Abstract

We propose a new kind of planar waveguide Bragg grating structure, i.e., planar waveguide moiré grating (MG), which is formed by two transverse adjacent gratings with slightly different Bragg wavelengths. It is found that this kind of structure shows the same light properties as the conventional MG that is realized by superimposing two Bragg gratings. Because the proposed MG structure is a planar pattern, the fabrication becomes much easier if applying a semiconductor microfabrication process, which is very beneficial for its applications in photonic integrated devices. Similar to the well-known Vernier effect, the coupling coefficient distribution can be easily adjusted by the alignment of the two adjacent gratings. Consequently, some special grating profiles can be achieved, such as perfect apodization with two sides of the coupling coefficient approaching zero. One important potential application of these specific features is the distributed feedback (DFB) semiconductor laser for improved properties, such as reduced spatial-hole burning and more power extraction. Some design examples are also given in this paper.

© 2017 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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2017 (3)

S. Liu, Y. Shi, L. Hao, R. Xiao, and X. Chen, “Experimental demonstration of the anti-symmetric sampled Bragg grating,” IEEE Photonics Technol. Lett. 29(4), 353–356 (2017).
[Crossref]

L. Li, Y. Shi, Y. Zhang, H. Zou, J. Shen, and X. Chen, “Study on a DFB laser diode based on sampled grating technique for suppression of the zeroth order resonance,” IEEE Photonics J. 9(2), 1501909 (2017).
[Crossref]

B. Liu, Y. Zhang, Y. He, X. Jiang, J. Peng, C. Qiu, and Y. Su, “Silicon photonic bandpass filter based on apodized subwavelength grating with high suppression ratio and short coupling length,” Opt. Express 25(10), 11359–11364 (2017).
[Crossref] [PubMed]

2016 (4)

K. Bédard, A. D. Simard, B. Filion, Y. Painchaud, L. A. Rusch, and S. LaRochelle, “Dual phase-shift Bragg grating silicon photonic modulator operating up to 60 Gb/s,” Opt. Express 24(3), 2413–2419 (2016).
[Crossref] [PubMed]

H. Qiu, J. Jiang, P. Yu, T. Dai, J. Yang, H. Yu, and X. Jiang, “Silicon band-rejection and band-pass filter based on asymmetric Bragg sidewall gratings in a multimode waveguide,” Opt. Lett. 41(11), 2450–2453 (2016).
[Crossref] [PubMed]

S. Sun, Y. Deng, N. Huang, J. Tang, N. Zhu, and M. Li, “A tunable photonic temporal integrator with ultra-long integration time windows based on Raman-gain assisted phase-shifted silicon Bragg gratings,” Opt. Commun. 373, 91–94 (2016).
[Crossref]

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 (2016).
[Crossref] [PubMed]

2015 (3)

2014 (7)

J. J. Guo, M. Li, Y. Deng, N. Huang, J. Liu, and N. Zhu, “Multichannel optical filters with an ultranarrow bandwidth based on sampled Brillouin dynamic gratings,” Opt. Express 22(4), 4290–4300 (2014).
[Crossref] [PubMed]

J. Wang, P. Chen, S. Chen, Y. Shi, and D. Dai, “Improved 8-channel silicon mode demultiplexer with grating polarizers,” Opt. Express 22(11), 12799–12807 (2014).
[Crossref] [PubMed]

Z. Zou, L. Zhou, X. Li, and J. Chen, “Channel-spacing tunable silicon comb filter using two linearly chirped Bragg gratings,” Opt. Express 22(16), 19513–19522 (2014).
[Crossref] [PubMed]

S. Mokhov, D. Ott, I. Divliansky, B. Zeldovich, and L. Glebov, “Moiré volume Bragg grating filter with tunable bandwidth,” Opt. Express 22(17), 20375–20386 (2014).
[Crossref] [PubMed]

M. Burla, M. Li, L. R. Cortés, X. Wang, M. R. Fernández-Ruiz, L. Chrostowski, and J. Azaña, “Terahertz-bandwidth photonic fractional Hilbert transformer based on a phase-shifted waveguide Bragg grating on silicon,” Opt. Lett. 39(21), 6241–6244 (2014).
[Crossref] [PubMed]

J. Zheng, N. Song, Y. Zhang, Y. Shi, S. Tang, L. Li, R. Guo, and X. Chen, “An equivalent-asymmetric coupling coefficient DFB Laser with high output efficiency and stable single longitudinal mode operation,” IEEE Photonics J. 6(6), 1502809 (2014).
[Crossref]

Y. Shi, R. Liu, S. Liu, and X. Zhu, “A low-cost and high-wavelength-precision fabrication method for multiwavelength DFB semiconductor laser array,” IEEE Photonics J. 6(3), 2400112 (2014).
[Crossref]

2013 (3)

2012 (2)

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

M. Tang, H. Xie, J. Zhu, X. Li, and Y. Li, “Study of moiré grating fabrication on metal samples using nanoimprint lithography,” Opt. Express 20(3), 2942–2955 (2012).
[Crossref] [PubMed]

2010 (1)

H. Zhu, X. Xu, H. Wang, D. Kong, S. Liang, L. Zhao, and W. Wang, “The fabrication of eight-channel DFB laser array using sampled gratings,” IEEE Photonics Technol. Lett. 22(5), 353–355 (2010).
[Crossref]

