Abstract

This theoretical modeling-and-simulation paper presents designs and projected performance of ~1500-nm silicon-on-insulator 2 x 2 Mach-Zehnder interferometer (MZI) optical crossbar switches and tunable filters that are actuated by thermo-optical (TO) means. A TO heater stripe is assumed to be on the top of each waveguided arm in the interferometer. Each strip-waveguide arm contains an inline set of N-fold coupled, phase-shifted Bragg-grating resonators. To implement accurate and realistic designs, a mixed full-vectorial mathematical model based upon the finite-element, coupled-mode, and transfer-matrix approaches was employed. The Butterworth-filter technique for grating length and weighting was used. The resulting narrowband waveguide-transmission spectral shape was better-than-Lorentzian because of its steeper sidewalls (faster rolloff). The metrics of crossbar switching, insertion loss (IL) and crosstalk (CT), were evaluated for choices of grating strength and TO-induced change in the grating-waveguide refractive index. The predicted ILs and CTs were quite superior to those cited in the literature for experimental and theoretical MZI devices based upon silicon nanobeam resonators. This was true for the Type-I and Type-II resonator addressing discussed here. Finally, we examined the TO-tunable composite filter profiles that are feasible by connecting two or more Type-I MZIs in an optical series arrangement. A variety of narrow filter shapes, tunable over ~2 nm, was found.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (4)

2017 (3)

2016 (3)

W. Zhang and J. Yao, “Silicon-based integrated microwave photonics,” IEEE J. Quantum Electron. 52, 1–12 (2016).

M. Burla, X. Wang, M. Li, L. Chrostowski, and J. Azaña, “Wideband dynamic microwave frequency identification system using a low-power ultracompact silicon photonic chip,” Nat. Commun. 7, 13004–13012 (2016).
[Crossref] [PubMed]

R. Soref, J. R. Hendrickson, and J. Sweet, “Simulation of germanium nanobeam electro-optical 2 × 2 switches and 1 × 1 modulators for the 2 to 5 mm infrared region,” Opt. Express 24(9), 9369–9382 (2016).
[Crossref] [PubMed]

2015 (5)

2014 (4)

2013 (1)

M. Spasojevic and L. R. Chen, “Tunable optical delay line in SOI implemented with step chirped Bragg gratings and serial grating arrays,” Proc. SPIE 8915, 89150S (2013).
[Crossref]

2012 (1)

2011 (2)

Q. Xu and R. Soref, “Reconfigurable optical directed-logic circuits using microresonator-based optical switches,” Opt. Express 19(6), 5244–5259 (2011).
[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, 290–292 (2011).

2008 (1)

V. M. N. Passaro, R. Loiacono, G. D’Amico, and F. De Leonardis, “Design of Bragg Grating Sensors Based on Submicrometer Optical Rib Waveguides in SOI,” IEEE Sens. J. 8(9), 1603–1611 (2008).
[Crossref]

Aimez, V.

Azaña, J.

M. Burla, X. Wang, M. Li, L. Chrostowski, and J. Azaña, “Wideband dynamic microwave frequency identification system using a low-power ultracompact silicon photonic chip,” Nat. Commun. 7, 13004–13012 (2016).
[Crossref] [PubMed]

Bazargani, H. P.

M. Burla, H. P. Bazargani, and J. St-Yves, 2, W. Shi, L. Chrostowski, J. Azaña, “Frequency Agile Microwave Photonics Notch Filter based on a Waveguide Bragg Grating on Silicon,” in Int. Topic Meeting on Microwave Photonics and 9th Asia-Pacific Microwave Photonics (2014), pp. 392–394.

Beaudin, G.

Boller, K.-J.

Y. Xie, Z. Gen, L. Zhuang, M. Burla, C. Taddei, M. Hoekman, A. Leinse, C. G. H. Roeloffzen, K.-J. Boller, and A. J. Lowery, “Programmable optical processor chips: toward photonic RF filters with DSP-level flexibility and MHz-band selectivity,” Nanophotonics 7, 1–34 (2017).

Burla, M.

Y. Xie, Z. Gen, L. Zhuang, M. Burla, C. Taddei, M. Hoekman, A. Leinse, C. G. H. Roeloffzen, K.-J. Boller, and A. J. Lowery, “Programmable optical processor chips: toward photonic RF filters with DSP-level flexibility and MHz-band selectivity,” Nanophotonics 7, 1–34 (2017).

