Abstract

A new vectorial model (VSPIN) based on the Jones formalism is proposed to describe the polarization dynamics of spin injected V(e)CSELs. This general modelling framework accounts for spin injection effects as a gain circular dichroism in the active medium and provides guidelines for developing functional spin-controlled lasers. We investigate the detrimental role of phase anisotropy on polarization switching and show that it can be overcome by preparing the laser cavity to achieve efficient polarization switching under low effective spin injection. The VSPIN model predictions have been confirmed experimentally and explain the polarization behavior of spin-VCSELs reported in the literature.

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

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References

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    [Crossref] [PubMed]

2017 (2)

2015 (3)

P. E. Faria, G. Xu, G. Lee, N. C. Gerhardt, G. M. Sipahi, and I. Zutic, “Toward high-frequency operation of spin lasers,” Phys. Rev. B 92(7), 075311 (2015).
[Crossref]

E. Wasner, S. Bearden, J. Lee, and I. Žutić, “Digital operation and eye diagrams in spin-lasers,” Appl. Phys. Lett. 107(8), 082406 (2015).
[Crossref]

J. Frougier, G. Baili, I. Sagnes, D. Dolfi, J.-M. George, and M. Alouini, “Accurate measurement of the residual birefringence in VECSEL: Towards understanding of the polarization behavior under spin-polarized pumping,” Opt. Express 23(8), 9573–9588 (2015).
[Crossref] [PubMed]

2014 (3)

J. Lee, S. Bearden, E. Wasner, and I. Žutić, “Spin-lasers: From threshold reduction to large-signal analysis,” Appl. Phys. Lett. 105(4), 042411 (2014).
[Crossref]

T. Fördös, K. Postava, H. Jaffrès, and J. Pištora, “Matrix approach for modeling of emission from multilayer spin-polarized light-emitting diodes and lasers,” J. Opt. 16(6), 065008 (2014).
[Crossref]

S. De, V. Potapchuk, and F. Bretenaker, “Influence of spin-dependent carrier dynamics on the properties of a dual-frequency vertical-external-cavity surface-emitting laser,” Phys. Rev. A 90(1), 013841 (2014).
[Crossref]

2013 (1)

J. Frougier, G. Baili, M. Alouini, I. Sagnes, H. Jaffrès, A. Garnache, C. Deranlot, D. Dolfi, and J. M. George, “Control of light polarization using optically spin-injected vertical external cavity surface emitting lasers,” Appl. Phys. Lett. 103(25), 252402 (2013).
[Crossref]

2011 (2)

S. Iba, S. Koh, K. Ikeda, and H. Kawaguchi, “Room temperature circularly polarized lasing in an optically spin injected vertical-cavity surface-emitting laser with (110) GaAs quantum wells,” Appl. Phys. Lett. 98(8), 081113 (2011).
[Crossref]

N. C. Gerhardt, M. Y. Li, H. Jähme, H. Höpfner, T. Ackemann, and M. R. Hofmann, “Ultrafast spin-induced polarization oscillations with tunable lifetime in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 99(15), 151107 (2011).
[Crossref]

2010 (2)

2009 (2)

2008 (1)

C. Gøthgen, R. Oszwałdowski, A. Petrou, and I. Žutić, “Analytical model of spin-polarized semiconductor lasers,” Appl. 93(4), 042513 (2008).

2007 (2)

2006 (1)

N. Gerhardt, S. Hovel, M. Hofmann, J. Yang, D. Reuter, and A. Wieck, “Enhancement of spin information with vertical cavity surface emitting lasers,” Electron. Lett. 42(2), 88–89 (2006).
[Crossref]

2005 (4)

X. Jiang, R. Wang, R. M. Shelby, R. M. Macfarlane, S. R. Bank, J. S. Harris, and S. S. P. Parkin, “Highly Spin-Polarized Room-Temperature Tunnel Injector for Semiconductor Spintronics using MgO(100),” Phys. Rev. Lett. 94(5), 056601 (2005).
[Crossref] [PubMed]

S. Hovel, N. Gerhardt, M. Hofmann, J. Yang, D. Reuter, and A. Wieck, “Spin controlled optically pumped vertical cavity surface emitting laser,” Electron. Lett. 41(5), 251–253 (2005).
[Crossref]

M. Holub, J. Shin, S. Chakrabarti, and P. Bhattacharya, “Electrically injected spin-polarized vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 87(9), 091108 (2005).
[Crossref]

J. Rudolph, S. Döhrmann, D. Hägele, M. Oestreich, and W. Stolz, “Room-temperature threshold reduction in vertical-cavity surface-emitting lasers by injection of spin-polarized electrons,” Phys. Rev. Lett. 87(24), 241117 (2005).

2000 (2)

M. Alouini, F. Bretenaker, M. Brunel, A. Le Floch, M. Vallet, and P. Thony, “Existence of two coupling constants in microchip lasers,” Opt. Lett. 25(12), 896–898 (2000).
[Crossref] [PubMed]

M. B. Willemsen, J. P. Woerdman, and J. P. Woerdman, “Anatomy of a Polarization Switch of a Vertical-Cavity Semiconductor Laser,” Phys. Rev. Lett. 84(19), 4337–4340 (2000).
[Crossref] [PubMed]

1999 (3)

M. Vallet, M. Brunel, M. Alouini, F. Bretenaker, A. Le Floch, and G. P. Agrawal, “Polarization self-modulated lasers with circular eigenstates,” Appl. Phys. Lett. 74(22), 3266–3268 (1999).
[Crossref]

A. Gahl, S. Balle, and M. S. Miguel, “Polarization dynamics of optically pumped vcsels,” IEEE J. Quantum Electron. 35(3), 342–351 (1999).
[Crossref]

R. Fiederling, M. Keim, G. Reuscher, W. Ossau, G. Schmidt, A. Waag, and L. W. Molenkamp, “Injection and detection of a spin-polarized current in a light-emitting diode,” Nature 402(6763), 787–790 (1999).
[Crossref]

1998 (1)

H. Ando, T. Sogawa, and H. Gotoh, “Photon-spin controlled lasing oscillation in surface-emitting lasers,” Appl. Phys. Lett. 73(5), 566–568 (1998).
[Crossref]

