Abstract

We present the design, analysis, and experimental characterization of a novel integrated add-drop filter capable of filtering simultaneously two independent channels that is based on a contra-directional grating assisted coupler with two different periods. The device performance is explained using Fourier analysis and confirmed with numerical simulations using the eigenmode expansion method. The devices were fabricated using electron-beam lithography on a silicon-on-insulator wafer with a 220 nm thick device layer. The Fourier analysis, simulations and experimental results are in agreement and show that the drop port response of the two-period configuration is the superposition of the drop port responses of two single-period gratings. Therefore, the output channels at drop port can be designed independently and can have different bandwidths.

© 2016 Optical Society of America

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References

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  1. A. D. Simard, N. Belhadj, Y. Painchaud, and S. LaRochelle, “Apodized silicon-on-insulator Bragg gratings,” IEEE Photonics Technol. Lett. 24(12), 1033–1035 (2012).
    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  10. H. Qiu, G. Jiang, T. Hu, H. Shao, P. Yu, J. Yang, and X. Jiang, “FSR-free add-drop filter based on silicon grating-assisted contradirectional couplers,” Opt. Lett. 38(1), 1–3 (2013).
    [Crossref] [PubMed]
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    [Crossref]
  12. W. Shi, H. Yun, C. Lin, X. Wang, J. Flueckiger, N. Jaeger, and L. Chrostowski, “Silicon CWDM demultiplexers using contra-directional couplers,” in Proceedings of CLEO, OSA Technical Digest (online) (Optical Society of America, 2013), paper CTu3F.5.
    [Crossref]
  13. X. Wang, Y. Wang, J. Flueckiger, R. Bojko, A. Liu, A. Reid, J. Pond, N. A. Jaeger, and L. Chrostowski, “Precise control of the coupling coefficient through destructive interference in silicon waveguide Bragg gratings,” Opt. Lett. 39(19), 5519–5522 (2014).
    [Crossref] [PubMed]
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    [Crossref]

2015 (2)

2014 (1)

2013 (2)

2012 (1)

A. D. Simard, N. Belhadj, Y. Painchaud, and S. LaRochelle, “Apodized silicon-on-insulator Bragg gratings,” IEEE Photonics Technol. Lett. 24(12), 1033–1035 (2012).
[Crossref]

2011 (2)

X. Wang, W. Shi, R. Vafaei, N. A. F. Jaeger, and L. Chrostowski, “Uniform and sampled Bragg gratings in SOI strip waveguides with sidewall corrugations,” IEEE Photonics Technol. Lett. 23(5), 290–292 (2011).

G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photonics Technol. Lett. 23(1), 6–8 (2011).

2009 (1)

1997 (1)

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997).
[Crossref]

1987 (1)

D. Marcuse, “Directional couplers made of nonidentical asymmetric slabs part II: grating-assisted couplers,” J. Lightwave Technol. 5(2), 268–273 (1987).
[Crossref]

Baehr-Jones, T.

Belhadj, N.

A. D. Simard, N. Belhadj, Y. Painchaud, and S. LaRochelle, “Apodized silicon-on-insulator Bragg gratings,” IEEE Photonics Technol. Lett. 24(12), 1033–1035 (2012).
[Crossref]

Bojko, R.

Chen, R.

G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photonics Technol. Lett. 23(1), 6–8 (2011).

Chrostowski, L.

Erdogan, T.

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997).
[Crossref]

Fainman, Y.

Flueckiger, J.

Grieco, A.

Hochberg, M.

Hu, T.

Ikeda, K.

Jaeger, N. A.

Jaeger, N. A. F.

W. Shi, X. Wang, C. Lin, H. Yun, Y. Liu, T. Baehr-Jones, M. Hochberg, N. A. F. Jaeger, and L. Chrostowski, “Silicon photonic grating-assisted, contra-directional couplers,” Opt. Express 21(3), 3633–3650 (2013).
[Crossref] [PubMed]

X. Wang, W. Shi, R. Vafaei, N. A. F. Jaeger, and L. Chrostowski, “Uniform and sampled Bragg gratings in SOI strip waveguides with sidewall corrugations,” IEEE Photonics Technol. Lett. 23(5), 290–292 (2011).

Jiang, G.

H. Qiu, G. Jiang, T. Hu, H. Shao, P. Yu, J. Yang, and X. Jiang, “FSR-free add-drop filter based on silicon grating-assisted contradirectional couplers,” Opt. Lett. 38(1), 1–3 (2013).
[Crossref] [PubMed]

G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photonics Technol. Lett. 23(1), 6–8 (2011).

