Abstract

Light produced by most natural and artificial sources is unpolarized or partially polarized. At any instant of time, however, such random light can be regarded as fully polarized, but the polarization state may vary drastically within short time intervals. This rate of change is another attribute that separates one unpolarized beam from another. Here, we study such polarization dynamics and, for the first time to our knowledge, measure the characteristic time, called the polarization time, in which the instantaneous polarization state stays essentially unaltered. The technique employs a polarization-sensitive Michelson interferometer and two-photon absorption detection valid for electromagnetic light, yielding superior femtosecond time resolution. We analyze two unpolarized light sources: amplified spontaneous emission from a fiber amplifier and a dual-wavelength laser source. The characterization of polarization dynamics can have significant applications in optical sensing, polarimetry, telecommunication, and astronomy, as well as in quantum and atom optics.

© 2017 Optical Society of America

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References

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    [Crossref]

2015 (2)

D. Colas, L. Dominici, S. Donati, A. A. Pervishko, T. C. H. Liew, I. A. Shelykh, D. Ballarini, M. de Giorgi, A. Bramati, G. Gigli, E. del Valle, F. P. Laussy, A. V. Kavokin, and D. Sanvitto, “Polarization shaping of Poincaré beams by polariton oscillations,” Light: Sci. Appl. 4, e350 (2015).
[Crossref]

A. Shevchenko, M. Roussey, A. T. Friberg, and T. Setälä, “Ultrashort coherence times in partially polarized stationary optical beams measured by two-photon absorption,” Opt. Express 23, 31274–31285 (2015).
[Crossref]

2013 (1)

M. Virte, K. Panajotov, H. Thienpoint, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7, 60–65 (2013).
[Crossref]

2012 (2)

L. Z. Liu, K. O’Keeffe, and S. M. Hooker, “Quasi-phase-matching of high-order-harmonic generation using polarization beating in optical waveguides,” Phys. Rev. A 85, 053823 (2012).
[Crossref]

P. Réfrégier, T. Setälä, and A. T. Friberg, “Maximal polarization order of random optical beams: reversible and irreversible polarization variations,” Opt. Lett. 37, 3750–3752 (2012).
[Crossref]

2011 (2)

F. Boitier, A. Godard, N. Dubreuil, P. Delaye, C. Fabre, and E. Rosencher, “Photon extrabunching in ultrabright twin beams measured by two-photon counting in a semiconductor,” Nat. Commun. 2, 425–426 (2011).
[Crossref]

A. Hayat, A. Nevet, P. Ginzburg, and M. Orenstein, “Applications of two-photon processes in semiconductor photonic devices: invited review,” Semicond. Sci. Technol. 26, 083001 (2011).
[Crossref]

2010 (3)

A. Mohan, M. Felici, P. Gallo, B. Dwir, A. Rudra, J. Faist, and E. Kapon, “Polarization-entangled photons produced with high-symmetry site-controlled quantum dots,” Nat. Photonics 4, 302–306 (2010).
[Crossref]

A. Nevet, A. Hayat, and M. Orenstein, “Ultrafast pulse compression by semiconductor two-photon gain,” Opt. Lett. 35, 3877–3879 (2010).
[Crossref]

T. Voipio, T. Setälä, A. Shevchenko, and A. T. Friberg, “Polarization dynamics and polarization time of random three-dimensional electromagnetic fields,” Phys. Rev. A 82, 063807 (2010).
[Crossref]

2009 (2)

A. Shevchenko, T. Setälä, M. Kaivola, and A. T. Friberg, “Characterization of polarization fluctuations in random electromagnetic beams,” New J. Phys. 11, 073004 (2009).
[Crossref]

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nat. Phys. 5, 267–270 (2009).
[Crossref]

2008 (2)

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, “Polarization time and length for random optical beams,” Phys. Rev. A 78, 033817 (2008).
[Crossref]

L. S. Froufe-Pérez and R. Carminati, “Lifetime fluctuations of a single emitter in a disordered nanoscopic system: the influence of the transition dipole orientation,” Phys. Stat. Sol. 205, 1258–1265 (2008).
[Crossref]

2007 (1)

K. Lindfors, A. Priimagi, T. Setälä, A. Shevchenko, A. T. Friberg, and M. Kaivola, “Local polarization of tightly focused unpolarized light,” Nat. Photonics 1, 228–231 (2007).
[Crossref]

2006 (1)

A. Shevchenko, M. Kaivola, and J. Javanainen, “Spin-degenerate two-level atoms in on-resonance partially polarized light,” Phys. Rev. A 73, 035801 (2006).
[Crossref]

2005 (1)

M. Coles, “The state of the universe,” Nature 433, 248–256 (2005).
[Crossref]

2004 (1)

2003 (1)

I. Hajnsek, E. Pottier, and S. R. Cloude, “Inversion of surface parameters from polarimetric SAR,” IEEE Trans. Geosci. Remote Sens. 41, 727–744 (2003).
[Crossref]

2002 (4)

J. M. Kovac, E. M. Leitch, C. Pryke, J. E. Carlstrom, N. W. Halverson, and W. L. Holzapfel, “Detection of polarization in the cosmic microwave background using DASI,” Nature 420, 772–787 (2002).
[Crossref]

D. Mesa, C. Baccigalupi, G. De Zotti, L. Gregorini, K.-H. Mack, M. Vigotti, and U. Klein, “Polarization properties of extragalactic radio sources and their contribution to microwave polarization fluctuations,” Astron. Astrophys. 396, 463–471 (2002).
[Crossref]

