Broadening of Short Light Pulses by Many Reflections from Multilayer Dielectric Coatings

E. Spiller

doi:10.1364/AO.10.000557

Applied Optics
Vol. 10,
Issue 3,
pp. 557-566
(1971)
•https://doi.org/10.1364/AO.10.000557

Broadening of Short Light Pulses by Many Reflections from Multilayer Dielectric Coatings

E. Spiller

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E. Spiller, "Broadening of Short Light Pulses by Many Reflections from Multilayer Dielectric Coatings," Appl. Opt. 10, 557-566 (1971)

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Abstract

The broadening of short light pulses which are reflected from multilayer dielectric mirror coatings is calculated. The case when a pulse is reflected many times is treated in detail. The quarter-wave stack is the design for minimal pulse broadening. The broadening after many reflections is mainly due to the phase variations close to the edge of the reflection band of the coating. The shortest output pulses are obtained if only the center part of the reflection band of the mirror is used; an input pulse which contains only this part of the spectrum produces a much shorter output pulse than a δ-function input. Output pulses as short as 10⁻¹³ see are possible for typical mirror coatings and one-thousand reflections. The influence of errors in the fabrication of a coating on the calculated results is discussed.

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	Design^a	Number of layers	Refractive indices	Step width Δν^b/ν₀	Interval for ν/ν₀	Reflectivity r² (ν₀), %
1.	QW	7	2.38–1.4	0.01	0.001–2.49	95.7064
2.	QW	15	2.38–1.4	0.01	0.01–2.49	99.937133
3.	QW	23	2.38–1.4	0.01	0.01–2.49	99.999084
4.	QW	15	2.38–1.4	0.001	0.75–1.249	99.937133
5.	QW	23	2.38–1.4	0.001	0.75–1.249	99.999084
6.	QW	31	2.38–1.4	0.0005	1–1.2495	99.999980
7.	QW	3	3.5–1.4	0.005	1.0–1.5950	92.4615
8.	QW	7	3.5–1.4	0.005	1.0–1.395	99.79956
9.	QW	15	3.5–1.4	0.002	1.0–1.398	99.999893
10.	QW	19	3.5–1.4	0.002	1.0–1.398	99.999984
11.	QW	23	3.5–1.4	0.002	1.0–1.398	100
12.	QW	29	3.5–1.4	0.002	1.0–1.398	100
13.	QW	3	5.0–1.4	0.01	1.0–1.99	98.13597
14.	QW	5	5.0–1.4	0.005	1.0–1.695	99.8526
15.	QW	9	5.0–1.4	0.005	1.0–1.6950	99.99988
16.	QW	13	5.0–1.4	0.005	1.0–1.6950	99.99996
17.	QW	17	5.0–1.4	0.005	1.0–1.6950	100
18.	Broad band	15	2.38–1.4	0.002	0.60–1.598	96.469
19.	QW with dispersion	23	ZnS–1.38	0.001	0.75–1.249	99.99826
20.	QW with random thickness variations	23	2.38–1.4	0.001	0.60–1.5980	99.999038

	Quarter-wave stack n₁ = 2.38, n₂ = 1.4	Quarter-wave stack with random thickness variations	Quarter-wave stack with dispersion in high index layers n₁ = Zns, n₂ = 1.38
Δt/T₀	246	255	287
Δt_min/T₀	36	36	36

	Design^a	Number of layers	Refractive indices	Step width Δν^b/ν₀	Interval for ν/ν₀	Reflectivity r² (ν₀), %
1.	QW	7	2.38–1.4	0.01	0.001–2.49	95.7064
2.	QW	15	2.38–1.4	0.01	0.01–2.49	99.937133
3.	QW	23	2.38–1.4	0.01	0.01–2.49	99.999084
4.	QW	15	2.38–1.4	0.001	0.75–1.249	99.937133
5.	QW	23	2.38–1.4	0.001	0.75–1.249	99.999084
6.	QW	31	2.38–1.4	0.0005	1–1.2495	99.999980
7.	QW	3	3.5–1.4	0.005	1.0–1.5950	92.4615
8.	QW	7	3.5–1.4	0.005	1.0–1.395	99.79956
9.	QW	15	3.5–1.4	0.002	1.0–1.398	99.999893
10.	QW	19	3.5–1.4	0.002	1.0–1.398	99.999984
11.	QW	23	3.5–1.4	0.002	1.0–1.398	100
12.	QW	29	3.5–1.4	0.002	1.0–1.398	100
13.	QW	3	5.0–1.4	0.01	1.0–1.99	98.13597
14.	QW	5	5.0–1.4	0.005	1.0–1.695	99.8526
15.	QW	9	5.0–1.4	0.005	1.0–1.6950	99.99988
16.	QW	13	5.0–1.4	0.005	1.0–1.6950	99.99996
17.	QW	17	5.0–1.4	0.005	1.0–1.6950	100
18.	Broad band	15	2.38–1.4	0.002	0.60–1.598	96.469
19.	QW with dispersion	23	ZnS–1.38	0.001	0.75–1.249	99.99826
20.	QW with random thickness variations	23	2.38–1.4	0.001	0.60–1.5980	99.999038

	Quarter-wave stack n₁ = 2.38, n₂ = 1.4	Quarter-wave stack with random thickness variations	Quarter-wave stack with dispersion in high index layers n₁ = Zns, n₂ = 1.38
Δt/T₀	246	255	287
Δt_min/T₀	36	36	36

Abstract

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Tables (2)

Equations (16)

Applied Optics