Jiang, X.

H. Qiu, G. Jiang, T. Hu, H. Shao, P. Yu, J. Yang, and X. Jiang, “FSR-free add-drop filter based on silicon grating-assisted contradirectional couplers,” Opt. Lett. 38(1), 1–3 (2013).
[Crossref] [PubMed]

G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photonics Technol. Lett. 23(1), 6–8 (2011).

LaRochelle, S.

A. D. Simard and S. LaRochelle, “Complex apodized Bragg grating filters without circulators in silicon-on-insulator,” Opt. Express 23(13), 16662–16675 (2015).
[Crossref] [PubMed]

A. D. Simard, N. Belhadj, Y. Painchaud, and S. LaRochelle, “Apodized silicon-on-insulator Bragg gratings,” IEEE Photonics Technol. Lett. 24(12), 1033–1035 (2012).
[Crossref]

Lin, C.

Liu, A.

Liu, Y.

Marcuse, D.

D. Marcuse, “Directional couplers made of nonidentical asymmetric slabs part II: grating-assisted couplers,” J. Lightwave Technol. 5(2), 268–273 (1987).
[Crossref]

Painchaud, Y.

A. D. Simard, N. Belhadj, Y. Painchaud, and S. LaRochelle, “Apodized silicon-on-insulator Bragg gratings,” IEEE Photonics Technol. Lett. 24(12), 1033–1035 (2012).
[Crossref]

Pond, J.

Puckett, M. W.

Qiu, H.

Reid, A.

Shao, H.

Shi, W.

W. Shi, X. Wang, C. Lin, H. Yun, Y. Liu, T. Baehr-Jones, M. Hochberg, N. A. F. Jaeger, and L. Chrostowski, “Silicon photonic grating-assisted, contra-directional couplers,” Opt. Express 21(3), 3633–3650 (2013).
[Crossref] [PubMed]

X. Wang, W. Shi, R. Vafaei, N. A. F. Jaeger, and L. Chrostowski, “Uniform and sampled Bragg gratings in SOI strip waveguides with sidewall corrugations,” IEEE Photonics Technol. Lett. 23(5), 290–292 (2011).

Simard, A. D.

A. D. Simard and S. LaRochelle, “Complex apodized Bragg grating filters without circulators in silicon-on-insulator,” Opt. Express 23(13), 16662–16675 (2015).
[Crossref] [PubMed]

A. D. Simard, N. Belhadj, Y. Painchaud, and S. LaRochelle, “Apodized silicon-on-insulator Bragg gratings,” IEEE Photonics Technol. Lett. 24(12), 1033–1035 (2012).
[Crossref]

Tan, D. T. H.

Vafaei, R.

X. Wang, W. Shi, R. Vafaei, N. A. F. Jaeger, and L. Chrostowski, “Uniform and sampled Bragg gratings in SOI strip waveguides with sidewall corrugations,” IEEE Photonics Technol. Lett. 23(5), 290–292 (2011).

Vallini, F.

Wang, M.

G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photonics Technol. Lett. 23(1), 6–8 (2011).

Wang, X.

Wang, Y.

Yang, J.

H. Qiu, G. Jiang, T. Hu, H. Shao, P. Yu, J. Yang, and X. Jiang, “FSR-free add-drop filter based on silicon grating-assisted contradirectional couplers,” Opt. Lett. 38(1), 1–3 (2013).
[Crossref] [PubMed]

G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photonics Technol. Lett. 23(1), 6–8 (2011).

Yu, P.

Yun, H.

Zhou, Q.

G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photonics Technol. Lett. 23(1), 6–8 (2011).

IEEE Photonics Technol. Lett. (3)

A. D. Simard, N. Belhadj, Y. Painchaud, and S. LaRochelle, “Apodized silicon-on-insulator Bragg gratings,” IEEE Photonics Technol. Lett. 24(12), 1033–1035 (2012).
[Crossref]

X. Wang, W. Shi, R. Vafaei, N. A. F. Jaeger, and L. Chrostowski, “Uniform and sampled Bragg gratings in SOI strip waveguides with sidewall corrugations,” IEEE Photonics Technol. Lett. 23(5), 290–292 (2011).

G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photonics Technol. Lett. 23(1), 6–8 (2011).

