Abstract

We measure the coupling constant between the two perpendicularly polarized eigenstates of a two-frequency Vertical External Cavity Surface Emitting Laser (VECSEL). This measurement is performed for different values of the transverse spatial separation between the two perpendicularly polarized modes. The consequences of these measurements on the two-frequency operation of such class-A semiconductor lasers are discussed.

© 2010 Optical Society of America

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  1. G. Pillet, L. Morvan, M. Brunel, F. Bretenaker, D. Dolfi, M. Vallet, J.-P. Huignard, and A. Le Floch, "Dualfrequency laser at 1.5 μm for optical distribution and generation of high-purity microwave signals," J. Lightwave Technol. 26, 2764-2773 (2008).
    [CrossRef]
  2. R. Czarny, M. Alouini, C. Larat, M. Krakowski, and D. Dolfi, "THz-dual-frequency Yb3+:KGd(WO4)2 laser for continuous-wave THz generation through photomixing," Electron. Lett. 40, 942-943 (2004).
    [CrossRef]
  3. L. Morvan, N. D. Lai, D. Dolfi, J.-P. Huignard, M. Brunel, F. Bretenaker, and A. Le Floch, "Building blocks for a two-frequency laser lidar-radar: a preliminary study," Appl. Opt. 41, 5702-5712 (2002).
    [CrossRef] [PubMed]
  4. K. Otsuka, P. Mandel, S. Bielawski, D. Derozier, and P. Glorieux, "Alternate time scales in multimode lasers," Phys. Rev. A 46, 1692-1695 (1992).
    [CrossRef] [PubMed]
  5. M. Brunel, A. Amon, and M. Vallet, "Dual-polarization microchip laser at 1.53 μm," Opt. Lett. 30, 2418-2420 (2005).
    [CrossRef] [PubMed]
  6. M. Brunel, F. Bretenaker, S. Blanc, V. Crozatier, J. Brisset, T. Merlet, and A. Poezevara, "High-spectral purity RF beat note generated by a two-frequency solid-state laser in a dual thermooptic and electrooptic phase-locked loop," IEEE Photon. Technol. Lett. 16, 870-872 (2004).
    [CrossRef]
  7. L. Morvan, D. Dolfi, J.-P. Huignard, S. Blanc, M. Brunel, M. Vallet, F. Bretenaker, and A. Le Floch, "Dualfrequency laser at 1.53 μm for generating high-purity optically carried microwave signals up to 20 GHz," in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2004), paper CTuL5.
    [PubMed]
  8. G. Baili, M. Alouini, D. Dolfi, F. Bretenaker, I. Sagnes, and A. Garnache, "Shot-noise limited operation of a monomode high cavity finesse semiconductor laser for microwave photonics applications," Opt. Lett. 32, 650-652 (2007).
    [CrossRef] [PubMed]
  9. G. Baili, F. Bretenaker,M. Alouini, D. Dolfi, and I. Sagnes, "Experimental investigation and analytical modeling of excess intensity noise in semiconductor class-A lasers," J. Lightwave Technol. 26, 952-961 (2008).
    [CrossRef]
  10. 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, 3421-3423 (2009).
    [CrossRef] [PubMed]
  11. M. SargentIII, M. O. Scully, and W. E. Lamb, Jr., Laser Physics (Addison-Wesley, 1974).
  12. M. M.-Tehrani and L. Mandel, "Coherence theory of the ring laser," Phys. Rev. A 17, 677-693 (1978).
    [CrossRef]
  13. A. Laurain, M. Myara, G. Beaudoin, I. Sagnes, and A. Garnache, "High power single-frequency continuouslytunable compact extended-cavity semiconductor laser," Opt. Express 17, 9503-9508 (2009).
    [CrossRef]
  14. A. E. Siegman, Lasers (University Science Books, 1986), pp. 992-999.
  15. M. Brunel, M. Vallet, A. Le Floch, and F. Bretenaker, "Differential measurement of the coupling constant between laser eigenstates," Appl. Phys. Lett. 70, 2070-2072 (1997).
    [CrossRef]
  16. 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, 896-898 (2000).
    [CrossRef]
  17. A. McKay, J. M. Dawes, and J.-D. Park, "Polarisation-mode coupling in (100)-cut Nd:YAG," Opt. Express 15, 16342-16347 (2007).
    [CrossRef]
  18. S. Schwartz, G. Feugnet, M. Rebut, F. Bretenaker, and J.-P. Pocholle, "Orientation of Nd3+ dipoles in yttrium aluminum garnet: Experiment and model," Phys. Rev. A 79, 063814 (2009).
    [CrossRef]
  19. J. Talghader and J. S. Smith, "Thermal dependence of the refractive index of GaAs and AlAs measured using semiconductor multilayer optical cavities," Appl. Phys. Lett. 66, 335-337 (1995).
    [CrossRef]
  20. M. San Miguel, Q. Feng, and J. V. Moloney, "Light-polarization dynamics in surface-emitting semiconductor lasers," Phys. Rev. A 52, 1728-1739 (1995).
    [CrossRef] [PubMed]
  21. M. P. van Exter, R. F. M. Hendriks, and J. P. Woerdman, "Physical insight into the polarization dynamics of semiconductor vertical-cavity lasers," Phys. Rev. A 57, 2080-2090 (1998).
    [CrossRef]
  22. D. Burak, J. V. Moloney, and R. Binder, "Microscopic theory of polarization properties of optically anisotropic vertical-cavity surface-emitting lasers," Phys. Rev. A 61, 053809 (2000).
    [CrossRef]

