Fan-out elements recorded as volume holograms: optimized recording conditions

H. P. Herzig; P. Ehbets; D. Prongué; R. Dändliker

doi:10.1364/AO.31.005716

Applied Optics
Vol. 31,
Issue 26,
pp. 5716-5723
(1992)
•https://doi.org/10.1364/AO.31.005716

Fan-out elements recorded as volume holograms: optimized recording conditions

H. P. Herzig, P. Ehbets, D. Prongué, and R. Dändliker

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H. P. Herzig, P. Ehbets, D. Prongué, and R. Dändliker, "Fan-out elements recorded as volume holograms: optimized recording conditions," Appl. Opt. 31, 5716-5723 (1992)

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Abstract

The recording of efficient fan-out elements as volume holograms is investigated by using the coupled-wave theory. In contrast to the results published in the standard literature, we find that the efficiency and the uniformity of regular fan-out elements depend strongly on the relative phases of the object waves, at least, if the thickness of the hologram is less than ~50 wavelengths. High efficiency and uniformity can be achieved by optimized recording conditions. At the same time, the required dynamic range of the holographic material becomes minimum.

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Interbeam Angle, Δα	Beam Ratio, B	Modulation, Δ∊	Maximum Useful Diffraction Efficiency, η_T	Uniformity Error, e
0.1°	1	0.013	0.23	0.63	uncorrected
	5	0.017	0.40	0.15
	10	0.018	0.44	0.12
0.1°	1	0.021	0.62	0.20	corrected
	5	0.022	0.78	0.28
	10	0.024	0.81	0.30
0.1°	1	0.021	0.62	0.20	correctedb
1°	1	0.016	0.32	1.10	uncorrected
	5	0.020	0.55	0.58
	10	0.021	0.60	0.41
1°	1	0.024	0.82	0.33	corrected
	5	0.026	0.94	0.16
	10	0.026	0.95	0.12
1°	1	0.024	0.82	0.32	correctedb
5°	1	0.024	0.75	1.73	uncorrected
	5	0.026	0.94	0.75
	10	0.026	0.97	0.51
5°	1	0.025	0.85	1.35	corrected
	5	0.026	0.96	0.80
	10	0.026	0.97	0.60
5°	1	0.025	0.96	0.60	correctedb

Interbeam Angle, Δα	Beam Ratio, B	Modulation, Δ∊	Maximum Useful Diffraction Efficiency, η_T	Uniformity Error, e
0.1°	1	0.030	0.45	4.20	uncorrected
	5	0.050	0.34	4.10
	10	0.038	0.47	3.91
0.1°	1	0.015	0.94	0.19	corrected
	5	0.015	0.97	0.12
	10	0.015	0.98	0.12
0.1°	1	0.015	0.94	0.19	correctedb
1°	1	0.021	0.30	3.21	uncorrected
	5	0.036	0.41	2.93
	10	0.042	0.42	4.70
1°	1	0.015	0.96	1.51	corrected
	5	0.015	0.97	0.73
	10	0.015	0.98	0.57
1°	1	0.015	0.98	0.35	correctedb
3°	1	0.024	0.77	1.09	uncorrected
	5	0.016	0.89	0.86
	10	0.016	0.94	0.79
3°	1	0.016	0.83	3.95	corrected
	5	0.015	0.95	1.68
	10	0.015	0.97	1.11
3°	1	0.016	0.83	2.44	correctedb

Interbeam Angle, Δα	Beam Ratio, B	Modulation, Δ∊	Maximum Useful Diffraction Efficiency, η_T	Uniformity Error, e
0.1°	1	0.013	0.23	0.63	uncorrected
	5	0.017	0.40	0.15
	10	0.018	0.44	0.12
0.1°	1	0.021	0.62	0.20	corrected
	5	0.022	0.78	0.28
	10	0.024	0.81	0.30
0.1°	1	0.021	0.62	0.20	correctedb
1°	1	0.016	0.32	1.10	uncorrected
	5	0.020	0.55	0.58
	10	0.021	0.60	0.41
1°	1	0.024	0.82	0.33	corrected
	5	0.026	0.94	0.16
	10	0.026	0.95	0.12
1°	1	0.024	0.82	0.32	correctedb
5°	1	0.024	0.75	1.73	uncorrected
	5	0.026	0.94	0.75
	10	0.026	0.97	0.51
5°	1	0.025	0.85	1.35	corrected
	5	0.026	0.96	0.80
	10	0.026	0.97	0.60
5°	1	0.025	0.96	0.60	correctedb

Interbeam Angle, Δα	Beam Ratio, B	Modulation, Δ∊	Maximum Useful Diffraction Efficiency, η_T	Uniformity Error, e
0.1°	1	0.030	0.45	4.20	uncorrected
	5	0.050	0.34	4.10
	10	0.038	0.47	3.91
0.1°	1	0.015	0.94	0.19	corrected
	5	0.015	0.97	0.12
	10	0.015	0.98	0.12
0.1°	1	0.015	0.94	0.19	correctedb
1°	1	0.021	0.30	3.21	uncorrected
	5	0.036	0.41	2.93
	10	0.042	0.42	4.70
1°	1	0.015	0.96	1.51	corrected
	5	0.015	0.97	0.73
	10	0.015	0.98	0.57
1°	1	0.015	0.98	0.35	correctedb
3°	1	0.024	0.77	1.09	uncorrected
	5	0.016	0.89	0.86
	10	0.016	0.94	0.79
3°	1	0.016	0.83	3.95	corrected
	5	0.015	0.95	1.68
	10	0.015	0.97	1.11
3°	1	0.016	0.83	2.44	correctedb

Abstract

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Equations (23)

Applied Optics