2000 (2)

L. Chen and P. Smith, “Demonstration of incoherent wavelength-encoding/time-spreading optical CDMA using chirped moiré gratings,” IEEE Photonics Technol. Lett. 12(9), 1281–1283 (2000).
[Crossref]

H. Chen, D. Liu, and A. Lee, “Moiré in atomic force microscope,” Exp. Mech. 24(1), 31–32 (2000).

1998 (1)

M. Ibsen, M. K. Durkin, and R. I. Laming, “Chirped moiré fiber gratings operating on two-wavelength channels for use as dual-channel dispersion compensators,” IEEE Photonics Technol. Lett. 10(1), 84–86 (1998).
[Crossref]

1997 (1)

1995 (1)

S. Radic, N. George, and G. P. Agrawal, “Analysis of nonuniform nonlinear distributed feedback structures: generalized transfer matrix method,” IEEE J. Quantum Electron. 31(7), 1326–1336 (1995).
[Crossref]

1991 (1)

S. Kishimoto, M. Egashira, and N. Shinya, “Observation of micro-deformation by moiré method using a scanning electron microscope,” J. Soc. Mater. Sci. 40(452), 637–641 (1991).
[Crossref]

1990 (2)

D. C. J. Reid, C. M. Ragdale, I. Bennion, D. J. Robbins, J. Buus, and W. J. Stewart, “Phase-shiftd moiré grating fiber resonators,” Electron. Lett. 26(1), 10–12 (1990).
[Crossref]

G. Morthier, K. David, P. Vankwikelberge, and R. Baets, “A new DFB-Laser diode with reduced spatial hole burning,” IEEE Photonics Technol. Lett. 2(6), 388–390 (1990).
[Crossref]

Agrawal, G. P.

S. Radic, N. George, and G. P. Agrawal, “Analysis of nonuniform nonlinear distributed feedback structures: generalized transfer matrix method,” IEEE J. Quantum Electron. 31(7), 1326–1336 (1995).
[Crossref]

Aitchison, J. S.

Azaña, J.

Baehr-Jones, T.

Baets, R.

G. Morthier, K. David, P. Vankwikelberge, and R. Baets, “A new DFB-Laser diode with reduced spatial hole burning,” IEEE Photonics Technol. Lett. 2(6), 388–390 (1990).
[Crossref]

Bahrami, H.

Bédard, K.

Belhadj, N.

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

Bennion, I.

Bruck, R.

Burla, M.

Buus, J.

D. C. J. Reid, C. M. Ragdale, I. Bennion, D. J. Robbins, J. Buus, and W. J. Stewart, “Phase-shiftd moiré grating fiber resonators,” Electron. Lett. 26(1), 10–12 (1990).
[Crossref]

Chen, H.

H. Chen, D. Liu, and A. Lee, “Moiré in atomic force microscope,” Exp. Mech. 24(1), 31–32 (2000).

Chen, J.

Chen, L.

L. Chen and P. Smith, “Demonstration of incoherent wavelength-encoding/time-spreading optical CDMA using chirped moiré gratings,” IEEE Photonics Technol. Lett. 12(9), 1281–1283 (2000).
[Crossref]

Chen, P.

Chen, S.

Chen, X.

S. Liu, Y. Shi, L. Hao, R. Xiao, and X. Chen, “Experimental demonstration of the anti-symmetric sampled Bragg grating,” IEEE Photonics Technol. Lett. 29(4), 353–356 (2017).
[Crossref]

L. Li, Y. Shi, Y. Zhang, H. Zou, J. Shen, and X. Chen, “Study on a DFB laser diode based on sampled grating technique for suppression of the zeroth order resonance,” IEEE Photonics J. 9(2), 1501909 (2017).
[Crossref]

L. Hao, Y. Shi, R. Xiao, Y. Qian, and X. Chen, “Study on sampled waveguide grating with anti-symmetric periodic structure,” Opt. Express 23(12), 15784–15791 (2015).
[Crossref] [PubMed]

J. Zheng, N. Song, Y. Zhang, Y. Shi, S. Tang, L. Li, R. Guo, and X. Chen, “An equivalent-asymmetric coupling coefficient DFB Laser with high output efficiency and stable single longitudinal mode operation,” IEEE Photonics J. 6(6), 1502809 (2014).
[Crossref]

Y. Shi, S. Li, R. Guo, R. Liu, Y. Zhou, and X. Chen, “A novel concavely apodized DFB semiconductor laser using common holographic exposure,” Opt. Express 21(13), 16022–16028 (2013).
[Crossref] [PubMed]

Chrostowski, L.

Cortés, L. R.

Dai, D.

Dai, T.

David, K.

G. Morthier, K. David, P. Vankwikelberge, and R. Baets, “A new DFB-Laser diode with reduced spatial hole burning,” IEEE Photonics Technol. Lett. 2(6), 388–390 (1990).
[Crossref]

De La Rue, R. M.

Deng, Y.