G. D. VanWiggeren and R. Roy, “Communication with dynamically fluctuating states of light polarization,” Phys. Rev. Lett. 88, 097903 (2002).
[Crossref]

J. M. Roth, T. E. Murphy, and C. Xu, “Ultrasensitive and high-dynamic-range two-photon absorption in a GaAs photomultiplier tube,” Opt. Lett. 27, 2076–2078 (2002).
[Crossref]

2000 (1)

J. P. Gordon and H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. USA 97, 4541–4550 (2000).
[Crossref]

1998 (1)

H. F. Hofmann and O. Hess, “Polarization fluctuations in vertical-cavity surface-emitting lasers: a key to the mechanism behind polarization stability,” Quantum Semiclass. Opt. 10, 87–96 (1998).
[Crossref]

1997 (1)

1994 (1)

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30, 256–268 (1994).
[Crossref]

1968 (1)

B. R. Mollow, “Two-photon absorption and field correlation functions,” Phys. Rev. 175, 1555–1563 (1968).
[Crossref]

Andersen, D. R.

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30, 256–268 (1994).
[Crossref]

Baccigalupi, C.

D. Mesa, C. Baccigalupi, G. De Zotti, L. Gregorini, K.-H. Mack, M. Vigotti, and U. Klein, “Polarization properties of extragalactic radio sources and their contribution to microwave polarization fluctuations,” Astron. Astrophys. 396, 463–471 (2002).
[Crossref]

Ballarini, D.

D. Colas, L. Dominici, S. Donati, A. A. Pervishko, T. C. H. Liew, I. A. Shelykh, D. Ballarini, M. de Giorgi, A. Bramati, G. Gigli, E. del Valle, F. P. Laussy, A. V. Kavokin, and D. Sanvitto, “Polarization shaping of Poincaré beams by polariton oscillations,” Light: Sci. Appl. 4, e350 (2015).
[Crossref]

Bates, A. P.

Boitier, F.

F. Boitier, A. Godard, N. Dubreuil, P. Delaye, C. Fabre, and E. Rosencher, “Photon extrabunching in ultrabright twin beams measured by two-photon counting in a semiconductor,” Nat. Commun. 2, 425–426 (2011).
[Crossref]

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nat. Phys. 5, 267–270 (2009).
[Crossref]

Bramati, A.

D. Colas, L. Dominici, S. Donati, A. A. Pervishko, T. C. H. Liew, I. A. Shelykh, D. Ballarini, M. de Giorgi, A. Bramati, G. Gigli, E. del Valle, F. P. Laussy, A. V. Kavokin, and D. Sanvitto, “Polarization shaping of Poincaré beams by polariton oscillations,” Light: Sci. Appl. 4, e350 (2015).
[Crossref]

Brosseau, C.

C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley, 1998).

Brown, T. G.

Carlstrom, J. E.

J. M. Kovac, E. M. Leitch, C. Pryke, J. E. Carlstrom, N. W. Halverson, and W. L. Holzapfel, “Detection of polarization in the cosmic microwave background using DASI,” Nature 420, 772–787 (2002).
[Crossref]

Carminati, R.

L. S. Froufe-Pérez and R. Carminati, “Lifetime fluctuations of a single emitter in a disordered nanoscopic system: the influence of the transition dipole orientation,” Phys. Stat. Sol. 205, 1258–1265 (2008).
[Crossref]

Cloude, S. R.

I. Hajnsek, E. Pottier, and S. R. Cloude, “Inversion of surface parameters from polarimetric SAR,” IEEE Trans. Geosci. Remote Sens. 41, 727–744 (2003).
[Crossref]

Colas, D.

D. Colas, L. Dominici, S. Donati, A. A. Pervishko, T. C. H. Liew, I. A. Shelykh, D. Ballarini, M. de Giorgi, A. Bramati, G. Gigli, E. del Valle, F. P. Laussy, A. V. Kavokin, and D. Sanvitto, “Polarization shaping of Poincaré beams by polariton oscillations,” Light: Sci. Appl. 4, e350 (2015).
[Crossref]

Coles, M.

M. Coles, “The state of the universe,” Nature 433, 248–256 (2005).
[Crossref]

de Giorgi, M.

D. Colas, L. Dominici, S. Donati, A. A. Pervishko, T. C. H. Liew, I. A. Shelykh, D. Ballarini, M. de Giorgi, A. Bramati, G. Gigli, E. del Valle, F. P. Laussy, A. V. Kavokin, and D. Sanvitto, “Polarization shaping of Poincaré beams by polariton oscillations,” Light: Sci. Appl. 4, e350 (2015).
[Crossref]

De Zotti, G.

D. Mesa, C. Baccigalupi, G. De Zotti, L. Gregorini, K.-H. Mack, M. Vigotti, and U. Klein, “Polarization properties of extragalactic radio sources and their contribution to microwave polarization fluctuations,” Astron. Astrophys. 396, 463–471 (2002).
[Crossref]

del Valle, E.

D. Colas, L. Dominici, S. Donati, A. A. Pervishko, T. C. H. Liew, I. A. Shelykh, D. Ballarini, M. de Giorgi, A. Bramati, G. Gigli, E. del Valle, F. P. Laussy, A. V. Kavokin, and D. Sanvitto, “Polarization shaping of Poincaré beams by polariton oscillations,” Light: Sci. Appl. 4, e350 (2015).
[Crossref]

Delaye, P.