2009

2008

2007

2005

2004

M. Brunel, F. Bretenaker, S. Blanc, V. Crozatier, J. Brisset, T. Merlet, and A. Poezevara, "High-spectral purity RF beat note generated by a two-frequency solid-state laser in a dual thermooptic and electrooptic phase-locked loop," IEEE Photon. Technol. Lett. 16, 870-872 (2004).
[CrossRef]

R. Czarny, M. Alouini, C. Larat, M. Krakowski, and D. Dolfi, "THz-dual-frequency Yb3+:KGd(WO4)2 laser for continuous-wave THz generation through photomixing," Electron. Lett. 40, 942-943 (2004).
[CrossRef]

2002

2000

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, 896-898 (2000).
[CrossRef]

D. Burak, J. V. Moloney, and R. Binder, "Microscopic theory of polarization properties of optically anisotropic vertical-cavity surface-emitting lasers," Phys. Rev. A 61, 053809 (2000).
[CrossRef]

1998

M. P. van Exter, R. F. M. Hendriks, and J. P. Woerdman, "Physical insight into the polarization dynamics of semiconductor vertical-cavity lasers," Phys. Rev. A 57, 2080-2090 (1998).
[CrossRef]

1997

M. Brunel, M. Vallet, A. Le Floch, and F. Bretenaker, "Differential measurement of the coupling constant between laser eigenstates," Appl. Phys. Lett. 70, 2070-2072 (1997).
[CrossRef]

1995

J. Talghader and J. S. Smith, "Thermal dependence of the refractive index of GaAs and AlAs measured using semiconductor multilayer optical cavities," Appl. Phys. Lett. 66, 335-337 (1995).
[CrossRef]

M. San Miguel, Q. Feng, and J. V. Moloney, "Light-polarization dynamics in surface-emitting semiconductor lasers," Phys. Rev. A 52, 1728-1739 (1995).
[CrossRef] [PubMed]

1992

K. Otsuka, P. Mandel, S. Bielawski, D. Derozier, and P. Glorieux, "Alternate time scales in multimode lasers," Phys. Rev. A 46, 1692-1695 (1992).
[CrossRef] [PubMed]

1978

M. M.-Tehrani and L. Mandel, "Coherence theory of the ring laser," Phys. Rev. A 17, 677-693 (1978).
[CrossRef]

Alouini, M.

