virtual stopband at 0.75 and harmonics
9	0.5, 0.8, 1.0, 1.2, 1.45, 1.67, 1.9, 2.1, 2.75	Same as T _base = 5
10	0.55, 0.8, 1.2, 1.4, 1.6, 1.8, 2.0, 2.2, 2.4, 2.6	Same as T _base = 5

Layer	Film Material	Actual Period (T _actual)
Layer	Film Material	1	2	3	4	5	6	7	8	9	10
1	H	1.50	0.50	0.75	1.00	1.1545	1.25	1.3117	1.3536	1.383	1.4045
2	L	1.50	1.50	0.75	0.50	0.5955	0.75	0.8887	1.0000	1.0868	1.1545
3	H			1.50	1.00	0.5955	0.50	0.5495	0.6464	0.7500	0.8455
4	L			0.75	1.50	1.1545	0.75	0.5495	0.5000	0.5302	0.5955
5	H			0.75		1.5000	1.25	0.8887	0.6464	0.5302	0.5000
6	L			1.50		1.1545	1.50	1.3117	1.0000	0.7500	0.5955
7	H					0.5955		1.5000	1.3536	1.0868	0.8455
8	L					0.5955		1.3117	1.5000	1.3830	1.1545
9	H					1.1545		0.8887		1.5000	1.4045
10	L					1.5000		0.5495		1.3830	1.5000
11	H							0.5495		1.0868
12	L							0.8887		0.7500
13	H							1.3117		0.5302
14	L							1.5000		0.5302
15	H									0.7500
16	L									1.0868
17	H									1.3830
18	L									1.5000
No. layers		20	20	18	20	20	24	28	24	36	30
No. periods		10	10	3	5	2	4	2	3	2	3
Trans. Fig. No.		2(a)	2(b)	2(c)	2(d)	2(e)	2(f)	2(g)	2(h)	2(i)	2(j)

T _base	Stop-band Positions [wave number (μm^-1)]	Comments on TMD
1	0.67, 2.0	Degenerate, quarter-wave stack
2	1.0, 2.0	Degenerate, detuned, high-order stack
3	1.0, 1.66	First TMD, nonharmonic stop band
4	0.5, 1.0, 1.5, 2.5	TMD, virtual stopband at 0.5 and harmonics
5	0.57, 1.0, 1.4, 1.8, 2.25	TMD, virtual and nonharmonic stop bands
6	0.66, 1.0, 1.33, 1.65, 2.0	Same as T _base = 5
7	0.7, 1.0, 1.3, 1.6, 1.85, 2.45, 2.75	Same as T _base = 5
8	0.75, 1.0, 1.25, 1.5, 1.75, 2.25	TMD, virtual stopband at 0.75 and harmonics
9	0.5, 0.8, 1.0, 1.2, 1.45, 1.67, 1.9, 2.1, 2.75	Same as T _base = 5
10	0.55, 0.8, 1.2, 1.4, 1.6, 1.8, 2.0, 2.2, 2.4, 2.6	Same as T _base = 5

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Applied Optics