S. Sun, Y. Deng, N. Huang, J. Tang, N. Zhu, and M. Li, “A tunable photonic temporal integrator with ultra-long integration time windows based on Raman-gain assisted phase-shifted silicon Bragg gratings,” Opt. Commun. 373, 91–94 (2016).
[Crossref]

J. J. Guo, M. Li, Y. Deng, N. Huang, J. Liu, and N. Zhu, “Multichannel optical filters with an ultranarrow bandwidth based on sampled Brillouin dynamic gratings,” Opt. Express 22(4), 4290–4300 (2014).
[Crossref] [PubMed]

Divliansky, I.

Durkin, M. K.

M. Ibsen, M. K. Durkin, and R. I. Laming, “Chirped moiré fiber gratings operating on two-wavelength channels for use as dual-channel dispersion compensators,” IEEE Photonics Technol. Lett. 10(1), 84–86 (1998).
[Crossref]

Egashira, M.

S. Kishimoto, M. Egashira, and N. Shinya, “Observation of micro-deformation by moiré method using a scanning electron microscope,” J. Soc. Mater. Sci. 40(452), 637–641 (1991).
[Crossref]

Everall, L. A.

Fernández-Ruiz, M. R.

Filion, B.

George, N.

S. Radic, N. George, and G. P. Agrawal, “Analysis of nonuniform nonlinear distributed feedback structures: generalized transfer matrix method,” IEEE J. Quantum Electron. 31(7), 1326–1336 (1995).
[Crossref]

Glebov, L.

Guo, J. J.

Guo, R.

J. Zheng, N. Song, Y. Zhang, Y. Shi, S. Tang, L. Li, R. Guo, and X. Chen, “An equivalent-asymmetric coupling coefficient DFB Laser with high output efficiency and stable single longitudinal mode operation,” IEEE Photonics J. 6(6), 1502809 (2014).
[Crossref]

Y. Shi, S. Li, R. Guo, R. Liu, Y. Zhou, and X. Chen, “A novel concavely apodized DFB semiconductor laser using common holographic exposure,” Opt. Express 21(13), 16022–16028 (2013).
[Crossref] [PubMed]

Hao, L.

S. Liu, Y. Shi, L. Hao, R. Xiao, and X. Chen, “Experimental demonstration of the anti-symmetric sampled Bragg grating,” IEEE Photonics Technol. Lett. 29(4), 353–356 (2017).
[Crossref]

L. Hao, Y. Shi, R. Xiao, Y. Qian, and X. Chen, “Study on sampled waveguide grating with anti-symmetric periodic structure,” Opt. Express 23(12), 15784–15791 (2015).
[Crossref] [PubMed]

He, Y.

Hochberg, M.

Huang, N.

S. Sun, Y. Deng, N. Huang, J. Tang, N. Zhu, and M. Li, “A tunable photonic temporal integrator with ultra-long integration time windows based on Raman-gain assisted phase-shifted silicon Bragg gratings,” Opt. Commun. 373, 91–94 (2016).
[Crossref]

J. J. Guo, M. Li, Y. Deng, N. Huang, J. Liu, and N. Zhu, “Multichannel optical filters with an ultranarrow bandwidth based on sampled Brillouin dynamic gratings,” Opt. Express 22(4), 4290–4300 (2014).
[Crossref] [PubMed]

Ibsen, M.

M. Ibsen, M. K. Durkin, and R. I. Laming, “Chirped moiré fiber gratings operating on two-wavelength channels for use as dual-channel dispersion compensators,” IEEE Photonics Technol. Lett. 10(1), 84–86 (1998).
[Crossref]

Jaeger, N. A.

Jean, P.

Jiang, J.

Jiang, X.

Kishimoto, S.

S. Kishimoto, M. Egashira, and N. Shinya, “Observation of micro-deformation by moiré method using a scanning electron microscope,” J. Soc. Mater. Sci. 40(452), 637–641 (1991).
[Crossref]

Kong, D.

H. Zhu, X. Xu, H. Wang, D. Kong, S. Liang, L. Zhao, and W. Wang, “The fabrication of eight-channel DFB laser array using sampled gratings,” IEEE Photonics Technol. Lett. 22(5), 353–355 (2010).
[Crossref]

Laming, R. I.

M. Ibsen, M. K. Durkin, and R. I. Laming, “Chirped moiré fiber gratings operating on two-wavelength channels for use as dual-channel dispersion compensators,” IEEE Photonics Technol. Lett. 10(1), 84–86 (1998).
[Crossref]

LaRochelle, S.

Lee, A.

H. Chen, D. Liu, and A. Lee, “Moiré in atomic force microscope,” Exp. Mech. 24(1), 31–32 (2000).

Li, L.

L. Li, Y. Shi, Y. Zhang, H. Zou, J. Shen, and X. Chen, “Study on a DFB laser diode based on sampled grating technique for suppression of the zeroth order resonance,” IEEE Photonics J. 9(2), 1501909 (2017).
[Crossref]

J. Zheng, N. Song, Y. Zhang, Y. Shi, S. Tang, L. Li, R. Guo, and X. Chen, “An equivalent-asymmetric coupling coefficient DFB Laser with high output efficiency and stable single longitudinal mode operation,” IEEE Photonics J. 6(6), 1502809 (2014).
[Crossref]

Li, M.

Li, S.

Li, X.

Li, Y.

Liang, S.

