Design and rigorous analysis of high-efficiency array
generators

Erkin Sidick; André Knoesen; Joseph N. Mait

doi:10.1364/AO.32.002599

Applied Optics
Vol. 32,
Issue 14,
pp. 2599-2605
(1993)
•https://doi.org/10.1364/AO.32.002599

Design and rigorous analysis of high-efficiency array generators

Erkin Sidick, André Knoesen, and Joseph N. Mait

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Erkin Sidick, André Knoesen, and Joseph N. Mait, "Design and rigorous analysis of high-efficiency array generators," Appl. Opt. 32, 2599-2605 (1993)

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Abstract

One-dimensional array generators with seven to fifteen spots are designed by the method of virtual sources in combination with simulated-annealing optimization. Continuous surface-relief grating array generators and their discretized versions are analyzed with rigorous diffraction theory, and the results are compared with those obtained from Fourier-optics theory. The array-generator designs have high diffraction efficiency and good uniformity.

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Parameter	n	N_s
Parameter	n	7	9	11	13	15
a_n	0	0.771	1.002	0.601	1.134	0.716
	1	0.976	0.976	0.722	1.098	1.260
	2	1.107	0.969	0.776	1.092	1.192
	3	0.954	0.936	0.884	0.919	1.369
	4		1.030	0.852	0.916	1.062
	5			0.763	1.148	1.005
	6				1.059	0.943
	7					1.259
φ_n	0	3.206	−0.906	−1.469	3.787	−0.755
	1	−0.911	2.966	1.985	1.379	1.839
	2	−1.179	−1.601	−3.259	5.524	−0.026
	3	0.824	−1.015	−1.765	2.138	−1.798
	4		0.488	−2.204	1.924	0.539
	5			−0.205	3.588	0.473
	6				3.671	1.739
	7					2.950
η (%)		96.88	99.28	97.73	97.55	94.54
		(95.15)^a	(98.37)^a	(96.46)^a	(96.12)^a	(93.73)^a
ΔR (%)		0.710	0.024	0.555	0.399	2.602
		(3.312)^a	(3.070)^a	(4.289)^a	(5.241)^a	(7.934)^a

Parameter	n	I(n) %
Parameter	n	FOT	Λ/λ = 100	Λ/λ = 50	Λ/λ = 10	Λ/λ = 5	Λ/λ = 3
	−8	0.0213	0.0252	0.0285	0.1807
	−7	0.0232	0.0618	0.0639	0.0133	0.6007
	−6	0.0330	0.0523	0.0503	0.0042	1.0158
	−5	0.0772	0.1243	0.1119	0.1112	1.5956
	−4	11.0278	10.9588	10.8878	8.2687	2.2038	1.0611
	−3	11.0336	10.8798	10.9291	12.6008	18.9608	12.0948
	−2	11.0321	11.2513	11.2659	11.4508	13.3230	3.7407
	−1	11.0314	10.7701	10.7857	11.2414	8.4109	19.1772
	0	11.0290	10.6420	10.6360	10.6592	6.4636	27.3299
	1	11.0314	10.7701	10.7857	11.2414	8.4109	19.1801
	2	11.0321	11.2513	11.2659	11.4508	13.3230	3.7387
	3	11.0336	10.8798	10.9291	12.6008	18.9608	12.1064
	4	11.0278	10.9588	10.8878	8.2687	2.2038	1.0652
	5	0.0772	0.1243	0.1119	0.1112	1.5956
	6	0.0330	0.0523	0.0503	0.0042	1.0158
	7	0.0232	0.0618	0.0639	0.0133	0.6007
	8	0.0213	0.0252	0.0285	0.1807
η (%)		99.28	98.36	98.37	97.78	92.26	99.49
ΔR (%)		0.0238	2.948	3.070	23.894	84.962	147.220

Parameter	n	N_s
Parameter	n	7	9	11	13	15
a_n	0	0.771	1.002	0.601	1.134	0.716
	1	0.976	0.976	0.722	1.098	1.260
	2	1.107	0.969	0.776	1.092	1.192
	3	0.954	0.936	0.884	0.919	1.369
	4		1.030	0.852	0.916	1.062
	5			0.763	1.148	1.005
	6				1.059	0.943
	7					1.259
φ_n	0	3.206	−0.906	−1.469	3.787	−0.755
	1	−0.911	2.966	1.985	1.379	1.839
	2	−1.179	−1.601	−3.259	5.524	−0.026
	3	0.824	−1.015	−1.765	2.138	−1.798
	4		0.488	−2.204	1.924	0.539
	5			−0.205	3.588	0.473
	6				3.671	1.739
	7					2.950
η (%)		96.88	99.28	97.73	97.55	94.54
		(95.15)^a	(98.37)^a	(96.46)^a	(96.12)^a	(93.73)^a
ΔR (%)		0.710	0.024	0.555	0.399	2.602
		(3.312)^a	(3.070)^a	(4.289)^a	(5.241)^a	(7.934)^a

Parameter	n	I(n) %
Parameter	n	FOT	Λ/λ = 100	Λ/λ = 50	Λ/λ = 10	Λ/λ = 5	Λ/λ = 3
	−8	0.0213	0.0252	0.0285	0.1807
	−7	0.0232	0.0618	0.0639	0.0133	0.6007
	−6	0.0330	0.0523	0.0503	0.0042	1.0158
	−5	0.0772	0.1243	0.1119	0.1112	1.5956
	−4	11.0278	10.9588	10.8878	8.2687	2.2038	1.0611
	−3	11.0336	10.8798	10.9291	12.6008	18.9608	12.0948
	−2	11.0321	11.2513	11.2659	11.4508	13.3230	3.7407
	−1	11.0314	10.7701	10.7857	11.2414	8.4109	19.1772
	0	11.0290	10.6420	10.6360	10.6592	6.4636	27.3299
	1	11.0314	10.7701	10.7857	11.2414	8.4109	19.1801
	2	11.0321	11.2513	11.2659	11.4508	13.3230	3.7387
	3	11.0336	10.8798	10.9291	12.6008	18.9608	12.1064
	4	11.0278	10.9588	10.8878	8.2687	2.2038	1.0652
	5	0.0772	0.1243	0.1119	0.1112	1.5956
	6	0.0330	0.0523	0.0503	0.0042	1.0158
	7	0.0232	0.0618	0.0639	0.0133	0.6007
	8	0.0213	0.0252	0.0285	0.1807
η (%)		99.28	98.36	98.37	97.78	92.26	99.49
ΔR (%)		0.0238	2.948	3.070	23.894	84.962	147.220

Abstract

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Figures (8)

Tables (2)

Equations (11)

Applied Optics