M. Burla, X. Wang, M. Li, L. Chrostowski, and J. Azaña, “Wideband dynamic microwave frequency identification system using a low-power ultracompact silicon photonic chip,” Nat. Commun. 7, 13004–13012 (2016).
[Crossref] [PubMed]

M. Burla, H. P. Bazargani, and J. St-Yves, 2, W. Shi, L. Chrostowski, J. Azaña, “Frequency Agile Microwave Photonics Notch Filter based on a Waveguide Bragg Grating on Silicon,” in Int. Topic Meeting on Microwave Photonics and 9th Asia-Pacific Microwave Photonics (2014), pp. 392–394.

Capmany, J.

Caverley, M.

Chen, J.

Chen, L. R.

M. Spasojevic and L. R. Chen, “Tunable optical delay line in SOI implemented with step chirped Bragg gratings and serial grating arrays,” Proc. SPIE 8915, 89150S (2013).
[Crossref]

Chen, Z.

Chrostowski, L.

M. Burla, X. Wang, M. Li, L. Chrostowski, and J. Azaña, “Wideband dynamic microwave frequency identification system using a low-power ultracompact silicon photonic chip,” Nat. Commun. 7, 13004–13012 (2016).
[Crossref] [PubMed]

Z. Chen, J. Flueckiger, X. Wang, F. Zhang, H. Yun, Z. Lu, M. Caverley, Y. Wang, N. A. F. Jaeger, and L. Chrostowski, “Spiral Bragg grating waveguides for TM mode silicon photonics,” Opt. Express 23(19), 25295–25307 (2015).
[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, 290–292 (2011).

D’Amico, G.

V. M. N. Passaro, R. Loiacono, G. D’Amico, and F. De Leonardis, “Design of Bragg Grating Sensors Based on Submicrometer Optical Rib Waveguides in SOI,” IEEE Sens. J. 8(9), 1603–1611 (2008).
[Crossref]

Dai, T.

De Leonardis, F.

B. Troia, F. De Leonardis, and V. M. N. Passaro, “Generalized modelling for the design of guided-wave optical directional couplers,” Opt. Lett. 39(5), 1161–1164 (2014).
[Crossref] [PubMed]

V. M. N. Passaro, R. Loiacono, G. D’Amico, and F. De Leonardis, “Design of Bragg Grating Sensors Based on Submicrometer Optical Rib Waveguides in SOI,” IEEE Sens. J. 8(9), 1603–1611 (2008).
[Crossref]

Doerr, C.

C. Doerr, “Silicon photonic integration in telecommunications,” Front. Phys. 3, 7 (2015).
[Crossref]

Flueckiger, J.

Gen, Z.

Y. Xie, Z. Gen, L. Zhuang, M. Burla, C. Taddei, M. Hoekman, A. Leinse, C. G. H. Roeloffzen, K.-J. Boller, and A. J. Lowery, “Programmable optical processor chips: toward photonic RF filters with DSP-level flexibility and MHz-band selectivity,” Nanophotonics 7, 1–34 (2017).

Gibson, R.

Giguère, A.

Guo, Z.

He, Y.

Hendrickson, J.

Hendrickson, J. R.

Hoekman, M.

Y. Xie, Z. Gen, L. Zhuang, M. Burla, C. Taddei, M. Hoekman, A. Leinse, C. G. H. Roeloffzen, K.-J. Boller, and A. J. Lowery, “Programmable optical processor chips: toward photonic RF filters with DSP-level flexibility and MHz-band selectivity,” Nanophotonics 7, 1–34 (2017).

Jaeger, N. A. F.

Z. Chen, J. Flueckiger, X. Wang, F. Zhang, H. Yun, Z. Lu, M. Caverley, Y. Wang, N. A. F. Jaeger, and L. Chrostowski, “Spiral Bragg grating waveguides for TM mode silicon photonics,” Opt. Express 23(19), 25295–25307 (2015).
[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, 290–292 (2011).

Jiang, J.

Jiang, X.

Kirk, A. G.

LaRochelle, S.

Le Drogoff, B.

Leinse, A.

Y. Xie, Z. Gen, L. Zhuang, M. Burla, C. Taddei, M. Hoekman, A. Leinse, C. G. H. Roeloffzen, K.-J. Boller, and A. J. Lowery, “Programmable optical processor chips: toward photonic RF filters with DSP-level flexibility and MHz-band selectivity,” Nanophotonics 7, 1–34 (2017).