1997 (3)

M. Travagnin, M. P. van Exter, A. K. Jansen van Doorn, and J. P. Woerdman, “Erratum: Role of optical anisotropies in the polarization properties of surface emitting semiconductor lasers [phys. rev. a 54, 1647 (1996)],” Phys. Rev. A 55(6), 4641 (1997).
[Crossref]

S. A. Crooker, D. D. Awschalom, J. J. Baumberg, F. Flack, and N. Samarth, “Optical spin resonance and transverse spin relaxation in magnetic semiconductor quantum wells,” Phys. Rev. B 56(12), 7574–7588 (1997).
[Crossref]

M. Brunel, M. Vallet, A. Le Floch, and F. Bretenaker, “Differential measurement of the coupling constant between laser eigenstates,” Appl. Phys. Lett. 70(16), 2070–2072 (1997).
[Crossref]

1996 (1)

M. Travagnin, J. P. Woerdman, A. K. Jansen van Doorn, and J. P. Woerdman, “Role of optical anisotropies in the polarization properties of surface-emitting semiconductor lasers,” Phys. Rev. A 54(2), 1647–1660 (1996).
[Crossref] [PubMed]

1995 (1)

Q. Feng, J. V. Moloney, and J. V. Moloney,“Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52(2), 1728–1739 (1995).
[Crossref] [PubMed]

1984 (1)

A. Le Floch, G. Ropars, J. M. Lenormand, and R. Le Naour, “Dynamics of Laser Eigenstates,” Phys. Rev. Lett. 52(11), 918–921 (1984).
[Crossref]

1941 (1)

Ackemann, T.

N. C. Gerhardt, M. Y. Li, H. Jähme, H. Höpfner, T. Ackemann, and M. R. Hofmann, “Ultrafast spin-induced polarization oscillations with tunable lifetime in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 99(15), 151107 (2011).
[Crossref]

Agrawal, G. P.

M. Vallet, M. Brunel, M. Alouini, F. Bretenaker, A. Le Floch, and G. P. Agrawal, “Polarization self-modulated lasers with circular eigenstates,” Appl. Phys. Lett. 74(22), 3266–3268 (1999).
[Crossref]

Alouini, M.

N. Ortega-Quijano, J. Fade, F. Parnet, and M. Alouini, “Generation of a coherent light beam with precise and fast dynamic control of the state and degree of polarization,” Opt. Lett. 42(15), 2898–2901 (2017).
[Crossref] [PubMed]

A. Joly, G. Baili, M. Alouini, J.-M. George, I. Sagnes, G. Pillet, and D. Dolfi, “Compensation of the residual linear anisotropy of phase in a vertical-external-cavity-surface-emitting laser for spin injection,” Opt. Lett. 42(3), 651–654 (2017).
[Crossref] [PubMed]

J. Frougier, G. Baili, I. Sagnes, D. Dolfi, J.-M. George, and M. Alouini, “Accurate measurement of the residual birefringence in VECSEL: Towards understanding of the polarization behavior under spin-polarized pumping,” Opt. Express 23(8), 9573–9588 (2015).
[Crossref] [PubMed]

J. Frougier, G. Baili, M. Alouini, I. Sagnes, H. Jaffrès, A. Garnache, C. Deranlot, D. Dolfi, and J. M. George, “Control of light polarization using optically spin-injected vertical external cavity surface emitting lasers,” Appl. Phys. Lett. 103(25), 252402 (2013).
[Crossref]

V. Pal, P. Trofimoff, B.-X. Miranda, G. Baili, M. Alouini, L. Morvan, D. Dolfi, F. Goldfarb, I. Sagnes, R. Ghosh, and F. Bretenaker, “Measurement of the coupling constant in a two-frequency VECSEL,” Opt. Express 18(5), 5008–5014 (2010).
[Crossref] [PubMed]

G. Baili, L. Morvan, M. Alouini, D. Dolfi, F. Bretenaker, I. Sagnes, and A. Garnache, “Experimental demonstration of a tunable dual-frequency semiconductor laser free of relaxation oscillations,” Opt. Lett. 34(21), 3421–3423 (2009).
[Crossref] [PubMed]

M. Alouini, F. Bretenaker, M. Brunel, A. Le Floch, M. Vallet, and P. Thony, “Existence of two coupling constants in microchip lasers,” Opt. Lett. 25(12), 896–898 (2000).
[Crossref] [PubMed]

M. Vallet, M. Brunel, M. Alouini, F. Bretenaker, A. Le Floch, and G. P. Agrawal, “Polarization self-modulated lasers with circular eigenstates,” Appl. Phys. Lett. 74(22), 3266–3268 (1999).
[Crossref]

Ando, H.

H. Ando, T. Sogawa, and H. Gotoh, “Photon-spin controlled lasing oscillation in surface-emitting lasers,” Appl. Phys. Lett. 73(5), 566–568 (1998).
[Crossref]

Awschalom, D. D.

S. A. Crooker, D. D. Awschalom, J. J. Baumberg, F. Flack, and N. Samarth, “Optical spin resonance and transverse spin relaxation in magnetic semiconductor quantum wells,” Phys. Rev. B 56(12), 7574–7588 (1997).
[Crossref]

Baili, G.

Balle, S.

A. Gahl, S. Balle, and M. S. Miguel, “Polarization dynamics of optically pumped vcsels,” IEEE J. Quantum Electron. 35(3), 342–351 (1999).
[Crossref]

Bank, S. R.

X. Jiang, R. Wang, R. M. Shelby, R. M. Macfarlane, S. R. Bank, J. S. Harris, and S. S. P. Parkin, “Highly Spin-Polarized Room-Temperature Tunnel Injector for Semiconductor Spintronics using MgO(100),” Phys. Rev. Lett. 94(5), 056601 (2005).
[Crossref] [PubMed]

Basu, D.

D. Basu, D. Saha, and P. Bhattacharya, “Optical polarization modulation and gain anisotropy in an electrically injected spin laser,” Phys. Rev. Lett. 102(9), 093904 (2009).
[Crossref] [PubMed]

Baumberg, J. J.