F. Boitier, A. Godard, N. Dubreuil, P. Delaye, C. Fabre, and E. Rosencher, “Photon extrabunching in ultrabright twin beams measured by two-photon counting in a semiconductor,” Nat. Commun. 2, 425–426 (2011).
[Crossref]

Dominici, L.

D. Colas, L. Dominici, S. Donati, A. A. Pervishko, T. C. H. Liew, I. A. Shelykh, D. Ballarini, M. de Giorgi, A. Bramati, G. Gigli, E. del Valle, F. P. Laussy, A. V. Kavokin, and D. Sanvitto, “Polarization shaping of Poincaré beams by polariton oscillations,” Light: Sci. Appl. 4, e350 (2015).
[Crossref]

Donati, S.

D. Colas, L. Dominici, S. Donati, A. A. Pervishko, T. C. H. Liew, I. A. Shelykh, D. Ballarini, M. de Giorgi, A. Bramati, G. Gigli, E. del Valle, F. P. Laussy, A. V. Kavokin, and D. Sanvitto, “Polarization shaping of Poincaré beams by polariton oscillations,” Light: Sci. Appl. 4, e350 (2015).
[Crossref]

Dubreuil, N.

F. Boitier, A. Godard, N. Dubreuil, P. Delaye, C. Fabre, and E. Rosencher, “Photon extrabunching in ultrabright twin beams measured by two-photon counting in a semiconductor,” Nat. Commun. 2, 425–426 (2011).
[Crossref]

Dvorak, M. D.

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30, 256–268 (1994).
[Crossref]

Dwir, B.

A. Mohan, M. Felici, P. Gallo, B. Dwir, A. Rudra, J. Faist, and E. Kapon, “Polarization-entangled photons produced with high-symmetry site-controlled quantum dots,” Nat. Photonics 4, 302–306 (2010).
[Crossref]

Fabre, C.

F. Boitier, A. Godard, N. Dubreuil, P. Delaye, C. Fabre, and E. Rosencher, “Photon extrabunching in ultrabright twin beams measured by two-photon counting in a semiconductor,” Nat. Commun. 2, 425–426 (2011).
[Crossref]

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nat. Phys. 5, 267–270 (2009).
[Crossref]

Faist, J.

A. Mohan, M. Felici, P. Gallo, B. Dwir, A. Rudra, J. Faist, and E. Kapon, “Polarization-entangled photons produced with high-symmetry site-controlled quantum dots,” Nat. Photonics 4, 302–306 (2010).
[Crossref]

Felici, M.

A. Mohan, M. Felici, P. Gallo, B. Dwir, A. Rudra, J. Faist, and E. Kapon, “Polarization-entangled photons produced with high-symmetry site-controlled quantum dots,” Nat. Photonics 4, 302–306 (2010).
[Crossref]

Friberg, A. T.

A. Shevchenko, M. Roussey, A. T. Friberg, and T. Setälä, “Ultrashort coherence times in partially polarized stationary optical beams measured by two-photon absorption,” Opt. Express 23, 31274–31285 (2015).
[Crossref]

P. Réfrégier, T. Setälä, and A. T. Friberg, “Maximal polarization order of random optical beams: reversible and irreversible polarization variations,” Opt. Lett. 37, 3750–3752 (2012).
[Crossref]

T. Voipio, T. Setälä, A. Shevchenko, and A. T. Friberg, “Polarization dynamics and polarization time of random three-dimensional electromagnetic fields,” Phys. Rev. A 82, 063807 (2010).
[Crossref]

A. Shevchenko, T. Setälä, M. Kaivola, and A. T. Friberg, “Characterization of polarization fluctuations in random electromagnetic beams,” New J. Phys. 11, 073004 (2009).
[Crossref]

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, “Polarization time and length for random optical beams,” Phys. Rev. A 78, 033817 (2008).
[Crossref]

K. Lindfors, A. Priimagi, T. Setälä, A. Shevchenko, A. T. Friberg, and M. Kaivola, “Local polarization of tightly focused unpolarized light,” Nat. Photonics 1, 228–231 (2007).
[Crossref]

Froufe-Pérez, L. S.

L. S. Froufe-Pérez and R. Carminati, “Lifetime fluctuations of a single emitter in a disordered nanoscopic system: the influence of the transition dipole orientation,” Phys. Stat. Sol. 205, 1258–1265 (2008).
[Crossref]

Gallo, P.

A. Mohan, M. Felici, P. Gallo, B. Dwir, A. Rudra, J. Faist, and E. Kapon, “Polarization-entangled photons produced with high-symmetry site-controlled quantum dots,” Nat. Photonics 4, 302–306 (2010).
[Crossref]

Gigli, G.

D. Colas, L. Dominici, S. Donati, A. A. Pervishko, T. C. H. Liew, I. A. Shelykh, D. Ballarini, M. de Giorgi, A. Bramati, G. Gigli, E. del Valle, F. P. Laussy, A. V. Kavokin, and D. Sanvitto, “Polarization shaping of Poincaré beams by polariton oscillations,” Light: Sci. Appl. 4, e350 (2015).
[Crossref]

Ginzburg, P.

A. Hayat, A. Nevet, P. Ginzburg, and M. Orenstein, “Applications of two-photon processes in semiconductor photonic devices: invited review,” Semicond. Sci. Technol. 26, 083001 (2011).
[Crossref]

Godard, A.

