Abstract

A transverse Bragg resonance (TBR) waveguide semiconductor laser with sampled grating is proposed and analyzed. The transverse phase shift in the middle of the grating is realized by shifting half of the sampling period, resulting in a good single transverse mode resonance. The characteristics such as the modal gain, the electric field distribution, the near and far field beam patterns are theoretically studied. Since the sampled grating is designed by combining a uniform basic grating with a micrometer scale sampling pattern, it can be easily fabricated by holographic exposure and conventional photolithography with low cost. Therefore, the proposed method would be beneficial to volume fabrication of wide-stripe high power semiconductor lasers.

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

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References

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  1. L. Zhu, A. Scherer, and A. Yariv, “Modal gain analysis of transverse Bragg resonance waveguide lasers with and without transverse defects,” IEEE J. Quantum Electron. 43(10), 934–940 (2007).
    [Crossref]
  2. R. J. Lang, D. Mehuys, D. F. Welch, and L. Goldberg, “Spontaneous filament formation in broad area diode laser amplifiers,” IEEE J. Quantum Electron. 30(3), 685–694 (1994).
    [Crossref]
  3. R. J. Lang, K. Dzurko, A. Hardy, S. Demars, A. Schoenfelder, and D. F. Welch, “Theory of Grating-Confined Broad-Area Lasers,” IEEE J. Quantum Electron. 34(11), 2196–2210 (1998).
    [Crossref]
  4. Y. Zhu, Y. Zhao, and L. Zhu, “Two-dimensional photonic crystal Bragg lasers with triangular lattice for monolithic coherent beam combining,” Sci. Rep. 7(1), 10610 (2017).
    [Crossref] [PubMed]
  5. A. M. Sarangan, M. W. Wright, J. R. Marciante, and D. J. Bossert, “Spectral Properties of Angled-Grating High-Power Semiconductor Lasers,” IEEE J. Quantum Electron. 35(8), 1220–1230 (1999).
    [Crossref]
  6. L. Zhu, G. A. Derose, A. Scherer, and A. Yariv, “Electrically pumped edge-emitting photonic crystal lasers with angled facets,” Opt. Lett. 32(10), 1256–1258 (2007).
    [Crossref] [PubMed]
  7. P. Yeh and A. Yariv, “Bragg reflection waveguides,” Opt. Commun. 19(3), 427–430 (1976).
    [Crossref]
  8. J.-S. Lee and S.-Y. Shin, “Strong discrimination of transverse modes in high-power laser diodes using Bragg channel waveguiding,” Opt. Lett. 14(2), 143–145 (1989).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  13. Y. Dai and X. Chen, “DFB semiconductor lasers based on reconstruction-equivalent-chirp technology,” Opt. Express 15(5), 2348–2353 (2007).
    [Crossref] [PubMed]
  14. Y. Shi, S. Li, X. Chen, L. Li, J. Li, T. Zhang, J. Zheng, Y. Zhang, S. Tang, L. Hou, J. H. Marsh, and B. Qiu, “High channel count and high precision channel spacing multi-wavelength laser array for future PICs,” Sci. Rep. 4(1), 7377 (2015).
    [Crossref] [PubMed]
  15. Y. Shi, S. Li, J. Li, L. Jia, S. Liu, and X. Chen, “An apodized DFB semiconductor laser realized by varying duty cycle of sampling Bragg grating and reconstruction-equivalent-chirp technology,” Opt. Commun. 283(9), 1840–1844 (2010).
    [Crossref]
  16. H. Ghafouri-Shiraz, Distributed feedback laser diodes and optical tunable filters (Wiley, 2003).
  17. D. Marcuse, “Reflection loss of laser mode from tilted end mirror,” J. Lightwave Technol. 7(2), 336–339 (1989).
    [Crossref]
  18. J. M. Choi, Design, fabrication, and characterization of semiconductor transverse Bragg resonance lasers, (Ph.D. dissertation, California Institute of Technology, 2007).
  19. Y. Shi, X. Tu, S. Li, Y. Zhou, L. Jia, and X. Chen, “Numerical study of three phase shifts and dual corrugation pitch modulated (CPM) DFB semiconductor lasers based on reconstruction equivalent chirp technology,” Chin. Sci. Bull. 55(35), 4083–4088 (2010).
    [Crossref]

2017 (1)

Y. Zhu, Y. Zhao, and L. Zhu, “Two-dimensional photonic crystal Bragg lasers with triangular lattice for monolithic coherent beam combining,” Sci. Rep. 7(1), 10610 (2017).
[Crossref] [PubMed]

2015 (1)

Y. Shi, S. Li, X. Chen, L. Li, J. Li, T. Zhang, J. Zheng, Y. Zhang, S. Tang, L. Hou, J. H. Marsh, and B. Qiu, “High channel count and high precision channel spacing multi-wavelength laser array for future PICs,” Sci. Rep. 4(1), 7377 (2015).
[Crossref] [PubMed]

2010 (2)

Y. Shi, S. Li, J. Li, L. Jia, S. Liu, and X. Chen, “An apodized DFB semiconductor laser realized by varying duty cycle of sampling Bragg grating and reconstruction-equivalent-chirp technology,” Opt. Commun. 283(9), 1840–1844 (2010).
[Crossref]

Y. Shi, X. Tu, S. Li, Y. Zhou, L. Jia, and X. Chen, “Numerical study of three phase shifts and dual corrugation pitch modulated (CPM) DFB semiconductor lasers based on reconstruction equivalent chirp technology,” Chin. Sci. Bull. 55(35), 4083–4088 (2010).
[Crossref]

2007 (3)

2006 (1)

2003 (2)

2002 (1)

1999 (1)

A. M. Sarangan, M. W. Wright, J. R. Marciante, and D. J. Bossert, “Spectral Properties of Angled-Grating High-Power Semiconductor Lasers,” IEEE J. Quantum Electron. 35(8), 1220–1230 (1999).
[Crossref]

1998 (1)

R. J. Lang, K. Dzurko, A. Hardy, S. Demars, A. Schoenfelder, and D. F. Welch, “Theory of Grating-Confined Broad-Area Lasers,” IEEE J. Quantum Electron. 34(11), 2196–2210 (1998).
[Crossref]

1994 (1)

R. J. Lang, D. Mehuys, D. F. Welch, and L. Goldberg, “Spontaneous filament formation in broad area diode laser amplifiers,” IEEE J. Quantum Electron. 30(3), 685–694 (1994).
[Crossref]

1989 (2)

1976 (1)

P. Yeh and A. Yariv, “Bragg reflection waveguides,” Opt. Commun. 19(3), 427–430 (1976).
[Crossref]

Bossert, D. J.

A. M. Sarangan, M. W. Wright, J. R. Marciante, and D. J. Bossert, “Spectral Properties of Angled-Grating High-Power Semiconductor Lasers,” IEEE J. Quantum Electron. 35(8), 1220–1230 (1999).
[Crossref]

Chen, X.

Y. Shi, S. Li, X. Chen, L. Li, J. Li, T. Zhang, J. Zheng, Y. Zhang, S. Tang, L. Hou, J. H. Marsh, and B. Qiu, “High channel count and high precision channel spacing multi-wavelength laser array for future PICs,” Sci. Rep. 4(1), 7377 (2015).
[Crossref] [PubMed]

Y. Shi, S. Li, J. Li, L. Jia, S. Liu, and X. Chen, “An apodized DFB semiconductor laser realized by varying duty cycle of sampling Bragg grating and reconstruction-equivalent-chirp technology,” Opt. Commun. 283(9), 1840–1844 (2010).
[Crossref]

Y. Shi, X. Tu, S. Li, Y. Zhou, L. Jia, and X. Chen, “Numerical study of three phase shifts and dual corrugation pitch modulated (CPM) DFB semiconductor lasers based on reconstruction equivalent chirp technology,” Chin. Sci. Bull. 55(35), 4083–4088 (2010).
[Crossref]

Y. Dai and X. Chen, “DFB semiconductor lasers based on reconstruction-equivalent-chirp technology,” Opt. Express 15(5), 2348–2353 (2007).
[Crossref] [PubMed]

Choi, J. M.

Dai, Y.

Demars, S.

R. J. Lang, K. Dzurko, A. Hardy, S. Demars, A. Schoenfelder, and D. F. Welch, “Theory of Grating-Confined Broad-Area Lasers,” IEEE J. Quantum Electron. 34(11), 2196–2210 (1998).
[Crossref]

Derose, G. A.

Dzurko, K.

R. J. Lang, K. Dzurko, A. Hardy, S. Demars, A. Schoenfelder, and D. F. Welch, “Theory of Grating-Confined Broad-Area Lasers,” IEEE J. Quantum Electron. 34(11), 2196–2210 (1998).
[Crossref]

Goldberg, L.

R. J. Lang, D. Mehuys, D. F. Welch, and L. Goldberg, “Spontaneous filament formation in broad area diode laser amplifiers,” IEEE J. Quantum Electron. 30(3), 685–694 (1994).
[Crossref]

Hardy, A.

R. J. Lang, K. Dzurko, A. Hardy, S. Demars, A. Schoenfelder, and D. F. Welch, “Theory of Grating-Confined Broad-Area Lasers,” IEEE J. Quantum Electron. 34(11), 2196–2210 (1998).
[Crossref]

Hou, L.

Y. Shi, S. Li, X. Chen, L. Li, J. Li, T. Zhang, J. Zheng, Y. Zhang, S. Tang, L. Hou, J. H. Marsh, and B. Qiu, “High channel count and high precision channel spacing multi-wavelength laser array for future PICs,” Sci. Rep. 4(1), 7377 (2015).
[Crossref] [PubMed]

Jia, L.

Y. Shi, X. Tu, S. Li, Y. Zhou, L. Jia, and X. Chen, “Numerical study of three phase shifts and dual corrugation pitch modulated (CPM) DFB semiconductor lasers based on reconstruction equivalent chirp technology,” Chin. Sci. Bull. 55(35), 4083–4088 (2010).
[Crossref]

Y. Shi, S. Li, J. Li, L. Jia, S. Liu, and X. Chen, “An apodized DFB semiconductor laser realized by varying duty cycle of sampling Bragg grating and reconstruction-equivalent-chirp technology,” Opt. Commun. 283(9), 1840–1844 (2010).
[Crossref]

Lang, R. J.

R. J. Lang, K. Dzurko, A. Hardy, S. Demars, A. Schoenfelder, and D. F. Welch, “Theory of Grating-Confined Broad-Area Lasers,” IEEE J. Quantum Electron. 34(11), 2196–2210 (1998).
[Crossref]

R. J. Lang, D. Mehuys, D. F. Welch, and L. Goldberg, “Spontaneous filament formation in broad area diode laser amplifiers,” IEEE J. Quantum Electron. 30(3), 685–694 (1994).
[Crossref]

Lee, J.-S.

Li, J.

Y. Shi, S. Li, X. Chen, L. Li, J. Li, T. Zhang, J. Zheng, Y. Zhang, S. Tang, L. Hou, J. H. Marsh, and B. Qiu, “High channel count and high precision channel spacing multi-wavelength laser array for future PICs,” Sci. Rep. 4(1), 7377 (2015).
[Crossref] [PubMed]

Y. Shi, S. Li, J. Li, L. Jia, S. Liu, and X. Chen, “An apodized DFB semiconductor laser realized by varying duty cycle of sampling Bragg grating and reconstruction-equivalent-chirp technology,” Opt. Commun. 283(9), 1840–1844 (2010).
[Crossref]

Li, L.

Y. Shi, S. Li, X. Chen, L. Li, J. Li, T. Zhang, J. Zheng, Y. Zhang, S. Tang, L. Hou, J. H. Marsh, and B. Qiu, “High channel count and high precision channel spacing multi-wavelength laser array for future PICs,” Sci. Rep. 4(1), 7377 (2015).
[Crossref] [PubMed]

Li, S.

Y. Shi, S. Li, X. Chen, L. Li, J. Li, T. Zhang, J. Zheng, Y. Zhang, S. Tang, L. Hou, J. H. Marsh, and B. Qiu, “High channel count and high precision channel spacing multi-wavelength laser array for future PICs,” Sci. Rep. 4(1), 7377 (2015).
[Crossref] [PubMed]

Y. Shi, X. Tu, S. Li, Y. Zhou, L. Jia, and X. Chen, “Numerical study of three phase shifts and dual corrugation pitch modulated (CPM) DFB semiconductor lasers based on reconstruction equivalent chirp technology,” Chin. Sci. Bull. 55(35), 4083–4088 (2010).
[Crossref]

Y. Shi, S. Li, J. Li, L. Jia, S. Liu, and X. Chen, “An apodized DFB semiconductor laser realized by varying duty cycle of sampling Bragg grating and reconstruction-equivalent-chirp technology,” Opt. Commun. 283(9), 1840–1844 (2010).
[Crossref]

Liang, W.

Liu, S.

Y. Shi, S. Li, J. Li, L. Jia, S. Liu, and X. Chen, “An apodized DFB semiconductor laser realized by varying duty cycle of sampling Bragg grating and reconstruction-equivalent-chirp technology,” Opt. Commun. 283(9), 1840–1844 (2010).
[Crossref]

Marciante, J. R.

A. M. Sarangan, M. W. Wright, J. R. Marciante, and D. J. Bossert, “Spectral Properties of Angled-Grating High-Power Semiconductor Lasers,” IEEE J. Quantum Electron. 35(8), 1220–1230 (1999).
[Crossref]

Marcuse, D.

D. Marcuse, “Reflection loss of laser mode from tilted end mirror,” J. Lightwave Technol. 7(2), 336–339 (1989).
[Crossref]

Marsh, J. H.

Y. Shi, S. Li, X. Chen, L. Li, J. Li, T. Zhang, J. Zheng, Y. Zhang, S. Tang, L. Hou, J. H. Marsh, and B. Qiu, “High channel count and high precision channel spacing multi-wavelength laser array for future PICs,” Sci. Rep. 4(1), 7377 (2015).
[Crossref] [PubMed]

Mehuys, D.

R. J. Lang, D. Mehuys, D. F. Welch, and L. Goldberg, “Spontaneous filament formation in broad area diode laser amplifiers,” IEEE J. Quantum Electron. 30(3), 685–694 (1994).
[Crossref]

Mookherjea, S.

Qiu, B.

Y. Shi, S. Li, X. Chen, L. Li, J. Li, T. Zhang, J. Zheng, Y. Zhang, S. Tang, L. Hou, J. H. Marsh, and B. Qiu, “High channel count and high precision channel spacing multi-wavelength laser array for future PICs,” Sci. Rep. 4(1), 7377 (2015).
[Crossref] [PubMed]

Sarangan, A. M.

A. M. Sarangan, M. W. Wright, J. R. Marciante, and D. J. Bossert, “Spectral Properties of Angled-Grating High-Power Semiconductor Lasers,” IEEE J. Quantum Electron. 35(8), 1220–1230 (1999).
[Crossref]

Scherer, A.

Schoenfelder, A.

R. J. Lang, K. Dzurko, A. Hardy, S. Demars, A. Schoenfelder, and D. F. Welch, “Theory of Grating-Confined Broad-Area Lasers,” IEEE J. Quantum Electron. 34(11), 2196–2210 (1998).
[Crossref]

Shi, Y.

Y. Shi, S. Li, X. Chen, L. Li, J. Li, T. Zhang, J. Zheng, Y. Zhang, S. Tang, L. Hou, J. H. Marsh, and B. Qiu, “High channel count and high precision channel spacing multi-wavelength laser array for future PICs,” Sci. Rep. 4(1), 7377 (2015).
[Crossref] [PubMed]

Y. Shi, S. Li, J. Li, L. Jia, S. Liu, and X. Chen, “An apodized DFB semiconductor laser realized by varying duty cycle of sampling Bragg grating and reconstruction-equivalent-chirp technology,” Opt. Commun. 283(9), 1840–1844 (2010).
[Crossref]

Y. Shi, X. Tu, S. Li, Y. Zhou, L. Jia, and X. Chen, “Numerical study of three phase shifts and dual corrugation pitch modulated (CPM) DFB semiconductor lasers based on reconstruction equivalent chirp technology,” Chin. Sci. Bull. 55(35), 4083–4088 (2010).
[Crossref]

Shin, S.-Y.

Tang, S.

Y. Shi, S. Li, X. Chen, L. Li, J. Li, T. Zhang, J. Zheng, Y. Zhang, S. Tang, L. Hou, J. H. Marsh, and B. Qiu, “High channel count and high precision channel spacing multi-wavelength laser array for future PICs,” Sci. Rep. 4(1), 7377 (2015).
[Crossref] [PubMed]

Tu, X.

Y. Shi, X. Tu, S. Li, Y. Zhou, L. Jia, and X. Chen, “Numerical study of three phase shifts and dual corrugation pitch modulated (CPM) DFB semiconductor lasers based on reconstruction equivalent chirp technology,” Chin. Sci. Bull. 55(35), 4083–4088 (2010).
[Crossref]

Welch, D. F.

R. J. Lang, K. Dzurko, A. Hardy, S. Demars, A. Schoenfelder, and D. F. Welch, “Theory of Grating-Confined Broad-Area Lasers,” IEEE J. Quantum Electron. 34(11), 2196–2210 (1998).
[Crossref]

R. J. Lang, D. Mehuys, D. F. Welch, and L. Goldberg, “Spontaneous filament formation in broad area diode laser amplifiers,” IEEE J. Quantum Electron. 30(3), 685–694 (1994).
[Crossref]

Wright, M. W.

A. M. Sarangan, M. W. Wright, J. R. Marciante, and D. J. Bossert, “Spectral Properties of Angled-Grating High-Power Semiconductor Lasers,” IEEE J. Quantum Electron. 35(8), 1220–1230 (1999).
[Crossref]

Xu, Y.

Yariv, A.

Yeh, P.

P. Yeh and A. Yariv, “Bragg reflection waveguides,” Opt. Commun. 19(3), 427–430 (1976).
[Crossref]

Zhang, T.

Y. Shi, S. Li, X. Chen, L. Li, J. Li, T. Zhang, J. Zheng, Y. Zhang, S. Tang, L. Hou, J. H. Marsh, and B. Qiu, “High channel count and high precision channel spacing multi-wavelength laser array for future PICs,” Sci. Rep. 4(1), 7377 (2015).
[Crossref] [PubMed]

Zhang, Y.

Y. Shi, S. Li, X. Chen, L. Li, J. Li, T. Zhang, J. Zheng, Y. Zhang, S. Tang, L. Hou, J. H. Marsh, and B. Qiu, “High channel count and high precision channel spacing multi-wavelength laser array for future PICs,” Sci. Rep. 4(1), 7377 (2015).
[Crossref] [PubMed]

Zhao, Y.

Y. Zhu, Y. Zhao, and L. Zhu, “Two-dimensional photonic crystal Bragg lasers with triangular lattice for monolithic coherent beam combining,” Sci. Rep. 7(1), 10610 (2017).
[Crossref] [PubMed]

Zheng, J.

Y. Shi, S. Li, X. Chen, L. Li, J. Li, T. Zhang, J. Zheng, Y. Zhang, S. Tang, L. Hou, J. H. Marsh, and B. Qiu, “High channel count and high precision channel spacing multi-wavelength laser array for future PICs,” Sci. Rep. 4(1), 7377 (2015).
[Crossref] [PubMed]

Zhou, Y.

Y. Shi, X. Tu, S. Li, Y. Zhou, L. Jia, and X. Chen, “Numerical study of three phase shifts and dual corrugation pitch modulated (CPM) DFB semiconductor lasers based on reconstruction equivalent chirp technology,” Chin. Sci. Bull. 55(35), 4083–4088 (2010).
[Crossref]

Zhu, L.

Y. Zhu, Y. Zhao, and L. Zhu, “Two-dimensional photonic crystal Bragg lasers with triangular lattice for monolithic coherent beam combining,” Sci. Rep. 7(1), 10610 (2017).
[Crossref] [PubMed]

L. Zhu, A. Scherer, and A. Yariv, “Modal gain analysis of transverse Bragg resonance waveguide lasers with and without transverse defects,” IEEE J. Quantum Electron. 43(10), 934–940 (2007).
[Crossref]

L. Zhu, G. A. Derose, A. Scherer, and A. Yariv, “Electrically pumped edge-emitting photonic crystal lasers with angled facets,” Opt. Lett. 32(10), 1256–1258 (2007).
[Crossref] [PubMed]

L. Zhu, J. M. Choi, G. A. DeRose, A. Yariv, and A. Scherer, “Electrically pumped two-dimensional Bragg grating lasers,” Opt. Lett. 31(12), 1863–1865 (2006).
[Crossref] [PubMed]

Zhu, Y.

Y. Zhu, Y. Zhao, and L. Zhu, “Two-dimensional photonic crystal Bragg lasers with triangular lattice for monolithic coherent beam combining,” Sci. Rep. 7(1), 10610 (2017).
[Crossref] [PubMed]

Chin. Sci. Bull. (1)

Y. Shi, X. Tu, S. Li, Y. Zhou, L. Jia, and X. Chen, “Numerical study of three phase shifts and dual corrugation pitch modulated (CPM) DFB semiconductor lasers based on reconstruction equivalent chirp technology,” Chin. Sci. Bull. 55(35), 4083–4088 (2010).
[Crossref]

IEEE J. Quantum Electron. (4)

L. Zhu, A. Scherer, and A. Yariv, “Modal gain analysis of transverse Bragg resonance waveguide lasers with and without transverse defects,” IEEE J. Quantum Electron. 43(10), 934–940 (2007).
[Crossref]

R. J. Lang, D. Mehuys, D. F. Welch, and L. Goldberg, “Spontaneous filament formation in broad area diode laser amplifiers,” IEEE J. Quantum Electron. 30(3), 685–694 (1994).
[Crossref]

R. J. Lang, K. Dzurko, A. Hardy, S. Demars, A. Schoenfelder, and D. F. Welch, “Theory of Grating-Confined Broad-Area Lasers,” IEEE J. Quantum Electron. 34(11), 2196–2210 (1998).
[Crossref]

A. M. Sarangan, M. W. Wright, J. R. Marciante, and D. J. Bossert, “Spectral Properties of Angled-Grating High-Power Semiconductor Lasers,” IEEE J. Quantum Electron. 35(8), 1220–1230 (1999).
[Crossref]

J. Lightwave Technol. (1)

D. Marcuse, “Reflection loss of laser mode from tilted end mirror,” J. Lightwave Technol. 7(2), 336–339 (1989).
[Crossref]

Opt. Commun. (2)

Y. Shi, S. Li, J. Li, L. Jia, S. Liu, and X. Chen, “An apodized DFB semiconductor laser realized by varying duty cycle of sampling Bragg grating and reconstruction-equivalent-chirp technology,” Opt. Commun. 283(9), 1840–1844 (2010).
[Crossref]

P. Yeh and A. Yariv, “Bragg reflection waveguides,” Opt. Commun. 19(3), 427–430 (1976).
[Crossref]

Opt. Express (1)

Opt. Lett. (6)

Sci. Rep. (2)

Y. Zhu, Y. Zhao, and L. Zhu, “Two-dimensional photonic crystal Bragg lasers with triangular lattice for monolithic coherent beam combining,” Sci. Rep. 7(1), 10610 (2017).
[Crossref] [PubMed]

Y. Shi, S. Li, X. Chen, L. Li, J. Li, T. Zhang, J. Zheng, Y. Zhang, S. Tang, L. Hou, J. H. Marsh, and B. Qiu, “High channel count and high precision channel spacing multi-wavelength laser array for future PICs,” Sci. Rep. 4(1), 7377 (2015).
[Crossref] [PubMed]

Other (2)

H. Ghafouri-Shiraz, Distributed feedback laser diodes and optical tunable filters (Wiley, 2003).

J. M. Choi, Design, fabrication, and characterization of semiconductor transverse Bragg resonance lasers, (Ph.D. dissertation, California Institute of Technology, 2007).

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Figures (7)

Fig. 1
Fig. 1 (a) Schematic of the proposed TBR waveguide laser; (b) the top view of the sampled grating.
Fig. 2
Fig. 2 Calculated transmission spectrum and modal gain of the proposed TBR waveguide.
Fig. 3
Fig. 3 (a) Normalized E(x)and (b) normalized electric field amplitude of the + 1st order resonance mode.
Fig. 4
Fig. 4 Modal gain versus modal angle for the TBR waveguide with sampled grating and uniform grating. The inset shows the difference between TBR mode and SMA mode.
Fig. 5
Fig. 5 The r f of the facet with different facet angles. The inset shows the top view of the grating with angled facet.
Fig. 6
Fig. 6 The normalized flatness value with different duty cycles. The inset shows the structure of the grating.
Fig. 7
Fig. 7 Calculated (a) near field and (b) far field beam patterns of the proposed TBR laser.

Tables (3)

Tables Icon

Table 1 Parameters used in the simulation

Tables Icon

Table 2 Calculated modal gains of the ± 1st and 0th order subgratings

Tables Icon

Table 3 Effective modal width with different etch depth

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

ε(x)= ε r0 +Δε(x)+i ε i (x)
Δε(x)= 1 2 S(x)[ Δ ε 0 exp( i 2π Λ 0 x )+c.c ]
S(x)= s m exp( i 2πm P x )
Δε(x)= 1 2 s m [ Δ ε 0 exp( i 2π Λ 0 x+i 2πm P x )+c.c ]
1 Λ m = 1 Λ 0 + m P
Δ ε +1 (x)= 1 2 Δ ε 0 s +1 exp[ i2π( 1 Λ 0 + 1 P )x ]+c.c
Δ ε +1 (x)={ 1 2 Δ ε 0 s +1 exp[ i2π( 1 Λ 0 + 1 P )x ]+c.c,x< x 0 1 2 Δ ε 0 s +1 exp[ i2π( 1 Λ 0 + 1 P )x ]exp( i2π ΔP P x )+c.c,x x 0
β r(+1) = k 0 n 1 [ λ 2n ( 1 Λ 0 + 1 P ) ] 2
Δ ε 1 (x)={ 1 2 Δ ε 0 s 1 exp[ i2π( 1 Λ 0 1 P )x ]+c.c,x< x 0 1 2 Δ ε 0 s 1 exp[ i2π( 1 Λ 0 1 P )x ]exp( i2π ΔP P x )+c.c,x x 0
β r(1) = k 0 n 1 [ λ 2n ( 1 Λ 0 1 P ) ] 2
Δ ε 0 (x)= 1 2 Δ ε 0 s 0 exp( i2π 1 Λ 0 x )+c.c
β r(0) = k 0 n[ 1 ( λ 2n Λ 0 ) 2 ± 2Δn Λ 0 πλ ]
r f = Re(β) 2ω μ 0 P 0 + E f (x) E b (x) e i2Re(β)sin(αθ)x dx
L beat = 2π | β m+1 β m |
F= 1 W 0 W [ P(x) P ¯ ] 2 dx

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