S. A. Crooker, D. D. Awschalom, J. J. Baumberg, F. Flack, and N. Samarth, “Optical spin resonance and transverse spin relaxation in magnetic semiconductor quantum wells,” Phys. Rev. B 56(12), 7574–7588 (1997).
[Crossref]

Bearden, S.

E. Wasner, S. Bearden, J. Lee, and I. Žutić, “Digital operation and eye diagrams in spin-lasers,” Appl. Phys. Lett. 107(8), 082406 (2015).
[Crossref]

J. Lee, S. Bearden, E. Wasner, and I. Žutić, “Spin-lasers: From threshold reduction to large-signal analysis,” Appl. Phys. Lett. 105(4), 042411 (2014).
[Crossref]

Bhattacharya, P.

D. Basu, D. Saha, and P. Bhattacharya, “Optical polarization modulation and gain anisotropy in an electrically injected spin laser,” Phys. Rev. Lett. 102(9), 093904 (2009).
[Crossref] [PubMed]

M. Holub, J. Shin, S. Chakrabarti, and P. Bhattacharya, “Electrically injected spin-polarized vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 87(9), 091108 (2005).
[Crossref]

Bretenaker, F.

S. De, V. Potapchuk, and F. Bretenaker, “Influence of spin-dependent carrier dynamics on the properties of a dual-frequency vertical-external-cavity surface-emitting laser,” Phys. Rev. A 90(1), 013841 (2014).
[Crossref]

V. Pal, P. Trofimoff, B.-X. Miranda, G. Baili, M. Alouini, L. Morvan, D. Dolfi, F. Goldfarb, I. Sagnes, R. Ghosh, and F. Bretenaker, “Measurement of the coupling constant in a two-frequency VECSEL,” Opt. Express 18(5), 5008–5014 (2010).
[Crossref] [PubMed]

G. Baili, L. Morvan, M. Alouini, D. Dolfi, F. Bretenaker, I. Sagnes, and A. Garnache, “Experimental demonstration of a tunable dual-frequency semiconductor laser free of relaxation oscillations,” Opt. Lett. 34(21), 3421–3423 (2009).
[Crossref] [PubMed]

M. Alouini, F. Bretenaker, M. Brunel, A. Le Floch, M. Vallet, and P. Thony, “Existence of two coupling constants in microchip lasers,” Opt. Lett. 25(12), 896–898 (2000).
[Crossref] [PubMed]

M. Vallet, M. Brunel, M. Alouini, F. Bretenaker, A. Le Floch, and G. P. Agrawal, “Polarization self-modulated lasers with circular eigenstates,” Appl. Phys. Lett. 74(22), 3266–3268 (1999).
[Crossref]

M. Brunel, M. Vallet, A. Le Floch, and F. Bretenaker, “Differential measurement of the coupling constant between laser eigenstates,” Appl. Phys. Lett. 70(16), 2070–2072 (1997).
[Crossref]

Brunel, M.

M. Alouini, F. Bretenaker, M. Brunel, A. Le Floch, M. Vallet, and P. Thony, “Existence of two coupling constants in microchip lasers,” Opt. Lett. 25(12), 896–898 (2000).
[Crossref] [PubMed]

M. Vallet, M. Brunel, M. Alouini, F. Bretenaker, A. Le Floch, and G. P. Agrawal, “Polarization self-modulated lasers with circular eigenstates,” Appl. Phys. Lett. 74(22), 3266–3268 (1999).
[Crossref]

M. Brunel, M. Vallet, A. Le Floch, and F. Bretenaker, “Differential measurement of the coupling constant between laser eigenstates,” Appl. Phys. Lett. 70(16), 2070–2072 (1997).
[Crossref]

Chakrabarti, S.

M. Holub, J. Shin, S. Chakrabarti, and P. Bhattacharya, “Electrically injected spin-polarized vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 87(9), 091108 (2005).
[Crossref]

Crooker, S. A.

S. A. Crooker, D. D. Awschalom, J. J. Baumberg, F. Flack, and N. Samarth, “Optical spin resonance and transverse spin relaxation in magnetic semiconductor quantum wells,” Phys. Rev. B 56(12), 7574–7588 (1997).
[Crossref]

Dawes, J. M.

De, S.

S. De, V. Potapchuk, and F. Bretenaker, “Influence of spin-dependent carrier dynamics on the properties of a dual-frequency vertical-external-cavity surface-emitting laser,” Phys. Rev. A 90(1), 013841 (2014).
[Crossref]

Deranlot, C.

J. Frougier, G. Baili, M. Alouini, I. Sagnes, H. Jaffrès, A. Garnache, C. Deranlot, D. Dolfi, and J. M. George, “Control of light polarization using optically spin-injected vertical external cavity surface emitting lasers,” Appl. Phys. Lett. 103(25), 252402 (2013).
[Crossref]

Döhrmann, S.

J. Rudolph, S. Döhrmann, D. Hägele, M. Oestreich, and W. Stolz, “Room-temperature threshold reduction in vertical-cavity surface-emitting lasers by injection of spin-polarized electrons,” Phys. Rev. Lett. 87(24), 241117 (2005).

Dolfi, D.

Fade, J.

Falls, W.

J. Lee, W. Falls, R. Oszwaldowski, and I. Zutic, “Spin modulation in semiconductor lasers,” Appl. Phys. Lett. 97(4), 041116 (2010).
[Crossref]

Faria, P. E.

P. E. Faria, G. Xu, G. Lee, N. C. Gerhardt, G. M. Sipahi, and I. Zutic, “Toward high-frequency operation of spin lasers,” Phys. Rev. B 92(7), 075311 (2015).
[Crossref]

Feng, Q.

Q. Feng, J. V. Moloney, and J. V. Moloney,“Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52(2), 1728–1739 (1995).
[Crossref] [PubMed]

Fiederling, R.

R. Fiederling, M. Keim, G. Reuscher, W. Ossau, G. Schmidt, A. Waag, and L. W. Molenkamp, “Injection and detection of a spin-polarized current in a light-emitting diode,” Nature 402(6763), 787–790 (1999).
[Crossref]

Flack, F.

S. A. Crooker, D. D. Awschalom, J. J. Baumberg, F. Flack, and N. Samarth, “Optical spin resonance and transverse spin relaxation in magnetic semiconductor quantum wells,” Phys. Rev. B 56(12), 7574–7588 (1997).
[Crossref]

Fördös, T.