H. Zhu, X. Xu, H. Wang, D. Kong, S. Liang, L. Zhao, and W. Wang, “The fabrication of eight-channel DFB laser array using sampled gratings,” IEEE Photonics Technol. Lett. 22(5), 353–355 (2010).
[Crossref]

Lin, C.

Liu, B.

Liu, D.

H. Chen, D. Liu, and A. Lee, “Moiré in atomic force microscope,” Exp. Mech. 24(1), 31–32 (2000).

Liu, J.

Liu, R.

Y. Shi, R. Liu, S. Liu, and X. Zhu, “A low-cost and high-wavelength-precision fabrication method for multiwavelength DFB semiconductor laser array,” IEEE Photonics J. 6(3), 2400112 (2014).
[Crossref]

Y. Shi, S. Li, R. Guo, R. Liu, Y. Zhou, and X. Chen, “A novel concavely apodized DFB semiconductor laser using common holographic exposure,” Opt. Express 21(13), 16022–16028 (2013).
[Crossref] [PubMed]

Liu, S.

S. Liu, Y. Shi, L. Hao, R. Xiao, and X. Chen, “Experimental demonstration of the anti-symmetric sampled Bragg grating,” IEEE Photonics Technol. Lett. 29(4), 353–356 (2017).
[Crossref]

Y. Shi, R. Liu, S. Liu, and X. Zhu, “A low-cost and high-wavelength-precision fabrication method for multiwavelength DFB semiconductor laser array,” IEEE Photonics J. 6(3), 2400112 (2014).
[Crossref]

Liu, X.

Liu, Y.

Mashanovich, G. Z.

Mills, B.

Mokhov, S.

Morthier, G.

G. Morthier, K. David, P. Vankwikelberge, and R. Baets, “A new DFB-Laser diode with reduced spatial hole burning,” IEEE Photonics Technol. Lett. 2(6), 388–390 (1990).
[Crossref]

Muskens, O. L.

Ott, D.

Painchaud, Y.

K. Bédard, A. D. Simard, B. Filion, Y. Painchaud, L. A. Rusch, and S. LaRochelle, “Dual phase-shift Bragg grating silicon photonic modulator operating up to 60 Gb/s,” Opt. Express 24(3), 2413–2419 (2016).
[Crossref] [PubMed]

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

Passaro, V. M.

Peng, J.

Qian, Y.

Qiu, C.

Qiu, H.

Radic, S.

S. Radic, N. George, and G. P. Agrawal, “Analysis of nonuniform nonlinear distributed feedback structures: generalized transfer matrix method,” IEEE J. Quantum Electron. 31(7), 1326–1336 (1995).
[Crossref]

Ragdale, C. M.

D. C. J. Reid, C. M. Ragdale, I. Bennion, D. J. Robbins, J. Buus, and W. J. Stewart, “Phase-shiftd moiré grating fiber resonators,” Electron. Lett. 26(1), 10–12 (1990).
[Crossref]

Reed, G. T.

Reid, D. C. J.

D. C. J. Reid, C. M. Ragdale, I. Bennion, D. J. Robbins, J. Buus, and W. J. Stewart, “Phase-shiftd moiré grating fiber resonators,” Electron. Lett. 26(1), 10–12 (1990).
[Crossref]

Robbins, D. J.

D. C. J. Reid, C. M. Ragdale, I. Bennion, D. J. Robbins, J. Buus, and W. J. Stewart, “Phase-shiftd moiré grating fiber resonators,” Electron. Lett. 26(1), 10–12 (1990).
[Crossref]

Rusch, L. A.

Shen, J.

L. Li, Y. Shi, Y. Zhang, H. Zou, J. Shen, and X. Chen, “Study on a DFB laser diode based on sampled grating technique for suppression of the zeroth order resonance,” IEEE Photonics J. 9(2), 1501909 (2017).
[Crossref]

Shi, W.

Shi, Y.

S. Liu, Y. Shi, L. Hao, R. Xiao, and X. Chen, “Experimental demonstration of the anti-symmetric sampled Bragg grating,” IEEE Photonics Technol. Lett. 29(4), 353–356 (2017).
[Crossref]

L. Li, Y. Shi, Y. Zhang, H. Zou, J. Shen, and X. Chen, “Study on a DFB laser diode based on sampled grating technique for suppression of the zeroth order resonance,” IEEE Photonics J. 9(2), 1501909 (2017).
[Crossref]

L. Hao, Y. Shi, R. Xiao, Y. Qian, and X. Chen, “Study on sampled waveguide grating with anti-symmetric periodic structure,” Opt. Express 23(12), 15784–15791 (2015).
[Crossref] [PubMed]

J. Zheng, N. Song, Y. Zhang, Y. Shi, S. Tang, L. Li, R. Guo, and X. Chen, “An equivalent-asymmetric coupling coefficient DFB Laser with high output efficiency and stable single longitudinal mode operation,” IEEE Photonics J. 6(6), 1502809 (2014).
[Crossref]

J. Wang, P. Chen, S. Chen, Y. Shi, and D. Dai, “Improved 8-channel silicon mode demultiplexer with grating polarizers,” Opt. Express 22(11), 12799–12807 (2014).
[Crossref] [PubMed]

Y. Shi, R. Liu, S. Liu, and X. Zhu, “A low-cost and high-wavelength-precision fabrication method for multiwavelength DFB semiconductor laser array,” IEEE Photonics J. 6(3), 2400112 (2014).
[Crossref]

Y. Shi, S. Li, R. Guo, R. Liu, Y. Zhou, and X. Chen, “A novel concavely apodized DFB semiconductor laser using common holographic exposure,” Opt. Express 21(13), 16022–16028 (2013).
[Crossref] [PubMed]

Shinya, N.

