Abstract

Polarization correlation functions that characterize the rate of change of the instantaneous polarization state of an arbitrary fluctuating electromagnetic beam were recently introduced. In this work, we describe techniques that enable the measurement of these functions leading to the determination of the so-called polarization time of a random field.

© 2012 Optical Society of America

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References

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  1. C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley, 1998).
  2. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
  3. J. J. Gil, “Polarimetric characterization of light and media: physical quantities involved in polarimetric phenomena,” Eur. Phys. J. Appl. Phys. 40, 1–47 (2007).
    [CrossRef]
  4. T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, “Polarization time,” J. Phys.: Conf. Ser. 139, 012011 (2008).
    [CrossRef]
  5. 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]
  6. 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]
  7. 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]
  8. G. D. Van Wiggeren and R. Roy, “Communication with dynamically fluctuating states of light polarization,” Phys. Rev. Lett. 88, 097903 (2002).
    [CrossRef]
  9. B. Kanseri and H. C. Kandpal, “Experimental determination of two-point Stokes parameters for a partially coherent broadband light beam,” Opt. Commun. 283, 4558–4562 (2010).
    [CrossRef]
  10. J. Tervo, T. Setälä, A. Roueff, Ph. Réfrégier, and A. T. Friberg, “Two-point Stokes parameters: interpretation and properties,” Opt. Lett. 34, 3074–3076 (2009).
    [CrossRef]
  11. 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).
  12. K. Lindfors, A. Priimagi, T. Setälä, A. Shevchenko, and A. T. Friberg, “Local polarization of tightly focused unpolarized light,” Nat. Photon. 1, 228–231 (2007).

2010

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]

B. Kanseri and H. C. Kandpal, “Experimental determination of two-point Stokes parameters for a partially coherent broadband light beam,” Opt. Commun. 283, 4558–4562 (2010).
[CrossRef]

2009

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).

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]

J. Tervo, T. Setälä, A. Roueff, Ph. Réfrégier, and A. T. Friberg, “Two-point Stokes parameters: interpretation and properties,” Opt. Lett. 34, 3074–3076 (2009).
[CrossRef]

2008

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, “Polarization time,” J. Phys.: Conf. Ser. 139, 012011 (2008).
[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]

2007

J. J. Gil, “Polarimetric characterization of light and media: physical quantities involved in polarimetric phenomena,” Eur. Phys. J. Appl. Phys. 40, 1–47 (2007).
[CrossRef]

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

2002

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

Boitier, F.

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).

Brosseau, C.

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

Fabre, C.

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).

Friberg, A. 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]

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]

J. Tervo, T. Setälä, A. Roueff, Ph. Réfrégier, and A. T. Friberg, “Two-point Stokes parameters: interpretation and properties,” Opt. Lett. 34, 3074–3076 (2009).
[CrossRef]

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, “Polarization time,” J. Phys.: Conf. Ser. 139, 012011 (2008).
[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, and A. T. Friberg, “Local polarization of tightly focused unpolarized light,” Nat. Photon. 1, 228–231 (2007).

Gil, J. J.

J. J. Gil, “Polarimetric characterization of light and media: physical quantities involved in polarimetric phenomena,” Eur. Phys. J. Appl. Phys. 40, 1–47 (2007).
[CrossRef]

Godard, A.

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).

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]

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, “Polarization time,” J. Phys.: Conf. Ser. 139, 012011 (2008).
[CrossRef]

Kandpal, H. C.

B. Kanseri and H. C. Kandpal, “Experimental determination of two-point Stokes parameters for a partially coherent broadband light beam,” Opt. Commun. 283, 4558–4562 (2010).
[CrossRef]

Kanseri, B.

B. Kanseri and H. C. Kandpal, “Experimental determination of two-point Stokes parameters for a partially coherent broadband light beam,” Opt. Commun. 283, 4558–4562 (2010).
[CrossRef]

Lindfors, K.

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

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Priimagi, A.

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

Réfrégier, Ph.

Rosencher, E.

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).

Roueff, A.

Roy, R.