T. Fördös, K. Postava, H. Jaffrès, and J. Pištora, “Matrix approach for modeling of emission from multilayer spin-polarized light-emitting diodes and lasers,” J. Opt. 16(6), 065008 (2014).
[Crossref]

Frougier, J.

J. Frougier, G. Baili, I. Sagnes, D. Dolfi, J.-M. George, and M. Alouini, “Accurate measurement of the residual birefringence in VECSEL: Towards understanding of the polarization behavior under spin-polarized pumping,” Opt. Express 23(8), 9573–9588 (2015).
[Crossref] [PubMed]

J. Frougier, G. Baili, M. Alouini, I. Sagnes, H. Jaffrès, A. Garnache, C. Deranlot, D. Dolfi, and J. M. George, “Control of light polarization using optically spin-injected vertical external cavity surface emitting lasers,” Appl. Phys. Lett. 103(25), 252402 (2013).
[Crossref]

Gahl, A.

A. Gahl, S. Balle, and M. S. Miguel, “Polarization dynamics of optically pumped vcsels,” IEEE J. Quantum Electron. 35(3), 342–351 (1999).
[Crossref]

Garnache, A.

George, J. M.

J. Frougier, G. Baili, M. Alouini, I. Sagnes, H. Jaffrès, A. Garnache, C. Deranlot, D. Dolfi, and J. M. George, “Control of light polarization using optically spin-injected vertical external cavity surface emitting lasers,” Appl. Phys. Lett. 103(25), 252402 (2013).
[Crossref]

George, J.-M.

Gerhardt, N.

N. Gerhardt, S. Hovel, M. Hofmann, J. Yang, D. Reuter, and A. Wieck, “Enhancement of spin information with vertical cavity surface emitting lasers,” Electron. Lett. 42(2), 88–89 (2006).
[Crossref]

S. Hovel, N. Gerhardt, M. Hofmann, J. Yang, D. Reuter, and A. Wieck, “Spin controlled optically pumped vertical cavity surface emitting laser,” Electron. Lett. 41(5), 251–253 (2005).
[Crossref]

Gerhardt, N. C.

P. E. Faria, G. Xu, G. Lee, N. C. Gerhardt, G. M. Sipahi, and I. Zutic, “Toward high-frequency operation of spin lasers,” Phys. Rev. B 92(7), 075311 (2015).
[Crossref]

N. C. Gerhardt, M. Y. Li, H. Jähme, H. Höpfner, T. Ackemann, and M. R. Hofmann, “Ultrafast spin-induced polarization oscillations with tunable lifetime in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 99(15), 151107 (2011).
[Crossref]

Ghosh, R.

Goldfarb, F.

Gøthgen, C.

C. Gøthgen, R. Oszwałdowski, A. Petrou, and I. Žutić, “Analytical model of spin-polarized semiconductor lasers,” Appl. 93(4), 042513 (2008).

Gotoh, H.

H. Ando, T. Sogawa, and H. Gotoh, “Photon-spin controlled lasing oscillation in surface-emitting lasers,” Appl. Phys. Lett. 73(5), 566–568 (1998).
[Crossref]

Hägele, D.

J. Rudolph, S. Döhrmann, D. Hägele, M. Oestreich, and W. Stolz, “Room-temperature threshold reduction in vertical-cavity surface-emitting lasers by injection of spin-polarized electrons,” Phys. Rev. Lett. 87(24), 241117 (2005).

Harris, J. S.

X. Jiang, R. Wang, R. M. Shelby, R. M. Macfarlane, S. R. Bank, J. S. Harris, and S. S. P. Parkin, “Highly Spin-Polarized Room-Temperature Tunnel Injector for Semiconductor Spintronics using MgO(100),” Phys. Rev. Lett. 94(5), 056601 (2005).
[Crossref] [PubMed]

Hofmann, M.

N. Gerhardt, S. Hovel, M. Hofmann, J. Yang, D. Reuter, and A. Wieck, “Enhancement of spin information with vertical cavity surface emitting lasers,” Electron. Lett. 42(2), 88–89 (2006).
[Crossref]

S. Hovel, N. Gerhardt, M. Hofmann, J. Yang, D. Reuter, and A. Wieck, “Spin controlled optically pumped vertical cavity surface emitting laser,” Electron. Lett. 41(5), 251–253 (2005).
[Crossref]

Hofmann, M. R.

N. C. Gerhardt, M. Y. Li, H. Jähme, H. Höpfner, T. Ackemann, and M. R. Hofmann, “Ultrafast spin-induced polarization oscillations with tunable lifetime in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 99(15), 151107 (2011).
[Crossref]

Holub, M.

M. Holub, J. Shin, S. Chakrabarti, and P. Bhattacharya, “Electrically injected spin-polarized vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 87(9), 091108 (2005).
[Crossref]

Höpfner, H.

N. C. Gerhardt, M. Y. Li, H. Jähme, H. Höpfner, T. Ackemann, and M. R. Hofmann, “Ultrafast spin-induced polarization oscillations with tunable lifetime in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 99(15), 151107 (2011).
[Crossref]

Hovel, S.

N. Gerhardt, S. Hovel, M. Hofmann, J. Yang, D. Reuter, and A. Wieck, “Enhancement of spin information with vertical cavity surface emitting lasers,” Electron. Lett. 42(2), 88–89 (2006).
[Crossref]

S. Hovel, N. Gerhardt, M. Hofmann, J. Yang, D. Reuter, and A. Wieck, “Spin controlled optically pumped vertical cavity surface emitting laser,” Electron. Lett. 41(5), 251–253 (2005).
[Crossref]

Iba, S.

S. Iba, S. Koh, K. Ikeda, and H. Kawaguchi, “Room temperature circularly polarized lasing in an optically spin injected vertical-cavity surface-emitting laser with (110) GaAs quantum wells,” Appl. Phys. Lett. 98(8), 081113 (2011).
[Crossref]

Ikeda, K.

S. Iba, S. Koh, K. Ikeda, and H. Kawaguchi, “Room temperature circularly polarized lasing in an optically spin injected vertical-cavity surface-emitting laser with (110) GaAs quantum wells,” Appl. Phys. Lett. 98(8), 081113 (2011).
[Crossref]

Jaffrès, H.