F. Boitier, A. Godard, N. Dubreuil, P. Delaye, C. Fabre, and E. Rosencher, “Photon extrabunching in ultrabright twin beams measured by two-photon counting in a semiconductor,” Nat. Commun. 2, 425–426 (2011).
[Crossref]

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nat. Phys. 5, 267–270 (2009).
[Crossref]

Gordon, J. P.

J. P. Gordon and H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. USA 97, 4541–4550 (2000).
[Crossref]

Gregorini, L.

D. Mesa, C. Baccigalupi, G. De Zotti, L. Gregorini, K.-H. Mack, M. Vigotti, and U. Klein, “Polarization properties of extragalactic radio sources and their contribution to microwave polarization fluctuations,” Astron. Astrophys. 396, 463–471 (2002).
[Crossref]

Hajnsek, I.

I. Hajnsek, E. Pottier, and S. R. Cloude, “Inversion of surface parameters from polarimetric SAR,” IEEE Trans. Geosci. Remote Sens. 41, 727–744 (2003).
[Crossref]

Halverson, N. W.

J. M. Kovac, E. M. Leitch, C. Pryke, J. E. Carlstrom, N. W. Halverson, and W. L. Holzapfel, “Detection of polarization in the cosmic microwave background using DASI,” Nature 420, 772–787 (2002).
[Crossref]

Hayat, A.

A. Hayat, A. Nevet, P. Ginzburg, and M. Orenstein, “Applications of two-photon processes in semiconductor photonic devices: invited review,” Semicond. Sci. Technol. 26, 083001 (2011).
[Crossref]

A. Nevet, A. Hayat, and M. Orenstein, “Ultrafast pulse compression by semiconductor two-photon gain,” Opt. Lett. 35, 3877–3879 (2010).
[Crossref]

Hess, O.

H. F. Hofmann and O. Hess, “Polarization fluctuations in vertical-cavity surface-emitting lasers: a key to the mechanism behind polarization stability,” Quantum Semiclass. Opt. 10, 87–96 (1998).
[Crossref]

Hofmann, H. F.

H. F. Hofmann and O. Hess, “Polarization fluctuations in vertical-cavity surface-emitting lasers: a key to the mechanism behind polarization stability,” Quantum Semiclass. Opt. 10, 87–96 (1998).
[Crossref]

Holzapfel, W. L.

J. M. Kovac, E. M. Leitch, C. Pryke, J. E. Carlstrom, N. W. Halverson, and W. L. Holzapfel, “Detection of polarization in the cosmic microwave background using DASI,” Nature 420, 772–787 (2002).
[Crossref]

Hooker, S.

S. Hooker and C. Webb, Laser Physics (Oxford University, 2010).

Hooker, S. M.

L. Z. Liu, K. O’Keeffe, and S. M. Hooker, “Quasi-phase-matching of high-order-harmonic generation using polarization beating in optical waveguides,” Phys. Rev. A 85, 053823 (2012).
[Crossref]

Hopcraft, K. I.

Jakeman, E.

Javanainen, J.

A. Shevchenko, M. Kaivola, and J. Javanainen, “Spin-degenerate two-level atoms in on-resonance partially polarized light,” Phys. Rev. A 73, 035801 (2006).
[Crossref]

Kaivola, M.

A. Shevchenko, T. Setälä, M. Kaivola, and A. T. Friberg, “Characterization of polarization fluctuations in random electromagnetic beams,” New J. Phys. 11, 073004 (2009).
[Crossref]

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, “Polarization time and length for random optical beams,” Phys. Rev. A 78, 033817 (2008).
[Crossref]

K. Lindfors, A. Priimagi, T. Setälä, A. Shevchenko, A. T. Friberg, and M. Kaivola, “Local polarization of tightly focused unpolarized light,” Nat. Photonics 1, 228–231 (2007).
[Crossref]

A. Shevchenko, M. Kaivola, and J. Javanainen, “Spin-degenerate two-level atoms in on-resonance partially polarized light,” Phys. Rev. A 73, 035801 (2006).
[Crossref]

Kapon, E.

A. Mohan, M. Felici, P. Gallo, B. Dwir, A. Rudra, J. Faist, and E. Kapon, “Polarization-entangled photons produced with high-symmetry site-controlled quantum dots,” Nat. Photonics 4, 302–306 (2010).
[Crossref]

Kavokin, A. V.

D. Colas, L. Dominici, S. Donati, A. A. Pervishko, T. C. H. Liew, I. A. Shelykh, D. Ballarini, M. de Giorgi, A. Bramati, G. Gigli, E. del Valle, F. P. Laussy, A. V. Kavokin, and D. Sanvitto, “Polarization shaping of Poincaré beams by polariton oscillations,” Light: Sci. Appl. 4, e350 (2015).
[Crossref]

Klein, U.

D. Mesa, C. Baccigalupi, G. De Zotti, L. Gregorini, K.-H. Mack, M. Vigotti, and U. Klein, “Polarization properties of extragalactic radio sources and their contribution to microwave polarization fluctuations,” Astron. Astrophys. 396, 463–471 (2002).
[Crossref]

Kogelnik, H.

J. P. Gordon and H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. USA 97, 4541–4550 (2000).
[Crossref]

Kovac, J. M.

J. M. Kovac, E. M. Leitch, C. Pryke, J. E. Carlstrom, N. W. Halverson, and W. L. Holzapfel, “Detection of polarization in the cosmic microwave background using DASI,” Nature 420, 772–787 (2002).
[Crossref]

Laussy, F. P.