S. Kishimoto, M. Egashira, and N. Shinya, “Observation of micro-deformation by moiré method using a scanning electron microscope,” J. Soc. Mater. Sci. 40(452), 637–641 (1991).
[Crossref]

Simard, A.

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

Simard, A. D.

Smith, P.

L. Chen and P. Smith, “Demonstration of incoherent wavelength-encoding/time-spreading optical CDMA using chirped moiré gratings,” IEEE Photonics Technol. Lett. 12(9), 1281–1283 (2000).
[Crossref]

Song, N.

J. Zheng, N. Song, Y. Zhang, Y. Shi, S. Tang, L. Li, R. Guo, and X. Chen, “An equivalent-asymmetric coupling coefficient DFB Laser with high output efficiency and stable single longitudinal mode operation,” IEEE Photonics J. 6(6), 1502809 (2014).
[Crossref]

Stewart, W. J.

D. C. J. Reid, C. M. Ragdale, I. Bennion, D. J. Robbins, J. Buus, and W. J. Stewart, “Phase-shiftd moiré grating fiber resonators,” Electron. Lett. 26(1), 10–12 (1990).
[Crossref]

St-Yves, J.

Su, Y.

Sugden, K.

Sun, S.

S. Sun, Y. Deng, N. Huang, J. Tang, N. Zhu, and M. Li, “A tunable photonic temporal integrator with ultra-long integration time windows based on Raman-gain assisted phase-shifted silicon Bragg gratings,” Opt. Commun. 373, 91–94 (2016).
[Crossref]

Tang, J.

S. Sun, Y. Deng, N. Huang, J. Tang, N. Zhu, and M. Li, “A tunable photonic temporal integrator with ultra-long integration time windows based on Raman-gain assisted phase-shifted silicon Bragg gratings,” Opt. Commun. 373, 91–94 (2016).
[Crossref]

Tang, M.

Tang, S.

J. Zheng, N. Song, Y. Zhang, Y. Shi, S. Tang, L. Li, R. Guo, and X. Chen, “An equivalent-asymmetric coupling coefficient DFB Laser with high output efficiency and stable single longitudinal mode operation,” IEEE Photonics J. 6(6), 1502809 (2014).
[Crossref]

Thoms, S.

Thomson, D. J.

Troia, B.

Vankwikelberge, P.

G. Morthier, K. David, P. Vankwikelberge, and R. Baets, “A new DFB-Laser diode with reduced spatial hole burning,” IEEE Photonics Technol. Lett. 2(6), 388–390 (1990).
[Crossref]

Wang, H.

H. Zhu, X. Xu, H. Wang, D. Kong, S. Liang, L. Zhao, and W. Wang, “The fabrication of eight-channel DFB laser array using sampled gratings,” IEEE Photonics Technol. Lett. 22(5), 353–355 (2010).
[Crossref]

Wang, J.

Wang, W.

H. Zhu, X. Xu, H. Wang, D. Kong, S. Liang, L. Zhao, and W. Wang, “The fabrication of eight-channel DFB laser array using sampled gratings,” IEEE Photonics Technol. Lett. 22(5), 353–355 (2010).
[Crossref]

Wang, X.

Williams, J. A. R.

Xiao, R.

S. Liu, Y. Shi, L. Hao, R. Xiao, and X. Chen, “Experimental demonstration of the anti-symmetric sampled Bragg grating,” IEEE Photonics Technol. Lett. 29(4), 353–356 (2017).
[Crossref]

L. Hao, Y. Shi, R. Xiao, Y. Qian, and X. Chen, “Study on sampled waveguide grating with anti-symmetric periodic structure,” Opt. Express 23(12), 15784–15791 (2015).
[Crossref] [PubMed]

Xie, H.

Xu, X.

H. Zhu, X. Xu, H. Wang, D. Kong, S. Liang, L. Zhao, and W. Wang, “The fabrication of eight-channel DFB laser array using sampled gratings,” IEEE Photonics Technol. Lett. 22(5), 353–355 (2010).
[Crossref]

Yang, J.

Yu, H.

Yu, P.

Yun, H.

Zeldovich, B.

Zhang, Y.

B. Liu, Y. Zhang, Y. He, X. Jiang, J. Peng, C. Qiu, and Y. Su, “Silicon photonic bandpass filter based on apodized subwavelength grating with high suppression ratio and short coupling length,” Opt. Express 25(10), 11359–11364 (2017).
[Crossref] [PubMed]

L. Li, Y. Shi, Y. Zhang, H. Zou, J. Shen, and X. Chen, “Study on a DFB laser diode based on sampled grating technique for suppression of the zeroth order resonance,” IEEE Photonics J. 9(2), 1501909 (2017).
[Crossref]

J. Zheng, N. Song, Y. Zhang, Y. Shi, S. Tang, L. Li, R. Guo, and X. Chen, “An equivalent-asymmetric coupling coefficient DFB Laser with high output efficiency and stable single longitudinal mode operation,” IEEE Photonics J. 6(6), 1502809 (2014).
[Crossref]

Zhao, L.