T. Fördös, K. Postava, H. Jaffrès, and J. Pištora, “Matrix approach for modeling of emission from multilayer spin-polarized light-emitting diodes and lasers,” J. Opt. 16(6), 065008 (2014).
[Crossref]

J. Frougier, G. Baili, M. Alouini, I. Sagnes, H. Jaffrès, A. Garnache, C. Deranlot, D. Dolfi, and J. M. George, “Control of light polarization using optically spin-injected vertical external cavity surface emitting lasers,” Appl. Phys. Lett. 103(25), 252402 (2013).
[Crossref]

Jähme, H.

N. C. Gerhardt, M. Y. Li, H. Jähme, H. Höpfner, T. Ackemann, and M. R. Hofmann, “Ultrafast spin-induced polarization oscillations with tunable lifetime in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 99(15), 151107 (2011).
[Crossref]

Jansen van Doorn, A. K.

M. Travagnin, M. P. van Exter, A. K. Jansen van Doorn, and J. P. Woerdman, “Erratum: Role of optical anisotropies in the polarization properties of surface emitting semiconductor lasers [phys. rev. a 54, 1647 (1996)],” Phys. Rev. A 55(6), 4641 (1997).
[Crossref]

M. Travagnin, J. P. Woerdman, A. K. Jansen van Doorn, and J. P. Woerdman, “Role of optical anisotropies in the polarization properties of surface-emitting semiconductor lasers,” Phys. Rev. A 54(2), 1647–1660 (1996).
[Crossref] [PubMed]

Jiang, X.

X. Jiang, R. Wang, R. M. Shelby, R. M. Macfarlane, S. R. Bank, J. S. Harris, and S. S. P. Parkin, “Highly Spin-Polarized Room-Temperature Tunnel Injector for Semiconductor Spintronics using MgO(100),” Phys. Rev. Lett. 94(5), 056601 (2005).
[Crossref] [PubMed]

Joly, A.

Jones, R. C.

Kawaguchi, H.

S. Iba, S. Koh, K. Ikeda, and H. Kawaguchi, “Room temperature circularly polarized lasing in an optically spin injected vertical-cavity surface-emitting laser with (110) GaAs quantum wells,” Appl. Phys. Lett. 98(8), 081113 (2011).
[Crossref]

Keim, M.

R. Fiederling, M. Keim, G. Reuscher, W. Ossau, G. Schmidt, A. Waag, and L. W. Molenkamp, “Injection and detection of a spin-polarized current in a light-emitting diode,” Nature 402(6763), 787–790 (1999).
[Crossref]

Koh, S.

S. Iba, S. Koh, K. Ikeda, and H. Kawaguchi, “Room temperature circularly polarized lasing in an optically spin injected vertical-cavity surface-emitting laser with (110) GaAs quantum wells,” Appl. Phys. Lett. 98(8), 081113 (2011).
[Crossref]

Le Floch, A.

M. Alouini, F. Bretenaker, M. Brunel, A. Le Floch, M. Vallet, and P. Thony, “Existence of two coupling constants in microchip lasers,” Opt. Lett. 25(12), 896–898 (2000).
[Crossref] [PubMed]

M. Vallet, M. Brunel, M. Alouini, F. Bretenaker, A. Le Floch, and G. P. Agrawal, “Polarization self-modulated lasers with circular eigenstates,” Appl. Phys. Lett. 74(22), 3266–3268 (1999).
[Crossref]

M. Brunel, M. Vallet, A. Le Floch, and F. Bretenaker, “Differential measurement of the coupling constant between laser eigenstates,” Appl. Phys. Lett. 70(16), 2070–2072 (1997).
[Crossref]

A. Le Floch, G. Ropars, J. M. Lenormand, and R. Le Naour, “Dynamics of Laser Eigenstates,” Phys. Rev. Lett. 52(11), 918–921 (1984).
[Crossref]

Le Naour, R.

A. Le Floch, G. Ropars, J. M. Lenormand, and R. Le Naour, “Dynamics of Laser Eigenstates,” Phys. Rev. Lett. 52(11), 918–921 (1984).
[Crossref]

Lee, G.

P. E. Faria, G. Xu, G. Lee, N. C. Gerhardt, G. M. Sipahi, and I. Zutic, “Toward high-frequency operation of spin lasers,” Phys. Rev. B 92(7), 075311 (2015).
[Crossref]

Lee, J.

E. Wasner, S. Bearden, J. Lee, and I. Žutić, “Digital operation and eye diagrams in spin-lasers,” Appl. Phys. Lett. 107(8), 082406 (2015).
[Crossref]

J. Lee, S. Bearden, E. Wasner, and I. Žutić, “Spin-lasers: From threshold reduction to large-signal analysis,” Appl. Phys. Lett. 105(4), 042411 (2014).
[Crossref]

J. Lee, W. Falls, R. Oszwaldowski, and I. Zutic, “Spin modulation in semiconductor lasers,” Appl. Phys. Lett. 97(4), 041116 (2010).
[Crossref]

Lenormand, J. M.

A. Le Floch, G. Ropars, J. M. Lenormand, and R. Le Naour, “Dynamics of Laser Eigenstates,” Phys. Rev. Lett. 52(11), 918–921 (1984).
[Crossref]

Li, M. Y.

N. C. Gerhardt, M. Y. Li, H. Jähme, H. Höpfner, T. Ackemann, and M. R. Hofmann, “Ultrafast spin-induced polarization oscillations with tunable lifetime in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 99(15), 151107 (2011).
[Crossref]

Macfarlane, R. M.

X. Jiang, R. Wang, R. M. Shelby, R. M. Macfarlane, S. R. Bank, J. S. Harris, and S. S. P. Parkin, “Highly Spin-Polarized Room-Temperature Tunnel Injector for Semiconductor Spintronics using MgO(100),” Phys. Rev. Lett. 94(5), 056601 (2005).
[Crossref] [PubMed]

McKay, A.

Miguel, M. S.

A. Gahl, S. Balle, and M. S. Miguel, “Polarization dynamics of optically pumped vcsels,” IEEE J. Quantum Electron. 35(3), 342–351 (1999).
[Crossref]

Miranda, B.-X.