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

Setälä, 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]

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]

J. Tervo, T. Setälä, A. Roueff, Ph. Réfrégier, and A. T. Friberg, “Two-point Stokes parameters: interpretation and properties,” Opt. Lett. 34, 3074–3076 (2009).
[CrossRef]

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, “Polarization time,” J. Phys.: Conf. Ser. 139, 012011 (2008).
[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, and A. T. Friberg, “Local polarization of tightly focused unpolarized light,” Nat. Photon. 1, 228–231 (2007).

Shevchenko, A.

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]

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, “Polarization time,” J. Phys.: Conf. Ser. 139, 012011 (2008).
[CrossRef]

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

Tervo, J.

Van Wiggeren, G. D.

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

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Eur. Phys. J. Appl. Phys.

J. J. Gil, “Polarimetric characterization of light and media: physical quantities involved in polarimetric phenomena,” Eur. Phys. J. Appl. Phys. 40, 1–47 (2007).
[CrossRef]

J. Phys.: Conf. Ser.

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, “Polarization time,” J. Phys.: Conf. Ser. 139, 012011 (2008).
[CrossRef]

Nat. Photon.

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

Nat. Phys.

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).

New J. Phys.

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. Commun.

B. Kanseri and H. C. Kandpal, “Experimental determination of two-point Stokes parameters for a partially coherent broadband light beam,” Opt. Commun. 283, 4558–4562 (2010).
[CrossRef]

Opt. Lett.

Phys. Rev. A

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.

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

Other

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

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

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Figures (3)

Fig. 1.
Fig. 1.

Illustration of a Michelson-type interferometer to measure (a) |ϕxx(τ)|2 and |ϕyy(τ)|2, and (b) |ϕxy(τ)|2 and |ϕyx(τ)|2. If the optical lengths of the interferometer’s arms are l1 and l2, the delay time τ is calculated as τ=(l2l1)/(2c), where c is the speed of light. Labels: P, polarizer; M1 and M2, mirrors; BS, beam splitter; PBS, polarizing beam splitter; λ/4, quarter-wave plate; P45°, polarizer at an angle of 45°; D, photodetector.

Fig. 2.
Fig. 2.

Schematic of an experimental setup for recording the Stokes parameters. The optical elements are aligned to measure Ix(t), Iy(t), I+45(t), and IRCP(t). Labels: BS1 and BS2, beam splitters; PBS, polarizing beam splitter; λ/4, quarter-wave plate; P1 and P2, polarizers; D1, D2, D3, and D4, photodetectors.

Fig. 3.
Fig. 3.

Schematic of an optical depolarizer. A polarized laser beam is split into two beams with equal powers and orthogonal polarizations. The beams are combined into a single beam after introducing a time delay for one of them with respect to the other. The output beam is effectively unpolarized if the beam path difference exceeds the coherence time of the input beam. Labels: PBS1 and PBS2, polarizing beam splitters; M1 and M2, mirrors.

Equations (12)

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

γJ(τ)=|E*(t)·E(t+τ)|2I(t)I(t+τ),
γP(τ)=S(t)·S(t+τ)S0(t)S0(t+τ).
γP(τ)=2γJ(τ)1,
γJ(τ)=Ix2+Iy2+2IxIy|ϕxy(0)|2+|Ixϕxx(τ)+Iyϕyy(τ)|2(Ix+Iy)2+Ix2|ϕxx(τ)|2+Iy2|ϕyy(τ)|2+IxIy(|ϕxy(τ)|2+|ϕyx(τ)|2),
ϕij(τ)=Ei(t)Ej*(t+τ)IiIj
γJ(τ)=2+2|ϕxy(0)|2+|ϕxx(τ)|2+|ϕyy(τ)|2+2Re[ϕxx*(τ)ϕyy(τ)]4+|ϕxx(τ)|2+|ϕyy(τ)|2+|ϕxy(τ)|2+|ϕyx(τ)|2.
Re[ϕxx*(τ)ϕyy(τ)]=Vxx(τ)Vyy(τ)cosφ(τ).
γP(τ)=S1(t)S1(t+τ)+S2(t)S2(t+τ)+S3(t)S3(t+τ)S0(t)S0(t+τ).
S0(t)=Ix(t)+Iy(t)=I(t),
S1(t)=Ix(t)Iy(t),
S2(t)=I+45(t)I45(t),
S3(t)=IRCP(t)ILCP(t).

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