D. Colas, L. Dominici, S. Donati, A. A. Pervishko, T. C. H. Liew, I. A. Shelykh, D. Ballarini, M. de Giorgi, A. Bramati, G. Gigli, E. del Valle, F. P. Laussy, A. V. Kavokin, and D. Sanvitto, “Polarization shaping of Poincaré beams by polariton oscillations,” Light: Sci. Appl. 4, e350 (2015).
[Crossref]

Leitch, E. M.

J. M. Kovac, E. M. Leitch, C. Pryke, J. E. Carlstrom, N. W. Halverson, and W. L. Holzapfel, “Detection of polarization in the cosmic microwave background using DASI,” Nature 420, 772–787 (2002).
[Crossref]

Liew, T. C. H.

D. Colas, L. Dominici, S. Donati, A. A. Pervishko, T. C. H. Liew, I. A. Shelykh, D. Ballarini, M. de Giorgi, A. Bramati, G. Gigli, E. del Valle, F. P. Laussy, A. V. Kavokin, and D. Sanvitto, “Polarization shaping of Poincaré beams by polariton oscillations,” Light: Sci. Appl. 4, e350 (2015).
[Crossref]

Lindfors, K.

K. Lindfors, A. Priimagi, T. Setälä, A. Shevchenko, A. T. Friberg, and M. Kaivola, “Local polarization of tightly focused unpolarized light,” Nat. Photonics 1, 228–231 (2007).
[Crossref]

Liu, L. Z.

L. Z. Liu, K. O’Keeffe, and S. M. Hooker, “Quasi-phase-matching of high-order-harmonic generation using polarization beating in optical waveguides,” Phys. Rev. A 85, 053823 (2012).
[Crossref]

Loudon, R.

R. Loudon, The Quantum Theory of Light, 3rd ed. (Oxford University, 2000).

Mack, K.-H.

D. Mesa, C. Baccigalupi, G. De Zotti, L. Gregorini, K.-H. Mack, M. Vigotti, and U. Klein, “Polarization properties of extragalactic radio sources and their contribution to microwave polarization fluctuations,” Astron. Astrophys. 396, 463–471 (2002).
[Crossref]

Mesa, D.

D. Mesa, C. Baccigalupi, G. De Zotti, L. Gregorini, K.-H. Mack, M. Vigotti, and U. Klein, “Polarization properties of extragalactic radio sources and their contribution to microwave polarization fluctuations,” Astron. Astrophys. 396, 463–471 (2002).
[Crossref]

Mohan, A.

A. Mohan, M. Felici, P. Gallo, B. Dwir, A. Rudra, J. Faist, and E. Kapon, “Polarization-entangled photons produced with high-symmetry site-controlled quantum dots,” Nat. Photonics 4, 302–306 (2010).
[Crossref]

Mollow, B. R.

B. R. Mollow, “Two-photon absorption and field correlation functions,” Phys. Rev. 175, 1555–1563 (1968).
[Crossref]

Murphy, T. E.

Nevet, A.

A. Hayat, A. Nevet, P. Ginzburg, and M. Orenstein, “Applications of two-photon processes in semiconductor photonic devices: invited review,” Semicond. Sci. Technol. 26, 083001 (2011).
[Crossref]

A. Nevet, A. Hayat, and M. Orenstein, “Ultrafast pulse compression by semiconductor two-photon gain,” Opt. Lett. 35, 3877–3879 (2010).
[Crossref]

O’Keeffe, K.

L. Z. Liu, K. O’Keeffe, and S. M. Hooker, “Quasi-phase-matching of high-order-harmonic generation using polarization beating in optical waveguides,” Phys. Rev. A 85, 053823 (2012).
[Crossref]

Orenstein, M.

A. Hayat, A. Nevet, P. Ginzburg, and M. Orenstein, “Applications of two-photon processes in semiconductor photonic devices: invited review,” Semicond. Sci. Technol. 26, 083001 (2011).
[Crossref]

A. Nevet, A. Hayat, and M. Orenstein, “Ultrafast pulse compression by semiconductor two-photon gain,” Opt. Lett. 35, 3877–3879 (2010).
[Crossref]

Panajotov, K.

M. Virte, K. Panajotov, H. Thienpoint, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7, 60–65 (2013).
[Crossref]

Pervishko, A. A.

D. Colas, L. Dominici, S. Donati, A. A. Pervishko, T. C. H. Liew, I. A. Shelykh, D. Ballarini, M. de Giorgi, A. Bramati, G. Gigli, E. del Valle, F. P. Laussy, A. V. Kavokin, and D. Sanvitto, “Polarization shaping of Poincaré beams by polariton oscillations,” Light: Sci. Appl. 4, e350 (2015).
[Crossref]

Pottier, E.

I. Hajnsek, E. Pottier, and S. R. Cloude, “Inversion of surface parameters from polarimetric SAR,” IEEE Trans. Geosci. Remote Sens. 41, 727–744 (2003).
[Crossref]

Priimagi, A.

K. Lindfors, A. Priimagi, T. Setälä, A. Shevchenko, A. T. Friberg, and M. Kaivola, “Local polarization of tightly focused unpolarized light,” Nat. Photonics 1, 228–231 (2007).
[Crossref]

Pryke, C.

J. M. Kovac, E. M. Leitch, C. Pryke, J. E. Carlstrom, N. W. Halverson, and W. L. Holzapfel, “Detection of polarization in the cosmic microwave background using DASI,” Nature 420, 772–787 (2002).
[Crossref]

Réfrégier, P.

Rosencher, E.