Molenkamp, L. W.

R. Fiederling, M. Keim, G. Reuscher, W. Ossau, G. Schmidt, A. Waag, and L. W. Molenkamp, “Injection and detection of a spin-polarized current in a light-emitting diode,” Nature 402(6763), 787–790 (1999).
[Crossref]

Moloney, J. V.

Q. Feng, J. V. Moloney, and J. V. Moloney,“Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52(2), 1728–1739 (1995).
[Crossref] [PubMed]

Q. Feng, J. V. Moloney, and J. V. Moloney,“Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52(2), 1728–1739 (1995).
[Crossref] [PubMed]

Morvan, L.

Oestreich, M.

J. Rudolph, S. Döhrmann, D. Hägele, M. Oestreich, and W. Stolz, “Room-temperature threshold reduction in vertical-cavity surface-emitting lasers by injection of spin-polarized electrons,” Phys. Rev. Lett. 87(24), 241117 (2005).

Ortega-Quijano, N.

Ossau, W.

R. Fiederling, M. Keim, G. Reuscher, W. Ossau, G. Schmidt, A. Waag, and L. W. Molenkamp, “Injection and detection of a spin-polarized current in a light-emitting diode,” Nature 402(6763), 787–790 (1999).
[Crossref]

Oszwaldowski, R.

J. Lee, W. Falls, R. Oszwaldowski, and I. Zutic, “Spin modulation in semiconductor lasers,” Appl. Phys. Lett. 97(4), 041116 (2010).
[Crossref]

C. Gøthgen, R. Oszwałdowski, A. Petrou, and I. Žutić, “Analytical model of spin-polarized semiconductor lasers,” Appl. 93(4), 042513 (2008).

Ouvrard, A.

Pal, V.

Park, J. D.

Parkin, S. S. P.

X. Jiang, R. Wang, R. M. Shelby, R. M. Macfarlane, S. R. Bank, J. S. Harris, and S. S. P. Parkin, “Highly Spin-Polarized Room-Temperature Tunnel Injector for Semiconductor Spintronics using MgO(100),” Phys. Rev. Lett. 94(5), 056601 (2005).
[Crossref] [PubMed]

Parnet, F.

Petrou, A.

C. Gøthgen, R. Oszwałdowski, A. Petrou, and I. Žutić, “Analytical model of spin-polarized semiconductor lasers,” Appl. 93(4), 042513 (2008).

Pillet, G.

Pištora, J.

T. Fördös, K. Postava, H. Jaffrès, and J. Pištora, “Matrix approach for modeling of emission from multilayer spin-polarized light-emitting diodes and lasers,” J. Opt. 16(6), 065008 (2014).
[Crossref]

Postava, K.

T. Fördös, K. Postava, H. Jaffrès, and J. Pištora, “Matrix approach for modeling of emission from multilayer spin-polarized light-emitting diodes and lasers,” J. Opt. 16(6), 065008 (2014).
[Crossref]

Potapchuk, V.

S. De, V. Potapchuk, and F. Bretenaker, “Influence of spin-dependent carrier dynamics on the properties of a dual-frequency vertical-external-cavity surface-emitting laser,” Phys. Rev. A 90(1), 013841 (2014).
[Crossref]

Reuscher, G.

R. Fiederling, M. Keim, G. Reuscher, W. Ossau, G. Schmidt, A. Waag, and L. W. Molenkamp, “Injection and detection of a spin-polarized current in a light-emitting diode,” Nature 402(6763), 787–790 (1999).
[Crossref]

Reuter, D.

N. Gerhardt, S. Hovel, M. Hofmann, J. Yang, D. Reuter, and A. Wieck, “Enhancement of spin information with vertical cavity surface emitting lasers,” Electron. Lett. 42(2), 88–89 (2006).
[Crossref]

S. Hovel, N. Gerhardt, M. Hofmann, J. Yang, D. Reuter, and A. Wieck, “Spin controlled optically pumped vertical cavity surface emitting laser,” Electron. Lett. 41(5), 251–253 (2005).
[Crossref]

Romanini, D.

Ropars, G.

A. Le Floch, G. Ropars, J. M. Lenormand, and R. Le Naour, “Dynamics of Laser Eigenstates,” Phys. Rev. Lett. 52(11), 918–921 (1984).
[Crossref]

Rudolph, J.

J. Rudolph, S. Döhrmann, D. Hägele, M. Oestreich, and W. Stolz, “Room-temperature threshold reduction in vertical-cavity surface-emitting lasers by injection of spin-polarized electrons,” Phys. Rev. Lett. 87(24), 241117 (2005).

Sagnes, I.

Saha, D.

D. Basu, D. Saha, and P. Bhattacharya, “Optical polarization modulation and gain anisotropy in an electrically injected spin laser,” Phys. Rev. Lett. 102(9), 093904 (2009).
[Crossref] [PubMed]

Samarth, N.

S. A. Crooker, D. D. Awschalom, J. J. Baumberg, F. Flack, and N. Samarth, “Optical spin resonance and transverse spin relaxation in magnetic semiconductor quantum wells,” Phys. Rev. B 56(12), 7574–7588 (1997).
[Crossref]

Schmidt, G.

R. Fiederling, M. Keim, G. Reuscher, W. Ossau, G. Schmidt, A. Waag, and L. W. Molenkamp, “Injection and detection of a spin-polarized current in a light-emitting diode,” Nature 402(6763), 787–790 (1999).
[Crossref]

Shelby, R. M.

X. Jiang, R. Wang, R. M. Shelby, R. M. Macfarlane, S. R. Bank, J. S. Harris, and S. S. P. Parkin, “Highly Spin-Polarized Room-Temperature Tunnel Injector for Semiconductor Spintronics using MgO(100),” Phys. Rev. Lett. 94(5), 056601 (2005).
[Crossref] [PubMed]

Shin, J.

M. Holub, J. Shin, S. Chakrabarti, and P. Bhattacharya, “Electrically injected spin-polarized vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 87(9), 091108 (2005).
[Crossref]

Sipahi, G. M.

