Grating design for interlayer optical interconnection of in-plane waveguides

Congshan Wan; Thomas K. Gaylord; Muhannad S. Bakir

doi:10.1364/AO.55.002601

Applied Optics
Vol. 55,
Issue 10,
pp. 2601-2610
(2016)
•https://doi.org/10.1364/AO.55.002601

Grating design for interlayer optical interconnection of in-plane waveguides

Congshan Wan, Thomas K. Gaylord, and Muhannad S. Bakir

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Congshan Wan, Thomas K. Gaylord, and Muhannad S. Bakir, "Grating design for interlayer optical interconnection of in-plane waveguides," Appl. Opt. 55, 2601-2610 (2016)

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Abstract

Interlayer grating-to-grating optical interconnect coupling efficiency is simulated and optimized using rigorous coupled-wave analysis (RCWA) for the case of binary rectangular-groove gratings. The “equivalent index slab (EIS)” concept is proposed to alleviate the numerical sensitivity problem inherent in the RCWA-leaky-wave approach, making the method applicable to any multilayer structure that has an arbitrary grating profile, large refractive-index differences, and a limited grating length. The method is easy to implement and computationally efficient and can provide optimal designs based on the system designer’s need. To determine the viability of the RCWA-EIS approach, results are compared to those obtained using the finite-difference time-domain method, and an excellent agreement is found.

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Corrections

Congshan Wan, Thomas K. Gaylord, and Muhannad S. Bakir, "Grating design for interlayer optical interconnection of in-plane waveguides: erratum," Appl. Opt. 55, 7987-7987 (2016)
https://opg.optica.org/ao/abstract.cfm?uri=ao-55-28-7987

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Grating design for interlayer optical interconnection of in-plane waveguides: erratum

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Appl. Opt. 55(28) 7987-7987 (2016)

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Binary Case Number	Initial Guesses			Optimized Values
	$θ$	$Λ$	$t_{g}$	$θ$	$Λ$	$t_{g}$	$P C_{c, + 1}$	$D E_{c, + 1}$	$β$	$α$
	rad (deg)	μm	μm	rad (deg)	μm	μm	$P C_{c, + 1}$	$@ N = 50$	${μm}^{- 1}$	${μm}^{- 1}$
1	0.15 (8.59)	0.55	0.25	0.1761 (10.10)	0.5439	0.2337	0.5345	0.4417	10.8416	0.0322
2	0.20 (11.46)	0.55	0.25	0.2245 (12.86)	0.5462	0.2419	0.5474	0.5117	10.6020	0.0500
3	0.25 (14.32)	0.50	0.15	0.2499 (14.32)	0.5371	0.2071	0.5028	0.4812	10.6963	0.0301
4	0.15 (8.59)	0.55	0.10	0.1584 (9.08)	0.5701	0.2299	0.5328	0.4314	10.3822	0.0291
5	0.30 (17.19)	0.50	0.25	0.1014 (5.81)	0.5951	0.3555	0.8935	0.5142	10.1478	0.0144
6	0.25 (14.32)	0.50	0.30	0.2356 (13.50)	0.4845	0.3619	0.8295	0.5296	12.0212	0.0210
7	0.23 (13.18)	0.67	0.29	0.3137 (17.97)	0.5734	0.2836	0.6004	0.5718	9.7076	0.0531
8	0.20 (11.46)	0.80	0.25	0.2741 (15.70)	0.4968	0.2013	0.4690	0.3401	11.5492	0.0260
9	0.15 (8.59)	1.00	0.30	0.1479 (8.47)	0.6691	0.2629	0.4011	0.3115	8.7933	0.0224
10	0.10 (5.73)	0.70	0.25	0.3029 (17.35)	0.5919	0.2393	0.5000	0.2905	9.4064	0.0147

Case 4 Equivalent Indices
Iteration No.	1st Layer	2nd Layer	3rd Layer	4th Layer	5th Layer	Func. Value
1	$1.1467 - 5.2892 j$	$6.8679 + 1.5320 j$	$5.9505 - 4.2526 j$	$- 3.0528 - 1.7341 j$	–	$0.0002 < 0.01$
Case 7 Equivalent Indices
Iteration No.	1st Layer	2nd Layer	3rd Layer	4th Layer	5th Layer	Func. Value
1	$0.7738 - 2.1118 j$	$5.0964 + 1.1922 j$	$4.3978 - 3.0027 j$	$2.7236 + 1.8936 j$	–	$0.0264 > 0.01$
2	$- 0.9871 + 4.2330 j$	$5.4118 + 1.3204 j$	$3.6796 - 0.8072 j$	$4.5069 - 2.4320 j$	$2.5383 + 2.4434 j$	$0.0020 < 0.01$

Binary Case Number	Initial Guesses			Optimized Values
	$θ$	$Λ$	$t_{g}$	$θ$	$Λ$	$t_{g}$	$P C_{c, + 1}$	$D E_{c, + 1}$	$β$	$α$
	rad (deg)	μm	μm	rad (deg)	μm	μm	$P C_{c, + 1}$	$@ N = 50$	${μm}^{- 1}$	${μm}^{- 1}$
1	0.15 (8.59)	0.55	0.25	0.1761 (10.10)	0.5439	0.2337	0.5345	0.4417	10.8416	0.0322
2	0.20 (11.46)	0.55	0.25	0.2245 (12.86)	0.5462	0.2419	0.5474	0.5117	10.6020	0.0500
3	0.25 (14.32)	0.50	0.15	0.2499 (14.32)	0.5371	0.2071	0.5028	0.4812	10.6963	0.0301
4	0.15 (8.59)	0.55	0.10	0.1584 (9.08)	0.5701	0.2299	0.5328	0.4314	10.3822	0.0291
5	0.30 (17.19)	0.50	0.25	0.1014 (5.81)	0.5951	0.3555	0.8935	0.5142	10.1478	0.0144
6	0.25 (14.32)	0.50	0.30	0.2356 (13.50)	0.4845	0.3619	0.8295	0.5296	12.0212	0.0210
7	0.23 (13.18)	0.67	0.29	0.3137 (17.97)	0.5734	0.2836	0.6004	0.5718	9.7076	0.0531
8	0.20 (11.46)	0.80	0.25	0.2741 (15.70)	0.4968	0.2013	0.4690	0.3401	11.5492	0.0260
9	0.15 (8.59)	1.00	0.30	0.1479 (8.47)	0.6691	0.2629	0.4011	0.3115	8.7933	0.0224
10	0.10 (5.73)	0.70	0.25	0.3029 (17.35)	0.5919	0.2393	0.5000	0.2905	9.4064	0.0147

Case 4 Equivalent Indices
Iteration No.	1st Layer	2nd Layer	3rd Layer	4th Layer	5th Layer	Func. Value
1	$1.1467 - 5.2892 j$	$6.8679 + 1.5320 j$	$5.9505 - 4.2526 j$	$- 3.0528 - 1.7341 j$	–	$0.0002 < 0.01$
Case 7 Equivalent Indices
Iteration No.	1st Layer	2nd Layer	3rd Layer	4th Layer	5th Layer	Func. Value
1	$0.7738 - 2.1118 j$	$5.0964 + 1.1922 j$	$4.3978 - 3.0027 j$	$2.7236 + 1.8936 j$	–	$0.0264 > 0.01$
2	$- 0.9871 + 4.2330 j$	$5.4118 + 1.3204 j$	$3.6796 - 0.8072 j$	$4.5069 - 2.4320 j$	$2.5383 + 2.4434 j$	$0.0020 < 0.01$

Abstract

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Figures (9)

Tables (2)

Equations (39)

Applied Optics