F. Boitier, A. Godard, N. Dubreuil, P. Delaye, C. Fabre, and E. Rosencher, “Photon extrabunching in ultrabright twin beams measured by two-photon counting in a semiconductor,” Nat. Commun. 2, 425–426 (2011).
[Crossref]

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nat. Phys. 5, 267–270 (2009).
[Crossref]

Roth, J. M.

Roussey, M.

Roy, R.

G. D. VanWiggeren and R. Roy, “Communication with dynamically fluctuating states of light polarization,” Phys. Rev. Lett. 88, 097903 (2002).
[Crossref]

Rudra, A.

A. Mohan, M. Felici, P. Gallo, B. Dwir, A. Rudra, J. Faist, and E. Kapon, “Polarization-entangled photons produced with high-symmetry site-controlled quantum dots,” Nat. Photonics 4, 302–306 (2010).
[Crossref]

Sanvitto, D.

D. Colas, L. Dominici, S. Donati, A. A. Pervishko, T. C. H. Liew, I. A. Shelykh, D. Ballarini, M. de Giorgi, A. Bramati, G. Gigli, E. del Valle, F. P. Laussy, A. V. Kavokin, and D. Sanvitto, “Polarization shaping of Poincaré beams by polariton oscillations,” Light: Sci. Appl. 4, e350 (2015).
[Crossref]

Schroeder, W. A.

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30, 256–268 (1994).
[Crossref]

Sciamanna, M.

M. Virte, K. Panajotov, H. Thienpoint, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7, 60–65 (2013).
[Crossref]

Setälä, T.

A. Shevchenko, M. Roussey, A. T. Friberg, and T. Setälä, “Ultrashort coherence times in partially polarized stationary optical beams measured by two-photon absorption,” Opt. Express 23, 31274–31285 (2015).
[Crossref]

P. Réfrégier, T. Setälä, and A. T. Friberg, “Maximal polarization order of random optical beams: reversible and irreversible polarization variations,” Opt. Lett. 37, 3750–3752 (2012).
[Crossref]

T. Voipio, T. Setälä, A. Shevchenko, and A. T. Friberg, “Polarization dynamics and polarization time of random three-dimensional electromagnetic fields,” Phys. Rev. A 82, 063807 (2010).
[Crossref]

A. Shevchenko, T. Setälä, M. Kaivola, and A. T. Friberg, “Characterization of polarization fluctuations in random electromagnetic beams,” New J. Phys. 11, 073004 (2009).
[Crossref]

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, “Polarization time and length for random optical beams,” Phys. Rev. A 78, 033817 (2008).
[Crossref]

K. Lindfors, A. Priimagi, T. Setälä, A. Shevchenko, A. T. Friberg, and M. Kaivola, “Local polarization of tightly focused unpolarized light,” Nat. Photonics 1, 228–231 (2007).
[Crossref]

Shelykh, I. A.

D. Colas, L. Dominici, S. Donati, A. A. Pervishko, T. C. H. Liew, I. A. Shelykh, D. Ballarini, M. de Giorgi, A. Bramati, G. Gigli, E. del Valle, F. P. Laussy, A. V. Kavokin, and D. Sanvitto, “Polarization shaping of Poincaré beams by polariton oscillations,” Light: Sci. Appl. 4, e350 (2015).
[Crossref]

Shevchenko, A.

A. Shevchenko, M. Roussey, A. T. Friberg, and T. Setälä, “Ultrashort coherence times in partially polarized stationary optical beams measured by two-photon absorption,” Opt. Express 23, 31274–31285 (2015).
[Crossref]

T. Voipio, T. Setälä, A. Shevchenko, and A. T. Friberg, “Polarization dynamics and polarization time of random three-dimensional electromagnetic fields,” Phys. Rev. A 82, 063807 (2010).
[Crossref]

A. Shevchenko, T. Setälä, M. Kaivola, and A. T. Friberg, “Characterization of polarization fluctuations in random electromagnetic beams,” New J. Phys. 11, 073004 (2009).
[Crossref]

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, “Polarization time and length for random optical beams,” Phys. Rev. A 78, 033817 (2008).
[Crossref]

K. Lindfors, A. Priimagi, T. Setälä, A. Shevchenko, A. T. Friberg, and M. Kaivola, “Local polarization of tightly focused unpolarized light,” Nat. Photonics 1, 228–231 (2007).
[Crossref]

A. Shevchenko, M. Kaivola, and J. Javanainen, “Spin-degenerate two-level atoms in on-resonance partially polarized light,” Phys. Rev. A 73, 035801 (2006).
[Crossref]

Shore, B. W.

B. W. Shore, The Theory of Coherent Atomic Excitation (Wiley, 1990).

Smirl, A. L.

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30, 256–268 (1994).
[Crossref]

Thienpoint, H.

M. Virte, K. Panajotov, H. Thienpoint, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7, 60–65 (2013).
[Crossref]

VanWiggeren, G. D.

G. D. VanWiggeren and R. Roy, “Communication with dynamically fluctuating states of light polarization,” Phys. Rev. Lett. 88, 097903 (2002).
[Crossref]

Vigotti, M.

D. Mesa, C. Baccigalupi, G. De Zotti, L. Gregorini, K.-H. Mack, M. Vigotti, and U. Klein, “Polarization properties of extragalactic radio sources and their contribution to microwave polarization fluctuations,” Astron. Astrophys. 396, 463–471 (2002).
[Crossref]

Virte, M.