Amon, A.

Baili, G.

Beaudoin, G.

Bielawski, S.

K. Otsuka, P. Mandel, S. Bielawski, D. Derozier, and P. Glorieux, "Alternate time scales in multimode lasers," Phys. Rev. A 46, 1692-1695 (1992).
[CrossRef] [PubMed]

Binder, R.

D. Burak, J. V. Moloney, and R. Binder, "Microscopic theory of polarization properties of optically anisotropic vertical-cavity surface-emitting lasers," Phys. Rev. A 61, 053809 (2000).
[CrossRef]

Blanc, S.

M. Brunel, F. Bretenaker, S. Blanc, V. Crozatier, J. Brisset, T. Merlet, and A. Poezevara, "High-spectral purity RF beat note generated by a two-frequency solid-state laser in a dual thermooptic and electrooptic phase-locked loop," IEEE Photon. Technol. Lett. 16, 870-872 (2004).
[CrossRef]

Bretenaker, F.

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, 3421-3423 (2009).
[CrossRef] [PubMed]

S. Schwartz, G. Feugnet, M. Rebut, F. Bretenaker, and J.-P. Pocholle, "Orientation of Nd3+ dipoles in yttrium aluminum garnet: Experiment and model," Phys. Rev. A 79, 063814 (2009).
[CrossRef]

G. Baili, F. Bretenaker,M. Alouini, D. Dolfi, and I. Sagnes, "Experimental investigation and analytical modeling of excess intensity noise in semiconductor class-A lasers," J. Lightwave Technol. 26, 952-961 (2008).
[CrossRef]

G. Pillet, L. Morvan, M. Brunel, F. Bretenaker, D. Dolfi, M. Vallet, J.-P. Huignard, and A. Le Floch, "Dualfrequency laser at 1.5 μm for optical distribution and generation of high-purity microwave signals," J. Lightwave Technol. 26, 2764-2773 (2008).
[CrossRef]

G. Baili, M. Alouini, D. Dolfi, F. Bretenaker, I. Sagnes, and A. Garnache, "Shot-noise limited operation of a monomode high cavity finesse semiconductor laser for microwave photonics applications," Opt. Lett. 32, 650-652 (2007).
[CrossRef] [PubMed]

M. Brunel, F. Bretenaker, S. Blanc, V. Crozatier, J. Brisset, T. Merlet, and A. Poezevara, "High-spectral purity RF beat note generated by a two-frequency solid-state laser in a dual thermooptic and electrooptic phase-locked loop," IEEE Photon. Technol. Lett. 16, 870-872 (2004).
[CrossRef]

L. Morvan, N. D. Lai, D. Dolfi, J.-P. Huignard, M. Brunel, F. Bretenaker, and A. Le Floch, "Building blocks for a two-frequency laser lidar-radar: a preliminary study," Appl. Opt. 41, 5702-5712 (2002).
[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, 896-898 (2000).
[CrossRef]

M. Brunel, M. Vallet, A. Le Floch, and F. Bretenaker, "Differential measurement of the coupling constant between laser eigenstates," Appl. Phys. Lett. 70, 2070-2072 (1997).
[CrossRef]

Brisset, J.

M. Brunel, F. Bretenaker, S. Blanc, V. Crozatier, J. Brisset, T. Merlet, and A. Poezevara, "High-spectral purity RF beat note generated by a two-frequency solid-state laser in a dual thermooptic and electrooptic phase-locked loop," IEEE Photon. Technol. Lett. 16, 870-872 (2004).
[CrossRef]

Brunel, M.

Burak, D.

D. Burak, J. V. Moloney, and R. Binder, "Microscopic theory of polarization properties of optically anisotropic vertical-cavity surface-emitting lasers," Phys. Rev. A 61, 053809 (2000).
[CrossRef]

Crozatier, V.