Li, M.

M. Burla, X. Wang, M. Li, L. Chrostowski, and J. Azaña, “Wideband dynamic microwave frequency identification system using a low-power ultracompact silicon photonic chip,” Nat. Commun. 7, 13004–13012 (2016).
[Crossref] [PubMed]

Li, X.

Li, Y.

Loiacono, R.

V. M. N. Passaro, R. Loiacono, G. D’Amico, and F. De Leonardis, “Design of Bragg Grating Sensors Based on Submicrometer Optical Rib Waveguides in SOI,” IEEE Sens. J. 8(9), 1603–1611 (2008).
[Crossref]

Lowery, A. J.

Y. Xie, Z. Gen, L. Zhuang, M. Burla, C. Taddei, M. Hoekman, A. Leinse, C. G. H. Roeloffzen, K.-J. Boller, and A. J. Lowery, “Programmable optical processor chips: toward photonic RF filters with DSP-level flexibility and MHz-band selectivity,” Nanophotonics 7, 1–34 (2017).

Lu, L.

Lu, Z.

Madsen, C. K.

Muñoz, P.

Passaro, V. M. N.

B. Troia, F. De Leonardis, and V. M. N. Passaro, “Generalized modelling for the design of guided-wave optical directional couplers,” Opt. Lett. 39(5), 1161–1164 (2014).
[Crossref] [PubMed]

V. M. N. Passaro, R. Loiacono, G. D’Amico, and F. De Leonardis, “Design of Bragg Grating Sensors Based on Submicrometer Optical Rib Waveguides in SOI,” IEEE Sens. J. 8(9), 1603–1611 (2008).
[Crossref]

Poon, A. W.

Qi, C. U.

Qiu, C.

Qiu, H.

Roeloffzen, C. G. H.

Y. Xie, Z. Gen, L. Zhuang, M. Burla, C. Taddei, M. Hoekman, A. Leinse, C. G. H. Roeloffzen, K.-J. Boller, and A. J. Lowery, “Programmable optical processor chips: toward photonic RF filters with DSP-level flexibility and MHz-band selectivity,” Nanophotonics 7, 1–34 (2017).

Shen, L.

Shi, W.

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, 290–292 (2011).

Simard, A. D.

Soref, R.

Spasojevic, M.

M. Spasojevic and L. R. Chen, “Tunable optical delay line in SOI implemented with step chirped Bragg gratings and serial grating arrays,” Proc. SPIE 8915, 89150S (2013).
[Crossref]

St-Yves, J.

M. Burla, H. P. Bazargani, and J. St-Yves, 2, W. Shi, L. Chrostowski, J. Azaña, “Frequency Agile Microwave Photonics Notch Filter based on a Waveguide Bragg Grating on Silicon,” in Int. Topic Meeting on Microwave Photonics and 9th Asia-Pacific Microwave Photonics (2014), pp. 392–394.

Su, Y.

Sweet, J.

Taddei, C.

Y. Xie, Z. Gen, L. Zhuang, M. Burla, C. Taddei, M. Hoekman, A. Leinse, C. G. H. Roeloffzen, K.-J. Boller, and A. J. Lowery, “Programmable optical processor chips: toward photonic RF filters with DSP-level flexibility and MHz-band selectivity,” Nanophotonics 7, 1–34 (2017).

Troia, B.

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, 290–292 (2011).

Veerasubramanian, V.

Wang, G.

Wang, X.

Wang, Y.

Xie, Y.

Y. Xie, Z. Gen, L. Zhuang, M. Burla, C. Taddei, M. Hoekman, A. Leinse, C. G. H. Roeloffzen, K.-J. Boller, and A. J. Lowery, “Programmable optical processor chips: toward photonic RF filters with DSP-level flexibility and MHz-band selectivity,” Nanophotonics 7, 1–34 (2017).

Xu, Q.

Yang, J.

Yao, J.

W. Zhang and J. Yao, “Silicon-based integrated microwave photonics,” IEEE J. Quantum Electron. 52, 1–12 (2016).

Yu, H.

Yun, H.

Zhang, F.

Zhang, L.

Zhang, W.