P. E. Faria, G. Xu, G. Lee, N. C. Gerhardt, G. M. Sipahi, and I. Zutic, “Toward high-frequency operation of spin lasers,” Phys. Rev. B 92(7), 075311 (2015).
[Crossref]

Sogawa, T.

H. Ando, T. Sogawa, and H. Gotoh, “Photon-spin controlled lasing oscillation in surface-emitting lasers,” Appl. Phys. Lett. 73(5), 566–568 (1998).
[Crossref]

Stolz, W.

J. Rudolph, S. Döhrmann, D. Hägele, M. Oestreich, and W. Stolz, “Room-temperature threshold reduction in vertical-cavity surface-emitting lasers by injection of spin-polarized electrons,” Phys. Rev. Lett. 87(24), 241117 (2005).

Thony, P.

Travagnin, M.

M. Travagnin, M. P. van Exter, A. K. Jansen van Doorn, and J. P. Woerdman, “Erratum: Role of optical anisotropies in the polarization properties of surface emitting semiconductor lasers [phys. rev. a 54, 1647 (1996)],” Phys. Rev. A 55(6), 4641 (1997).
[Crossref]

M. Travagnin, J. P. Woerdman, A. K. Jansen van Doorn, and J. P. Woerdman, “Role of optical anisotropies in the polarization properties of surface-emitting semiconductor lasers,” Phys. Rev. A 54(2), 1647–1660 (1996).
[Crossref] [PubMed]

Trofimoff, P.

Vallet, M.

M. Alouini, F. Bretenaker, M. Brunel, A. Le Floch, M. Vallet, and P. Thony, “Existence of two coupling constants in microchip lasers,” Opt. Lett. 25(12), 896–898 (2000).
[Crossref] [PubMed]

M. Vallet, M. Brunel, M. Alouini, F. Bretenaker, A. Le Floch, and G. P. Agrawal, “Polarization self-modulated lasers with circular eigenstates,” Appl. Phys. Lett. 74(22), 3266–3268 (1999).
[Crossref]

M. Brunel, M. Vallet, A. Le Floch, and F. Bretenaker, “Differential measurement of the coupling constant between laser eigenstates,” Appl. Phys. Lett. 70(16), 2070–2072 (1997).
[Crossref]

van Exter, M. P.

M. Travagnin, M. P. van Exter, A. K. Jansen van Doorn, and J. P. Woerdman, “Erratum: Role of optical anisotropies in the polarization properties of surface emitting semiconductor lasers [phys. rev. a 54, 1647 (1996)],” Phys. Rev. A 55(6), 4641 (1997).
[Crossref]

Waag, A.

R. Fiederling, M. Keim, G. Reuscher, W. Ossau, G. Schmidt, A. Waag, and L. W. Molenkamp, “Injection and detection of a spin-polarized current in a light-emitting diode,” Nature 402(6763), 787–790 (1999).
[Crossref]

Wang, R.

X. Jiang, R. Wang, R. M. Shelby, R. M. Macfarlane, S. R. Bank, J. S. Harris, and S. S. P. Parkin, “Highly Spin-Polarized Room-Temperature Tunnel Injector for Semiconductor Spintronics using MgO(100),” Phys. Rev. Lett. 94(5), 056601 (2005).
[Crossref] [PubMed]

Wasner, E.

E. Wasner, S. Bearden, J. Lee, and I. Žutić, “Digital operation and eye diagrams in spin-lasers,” Appl. Phys. Lett. 107(8), 082406 (2015).
[Crossref]

J. Lee, S. Bearden, E. Wasner, and I. Žutić, “Spin-lasers: From threshold reduction to large-signal analysis,” Appl. Phys. Lett. 105(4), 042411 (2014).
[Crossref]

Wieck, A.

N. Gerhardt, S. Hovel, M. Hofmann, J. Yang, D. Reuter, and A. Wieck, “Enhancement of spin information with vertical cavity surface emitting lasers,” Electron. Lett. 42(2), 88–89 (2006).
[Crossref]

S. Hovel, N. Gerhardt, M. Hofmann, J. Yang, D. Reuter, and A. Wieck, “Spin controlled optically pumped vertical cavity surface emitting laser,” Electron. Lett. 41(5), 251–253 (2005).
[Crossref]

Willemsen, M. B.

M. B. Willemsen, J. P. Woerdman, and J. P. Woerdman, “Anatomy of a Polarization Switch of a Vertical-Cavity Semiconductor Laser,” Phys. Rev. Lett. 84(19), 4337–4340 (2000).
[Crossref] [PubMed]

Woerdman, J. P.

M. B. Willemsen, J. P. Woerdman, and J. P. Woerdman, “Anatomy of a Polarization Switch of a Vertical-Cavity Semiconductor Laser,” Phys. Rev. Lett. 84(19), 4337–4340 (2000).
[Crossref] [PubMed]

M. B. Willemsen, J. P. Woerdman, and J. P. Woerdman, “Anatomy of a Polarization Switch of a Vertical-Cavity Semiconductor Laser,” Phys. Rev. Lett. 84(19), 4337–4340 (2000).
[Crossref] [PubMed]

M. Travagnin, M. P. van Exter, A. K. Jansen van Doorn, and J. P. Woerdman, “Erratum: Role of optical anisotropies in the polarization properties of surface emitting semiconductor lasers [phys. rev. a 54, 1647 (1996)],” Phys. Rev. A 55(6), 4641 (1997).
[Crossref]

M. Travagnin, J. P. Woerdman, A. K. Jansen van Doorn, and J. P. Woerdman, “Role of optical anisotropies in the polarization properties of surface-emitting semiconductor lasers,” Phys. Rev. A 54(2), 1647–1660 (1996).
[Crossref] [PubMed]

M. Travagnin, J. P. Woerdman, A. K. Jansen van Doorn, and J. P. Woerdman, “Role of optical anisotropies in the polarization properties of surface-emitting semiconductor lasers,” Phys. Rev. A 54(2), 1647–1660 (1996).
[Crossref] [PubMed]

Xu, G.

P. E. Faria, G. Xu, G. Lee, N. C. Gerhardt, G. M. Sipahi, and I. Zutic, “Toward high-frequency operation of spin lasers,” Phys. Rev. B 92(7), 075311 (2015).
[Crossref]

Yang, J.