M. Virte, K. Panajotov, H. Thienpoint, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7, 60–65 (2013).
[Crossref]

Voipio, T.

T. Voipio, T. Setälä, A. Shevchenko, and A. T. Friberg, “Polarization dynamics and polarization time of random three-dimensional electromagnetic fields,” Phys. Rev. A 82, 063807 (2010).
[Crossref]

Webb, C.

S. Hooker and C. Webb, Laser Physics (Oxford University, 2010).

Weiner, A. M.

A. M. Weiner, Ultrafast Optics (Wiley, 2009).

Wherrett, B. S.

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30, 256–268 (1994).
[Crossref]

Xu, C.

Zhu, Z.

Astron. Astrophys. (1)

D. Mesa, C. Baccigalupi, G. De Zotti, L. Gregorini, K.-H. Mack, M. Vigotti, and U. Klein, “Polarization properties of extragalactic radio sources and their contribution to microwave polarization fluctuations,” Astron. Astrophys. 396, 463–471 (2002).
[Crossref]

IEEE J. Quantum Electron. (1)

M. D. Dvorak, W. A. Schroeder, D. R. Andersen, A. L. Smirl, and B. S. Wherrett, “Measurement of the anisotropy of two-photon absorption coefficients in zincblende semiconductors,” IEEE J. Quantum Electron. 30, 256–268 (1994).
[Crossref]

IEEE Trans. Geosci. Remote Sens. (1)

I. Hajnsek, E. Pottier, and S. R. Cloude, “Inversion of surface parameters from polarimetric SAR,” IEEE Trans. Geosci. Remote Sens. 41, 727–744 (2003).
[Crossref]

J. Opt. Soc. Am. A (1)

Light: Sci. Appl. (1)

D. Colas, L. Dominici, S. Donati, A. A. Pervishko, T. C. H. Liew, I. A. Shelykh, D. Ballarini, M. de Giorgi, A. Bramati, G. Gigli, E. del Valle, F. P. Laussy, A. V. Kavokin, and D. Sanvitto, “Polarization shaping of Poincaré beams by polariton oscillations,” Light: Sci. Appl. 4, e350 (2015).
[Crossref]

Nat. Commun. (1)

F. Boitier, A. Godard, N. Dubreuil, P. Delaye, C. Fabre, and E. Rosencher, “Photon extrabunching in ultrabright twin beams measured by two-photon counting in a semiconductor,” Nat. Commun. 2, 425–426 (2011).
[Crossref]

Nat. Photonics (3)

A. Mohan, M. Felici, P. Gallo, B. Dwir, A. Rudra, J. Faist, and E. Kapon, “Polarization-entangled photons produced with high-symmetry site-controlled quantum dots,” Nat. Photonics 4, 302–306 (2010).
[Crossref]

M. Virte, K. Panajotov, H. Thienpoint, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7, 60–65 (2013).
[Crossref]

K. Lindfors, A. Priimagi, T. Setälä, A. Shevchenko, A. T. Friberg, and M. Kaivola, “Local polarization of tightly focused unpolarized light,” Nat. Photonics 1, 228–231 (2007).
[Crossref]

Nat. Phys. (1)

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nat. Phys. 5, 267–270 (2009).
[Crossref]

Nature (2)

M. Coles, “The state of the universe,” Nature 433, 248–256 (2005).
[Crossref]

J. M. Kovac, E. M. Leitch, C. Pryke, J. E. Carlstrom, N. W. Halverson, and W. L. Holzapfel, “Detection of polarization in the cosmic microwave background using DASI,” Nature 420, 772–787 (2002).
[Crossref]

New J. Phys. (1)

A. Shevchenko, T. Setälä, M. Kaivola, and A. T. Friberg, “Characterization of polarization fluctuations in random electromagnetic beams,” New J. Phys. 11, 073004 (2009).
[Crossref]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. (1)

B. R. Mollow, “Two-photon absorption and field correlation functions,” Phys. Rev. 175, 1555–1563 (1968).
[Crossref]

Phys. Rev. A (4)

A. Shevchenko, M. Kaivola, and J. Javanainen, “Spin-degenerate two-level atoms in on-resonance partially polarized light,” Phys. Rev. A 73, 035801 (2006).
[Crossref]

L. Z. Liu, K. O’Keeffe, and S. M. Hooker, “Quasi-phase-matching of high-order-harmonic generation using polarization beating in optical waveguides,” Phys. Rev. A 85, 053823 (2012).
[Crossref]

T. Voipio, T. Setälä, A. Shevchenko, and A. T. Friberg, “Polarization dynamics and polarization time of random three-dimensional electromagnetic fields,” Phys. Rev. A 82, 063807 (2010).
[Crossref]

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, “Polarization time and length for random optical beams,” Phys. Rev. A 78, 033817 (2008).
[Crossref]

Phys. Rev. Lett. (1)

G. D. VanWiggeren and R. Roy, “Communication with dynamically fluctuating states of light polarization,” Phys. Rev. Lett. 88, 097903 (2002).
[Crossref]

Phys. Stat. Sol. (1)

L. S. Froufe-Pérez and R. Carminati, “Lifetime fluctuations of a single emitter in a disordered nanoscopic system: the influence of the transition dipole orientation,” Phys. Stat. Sol. 205, 1258–1265 (2008).
[Crossref]

Proc. Natl. Acad. Sci. USA (1)

J. P. Gordon and H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. USA 97, 4541–4550 (2000).
[Crossref]

Quantum Semiclass. Opt. (1)

H. F. Hofmann and O. Hess, “Polarization fluctuations in vertical-cavity surface-emitting lasers: a key to the mechanism behind polarization stability,” Quantum Semiclass. Opt. 10, 87–96 (1998).
[Crossref]

Semicond. Sci. Technol. (1)

A. Hayat, A. Nevet, P. Ginzburg, and M. Orenstein, “Applications of two-photon processes in semiconductor photonic devices: invited review,” Semicond. Sci. Technol. 26, 083001 (2011).
[Crossref]

Other (5)

R. Loudon, The Quantum Theory of Light, 3rd ed. (Oxford University, 2000).

A. M. Weiner, Ultrafast Optics (Wiley, 2009).

S. Hooker and C. Webb, Laser Physics (Oxford University, 2010).

C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley, 1998).