H. Zhu, X. Xu, H. Wang, D. Kong, S. Liang, L. Zhao, and W. Wang, “The fabrication of eight-channel DFB laser array using sampled gratings,” IEEE Photonics Technol. Lett. 22(5), 353–355 (2010).
[Crossref]

Zheng, J.

J. Zheng, N. Song, Y. Zhang, Y. Shi, S. Tang, L. Li, R. Guo, and X. Chen, “An equivalent-asymmetric coupling coefficient DFB Laser with high output efficiency and stable single longitudinal mode operation,” IEEE Photonics J. 6(6), 1502809 (2014).
[Crossref]

Zhou, L.

Zhou, Y.

Zhu, H.

H. Zhu, X. Xu, H. Wang, D. Kong, S. Liang, L. Zhao, and W. Wang, “The fabrication of eight-channel DFB laser array using sampled gratings,” IEEE Photonics Technol. Lett. 22(5), 353–355 (2010).
[Crossref]

Zhu, J.

Zhu, N.

S. Sun, Y. Deng, N. Huang, J. Tang, N. Zhu, and M. Li, “A tunable photonic temporal integrator with ultra-long integration time windows based on Raman-gain assisted phase-shifted silicon Bragg gratings,” Opt. Commun. 373, 91–94 (2016).
[Crossref]

J. J. Guo, M. Li, Y. Deng, N. Huang, J. Liu, and N. Zhu, “Multichannel optical filters with an ultranarrow bandwidth based on sampled Brillouin dynamic gratings,” Opt. Express 22(4), 4290–4300 (2014).
[Crossref] [PubMed]

Zhu, X.

Y. Shi, R. Liu, S. Liu, and X. Zhu, “A low-cost and high-wavelength-precision fabrication method for multiwavelength DFB semiconductor laser array,” IEEE Photonics J. 6(3), 2400112 (2014).
[Crossref]

Zou, H.

L. Li, Y. Shi, Y. Zhang, H. Zou, J. Shen, and X. Chen, “Study on a DFB laser diode based on sampled grating technique for suppression of the zeroth order resonance,” IEEE Photonics J. 9(2), 1501909 (2017).
[Crossref]

Zou, Z.

Electron. Lett. (1)

D. C. J. Reid, C. M. Ragdale, I. Bennion, D. J. Robbins, J. Buus, and W. J. Stewart, “Phase-shiftd moiré grating fiber resonators,” Electron. Lett. 26(1), 10–12 (1990).
[Crossref]

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H. Chen, D. Liu, and A. Lee, “Moiré in atomic force microscope,” Exp. Mech. 24(1), 31–32 (2000).

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L. Li, Y. Shi, Y. Zhang, H. Zou, J. Shen, and X. Chen, “Study on a DFB laser diode based on sampled grating technique for suppression of the zeroth order resonance,” IEEE Photonics J. 9(2), 1501909 (2017).
[Crossref]

Y. Shi, R. Liu, S. Liu, and X. Zhu, “A low-cost and high-wavelength-precision fabrication method for multiwavelength DFB semiconductor laser array,” IEEE Photonics J. 6(3), 2400112 (2014).
[Crossref]

J. Zheng, N. Song, Y. Zhang, Y. Shi, S. Tang, L. Li, R. Guo, and X. Chen, “An equivalent-asymmetric coupling coefficient DFB Laser with high output efficiency and stable single longitudinal mode operation,” IEEE Photonics J. 6(6), 1502809 (2014).
[Crossref]

IEEE Photonics Technol. Lett. (6)

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

H. Zhu, X. Xu, H. Wang, D. Kong, S. Liang, L. Zhao, and W. Wang, “The fabrication of eight-channel DFB laser array using sampled gratings,” IEEE Photonics Technol. Lett. 22(5), 353–355 (2010).
[Crossref]

M. Ibsen, M. K. Durkin, and R. I. Laming, “Chirped moiré fiber gratings operating on two-wavelength channels for use as dual-channel dispersion compensators,” IEEE Photonics Technol. Lett. 10(1), 84–86 (1998).
[Crossref]

L. Chen and P. Smith, “Demonstration of incoherent wavelength-encoding/time-spreading optical CDMA using chirped moiré gratings,” IEEE Photonics Technol. Lett. 12(9), 1281–1283 (2000).
[Crossref]

S. Liu, Y. Shi, L. Hao, R. Xiao, and X. Chen, “Experimental demonstration of the anti-symmetric sampled Bragg grating,” IEEE Photonics Technol. Lett. 29(4), 353–356 (2017).
[Crossref]

G. Morthier, K. David, P. Vankwikelberge, and R. Baets, “A new DFB-Laser diode with reduced spatial hole burning,” IEEE Photonics Technol. Lett. 2(6), 388–390 (1990).
[Crossref]

J. Soc. Mater. Sci. (1)

S. Kishimoto, M. Egashira, and N. Shinya, “Observation of micro-deformation by moiré method using a scanning electron microscope,” J. Soc. Mater. Sci. 40(452), 637–641 (1991).
[Crossref]