N. Gerhardt, S. Hovel, M. Hofmann, J. Yang, D. Reuter, and A. Wieck, “Enhancement of spin information with vertical cavity surface emitting lasers,” Electron. Lett. 42(2), 88–89 (2006).
[Crossref]

S. Hovel, N. Gerhardt, M. Hofmann, J. Yang, D. Reuter, and A. Wieck, “Spin controlled optically pumped vertical cavity surface emitting laser,” Electron. Lett. 41(5), 251–253 (2005).
[Crossref]

Zutic, I.

P. E. Faria, G. Xu, G. Lee, N. C. Gerhardt, G. M. Sipahi, and I. Zutic, “Toward high-frequency operation of spin lasers,” Phys. Rev. B 92(7), 075311 (2015).
[Crossref]

J. Lee, W. Falls, R. Oszwaldowski, and I. Zutic, “Spin modulation in semiconductor lasers,” Appl. Phys. Lett. 97(4), 041116 (2010).
[Crossref]

Žutic, I.

E. Wasner, S. Bearden, J. Lee, and I. Žutić, “Digital operation and eye diagrams in spin-lasers,” Appl. Phys. Lett. 107(8), 082406 (2015).
[Crossref]

J. Lee, S. Bearden, E. Wasner, and I. Žutić, “Spin-lasers: From threshold reduction to large-signal analysis,” Appl. Phys. Lett. 105(4), 042411 (2014).
[Crossref]

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Figures (9)

Fig. 1
Fig. 1 Schematic representation of the cavity.
Fig. 2
Fig. 2 Evolution of the frequency splitting between the two polarization eigenstates as a function of the ratio r between the circular dichroism of gain ΔGN and the linear birefringence of phase γ.
Fig. 3
Fig. 3 Ratio of the transverse components of the filed (left-hand side) and polarization angle (right-hand side) for the two possible eigenstates as a function of the ratio r between the circular dichroism of gain and the linear birefringence of phase.
Fig. 4
Fig. 4 Evolution of the two eigenpolarizations as a function of the ratio r between the circular dichroism of gain Δ G N and the linear birefringence of phase γ.
Fig. 5
Fig. 5 Evolution of the frequency splitting and the two eigenpolarizations as a function of the ratio r between the circular dichroism of gain Δ G N and the linear birefringence of phase γ.
Fig. 6
Fig. 6 Schematic representation of the cavity including a Faraday rotator.
Fig. 7
Fig. 7 Ratio of the transverse components of the two eigenstates with respect to the linear birefringence in the active medium.
Fig. 8
Fig. 8 (left) Evolution of the ellipticity and (right) Frequency difference between the two laser eigenstates as a function of the linear birefringence in the active medium.
Fig. 9
Fig. 9 Evolution of the intensities of the two modes as a function of the normalized circular dichroism of gain for three values of the nonlinear coupling constant: 0, 0.5 and 0.9.

Equations (48)

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[ J Δϕ ]= e i 2π λ 0 n ¯ l [ e i γ 2 0 0 e i γ 2 ],
γ= 2π λ 0 ( n e n 0 )l.
[ J ΔG ]=[ G ¯ i 2 ΔG i 2 ΔG G ¯ ].
[ J M ]= R [ 1 0 0 1 ].
[ J L ]= e iϕ [ J Δϕ ][ J G ][ J Δϕ ][ J M ].
[ J L ]= R G ¯ e 2ik( n ma e ma + n ¯ l+L) [ e iγ i 2 Δ G N i 2 Δ G N e iγ ],
[ J L ] E =λ E .
( λcos( γ ) ) 2 = 1 4 Δ G N 2 sin 2 ( γ ).
λ= 1 R G ¯ e 2ik L eff .
E y E x =0or E y E x .
Δν= ν + ν = cγ π L eff .
E y E x =±i= e ±i π 2 .
G ± = 1 R ( 1± 1 2 Δ G N ) .
λ ± =cos( γ )±i sin 2 ( γ ) 1 4 Δ G N 2 .
Δν= ν + ν = c π L eff arctan( tan( γ ) 1 ( Δ G N 2sin( γ ) ) 2 ).
E y E x = 2sin( γ ) Δ G N ( 1± 1 ( Δ G N 2sin( γ ) ) 2 ).
E y E x = 1 r ( 1± 1 r 2 ).
λ ± =cos( γ )± 1 4 Δ G N 2 sin 2 ( γ ) .
E y E x =2 e iγ λ ± iΔ G N ,
| E y E x |=1,
Φ ± =arg( E y E x )=arctan ( r 2 1 ) 1 2 .
G ± = R 1 ( cos( γ )±sin( γ ) r 2 1 ) 1 .
[ J F ]= R [ cosθ sinθ sinθ cosθ ],
[ J F ]= 1 2 [ 1 1 1 1 ].
[ J L ]= e iϕ [ J F ][ J Δϕ ][ J G ][ J Δϕ ][ J F ][ J M ].
ϕ=2k( n ma e ma + n ¯ l+ n F e F +L)=2k L eff ,
λ ± = e i π 2 ( 2Δ G N ).
λ ± =( 2±Δ G N ) e i π 2 .
G ± = 1 R ( 1± 1 2 Δ G N ) 1 ,
v ± =( q 1 4 ) c L eff ,
Δ v ± =| v + v |= c 4 L eff .
E x E y | ± =itan( γ )±i tan 2 ( γ )+1 ,
E x E y | ± =±i.
lim γ π 2 E x E y | + =
lim γ π 2 E x E y | =0.
I ˙ R = α R β R I R θ RL I L ,
I ˙ L = α L β L I L θ LR I R .
β R = β L =β,
θ RL = θ LR =θ,
α R =α+ δα/2 ,
α L =α δα/2 .
I R = α( βθ )+ δα 2 ( β+θ ) β 2 θ 2 ,
I L = α( βθ ) δα 2 ( β+θ ) β 2 θ 2 .
C= θ RL θ LR β R β L θ 2 β 2 .
I R = α β ( 1 C )+ δα 2α ( 1+ C ) 1C ,
I L = α β ( 1 C ) δα 2α ( 1+ C ) 1C .
I R = α β ( 1+ δα 2α ),
I L = α β ( 1 δα 2α ),

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