M. Brunel, F. Bretenaker, S. Blanc, V. Crozatier, J. Brisset, T. Merlet, and A. Poezevara, "High-spectral purity RF beat note generated by a two-frequency solid-state laser in a dual thermooptic and electrooptic phase-locked loop," IEEE Photon. Technol. Lett. 16, 870-872 (2004).
[CrossRef]

Czarny, R.

R. Czarny, M. Alouini, C. Larat, M. Krakowski, and D. Dolfi, "THz-dual-frequency Yb3+:KGd(WO4)2 laser for continuous-wave THz generation through photomixing," Electron. Lett. 40, 942-943 (2004).
[CrossRef]

Dawes, J. M.

Derozier, D.

K. Otsuka, P. Mandel, S. Bielawski, D. Derozier, and P. Glorieux, "Alternate time scales in multimode lasers," Phys. Rev. A 46, 1692-1695 (1992).
[CrossRef] [PubMed]

Dolfi, D.

Feng, Q.

M. San Miguel, Q. Feng, and J. V. Moloney, "Light-polarization dynamics in surface-emitting semiconductor lasers," Phys. Rev. A 52, 1728-1739 (1995).
[CrossRef] [PubMed]

Feugnet, G.

S. Schwartz, G. Feugnet, M. Rebut, F. Bretenaker, and J.-P. Pocholle, "Orientation of Nd3+ dipoles in yttrium aluminum garnet: Experiment and model," Phys. Rev. A 79, 063814 (2009).
[CrossRef]

Garnache, A.

Glorieux, P.

K. Otsuka, P. Mandel, S. Bielawski, D. Derozier, and P. Glorieux, "Alternate time scales in multimode lasers," Phys. Rev. A 46, 1692-1695 (1992).
[CrossRef] [PubMed]

Hendriks, R. F. M.

M. P. van Exter, R. F. M. Hendriks, and J. P. Woerdman, "Physical insight into the polarization dynamics of semiconductor vertical-cavity lasers," Phys. Rev. A 57, 2080-2090 (1998).
[CrossRef]

Huignard, J.-P.

Krakowski, M.

R. Czarny, M. Alouini, C. Larat, M. Krakowski, and D. Dolfi, "THz-dual-frequency Yb3+:KGd(WO4)2 laser for continuous-wave THz generation through photomixing," Electron. Lett. 40, 942-943 (2004).
[CrossRef]

Lai, N. D.

Larat, C.

R. Czarny, M. Alouini, C. Larat, M. Krakowski, and D. Dolfi, "THz-dual-frequency Yb3+:KGd(WO4)2 laser for continuous-wave THz generation through photomixing," Electron. Lett. 40, 942-943 (2004).
[CrossRef]

Laurain, A.

Le Floch, A.

Mandel, P.

K. Otsuka, P. Mandel, S. Bielawski, D. Derozier, and P. Glorieux, "Alternate time scales in multimode lasers," Phys. Rev. A 46, 1692-1695 (1992).
[CrossRef] [PubMed]

McKay, A.

Merlet, T.

M. Brunel, F. Bretenaker, S. Blanc, V. Crozatier, J. Brisset, T. Merlet, and A. Poezevara, "High-spectral purity RF beat note generated by a two-frequency solid-state laser in a dual thermooptic and electrooptic phase-locked loop," IEEE Photon. Technol. Lett. 16, 870-872 (2004).
[CrossRef]

Moloney, J. V.

D. Burak, J. V. Moloney, and R. Binder, "Microscopic theory of polarization properties of optically anisotropic vertical-cavity surface-emitting lasers," Phys. Rev. A 61, 053809 (2000).
[CrossRef]

M. San Miguel, Q. Feng, and J. V. Moloney, "Light-polarization dynamics in surface-emitting semiconductor lasers," Phys. Rev. A 52, 1728-1739 (1995).
[CrossRef] [PubMed]

Morvan, L.

Myara, M.

Otsuka, K.

K. Otsuka, P. Mandel, S. Bielawski, D. Derozier, and P. Glorieux, "Alternate time scales in multimode lasers," Phys. Rev. A 46, 1692-1695 (1992).
[CrossRef] [PubMed]

Park, J.-D.