J. Lightwave Technol. (2)

D. Marcuse, “Directional couplers made of nonidentical asymmetric slabs part II: grating-assisted couplers,” J. Lightwave Technol. 5(2), 268–273 (1987).
[Crossref]

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997).
[Crossref]

Opt. Express (2)

Opt. Lett. (4)

Other (4)

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford University, 2007).

W. Shi, H. Yun, C. Lin, X. Wang, J. Flueckiger, N. Jaeger, and L. Chrostowski, “Silicon CWDM demultiplexers using contra-directional couplers,” in Proceedings of CLEO, OSA Technical Digest (online) (Optical Society of America, 2013), paper CTu3F.5.
[Crossref]

L. Chrostowski, X. Wang, J. Flueckiger, Y. Wu, Y. Wang, and S. Talebi Fard, “Impact of fabrication non-uniformity on chip-scale silicon photonic integrated circuits,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2014), paper Th2A.37.
[Crossref]

X. Wang, H. Yun, N. A. F. Jaeger, and L. Chrostowski, “Multi-period Bragg gratings in silicon waveguides,” in Proceedings of IEEE Photonics Conference (IEEE 2013), pp. 442–443.

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Figures (6)

Fig. 1
Fig. 1 (a) Top view of a uniform CDGAC with a grating only on one of the waveguides; (b) Top view of a uniform two-period CDGAC.
Fig. 2
Fig. 2 Longitudinal phase match condition for the two-period configuration with Λ 1 = 312 nm, Λ 2 = 318 nm, Δ W 1 = 50 nm, and Δ W 2 = 50 nm.
Fig. 3
Fig. 3 Fourier coefficients of the two-period configuration with Λ 1 = 312 nm and Λ 2 = 318 nm having Ν p 3 = 20 super-periods.
Fig. 4
Fig. 4 Simulation results of a uniform two-period CDGAC with Δ W 1 = Δ W 2 = 50 nm, Λ 1 = 312 nm, Λ 2 = 318 nm, and Ν p 3 = 20.
Fig. 5
Fig. 5 Through and drop port response of (a) two-period CDGAC with Δ W 1 = Δ W 2 = 50 nm, Λ 1 = 312 nm, Λ 2 = 318 nm, and a = 10, (b) a single-period CDGAC with Δ W 1 = 50 nm, Δ W 2 = 0 nm, Λ = 312 nm, and a = 10, (c) a single-period CDGAC with Δ W 1 = 0 nm, Δ W 2 = 50 nm, Λ = 318 nm, and a = 10.
Fig. 6
Fig. 6 Transmission and drop port response of a two-period CDGAC with Δ W 1 = 24 nm, Δ W 2 = 50 nm, Λ 1 = 318 nm, Λ 2 = 312 nm, and a = 10.

Equations (13)

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β 1 ( λ 0 ) + β 2 ( λ 0 ) = 2 m π Λ 0
2 n e f f 1 a v e ( 2 π λ ) = m 2 π Λ 3
2 n e f f 2 a v e ( 2 π λ ) = m 2 π Λ 3
( n e f f 1 a v e + n e f f 2 a v e ) ( 2 π λ ) = m 2 π Λ 3
c ( z ) = a ( z ) p 1 ( z ) + b ( z ) p 2 ( z )
C ( ω ) = ( A ( ω ) + B ( ω ) ) * P ( ω ) = k A k P ( ω k 2 π Λ 1 ) + k B k P ( ω k 2 π Λ 2 )
ω 1 = 2 π Λ 1 = Λ 2 ( Λ 1 , Λ 2 ) × 2 π Λ 3 = Λ 2 ( Λ 1 , Λ 2 ) × ω 3 = l 1 ω 3
ω 2 = 2 π Λ 2 = Λ 1 ( Λ 1 , Λ 2 ) × 2 π Λ 3 = Λ 1 ( Λ 1 , Λ 2 ) × ω 3 = l 2 ω 3
C ( ω ) = k A k P ( ω k l 1 ω 3 ) + k B k P ( ω k l 2 ω 3 )
C m = C ( ω m = m ω 3 ) = k A k P ( ( m k l 1 ) ω 3 ) + k B k P ( ( m k l 2 ) ω 3 )
C m = k A k e j ω 3 ( m k l 1 ) sin c ( ( m k l 1 ) Ν p 3 ) + k B k e j ω 3 ( m k l 2 ) sin c ( ( m k l 2 ) Ν p 3 )
k c = ω ε 0 4 E 1 Δ ε m E 2 d x d y
Δ W = Δ W 0 e a ( x 0.5 N p N p ) 2

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