W. Zhang and J. Yao, “Silicon-based integrated microwave photonics,” IEEE J. Quantum Electron. 52, 1–12 (2016).

Zhang, Y.

Zhou, H.

Zhou, L.

Zhu, Q.

Zhuang, L.

Y. Xie, Z. Gen, L. Zhuang, M. Burla, C. Taddei, M. Hoekman, A. Leinse, C. G. H. Roeloffzen, K.-J. Boller, and A. J. Lowery, “Programmable optical processor chips: toward photonic RF filters with DSP-level flexibility and MHz-band selectivity,” Nanophotonics 7, 1–34 (2017).

APL Photonics (1)

R. Soref, “Tutorial: Integrated- Photonic Switching Structures,” APL Photonics 3(2), 021101 (2018).
[Crossref]

Appl. Opt. (1)

Front. Phys. (1)

C. Doerr, “Silicon photonic integration in telecommunications,” Front. Phys. 3, 7 (2015).
[Crossref]

IEEE J. Quantum Electron. (1)

W. Zhang and J. Yao, “Silicon-based integrated microwave photonics,” IEEE J. Quantum Electron. 52, 1–12 (2016).

IEEE Photonics Technol. Lett. (1)

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, 290–292 (2011).

IEEE Sens. J. (1)

V. M. N. Passaro, R. Loiacono, G. D’Amico, and F. De Leonardis, “Design of Bragg Grating Sensors Based on Submicrometer Optical Rib Waveguides in SOI,” IEEE Sens. J. 8(9), 1603–1611 (2008).
[Crossref]

J. Lightwave Technol. (2)

Nanophotonics (1)

Y. Xie, Z. Gen, L. Zhuang, M. Burla, C. Taddei, M. Hoekman, A. Leinse, C. G. H. Roeloffzen, K.-J. Boller, and A. J. Lowery, “Programmable optical processor chips: toward photonic RF filters with DSP-level flexibility and MHz-band selectivity,” Nanophotonics 7, 1–34 (2017).

Nat. Commun. (1)

M. Burla, X. Wang, M. Li, L. Chrostowski, and J. Azaña, “Wideband dynamic microwave frequency identification system using a low-power ultracompact silicon photonic chip,” Nat. Commun. 7, 13004–13012 (2016).
[Crossref] [PubMed]

Opt. Express (7)

Q. Xu and R. Soref, “Reconfigurable optical directed-logic circuits using microresonator-based optical switches,” Opt. Express 19(6), 5244–5259 (2011).
[Crossref] [PubMed]

V. Veerasubramanian, G. Beaudin, A. Giguère, B. Le Drogoff, V. Aimez, and A. G. Kirk, “Waveguide-coupled drop filters on SOI using quarter-wave shifted sidewalled grating resonators,” Opt. Express 20(14), 15983–15990 (2012).
[Crossref] [PubMed]

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]

J. Jiang, H. Qiu, G. Wang, Y. Li, T. Dai, X. Wang, H. Yu, J. Yang, and X. Jiang, “Broadband tunable filter based on the loop of multimode Bragg grating,” Opt. Express 26(1), 559–566 (2018).
[Crossref] [PubMed]

Z. Chen, J. Flueckiger, X. Wang, F. Zhang, H. Yun, Z. Lu, M. Caverley, Y. Wang, N. A. F. Jaeger, and L. Chrostowski, “Spiral Bragg grating waveguides for TM mode silicon photonics,” Opt. Express 23(19), 25295–25307 (2015).
[Crossref] [PubMed]

R. Soref and J. Hendrickson, “Proposed ultralow-energy dual photonic-crystal nanobeam devices for on-chip N x N switching, logic, and wavelength multiplexing,” Opt. Express 23(25), 32582–32596 (2015).
[Crossref] [PubMed]

R. Soref, J. R. Hendrickson, and J. Sweet, “Simulation of germanium nanobeam electro-optical 2 × 2 switches and 1 × 1 modulators for the 2 to 5 mm infrared region,” Opt. Express 24(9), 9369–9382 (2016).
[Crossref] [PubMed]

Opt. Lett. (3)

Photon. Res. (3)

Proc. SPIE (1)

M. Spasojevic and L. R. Chen, “Tunable optical delay line in SOI implemented with step chirped Bragg gratings and serial grating arrays,” Proc. SPIE 8915, 89150S (2013).
[Crossref]

Other (7)

S. LaRochelle, A. D. Simard, “Silicon Photonic Bragg Grating Devices,” in OFC (2017), paper Th1G.3.

M. Burla, H. P. Bazargani, and J. St-Yves, 2, W. Shi, L. Chrostowski, J. Azaña, “Frequency Agile Microwave Photonics Notch Filter based on a Waveguide Bragg Grating on Silicon,” in Int. Topic Meeting on Microwave Photonics and 9th Asia-Pacific Microwave Photonics (2014), pp. 392–394.