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 (2016).
[Crossref] [PubMed]

Opt. Commun. (1)

S. Sun, Y. Deng, N. Huang, J. Tang, N. Zhu, and M. Li, “A tunable photonic temporal integrator with ultra-long integration time windows based on Raman-gain assisted phase-shifted silicon Bragg gratings,” Opt. Commun. 373, 91–94 (2016).
[Crossref]

Opt. Express (12)

M. Tang, H. Xie, J. Zhu, X. Li, and Y. Li, “Study of moiré grating fabrication on metal samples using nanoimprint lithography,” Opt. Express 20(3), 2942–2955 (2012).
[Crossref] [PubMed]

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

Y. Shi, S. Li, R. Guo, R. Liu, Y. Zhou, and X. Chen, “A novel concavely apodized DFB semiconductor laser using common holographic exposure,” Opt. Express 21(13), 16022–16028 (2013).
[Crossref] [PubMed]

M. Burla, L. R. Cortés, M. Li, X. Wang, L. Chrostowski, and J. Azaña, “Integrated waveguide Bragg gratings for microwave photonics signal processing,” Opt. Express 21(21), 25120–25147 (2013).
[Crossref] [PubMed]

J. J. Guo, M. Li, Y. Deng, N. Huang, J. Liu, and N. Zhu, “Multichannel optical filters with an ultranarrow bandwidth based on sampled Brillouin dynamic gratings,” Opt. Express 22(4), 4290–4300 (2014).
[Crossref] [PubMed]

J. Wang, P. Chen, S. Chen, Y. Shi, and D. Dai, “Improved 8-channel silicon mode demultiplexer with grating polarizers,” Opt. Express 22(11), 12799–12807 (2014).
[Crossref] [PubMed]

Z. Zou, L. Zhou, X. Li, and J. Chen, “Channel-spacing tunable silicon comb filter using two linearly chirped Bragg gratings,” Opt. Express 22(16), 19513–19522 (2014).
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S. Mokhov, D. Ott, I. Divliansky, B. Zeldovich, and L. Glebov, “Moiré volume Bragg grating filter with tunable bandwidth,” Opt. Express 22(17), 20375–20386 (2014).
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R. Bruck, B. Mills, D. J. Thomson, B. Troia, V. M. Passaro, G. Z. Mashanovich, G. T. Reed, and O. L. Muskens, “Picosecond optically reconfigurable filters exploiting full free spectral range tuning of single ring and Vernier effect resonators,” Opt. Express 23(9), 12468–12477 (2015).
[Crossref] [PubMed]

L. Hao, Y. Shi, R. Xiao, Y. Qian, and X. Chen, “Study on sampled waveguide grating with anti-symmetric periodic structure,” Opt. Express 23(12), 15784–15791 (2015).
[Crossref] [PubMed]

K. Bédard, A. D. Simard, B. Filion, Y. Painchaud, L. A. Rusch, and S. LaRochelle, “Dual phase-shift Bragg grating silicon photonic modulator operating up to 60 Gb/s,” Opt. Express 24(3), 2413–2419 (2016).
[Crossref] [PubMed]

B. Liu, Y. Zhang, Y. He, X. Jiang, J. Peng, C. Qiu, and Y. Su, “Silicon photonic bandpass filter based on apodized subwavelength grating with high suppression ratio and short coupling length,” Opt. Express 25(10), 11359–11364 (2017).
[Crossref] [PubMed]

Opt. Lett. (4)

Other (2)

H. Ghafour-Shiraz, Distributed Feedback Laser Diodes and Optical Tunable Filters (Wiley, 2003), pp. 141–146.

C. Chen, Foundations for Guided-wave Optics (Wiley, 2006), pp. 175–180.

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Figures (10)

Fig. 1
Fig. 1 The schematic of the proposed MG with (a) the full view of the grating structure and detailed views of grating structures with (b) the low coupling coefficient region, (c) high coupling coefficient region, and (d) the low coupling coefficient region again.
Fig. 2
Fig. 2 (a) The equivalent refractive index modulation profile of the MG structure with the length of ΛC and the initial phase difference of π. The blue solid line and the red dash line mean the rapidly varying component and the slowly varying envelope, respectively. (b) The corresponding simulated transmission and reflection spectra of the planar MG and the reflection spectrum of the conventional MG.
Fig. 3
Fig. 3 The equivalent refractive index modulation profiles of (a) the HPC with the initial phase difference of π, (c) the QPC with the initial phase difference of π, and (e) the QPC with the initial phase difference of π/2, where the blue solid line and the red dash line mean the rapidly varying component and the slowly varying envelope, respectively. (b), (d) and (f) show the corresponding transmission and reflection spectra of (a), (c) and (e).
Fig. 4
Fig. 4 The schematic of the SMG structure with (a) the sampling pattern, (b) the basic grating and (c) the corresponding SMG.
Fig. 5
Fig. 5 (a) The simulated transmission and reflection spectra of the SMG. (b) The detailed light response of the −1st order sub-grating.
Fig. 6
Fig. 6 (a), (b) The normalized intensity distributions of different laser types, which have been shown in Table 1. (b), (d) The corresponding normalized threshold gain margins.
Fig. 7
Fig. 7 The simulated transmission and reflection spectra of the leaky mode in the MG with the initial phase difference of π and the grating length of (a) ΛC, (b) ΛC/4. The inserted figures are the profiles of the corresponding Δne01, where the blue solid line and the red dash line mean the rapidly varying component and the slowly varying envelope, respectively.
Fig. 8
Fig. 8 (a) The schematic of the random grating position error. (b) The random grating position error along the waveguide. (c)The schematic of the ideal, error, and real coupling coefficient distributions. (d) The corresponding simulated transmission spectra of the ideal and the MG with random grating position error.
Fig. 9
Fig. 9 (a) The schematic of the constant grating position error. (b) The coupling coefficient distributions curves versus different constant grating position errors. (c) The corresponding simulated transmission spectra with different constant grating position errors and the inserted figure is the transmission peak versus the constant grating position error.
Fig. 10
Fig. 10 (a) The schematic of the initial phase error. (b) The effective grating profiles with the different initial phase errors. (c) The corresponding transmission spectra and the inserted figure is the 3dB bandwidth of the transmission peak versus the initial phase error.

