Abstract

A simple device is presented that serves as a secondary source of light with prescribed polarization properties. The technique employed is based on the Schmidt purification of a mixed quantum state. Such a purification can be applied to quantum and to classical polarization states. The device presented here can be used with both classical and quantum primary sources of light. It allows controlling the degree of polarization as well as the Stokes vector that enters the decomposition of a light beam in a fully unpolarized and a fully polarized component.

© 2013 Optical Society of America

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References

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  1. A. S. Ostrovsky, G. Rodríguez-Zurita, C. Meneses-Fabián, M. A. Olvera-Santamaría, and C. Rickenstorff-Parrao, “Experimental generating the partially coherent and partially polarized electromagnetic source,” Opt. Express 18, 12864–12871 (2010).
    [CrossRef]
  2. A. S. Ostrovsky, M. A. Olvera, C. Rickenstorff, G. Martínez-Niconoff, and V. Arrizón, “Generation of a secondary electromagnetic source with desired statistical properties,” Opt. Commun. 283, 4490–4493 (2010).
    [CrossRef]
  3. T. Shirai and E. Wolf, “Coherence and polarization of electromagnetic beams modulated by random phase screens and their changes on propagation in free space,” J. Opt. Soc. Am. A 21, 1907–1916 (2004).
    [CrossRef]
  4. T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A 7, 232–237 (2005).
    [CrossRef]
  5. S.-Y. Lu and R. A. Chipman, “Mueller matrices and the degree of polarization,” Opt. Commun. 146, 11–14 (1998).
    [CrossRef]
  6. S. Başkal, E. Georgieva, Y. S. Kim, and M. E. Noz, “Lorentz group in classical ray optics,” J. Opt. B 6, S455–S472 (2004).
    [CrossRef]
  7. R. Simon, S. Chaturvedi, V. Srinivasan, and N. Mukunda, “Hamilton’s turns for the Lorentz group,” Int. J. Theor. Phys. 45, 2051–2070 (2006).
    [CrossRef]
  8. J. Audretsch, Entangled Systems: New Directions in Quantum Physics (Wiley-VCH, 2007).
  9. B.-G. Englert, C. Kurtsiefer, and H. Weinfurter, “Universal unitary gate for single-photon two-qubit states,” Phys. Rev. A 63, 032303 (2001).
    [CrossRef]
  10. F. De Zela, “Two-component gadget for transforming any two nonorthogonal polarization states into one another,” Phys. Lett. A 376, 1664–1668 (2012).
    [CrossRef]
  11. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
  12. K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nat. Photonics 7, 72–78 (2013).
    [CrossRef]

2013 (1)

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nat. Photonics 7, 72–78 (2013).
[CrossRef]

2012 (1)

F. De Zela, “Two-component gadget for transforming any two nonorthogonal polarization states into one another,” Phys. Lett. A 376, 1664–1668 (2012).
[CrossRef]

2010 (2)

A. S. Ostrovsky, G. Rodríguez-Zurita, C. Meneses-Fabián, M. A. Olvera-Santamaría, and C. Rickenstorff-Parrao, “Experimental generating the partially coherent and partially polarized electromagnetic source,” Opt. Express 18, 12864–12871 (2010).
[CrossRef]

A. S. Ostrovsky, M. A. Olvera, C. Rickenstorff, G. Martínez-Niconoff, and V. Arrizón, “Generation of a secondary electromagnetic source with desired statistical properties,” Opt. Commun. 283, 4490–4493 (2010).
[CrossRef]

2006 (1)

R. Simon, S. Chaturvedi, V. Srinivasan, and N. Mukunda, “Hamilton’s turns for the Lorentz group,” Int. J. Theor. Phys. 45, 2051–2070 (2006).
[CrossRef]

2005 (1)

T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A 7, 232–237 (2005).
[CrossRef]

2004 (2)

2001 (1)

B.-G. Englert, C. Kurtsiefer, and H. Weinfurter, “Universal unitary gate for single-photon two-qubit states,” Phys. Rev. A 63, 032303 (2001).
[CrossRef]

1998 (1)

S.-Y. Lu and R. A. Chipman, “Mueller matrices and the degree of polarization,” Opt. Commun. 146, 11–14 (1998).
[CrossRef]

Abouraddy, A. F.

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nat. Photonics 7, 72–78 (2013).
[CrossRef]

Arrizón, V.

A. S. Ostrovsky, M. A. Olvera, C. Rickenstorff, G. Martínez-Niconoff, and V. Arrizón, “Generation of a secondary electromagnetic source with desired statistical properties,” Opt. Commun. 283, 4490–4493 (2010).
[CrossRef]

Audretsch, J.

J. Audretsch, Entangled Systems: New Directions in Quantum Physics (Wiley-VCH, 2007).

Baskal, S.

S. Başkal, E. Georgieva, Y. S. Kim, and M. E. Noz, “Lorentz group in classical ray optics,” J. Opt. B 6, S455–S472 (2004).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

Chaturvedi, S.

R. Simon, S. Chaturvedi, V. Srinivasan, and N. Mukunda, “Hamilton’s turns for the Lorentz group,” Int. J. Theor. Phys. 45, 2051–2070 (2006).
[CrossRef]

Chipman, R. A.

S.-Y. Lu and R. A. Chipman, “Mueller matrices and the degree of polarization,” Opt. Commun. 146, 11–14 (1998).
[CrossRef]

De Zela, F.

F. De Zela, “Two-component gadget for transforming any two nonorthogonal polarization states into one another,” Phys. Lett. A 376, 1664–1668 (2012).
[CrossRef]

Di Giuseppe, G.

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nat. Photonics 7, 72–78 (2013).
[CrossRef]

Englert, B.-G.

B.-G. