Abstract

In this paper we report a new method of photonic generation of microwave signals using a multi-transverse mode VCSEL subject to two-frequency optical injection. Numerical simulations show that double injection locking involving two transverse modes can be obtained in these systems. We show that the higher-order transverse mode is excited with a much larger amplitude than that of the fundamental transverse mode. The comparison with the case of a single-transverse mode VCSEL subject to similar two-frequency optical injection shows that multi-transverse mode operation of the VCSEL enhances the performance of the photonic microwave generation system. Broad tuning ranges, beyond the THz region, and narrow linewidths are demonstrated in our system. The maximum frequency of the generated microwave signals can be substantially increased if multimode VCSELs are used instead of single-mode VCSELs.

© 2012 OSA

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  2. F. Koyama, “Recent advances of VCSEL photonics,” J. Lightwave Technol.24(12), 4502–4513 (2006).
    [CrossRef]
  3. C.-H. Chang, L. Chrostowski, and C. J. Chang-Hasnain, “Injection locking of VCSELs,” IEEE J. Sel. Top. Quantum Electron.9(5), 1386–1393 (2003).
    [CrossRef]
  4. D. Parekh, X. Zhao, W. Hofmann, M. C. Amann, L. A. Zenteno, and C. J. Chang-Hasnain, “Greatly enhanced modulation response of injection-locked multimode VCSELs,” Opt. Express16(26), 21582–21586 (2008).
    [CrossRef] [PubMed]
  5. H. Li, T. Lucas, J. G. McInerney, M. Wright, and R. A. Morgan, “Injection locking dynamics of vertical cavity semiconductor lasers under conventional and phase conjugate injection,” IEEE J. Quantum Electron.32(2), 227–235 (1996).
    [CrossRef]
  6. J. Altes, I. Gatare, K. Panajotov, H. Thienpont, and M. Sciamanna, “Mapping of the dynamics induced by orthogonal optical injection in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron.42(2), 198–207 (2006).
    [CrossRef]
  7. A. Valle, I. Gatare, K. Panajotov, and M. Sciamanna, “Transverse mode switching and locking in vertical-cavity surface-emitting lasers subject to orthogonal optical injection,” IEEE J. Quantum Electron.43(4), 322–333 (2007).
    [CrossRef]
  8. A. Quirce, A. Valle, A. Hurtado, C. Gimenez, L. Pesquera, and M. J. Adams, “Experimental study of transverse mode selection in VCSELs induced by parallel polarized optical injection,” IEEE J. Quantum Electron.46(4), 467–473 (2010).
    [CrossRef]
  9. A. Quirce, J. R. Cuesta, A. Valle, A. Hurtado, L. Pesquera, and M. J. Adams, “Polarization bistability induced by orthogonal optical injection in 1550-nm multimode VCSELs,” IEEE J. Sel. Top. Quantum Electron.18(2), 772–778 (2012).
    [CrossRef]
  10. H. Lin, Y. Zhang, D. W. Pierce, A. Quirce, and A. Valle, “Polarization dynamics of a multimode vertical-cavity surface-emitting laser subject to orthogonal optical injection,” J. Opt. Soc. Am. B29(4), 867–873 (2012).
    [CrossRef]
  11. C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Vonlehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization, and transverse-mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron.27(6), 1402–1409 (1991).
    [CrossRef]
  12. A. Valle, J. Sarma, and K. A. Shore, “Spatial holeburning effects on the dynamics of vertical-cavity surface-emitting laser diodes,” IEEE J. Quantum Electron.31(8), 1423–1431 (1995).
    [CrossRef]
  13. A. Hayat, A. Bacou, A. Rissons, J. C. Mollier, V. Iakovlev, A. Sirbu, and E. Kapon, “Long wavelength VCSEL-by-VCSEL optical injection locking,” IEEE Trans. Microw. Theory Tech.57(7), 1850–1858 (2009).
    [CrossRef]
  14. H. Lin, D. W. Pierce, A. J. Basnet, A. Quirce, Y. Zhang, and A. Valle, “Two-frequency injection on a multimode vertical-cavity surface-emitting laser,” Opt. Express19(23), 22437–22442 (2011).
    [CrossRef] [PubMed]
  15. S. C. Chan, R. Diaz, and J. M. Liu, “Novel photonic applications of nonlinear semiconductor laser dynamics,” Opt. Quantum Electron.40(2-4), 83–95 (2008).
    [CrossRef]
  16. S. C. Chan, S. K. Hwang, and J. M. Liu, “Radio-over-fiber transmission from an optically injected semiconductor laser in period-one state,” Proc. SPIE6468,46811–46811 (2007).
  17. S. C. Chan, “Analysis of an optically injected semiconductor laser for microwave generation,” IEEE J. Quantum Electron.46(3), 421–428 (2010).
    [CrossRef]
  18. S. C. Chan, S. K. Hwang, and J. M. Liu, “Radio-over-fiber AM-to-FM upconversion using an optically injected semiconductor laser,” Opt. Lett.31(15), 2254–2256 (2006).
    [CrossRef] [PubMed]
  19. X. Q. Qi and J. M. Liu, “Photonic microwave applications of the dynamics of semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron.17(5), 1198–1211 (2011).
    [CrossRef]
  20. X. Q. Qi and J. M. Liu, “Dynamics scenarios of dual-beam optically injected semiconductor lasers,” IEEE J. Quantum Electron.47(6), 762–769 (2011).
    [CrossRef]
  21. Y. S. Juan and F. Y. Lin, “Photonic generation of broadly tunable microwave signals utilizing a dual-beam optically injected semiconductor laser,” IEEE Photonics J.3(4), 644–650 (2011).
    [CrossRef]
  22. Y. C. Chen, Y. S. Juan, and F. Y. Lin, “High-frequency microwave signal generation in a semiconductor laser under double injection locking,” Proc. SPIE7936,793609 (2011).
  23. A. Valle, K. A. Shore, and L. Pesquera, “Polarization selection in birefringent vertical-cavity surface emitting lasers,” J. Lightwave Technol.14(9), 2062–2068 (1996).
    [CrossRef]
  24. A. Valle, J. Martin-Regalado, L. Pesquera, S. Balle, and M. San Miguel, “Polarization dynamics of birefringent index-guided vertical cavity surface-emitting lasers,” Proc. SPIE3283,280–291 (1998).
  25. J. Y. Law, G. H. M. vanTartwijk, and G. P. Agrawal, “Effects of transverse-mode competition on the injection dynamics of vertical-cavity surface-emitting lasers,” Quantum Semiclassic. Opt. J. Eu. Opt. Soc. Part B9(5), 737–747 (1997).
    [CrossRef]
  26. A. Valle and L. Pesquera, “Theoretical calculation of relative intensity noise of multimode vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron.40(6), 597–606 (2004).
    [CrossRef]
  27. S. Wieczorek and W. W. Chow, “Bifurcations and chaos in a semiconductor laser with coherent or noisy optical injection,” Opt. Commun.282(12), 2367–2379 (2009).
    [CrossRef]
  28. J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron.33(5), 765–783 (1997).
    [CrossRef]

2012

A. Quirce, J. R. Cuesta, A. Valle, A. Hurtado, L. Pesquera, and M. J. Adams, “Polarization bistability induced by orthogonal optical injection in 1550-nm multimode VCSELs,” IEEE J. Sel. Top. Quantum Electron.18(2), 772–778 (2012).
[CrossRef]

H. Lin, Y. Zhang, D. W. Pierce, A. Quirce, and A. Valle, “Polarization dynamics of a multimode vertical-cavity surface-emitting laser subject to orthogonal optical injection,” J. Opt. Soc. Am. B29(4), 867–873 (2012).
[CrossRef]

2011

H. Lin, D. W. Pierce, A. J. Basnet, A. Quirce, Y. Zhang, and A. Valle, “Two-frequency injection on a multimode vertical-cavity surface-emitting laser,” Opt. Express19(23), 22437–22442 (2011).
[CrossRef] [PubMed]

X. Q. Qi and J. M. Liu, “Photonic microwave applications of the dynamics of semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron.17(5), 1198–1211 (2011).
[CrossRef]

X. Q. Qi and J. M. Liu, “Dynamics scenarios of dual-beam optically injected semiconductor lasers,” IEEE J. Quantum Electron.47(6), 762–769 (2011).
[CrossRef]

Y. S. Juan and F. Y. Lin, “Photonic generation of broadly tunable microwave signals utilizing a dual-beam optically injected semiconductor laser,” IEEE Photonics J.3(4), 644–650 (2011).
[CrossRef]

Y. C. Chen, Y. S. Juan, and F. Y. Lin, “High-frequency microwave signal generation in a semiconductor laser under double injection locking,” Proc. SPIE7936,793609 (2011).

2010

A. Quirce, A. Valle, A. Hurtado, C. Gimenez, L. Pesquera, and M. J. Adams, “Experimental study of transverse mode selection in VCSELs induced by parallel polarized optical injection,” IEEE J. Quantum Electron.46(4), 467–473 (2010).
[CrossRef]

S. C. Chan, “Analysis of an optically injected semiconductor laser for microwave generation,” IEEE J. Quantum Electron.46(3), 421–428 (2010).
[CrossRef]

2009

A. Hayat, A. Bacou, A. Rissons, J. C. Mollier, V. Iakovlev, A. Sirbu, and E. Kapon, “Long wavelength VCSEL-by-VCSEL optical injection locking,” IEEE Trans. Microw. Theory Tech.57(7), 1850–1858 (2009).
[CrossRef]

S. Wieczorek and W. W. Chow, “Bifurcations and chaos in a semiconductor laser with coherent or noisy optical injection,” Opt. Commun.282(12), 2367–2379 (2009).
[CrossRef]

2008

S. C. Chan, R. Diaz, and J. M. Liu, “Novel photonic applications of nonlinear semiconductor laser dynamics,” Opt. Quantum Electron.40(2-4), 83–95 (2008).
[CrossRef]

D. Parekh, X. Zhao, W. Hofmann, M. C. Amann, L. A. Zenteno, and C. J. Chang-Hasnain, “Greatly enhanced modulation response of injection-locked multimode VCSELs,” Opt. Express16(26), 21582–21586 (2008).
[CrossRef] [PubMed]

2007

S. C. Chan, S. K. Hwang, and J. M. Liu, “Radio-over-fiber transmission from an optically injected semiconductor laser in period-one state,” Proc. SPIE6468,46811–46811 (2007).

A. Valle, I. Gatare, K. Panajotov, and M. Sciamanna, “Transverse mode switching and locking in vertical-cavity surface-emitting lasers subject to orthogonal optical injection,” IEEE J. Quantum Electron.43(4), 322–333 (2007).
[CrossRef]

2006

J. Altes, I. Gatare, K. Panajotov, H. Thienpont, and M. Sciamanna, “Mapping of the dynamics induced by orthogonal optical injection in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron.42(2), 198–207 (2006).
[CrossRef]

S. C. Chan, S. K. Hwang, and J. M. Liu, “Radio-over-fiber AM-to-FM upconversion using an optically injected semiconductor laser,” Opt. Lett.31(15), 2254–2256 (2006).
[CrossRef] [PubMed]

F. Koyama, “Recent advances of VCSEL photonics,” J. Lightwave Technol.24(12), 4502–4513 (2006).
[CrossRef]

2004

A. Valle and L. Pesquera, “Theoretical calculation of relative intensity noise of multimode vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron.40(6), 597–606 (2004).
[CrossRef]

2003

C.-H. Chang, L. Chrostowski, and C. J. Chang-Hasnain, “Injection locking of VCSELs,” IEEE J. Sel. Top. Quantum Electron.9(5), 1386–1393 (2003).
[CrossRef]

1998

A. Valle, J. Martin-Regalado, L. Pesquera, S. Balle, and M. San Miguel, “Polarization dynamics of birefringent index-guided vertical cavity surface-emitting lasers,” Proc. SPIE3283,280–291 (1998).

1997

J. Y. Law, G. H. M. vanTartwijk, and G. P. Agrawal, “Effects of transverse-mode competition on the injection dynamics of vertical-cavity surface-emitting lasers,” Quantum Semiclassic. Opt. J. Eu. Opt. Soc. Part B9(5), 737–747 (1997).
[CrossRef]

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron.33(5), 765–783 (1997).
[CrossRef]

1996

A. Valle, K. A. Shore, and L. Pesquera, “Polarization selection in birefringent vertical-cavity surface emitting lasers,” J. Lightwave Technol.14(9), 2062–2068 (1996).
[CrossRef]

H. Li, T. Lucas, J. G. McInerney, M. Wright, and R. A. Morgan, “Injection locking dynamics of vertical cavity semiconductor lasers under conventional and phase conjugate injection,” IEEE J. Quantum Electron.32(2), 227–235 (1996).
[CrossRef]

1995

A. Valle, J. Sarma, and K. A. Shore, “Spatial holeburning effects on the dynamics of vertical-cavity surface-emitting laser diodes,” IEEE J. Quantum Electron.31(8), 1423–1431 (1995).
[CrossRef]

1991

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Vonlehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization, and transverse-mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron.27(6), 1402–1409 (1991).
[CrossRef]

Abraham, N. B.

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron.33(5), 765–783 (1997).
[CrossRef]

Adams, M. J.

A. Quirce, J. R. Cuesta, A. Valle, A. Hurtado, L. Pesquera, and M. J. Adams, “Polarization bistability induced by orthogonal optical injection in 1550-nm multimode VCSELs,” IEEE J. Sel. Top. Quantum Electron.18(2), 772–778 (2012).
[CrossRef]

A. Quirce, A. Valle, A. Hurtado, C. Gimenez, L. Pesquera, and M. J. Adams, “Experimental study of transverse mode selection in VCSELs induced by parallel polarized optical injection,” IEEE J. Quantum Electron.46(4), 467–473 (2010).
[CrossRef]

Agrawal, G. P.

J. Y. Law, G. H. M. vanTartwijk, and G. P. Agrawal, “Effects of transverse-mode competition on the injection dynamics of vertical-cavity surface-emitting lasers,” Quantum Semiclassic. Opt. J. Eu. Opt. Soc. Part B9(5), 737–747 (1997).
[CrossRef]

Altes, J.

J. Altes, I. Gatare, K. Panajotov, H. Thienpont, and M. Sciamanna, “Mapping of the dynamics induced by orthogonal optical injection in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron.42(2), 198–207 (2006).
[CrossRef]

Amann, M. C.

Bacou, A.

A. Hayat, A. Bacou, A. Rissons, J. C. Mollier, V. Iakovlev, A. Sirbu, and E. Kapon, “Long wavelength VCSEL-by-VCSEL optical injection locking,” IEEE Trans. Microw. Theory Tech.57(7), 1850–1858 (2009).
[CrossRef]

Balle, S.

A. Valle, J. Martin-Regalado, L. Pesquera, S. Balle, and M. San Miguel, “Polarization dynamics of birefringent index-guided vertical cavity surface-emitting lasers,” Proc. SPIE3283,280–291 (1998).

Basnet, A. J.

Chan, S. C.

S. C. Chan, “Analysis of an optically injected semiconductor laser for microwave generation,” IEEE J. Quantum Electron.46(3), 421–428 (2010).
[CrossRef]

S. C. Chan, R. Diaz, and J. M. Liu, “Novel photonic applications of nonlinear semiconductor laser dynamics,” Opt. Quantum Electron.40(2-4), 83–95 (2008).
[CrossRef]

S. C. Chan, S. K. Hwang, and J. M. Liu, “Radio-over-fiber transmission from an optically injected semiconductor laser in period-one state,” Proc. SPIE6468,46811–46811 (2007).

S. C. Chan, S. K. Hwang, and J. M. Liu, “Radio-over-fiber AM-to-FM upconversion using an optically injected semiconductor laser,” Opt. Lett.31(15), 2254–2256 (2006).
[CrossRef] [PubMed]

Chang, C.-H.

C.-H. Chang, L. Chrostowski, and C. J. Chang-Hasnain, “Injection locking of VCSELs,” IEEE J. Sel. Top. Quantum Electron.9(5), 1386–1393 (2003).
[CrossRef]

Chang-Hasnain, C. J.

D. Parekh, X. Zhao, W. Hofmann, M. C. Amann, L. A. Zenteno, and C. J. Chang-Hasnain, “Greatly enhanced modulation response of injection-locked multimode VCSELs,” Opt. Express16(26), 21582–21586 (2008).
[CrossRef] [PubMed]

C.-H. Chang, L. Chrostowski, and C. J. Chang-Hasnain, “Injection locking of VCSELs,” IEEE J. Sel. Top. Quantum Electron.9(5), 1386–1393 (2003).
[CrossRef]

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Vonlehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization, and transverse-mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron.27(6), 1402–1409 (1991).
[CrossRef]

Chen, Y. C.

Y. C. Chen, Y. S. Juan, and F. Y. Lin, “High-frequency microwave signal generation in a semiconductor laser under double injection locking,” Proc. SPIE7936,793609 (2011).

Chow, W. W.

S. Wieczorek and W. W. Chow, “Bifurcations and chaos in a semiconductor laser with coherent or noisy optical injection,” Opt. Commun.282(12), 2367–2379 (2009).
[CrossRef]

Chrostowski, L.

C.-H. Chang, L. Chrostowski, and C. J. Chang-Hasnain, “Injection locking of VCSELs,” IEEE J. Sel. Top. Quantum Electron.9(5), 1386–1393 (2003).
[CrossRef]

Cuesta, J. R.

A. Quirce, J. R. Cuesta, A. Valle, A. Hurtado, L. Pesquera, and M. J. Adams, “Polarization bistability induced by orthogonal optical injection in 1550-nm multimode VCSELs,” IEEE J. Sel. Top. Quantum Electron.18(2), 772–778 (2012).
[CrossRef]

Diaz, R.

S. C. Chan, R. Diaz, and J. M. Liu, “Novel photonic applications of nonlinear semiconductor laser dynamics,” Opt. Quantum Electron.40(2-4), 83–95 (2008).
[CrossRef]

Florez, L. T.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Vonlehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization, and transverse-mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron.27(6), 1402–1409 (1991).
[CrossRef]

Gatare, I.

A. Valle, I. Gatare, K. Panajotov, and M. Sciamanna, “Transverse mode switching and locking in vertical-cavity surface-emitting lasers subject to orthogonal optical injection,” IEEE J. Quantum Electron.43(4), 322–333 (2007).
[CrossRef]

J. Altes, I. Gatare, K. Panajotov, H. Thienpont, and M. Sciamanna, “Mapping of the dynamics induced by orthogonal optical injection in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron.42(2), 198–207 (2006).
[CrossRef]

Gimenez, C.

A. Quirce, A. Valle, A. Hurtado, C. Gimenez, L. Pesquera, and M. J. Adams, “Experimental study of transverse mode selection in VCSELs induced by parallel polarized optical injection,” IEEE J. Quantum Electron.46(4), 467–473 (2010).
[CrossRef]

Harbison, J. P.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Vonlehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization, and transverse-mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron.27(6), 1402–1409 (1991).
[CrossRef]

Hasnain, G.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Vonlehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization, and transverse-mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron.27(6), 1402–1409 (1991).
[CrossRef]

Hayat, A.

A. Hayat, A. Bacou, A. Rissons, J. C. Mollier, V. Iakovlev, A. Sirbu, and E. Kapon, “Long wavelength VCSEL-by-VCSEL optical injection locking,” IEEE Trans. Microw. Theory Tech.57(7), 1850–1858 (2009).
[CrossRef]

Hofmann, W.

Hurtado, A.

A. Quirce, J. R. Cuesta, A. Valle, A. Hurtado, L. Pesquera, and M. J. Adams, “Polarization bistability induced by orthogonal optical injection in 1550-nm multimode VCSELs,” IEEE J. Sel. Top. Quantum Electron.18(2), 772–778 (2012).
[CrossRef]

A. Quirce, A. Valle, A. Hurtado, C. Gimenez, L. Pesquera, and M. J. Adams, “Experimental study of transverse mode selection in VCSELs induced by parallel polarized optical injection,” IEEE J. Quantum Electron.46(4), 467–473 (2010).
[CrossRef]

Hwang, S. K.

S. C. Chan, S. K. Hwang, and J. M. Liu, “Radio-over-fiber transmission from an optically injected semiconductor laser in period-one state,” Proc. SPIE6468,46811–46811 (2007).

S. C. Chan, S. K. Hwang, and J. M. Liu, “Radio-over-fiber AM-to-FM upconversion using an optically injected semiconductor laser,” Opt. Lett.31(15), 2254–2256 (2006).
[CrossRef] [PubMed]

Iakovlev, V.

A. Hayat, A. Bacou, A. Rissons, J. C. Mollier, V. Iakovlev, A. Sirbu, and E. Kapon, “Long wavelength VCSEL-by-VCSEL optical injection locking,” IEEE Trans. Microw. Theory Tech.57(7), 1850–1858 (2009).
[CrossRef]

Juan, Y. S.

Y. C. Chen, Y. S. Juan, and F. Y. Lin, “High-frequency microwave signal generation in a semiconductor laser under double injection locking,” Proc. SPIE7936,793609 (2011).

Y. S. Juan and F. Y. Lin, “Photonic generation of broadly tunable microwave signals utilizing a dual-beam optically injected semiconductor laser,” IEEE Photonics J.3(4), 644–650 (2011).
[CrossRef]

Kapon, E.

A. Hayat, A. Bacou, A. Rissons, J. C. Mollier, V. Iakovlev, A. Sirbu, and E. Kapon, “Long wavelength VCSEL-by-VCSEL optical injection locking,” IEEE Trans. Microw. Theory Tech.57(7), 1850–1858 (2009).
[CrossRef]

Koyama, F.

Law, J. Y.

J. Y. Law, G. H. M. vanTartwijk, and G. P. Agrawal, “Effects of transverse-mode competition on the injection dynamics of vertical-cavity surface-emitting lasers,” Quantum Semiclassic. Opt. J. Eu. Opt. Soc. Part B9(5), 737–747 (1997).
[CrossRef]

Li, H.

H. Li, T. Lucas, J. G. McInerney, M. Wright, and R. A. Morgan, “Injection locking dynamics of vertical cavity semiconductor lasers under conventional and phase conjugate injection,” IEEE J. Quantum Electron.32(2), 227–235 (1996).
[CrossRef]

Lin, F. Y.

Y. C. Chen, Y. S. Juan, and F. Y. Lin, “High-frequency microwave signal generation in a semiconductor laser under double injection locking,” Proc. SPIE7936,793609 (2011).

Y. S. Juan and F. Y. Lin, “Photonic generation of broadly tunable microwave signals utilizing a dual-beam optically injected semiconductor laser,” IEEE Photonics J.3(4), 644–650 (2011).
[CrossRef]

Lin, H.

Liu, J. M.

X. Q. Qi and J. M. Liu, “Dynamics scenarios of dual-beam optically injected semiconductor lasers,” IEEE J. Quantum Electron.47(6), 762–769 (2011).
[CrossRef]

X. Q. Qi and J. M. Liu, “Photonic microwave applications of the dynamics of semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron.17(5), 1198–1211 (2011).
[CrossRef]

S. C. Chan, R. Diaz, and J. M. Liu, “Novel photonic applications of nonlinear semiconductor laser dynamics,” Opt. Quantum Electron.40(2-4), 83–95 (2008).
[CrossRef]

S. C. Chan, S. K. Hwang, and J. M. Liu, “Radio-over-fiber transmission from an optically injected semiconductor laser in period-one state,” Proc. SPIE6468,46811–46811 (2007).

S. C. Chan, S. K. Hwang, and J. M. Liu, “Radio-over-fiber AM-to-FM upconversion using an optically injected semiconductor laser,” Opt. Lett.31(15), 2254–2256 (2006).
[CrossRef] [PubMed]

Lucas, T.

H. Li, T. Lucas, J. G. McInerney, M. Wright, and R. A. Morgan, “Injection locking dynamics of vertical cavity semiconductor lasers under conventional and phase conjugate injection,” IEEE J. Quantum Electron.32(2), 227–235 (1996).
[CrossRef]

Martin-Regalado, J.

A. Valle, J. Martin-Regalado, L. Pesquera, S. Balle, and M. San Miguel, “Polarization dynamics of birefringent index-guided vertical cavity surface-emitting lasers,” Proc. SPIE3283,280–291 (1998).

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron.33(5), 765–783 (1997).
[CrossRef]

McInerney, J. G.

H. Li, T. Lucas, J. G. McInerney, M. Wright, and R. A. Morgan, “Injection locking dynamics of vertical cavity semiconductor lasers under conventional and phase conjugate injection,” IEEE J. Quantum Electron.32(2), 227–235 (1996).
[CrossRef]

Mollier, J. C.

A. Hayat, A. Bacou, A. Rissons, J. C. Mollier, V. Iakovlev, A. Sirbu, and E. Kapon, “Long wavelength VCSEL-by-VCSEL optical injection locking,” IEEE Trans. Microw. Theory Tech.57(7), 1850–1858 (2009).
[CrossRef]

Morgan, R. A.

H. Li, T. Lucas, J. G. McInerney, M. Wright, and R. A. Morgan, “Injection locking dynamics of vertical cavity semiconductor lasers under conventional and phase conjugate injection,” IEEE J. Quantum Electron.32(2), 227–235 (1996).
[CrossRef]

Panajotov, K.

A. Valle, I. Gatare, K. Panajotov, and M. Sciamanna, “Transverse mode switching and locking in vertical-cavity surface-emitting lasers subject to orthogonal optical injection,” IEEE J. Quantum Electron.43(4), 322–333 (2007).
[CrossRef]

J. Altes, I. Gatare, K. Panajotov, H. Thienpont, and M. Sciamanna, “Mapping of the dynamics induced by orthogonal optical injection in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron.42(2), 198–207 (2006).
[CrossRef]

Parekh, D.

Pesquera, L.

A. Quirce, J. R. Cuesta, A. Valle, A. Hurtado, L. Pesquera, and M. J. Adams, “Polarization bistability induced by orthogonal optical injection in 1550-nm multimode VCSELs,” IEEE J. Sel. Top. Quantum Electron.18(2), 772–778 (2012).
[CrossRef]

A. Quirce, A. Valle, A. Hurtado, C. Gimenez, L. Pesquera, and M. J. Adams, “Experimental study of transverse mode selection in VCSELs induced by parallel polarized optical injection,” IEEE J. Quantum Electron.46(4), 467–473 (2010).
[CrossRef]

A. Valle and L. Pesquera, “Theoretical calculation of relative intensity noise of multimode vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron.40(6), 597–606 (2004).
[CrossRef]

A. Valle, J. Martin-Regalado, L. Pesquera, S. Balle, and M. San Miguel, “Polarization dynamics of birefringent index-guided vertical cavity surface-emitting lasers,” Proc. SPIE3283,280–291 (1998).

A. Valle, K. A. Shore, and L. Pesquera, “Polarization selection in birefringent vertical-cavity surface emitting lasers,” J. Lightwave Technol.14(9), 2062–2068 (1996).
[CrossRef]

Pierce, D. W.

Prati, F.

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron.33(5), 765–783 (1997).
[CrossRef]

Qi, X. Q.

X. Q. Qi and J. M. Liu, “Photonic microwave applications of the dynamics of semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron.17(5), 1198–1211 (2011).
[CrossRef]

X. Q. Qi and J. M. Liu, “Dynamics scenarios of dual-beam optically injected semiconductor lasers,” IEEE J. Quantum Electron.47(6), 762–769 (2011).
[CrossRef]

Quirce, A.

A. Quirce, J. R. Cuesta, A. Valle, A. Hurtado, L. Pesquera, and M. J. Adams, “Polarization bistability induced by orthogonal optical injection in 1550-nm multimode VCSELs,” IEEE J. Sel. Top. Quantum Electron.18(2), 772–778 (2012).
[CrossRef]

H. Lin, Y. Zhang, D. W. Pierce, A. Quirce, and A. Valle, “Polarization dynamics of a multimode vertical-cavity surface-emitting laser subject to orthogonal optical injection,” J. Opt. Soc. Am. B29(4), 867–873 (2012).
[CrossRef]

H. Lin, D. W. Pierce, A. J. Basnet, A. Quirce, Y. Zhang, and A. Valle, “Two-frequency injection on a multimode vertical-cavity surface-emitting laser,” Opt. Express19(23), 22437–22442 (2011).
[CrossRef] [PubMed]

A. Quirce, A. Valle, A. Hurtado, C. Gimenez, L. Pesquera, and M. J. Adams, “Experimental study of transverse mode selection in VCSELs induced by parallel polarized optical injection,” IEEE J. Quantum Electron.46(4), 467–473 (2010).
[CrossRef]

Rissons, A.

A. Hayat, A. Bacou, A. Rissons, J. C. Mollier, V. Iakovlev, A. Sirbu, and E. Kapon, “Long wavelength VCSEL-by-VCSEL optical injection locking,” IEEE Trans. Microw. Theory Tech.57(7), 1850–1858 (2009).
[CrossRef]

San Miguel, M.

A. Valle, J. Martin-Regalado, L. Pesquera, S. Balle, and M. San Miguel, “Polarization dynamics of birefringent index-guided vertical cavity surface-emitting lasers,” Proc. SPIE3283,280–291 (1998).

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron.33(5), 765–783 (1997).
[CrossRef]

Sarma, J.

A. Valle, J. Sarma, and K. A. Shore, “Spatial holeburning effects on the dynamics of vertical-cavity surface-emitting laser diodes,” IEEE J. Quantum Electron.31(8), 1423–1431 (1995).
[CrossRef]

Sciamanna, M.

A. Valle, I. Gatare, K. Panajotov, and M. Sciamanna, “Transverse mode switching and locking in vertical-cavity surface-emitting lasers subject to orthogonal optical injection,” IEEE J. Quantum Electron.43(4), 322–333 (2007).
[CrossRef]

J. Altes, I. Gatare, K. Panajotov, H. Thienpont, and M. Sciamanna, “Mapping of the dynamics induced by orthogonal optical injection in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron.42(2), 198–207 (2006).
[CrossRef]

Shore, K. A.

A. Valle, K. A. Shore, and L. Pesquera, “Polarization selection in birefringent vertical-cavity surface emitting lasers,” J. Lightwave Technol.14(9), 2062–2068 (1996).
[CrossRef]

A. Valle, J. Sarma, and K. A. Shore, “Spatial holeburning effects on the dynamics of vertical-cavity surface-emitting laser diodes,” IEEE J. Quantum Electron.31(8), 1423–1431 (1995).
[CrossRef]

Sirbu, A.

A. Hayat, A. Bacou, A. Rissons, J. C. Mollier, V. Iakovlev, A. Sirbu, and E. Kapon, “Long wavelength VCSEL-by-VCSEL optical injection locking,” IEEE Trans. Microw. Theory Tech.57(7), 1850–1858 (2009).
[CrossRef]

Stoffel, N. G.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Vonlehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization, and transverse-mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron.27(6), 1402–1409 (1991).
[CrossRef]

Thienpont, H.

J. Altes, I. Gatare, K. Panajotov, H. Thienpont, and M. Sciamanna, “Mapping of the dynamics induced by orthogonal optical injection in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron.42(2), 198–207 (2006).
[CrossRef]

Valle, A.

A. Quirce, J. R. Cuesta, A. Valle, A. Hurtado, L. Pesquera, and M. J. Adams, “Polarization bistability induced by orthogonal optical injection in 1550-nm multimode VCSELs,” IEEE J. Sel. Top. Quantum Electron.18(2), 772–778 (2012).
[CrossRef]

H. Lin, Y. Zhang, D. W. Pierce, A. Quirce, and A. Valle, “Polarization dynamics of a multimode vertical-cavity surface-emitting laser subject to orthogonal optical injection,” J. Opt. Soc. Am. B29(4), 867–873 (2012).
[CrossRef]

H. Lin, D. W. Pierce, A. J. Basnet, A. Quirce, Y. Zhang, and A. Valle, “Two-frequency injection on a multimode vertical-cavity surface-emitting laser,” Opt. Express19(23), 22437–22442 (2011).
[CrossRef] [PubMed]

A. Quirce, A. Valle, A. Hurtado, C. Gimenez, L. Pesquera, and M. J. Adams, “Experimental study of transverse mode selection in VCSELs induced by parallel polarized optical injection,” IEEE J. Quantum Electron.46(4), 467–473 (2010).
[CrossRef]

A. Valle, I. Gatare, K. Panajotov, and M. Sciamanna, “Transverse mode switching and locking in vertical-cavity surface-emitting lasers subject to orthogonal optical injection,” IEEE J. Quantum Electron.43(4), 322–333 (2007).
[CrossRef]

A. Valle and L. Pesquera, “Theoretical calculation of relative intensity noise of multimode vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron.40(6), 597–606 (2004).
[CrossRef]

A. Valle, J. Martin-Regalado, L. Pesquera, S. Balle, and M. San Miguel, “Polarization dynamics of birefringent index-guided vertical cavity surface-emitting lasers,” Proc. SPIE3283,280–291 (1998).

A. Valle, K. A. Shore, and L. Pesquera, “Polarization selection in birefringent vertical-cavity surface emitting lasers,” J. Lightwave Technol.14(9), 2062–2068 (1996).
[CrossRef]

A. Valle, J. Sarma, and K. A. Shore, “Spatial holeburning effects on the dynamics of vertical-cavity surface-emitting laser diodes,” IEEE J. Quantum Electron.31(8), 1423–1431 (1995).
[CrossRef]

vanTartwijk, G. H. M.

J. Y. Law, G. H. M. vanTartwijk, and G. P. Agrawal, “Effects of transverse-mode competition on the injection dynamics of vertical-cavity surface-emitting lasers,” Quantum Semiclassic. Opt. J. Eu. Opt. Soc. Part B9(5), 737–747 (1997).
[CrossRef]

Vonlehmen, A. C.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Vonlehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization, and transverse-mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron.27(6), 1402–1409 (1991).
[CrossRef]

Wieczorek, S.

S. Wieczorek and W. W. Chow, “Bifurcations and chaos in a semiconductor laser with coherent or noisy optical injection,” Opt. Commun.282(12), 2367–2379 (2009).
[CrossRef]

Wright, M.

H. Li, T. Lucas, J. G. McInerney, M. Wright, and R. A. Morgan, “Injection locking dynamics of vertical cavity semiconductor lasers under conventional and phase conjugate injection,” IEEE J. Quantum Electron.32(2), 227–235 (1996).
[CrossRef]

Zenteno, L. A.

Zhang, Y.

Zhao, X.

IEEE J. Quantum Electron.

H. Li, T. Lucas, J. G. McInerney, M. Wright, and R. A. Morgan, “Injection locking dynamics of vertical cavity semiconductor lasers under conventional and phase conjugate injection,” IEEE J. Quantum Electron.32(2), 227–235 (1996).
[CrossRef]

J. Altes, I. Gatare, K. Panajotov, H. Thienpont, and M. Sciamanna, “Mapping of the dynamics induced by orthogonal optical injection in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron.42(2), 198–207 (2006).
[CrossRef]

A. Valle, I. Gatare, K. Panajotov, and M. Sciamanna, “Transverse mode switching and locking in vertical-cavity surface-emitting lasers subject to orthogonal optical injection,” IEEE J. Quantum Electron.43(4), 322–333 (2007).
[CrossRef]

A. Quirce, A. Valle, A. Hurtado, C. Gimenez, L. Pesquera, and M. J. Adams, “Experimental study of transverse mode selection in VCSELs induced by parallel polarized optical injection,” IEEE J. Quantum Electron.46(4), 467–473 (2010).
[CrossRef]

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Vonlehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization, and transverse-mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron.27(6), 1402–1409 (1991).
[CrossRef]

A. Valle, J. Sarma, and K. A. Shore, “Spatial holeburning effects on the dynamics of vertical-cavity surface-emitting laser diodes,” IEEE J. Quantum Electron.31(8), 1423–1431 (1995).
[CrossRef]

S. C. Chan, “Analysis of an optically injected semiconductor laser for microwave generation,” IEEE J. Quantum Electron.46(3), 421–428 (2010).
[CrossRef]

X. Q. Qi and J. M. Liu, “Dynamics scenarios of dual-beam optically injected semiconductor lasers,” IEEE J. Quantum Electron.47(6), 762–769 (2011).
[CrossRef]

A. Valle and L. Pesquera, “Theoretical calculation of relative intensity noise of multimode vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron.40(6), 597–606 (2004).
[CrossRef]

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron.33(5), 765–783 (1997).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

X. Q. Qi and J. M. Liu, “Photonic microwave applications of the dynamics of semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron.17(5), 1198–1211 (2011).
[CrossRef]

A. Quirce, J. R. Cuesta, A. Valle, A. Hurtado, L. Pesquera, and M. J. Adams, “Polarization bistability induced by orthogonal optical injection in 1550-nm multimode VCSELs,” IEEE J. Sel. Top. Quantum Electron.18(2), 772–778 (2012).
[CrossRef]

C.-H. Chang, L. Chrostowski, and C. J. Chang-Hasnain, “Injection locking of VCSELs,” IEEE J. Sel. Top. Quantum Electron.9(5), 1386–1393 (2003).
[CrossRef]

IEEE Photonics J.

Y. S. Juan and F. Y. Lin, “Photonic generation of broadly tunable microwave signals utilizing a dual-beam optically injected semiconductor laser,” IEEE Photonics J.3(4), 644–650 (2011).
[CrossRef]

IEEE Trans. Microw. Theory Tech.

A. Hayat, A. Bacou, A. Rissons, J. C. Mollier, V. Iakovlev, A. Sirbu, and E. Kapon, “Long wavelength VCSEL-by-VCSEL optical injection locking,” IEEE Trans. Microw. Theory Tech.57(7), 1850–1858 (2009).
[CrossRef]

J. Lightwave Technol.

F. Koyama, “Recent advances of VCSEL photonics,” J. Lightwave Technol.24(12), 4502–4513 (2006).
[CrossRef]

A. Valle, K. A. Shore, and L. Pesquera, “Polarization selection in birefringent vertical-cavity surface emitting lasers,” J. Lightwave Technol.14(9), 2062–2068 (1996).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

S. Wieczorek and W. W. Chow, “Bifurcations and chaos in a semiconductor laser with coherent or noisy optical injection,” Opt. Commun.282(12), 2367–2379 (2009).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Quantum Electron.

S. C. Chan, R. Diaz, and J. M. Liu, “Novel photonic applications of nonlinear semiconductor laser dynamics,” Opt. Quantum Electron.40(2-4), 83–95 (2008).
[CrossRef]

Proc. SPIE

S. C. Chan, S. K. Hwang, and J. M. Liu, “Radio-over-fiber transmission from an optically injected semiconductor laser in period-one state,” Proc. SPIE6468,46811–46811 (2007).

Y. C. Chen, Y. S. Juan, and F. Y. Lin, “High-frequency microwave signal generation in a semiconductor laser under double injection locking,” Proc. SPIE7936,793609 (2011).

A. Valle, J. Martin-Regalado, L. Pesquera, S. Balle, and M. San Miguel, “Polarization dynamics of birefringent index-guided vertical cavity surface-emitting lasers,” Proc. SPIE3283,280–291 (1998).