Pillet, G.

Pocholle, J.-P.

S. Schwartz, G. Feugnet, M. Rebut, F. Bretenaker, and J.-P. Pocholle, "Orientation of Nd3+ dipoles in yttrium aluminum garnet: Experiment and model," Phys. Rev. A 79, 063814 (2009).
[CrossRef]

Poezevara, A.

M. Brunel, F. Bretenaker, S. Blanc, V. Crozatier, J. Brisset, T. Merlet, and A. Poezevara, "High-spectral purity RF beat note generated by a two-frequency solid-state laser in a dual thermooptic and electrooptic phase-locked loop," IEEE Photon. Technol. Lett. 16, 870-872 (2004).
[CrossRef]

Rebut, M.

S. Schwartz, G. Feugnet, M. Rebut, F. Bretenaker, and J.-P. Pocholle, "Orientation of Nd3+ dipoles in yttrium aluminum garnet: Experiment and model," Phys. Rev. A 79, 063814 (2009).
[CrossRef]

Sagnes, I.

San Miguel, M.

M. San Miguel, Q. Feng, and J. V. Moloney, "Light-polarization dynamics in surface-emitting semiconductor lasers," Phys. Rev. A 52, 1728-1739 (1995).
[CrossRef] [PubMed]

Schwartz, S.

S. Schwartz, G. Feugnet, M. Rebut, F. Bretenaker, and J.-P. Pocholle, "Orientation of Nd3+ dipoles in yttrium aluminum garnet: Experiment and model," Phys. Rev. A 79, 063814 (2009).
[CrossRef]

Smith, J. S.

J. Talghader and J. S. Smith, "Thermal dependence of the refractive index of GaAs and AlAs measured using semiconductor multilayer optical cavities," Appl. Phys. Lett. 66, 335-337 (1995).
[CrossRef]

Talghader, J.

J. Talghader and J. S. Smith, "Thermal dependence of the refractive index of GaAs and AlAs measured using semiconductor multilayer optical cavities," Appl. Phys. Lett. 66, 335-337 (1995).
[CrossRef]

Thony, P.

Vallet, M.

van Exter, M. P.

M. P. van Exter, R. F. M. Hendriks, and J. P. Woerdman, "Physical insight into the polarization dynamics of semiconductor vertical-cavity lasers," Phys. Rev. A 57, 2080-2090 (1998).
[CrossRef]

Woerdman, J. P.

M. P. van Exter, R. F. M. Hendriks, and J. P. Woerdman, "Physical insight into the polarization dynamics of semiconductor vertical-cavity lasers," Phys. Rev. A 57, 2080-2090 (1998).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

M. Brunel, M. Vallet, A. Le Floch, and F. Bretenaker, "Differential measurement of the coupling constant between laser eigenstates," Appl. Phys. Lett. 70, 2070-2072 (1997).
[CrossRef]

J. Talghader and J. S. Smith, "Thermal dependence of the refractive index of GaAs and AlAs measured using semiconductor multilayer optical cavities," Appl. Phys. Lett. 66, 335-337 (1995).
[CrossRef]

Electron. Lett.

R. Czarny, M. Alouini, C. Larat, M. Krakowski, and D. Dolfi, "THz-dual-frequency Yb3+:KGd(WO4)2 laser for continuous-wave THz generation through photomixing," Electron. Lett. 40, 942-943 (2004).
[CrossRef]

IEEE Photon. Technol. Lett.

M. Brunel, F. Bretenaker, S. Blanc, V. Crozatier, J. Brisset, T. Merlet, and A. Poezevara, "High-spectral purity RF beat note generated by a two-frequency solid-state laser in a dual thermooptic and electrooptic phase-locked loop," IEEE Photon. Technol. Lett. 16, 870-872 (2004).
[CrossRef]

J. Lightwave Technol.

Opt. Express

Opt. Lett.

Phys. Rev. A

K. Otsuka, P. Mandel, S. Bielawski, D. Derozier, and P. Glorieux, "Alternate time scales in multimode lasers," Phys. Rev. A 46, 1692-1695 (1992).
[CrossRef] [PubMed]

S. Schwartz, G. Feugnet, M. Rebut, F. Bretenaker, and J.-P. Pocholle, "Orientation of Nd3+ dipoles in yttrium aluminum garnet: Experiment and model," Phys. Rev. A 79, 063814 (2009).
[CrossRef]

M. San Miguel, Q. Feng, and J. V. Moloney, "Light-polarization dynamics in surface-emitting semiconductor lasers," Phys. Rev. A 52, 1728-1739 (1995).
[CrossRef] [PubMed]

M. P. van Exter, R. F. M. Hendriks, and J. P. Woerdman, "Physical insight into the polarization dynamics of semiconductor vertical-cavity lasers," Phys. Rev. A 57, 2080-2090 (1998).
[CrossRef]

D. Burak, J. V. Moloney, and R. Binder, "Microscopic theory of polarization properties of optically anisotropic vertical-cavity surface-emitting lasers," Phys. Rev. A 61, 053809 (2000).
[CrossRef]

M. M.-Tehrani and L. Mandel, "Coherence theory of the ring laser," Phys. Rev. A 17, 677-693 (1978).
[CrossRef]

Other

M. SargentIII, M. O. Scully, and W. E. Lamb, Jr., Laser Physics (Addison-Wesley, 1974).

A. E. Siegman, Lasers (University Science Books, 1986), pp. 992-999.

L. Morvan, D. Dolfi, J.-P. Huignard, S. Blanc, M. Brunel, M. Vallet, F. Bretenaker, and A. Le Floch, "Dualfrequency laser at 1.53 μm for generating high-purity optically carried microwave signals up to 20 GHz," in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2004), paper CTuL5.
[PubMed]

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Figures (4)

Fig. 1.
Fig. 1.

Experimental setup. BC: birefringent crystal; HWP: half-wave plate; M: cavity mirror; E: étalon; FPI: Fabry-Perot interferometer. PBS: polarization beam-splitter; BS: beam splitter; L: lens; D: detector; OI: optical isolator; OSA: optical spectrum analyzer.

Fig. 2.
Fig. 2.

Experimental results for a spatial separation d = 20 μm. (a) Evolution of the powers of the ordinary and extraordinary modes when the losses of the ordinary mode are modulated at 227 Hz. (b) Same as (a) when the losses of the extraordinary mode are modulated.

Fig. 3.
Fig. 3.

Same as Fig. 2 for d = 50 μm.

Fig. 4.
Fig. 4.

Evolution of the coupling constant C versus spatial separation d. The filled circles are the measurements and the full lines are given by Eq. (12) with C 0 = 0.8 and w 0 = 41 μm (full red line), C 0 = 0.75 and w 0 = 50 μm (dashed green line), and C 0 = 0.71 and w 0 = 60 μm (dot-dashed blue line)

Equations (12)

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

d I o d t = I o τ o [ 1 + r o 1 + ( I o + ξ oe I e ) / I sat ] ,
d I e d t = I e τ e [ 1 + r e 1 + ( I e + ξ eo I o ) / I sat ] ,
I o = I sat ( r o 1 ) ξ oe ( r e 1 ) 1 C ,
I e = I sat ( r e 1 ) ξ eo ( r o 1 ) 1 C ,
C = ξ oe ξ eo
ξ eo = I e / r o I o / r o ,
ξ eo = I o / r e I e / r e .
C d = 20 μ m = ξ oe ξ eo = 0.64 .
C d = 50 μ m = ξ oe ξ eo = 0.18 .
C d = 100 μ m 0 .
C = C 0 I 1 x y I 2 x y d x d y ( I 1 2 x y d x d y I 1 2 x y d x d y ) 1 / 2 ,
C = C 0 e d 2 / w 0 2 .

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