B. W. Shore, The Theory of Coherent Atomic Excitation (Wiley, 1990).

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Figures (6)

Fig. 1.
Fig. 1.

Illustration of polarization dynamics. (a) The instantaneous polarization state represented by the red ellipses does not, on average, significantly change within the polarization time τp. (b) The instantaneous Poincaré vectors s(t) and s(t+τ) determine how much the instantaneous polarization state changes on the Poincaré sphere within τ.

Fig. 2.
Fig. 2.

Polarization-sensitive Michelson interferometer and the source spectra. (a) Experimental setup: OF, optical fiber; L1 and L2, lenses; BS, beam splitter; WP, quarter-wave plate; P, polarizer; M, mirror; and PT, photomultiplier tube. One of the mirrors is translated with a piezoelectric transducer to alter τ. (b) Measured spectra of the optical beams from the ASE of an Er-doped fiber amplifier (blue line) and two independent lasers (red line). The polar plot in the inset illustrates the dependence of the two-photon absorption signal on the orientation angle α of the linear polarization of incident light derived from the ASE.

Fig. 3.
Fig. 3.

Two-photon absorption counts (left) and the related intensity correlation functions (ICFs) (right) measured for ASE light. Curves in (a) and (b) were measured by selecting x-polarized fields in both arms of the interferometer (blue XX curves), y-polarized fields in both arms (red YY curves), and x- and y-polarized fields in different arms (black XY curve). The curves in (c) and (d) were measured by selecting right-hand circular polarizations in both arms (blue RR curves), left-hand circular polarizations in both arms (red LL curves), and right-hand and left-hand circular polarizations in different arms (black RL curves). In (e) and (f), the selected components are linearly polarized at an angle of +45° in both arms (blue +45, +45 curves), 45° in both arms (red 45, 45 curves), and +45° in one arm and 45° in the other arm, respectively (black +45, 45 curves). The insets in (a), (c), and (e) illustrate the oscillation of the measured signals at τ[0,50  fs].

Fig. 4.
Fig. 4.

Polarization dynamics of ASE light. (a) Autocorrelation functions of the Stokes parameters (SPCFs) and (b) the polarization correlation function γP(τ). The illustrated polarization time τp is determined from γP(τp)=γP(0)/2.

Fig. 5.
Fig. 5.

Two-photon absorption counts (left) and the corresponding ICFs (right) measured for a two-laser beam. Curves in (a) and (b) were measured by selecting x-polarized fields in both arms of the interferometer (blue XX curves), y-polarized fields in both arms (red YY curves), and x- and y-polarized fields in different arms (black XY curve). Curves in (c) and (d) were measured by selecting right-hand circular polarizations in both arms (blue RR curves), left-hand circular polarizations in both arms (red LL curves), and right-hand and left-hand circular polarizations in different arms (black XY curves). In (e) and (f), the selected components are linearly polarized at an angle of +45° in both arms (blue +45, +45 curves), 45° in both arms (red 45, 45 curves), and +45° in one arm and 45° in the other arm, respectively (black +45, 45 curves).

Fig. 6.
Fig. 6.

Polarization dynamics of a two-laser beam. (a) Autocorrelation functions of the Stokes parameters (SPCFs) and (b) the polarization correlation function γP(τ). The polarization time τp is determined from γP(τp)=γP(0)/2. The time τ is equal to the time interval within which any original polarization state of the field will be transformed into the orthogonal polarization state.

Equations (12)

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

S0(t)=Ix(t)+Iy(t),
S1(t)=Ix(t)Iy(t),
S2(t)=I+45(t)I45(t),
S3(t)=IRCP(t)ILCP(t),
γP(τ)=[s(t)·s(t+τ)]S0(t)S0(t+τ)S0(t)S0(t+τ).
γP(τ)=n=13Sn(t)Sn(t+τ)S0(t)S0(t+τ),
S0(t)S0(t+τ)=Cx,x(τ)+Cx,y(τ)+Cy,x(τ)+Cy,y(τ),
S1(t)S1(t+τ)=Cx,x(τ)Cx,y(τ)Cy,x(τ)+Cy,y(τ),
S2(t)S2(t+τ)=C+45,+45(τ)C+45,45(τ)C45,+45(τ)+C45,45(τ),
S3(t)S3(t+τ)=CRCP,RCP(τ)CRCP,LCP(τ)CLCP,RCP(τ)+CLCP,LCP(τ).
S(τ)I2(t)=I12(t)+I22(t)+2I1(t)I2(t+τ)+2|A1T(t)A2*(t+τ)|2+Re[F(1)(τ)eiω0τ]+Re[F(2)(τ)e2iω0τ],
I1i(t)I2j(t+τ)=C[Sij(τ)S1iS2j]/ηij,

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