Tables (1)

Tables Icon

Table 1 Parameters of different DFB laser types

Equations (15)

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Δ ε 1 ( x , z ) = { 2 π n ¯ Δ n e x p ( j ( 2 π z Λ 1 + φ 1 ) ) r e c t ( x W ) ( 0 < x < W 2 ) 2 π n ¯ Δ n e x p ( j ( 2 π z Λ 2 + φ 2 ) ) r e c t ( x W ) ( W 2 < x < 0 ) ,
Δ ε 1 ( x , z ) = { 2 π n ¯ Δ n e x p ( j ( 2 π z Λ S + φ 1 + φ 2 2 ) ) exp ( j ( 2 π z Λ C φ 2 φ 1 2 ) ) r e c t ( x W ) ( 0 < x < W 2 ) 2 π n ¯ Δ n e x p ( j ( 2 π z Λ S + φ 1 + φ 2 2 ) ) exp ( j ( 2 π z Λ C φ 2 φ 1 2 ) ) r e c t ( x W ) ( W 2 < x < 0 ) ,
κ 00 ( x , z ) = ω ε 0 4 0 W 2 [ 2 π n ¯ Δ n e x p ( j ( 2 π z Λ C φ 2 φ 1 2 ) ) r e c t ( x W ) ] E 0 ( x ) E 0 * ( x ) d x + ω ε 0 4 W 2 0 [ 2 π n ¯ Δ n e x p ( j ( 2 π z Λ C φ 2 φ 1 2 ) ) r e c t ( x W ) ] E 0 ( x ) E 0 * ( x ) d x ,
κ 00 ( z ) = ω ε 0 π γ 00 n ¯ Δ n cos ( 2 π z Λ C φ 2 φ 1 2 ) ,
Δ n e ( z ) = Δ n cos ( 2 π z Λ C φ 2 φ 1 2 ) cos ( 2 π z Λ S + φ 1 + φ 2 2 ) .
Δ ε s 1 ( x , z ) = { 2 π n ¯ Δ n m F m e x p ( j 2 π z Λ 0 + j 2 π m z P 1 ) e x p ( j φ 0 + j φ s 1 m ) r e c t ( x W ) ( 0 < x < W 2 ) 2 π n ¯ Δ n m F m e x p ( j 2 π z Λ 0 + j 2 π m z P 2 ) e x p ( j φ 0 + j φ s 2 m ) r e c t ( x W ) ( W 2 < x < 0 ) ,
Δ n s e ( z ) = Δ n F - 1 cos ( 2 π z Λ S + φ s 1 + φ s 2 + 2 φ 0 2 ) cos ( 2 π z Λ C φ s 2 φ s 1 2 ) .
λ r = ( n e f f 0 + n e f f 1 ) Λ S ,
κ 01 ( z ) = ω ε 0 π γ 01 n ¯ Δ n cos ( 2 π z Λ C φ 2 φ 1 + π 2 ) ,
Δ n e 0 1 ( z ) = Δ n cos ( 2 π z Λ C φ 2 φ 1 + π 2 ) cos ( 2 π z Λ S + φ 1 + φ 2 π 2 ) .
Δ n e ( z ) = Δ n cos ( 2 π z Λ S + Φ 1 ( z ) + Φ 2 ( z ) 2 ) cos ( 2 π z Λ C Φ 2 ( z ) Φ 1 ( z ) 2 ) .
( n e f f 0 + n e f f 1 ) ( 1 + c ) ( Λ c 1 + Λ c 2 ) 2 < 2 n e f f 0 Λ c 1 .
c < 4 n e f f 0 Λ c 1 ( n e f f 0 + n e f f 1 ) ( Λ c 1 + Λ c 2 ) 1.
κ r ( z ) = ω ε 0 π γ m ( z ) n ¯ Δ n cos ( 2 π z Λ C φ 2 φ 1 2 ) + ω ε 0 π γ e ( z ) n ¯ Δ n ,
κ r ( z ) = ω ε 0 π γ m n ¯ Δ n cos ( 2 π z Λ C φ 2 φ 1 2 ) + ω ε 0 π γ u n ¯ Δ n ,

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