C. Qui, W. Gao, R. Soref, J. Robinson, and Q. Xu, “Demonstration of reconfigurable electro-optical directed-logic circuit using carrier-depletion micro-ring resonators,” in CLEO Science and Innovations (2015), paper SM2I.4.

X. Jiang, H. Zhang, C. Qiu, Y. Zhang, Y. Su, and R. Soref, “Compact and power-efficient 2 x 2 thermo-optical switch based on the dual-nanobeam MZI,” in Optical Fiber Communication Conference (2018), paper Th2A.7.
[Crossref]

R. Soref, “Resonant and slow-light 2 x 2 switches enabled by nanobeams and grating-assisted waveguides,” in Progress in Electromagnetics Research Symposium (2017), paper IP5.9.

S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communications Electronics (John Wiley & Sons, Inc., 1995).

R. Soref, F. De Leonardis, V. M. N. Passaro, “Reconfigurable optical-microwave filter banks using thermo-optically tuned Bragg Mach-Zehnder devices,” Opt. Express, in publication.

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Figures (5)

Fig. 1
Fig. 1 (a) Schematic architecture of on-chip 2 × 2 MZI switch (in orange the heating strips). (b) 2 × 2 MZI switch black box; (c) i-th waveguide Bragg resonator; (d) SOI waveguide cross section.
Fig. 2
Fig. 2 (a) Through spectrum for different values of M , assuming N = 3; (b) Drop spectrum for different values of M , assuming N = 3; c) Through spectrum for N = 3, and N = 4, assuming M = 20; d) Drop spectrum for N = 3, and N = 4, assuming M = 20. The simulations are performed by considering:   W = 450 nm, H = 250 nm, W t = 100 nm, Λ = 315 nm, and α l = 1 dB/cm.
Fig. 3
Fig. 3 Type-I Through and Drop spectra for N = 3, and M = 30, assuming W t = 100 nm (left panels) and W t = 80 nm (right panels); A zoom plot is shown in (c) and in (d). Red line represents the cross state, Blue and Green lines indicate the Bar state.
Fig. 4
Fig. 4 Type-II Through and Drop spectra for N = 3, M = 30, and W t = 100 nm; (a) All TOs are switched-off; (b) Cross state: TO1 switched-on and TO1 switched-off; (c) Bar state:TO1 switched-off and TO2 switched-on; (d). TO-induced refractive index change needed for Cross as a function of δ λ selection, (e) Insertion loss for Cross and Bar states as a function of δ λ ; (f) Crosstalk for Cross and Bar states as a function of Δ n .
Fig. 5
Fig. 5 One row of the proposed multi-row reconfigurable filter-cascade mesh. The example of the 2-cascade of resonant 2 x 2 TO MZI bulding blocks is shown.

Tables (6)

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Table 1 Ladder-circuit coefficients.

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Table 2 Coupled Bragg resonators parameters.

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Table 3 Filter performance for MZI-Type I.

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Table 4 Calculated 2 x 2 switching performance for MZI-Type I.

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Table 5 Comparison between WBR-MZI and NBR-MZI

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Table 6 Comparison between WBR-MZI and DR-MZI

Equations (4)

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[ b 2 a 2 b 4 a 4 ] = T M Z I [ b 1 a 1 b 3 a 3 ] = T c T a r m T c [ b 1 a 1 b 3 a 3 ]
T a r m = [ T a r m 1   0 0 T a r m 2 ]
T c = [ A B C D ] = [ S 12 0 S 23 0 0 S 34 S 12 S 34 S 14 S 23 0 S 14 S 12 S 34 S 14 S 23 S 14 0 S 34 0 0 S 23 S 12 S 34 S 14 S 23 0 S 12 S 12 S 34 S 14 S 23 ]
L B i = 1 2 κ c log ( g i g 1 ) + L B 1 ; i > 1

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