Quantum Semiclassic. Opt. J. Eu. Opt. Soc. Part B

J. Y. Law, G. H. M. vanTartwijk, and G. P. Agrawal, “Effects of transverse-mode competition on the injection dynamics of vertical-cavity surface-emitting lasers,” Quantum Semiclassic. Opt. J. Eu. Opt. Soc. Part B9(5), 737–747 (1997).
[CrossRef]

Other

J. Ohtsubo, Semiconductor Lasers. Stability, Instability and Chaos, Springer Series in Optical Sciences (Springer, 2007).

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Figures (9)

Fig. 1
Fig. 1

Temporal and spectral dynamics of a single-transverse mode VCSEL when (a) no optical injection is applied, (b) Δf = 100 GHz, Δν = 0 GHz, κs = 10−2, and κc = κs /2. Upper row: Time traces of the power of the polarized transverse modes. Middle row: RF spectra of the polarized powers. Lower row: x and y-polarized optical spectra.

Fig. 2
Fig. 2

Temporal and spectral dynamics of a multi-transverse mode VCSEL when (a) no optical injection is applied, (b) Δf = 100 GHz, Δν = 0 GHz, κs = 10−2, and κc = κs /2. Upper row: Time traces of the power of the polarized transverse modes. Middle row: RF spectra of the polarized powers. Lower row: x and y-polarized optical spectra.

Fig. 3
Fig. 3

Temporal and spectral dynamics of a multi-transverse mode VCSEL when (a) Δf = 200 GHz, κs = 10−2 (b) Δf = 200 GHz, κs = 3 10−2. Other parameters are Δν = 0 GHz and κc = κs /2. Upper row: Time traces of the power of the polarized transverse modes and total power. Total power for the single-mode case is also included. Middle row: RF spectra of the polarized powers. Lower row: x and y-polarized optical spectra.

Fig. 4
Fig. 4

(a) Peak-to-peak amplitude of the total power as a function of Δf. (b) Ratio between peak-to-peak amplitudes obtained with multi-transverse and single transverse-mode VCSELs. In this Fig. Δν = 0 and κc = κs /2.

Fig. 5
Fig. 5

Temporal and spectral dynamics of a multi-transverse mode VCSEL when (a) Δf = 500 GHz, κs = 3 10−2, κc = κs /2, Δν = 0 GHz (b) Δf = 200 GHz, κs = 3 10−2, κc = 0.1κs, Δν = 0 GHz. Upper row: Time traces of the power of the polarized transverse modes. Middle row: RF spectra of the polarized powers. Lower row: x and y-polarized optical spectra.

Fig. 6
Fig. 6

(a) Peak-to-peak amplitude of the total power as a function of κs. (b) Ratio between peak-to-peak amplitudes obtained with multi and single transverse-mode VCSELs. In this Fig. κc = κs/2, Δf = 200 GHz, and Δν = 0 GHz.

Fig. 7
Fig. 7

(a) Peak-to-peak amplitude of the total power as a function of κcs. (b) Ratio between peak-to-peak amplitudes obtained with multi and single transverse-mode VCSELs. In this Fig. Δf = 200 GHz, and Δν = 0 GHz.

Fig. 8
Fig. 8

(a) Peak-to-peak amplitude of the total power as a function of I/Ith when Δf = 200 GHz and κs = 3 10−2 (b) RF linewidth as a function of the linewidth of the master lasers when Δf = 100 GHz and κs = 10−2. In this Fig. κc = κs/2 and Δν = 0 GHz.

Fig. 9
Fig. 9

(a) Maximum frequency of the generated microwave signals as a function of the injection strength. (b) Ratio of the maximum frequencies obtained with multimode and single-mode VCSELs. In this Fig. A = 4 a.u., κc = κs/2 and Δν = 0 GHz.

Tables (1)

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Table 1 Parameters Used in the Model

Equations (8)

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E ˙ 0x =k(1+iα)( E 0x ( g 0x 1)+i E 0y g 0xy )( γ a +i γ p0 ) E 0x + κ 01 τ in e iΔ ω 1 t + κ 02 τ in e iΔ ω 2 t + β 2 ( N ¯ + n ¯ ξ 0+ + N ¯ n ¯ ξ 0 )
E ˙ 0y =k(1+iα)( E 0y ( g 0y 1)i E 0x g 0yx )+( γ a +i γ p0 ) E 0y i 0( N ¯ + n ¯ ξ 0+ N ¯ n ¯ ξ 0 )
E ˙ 1x =k(1+iα)( E 1x ( g 1x κ r )+i E 1y g 1xy )+i γ p tr E 1x ( γ a +i γ p1 ) E 1x + κ 11 τ in e iΔ ω 1 t + κ 12 τ in e iΔ ω 2 t + β 2 ( N ¯ + n ¯ ξ 1+ + N ¯ n ¯ ξ 1 )
E ˙ 1y =k(1+iα)( E 1y ( g 1y κ r )i E 1x g 1yx )+i γ p tr E 1y +( γ a +i γ p1 ) E 1y i β 2 ( N ¯ + n ¯ ξ 1+ N ¯ n ¯ ξ 1 )
N(r,t) t =I(r)+D 2 N γ e [ N( 1+ i=0,1 j=x,y | E ij | 2 ψ ij 2 (r) )in i=0,1 ( E ix E iy * E iy E ix * ) ψ ix (r) ψ iy (r) ]
n(r,t) t = γ s n+D 2 n γ e [ n i=0,1 j=x,y | E ij | 2 ψ ij 2 (r) iN i=0,1 ( E ix E iy * E iy E ix * ) ψ ix (r) ψ iy (r) ]
g i,jk = 0 n(r,t) ψ ij (r) ψ ik (r)rdr 0 ψ ij 2 (r)rdr g ij = 0 N(r,t) ψ ij 2 (r)rdr 0 ψ ij 2 (r)rdr
k im =( 1 R R ) η inj P inj,im

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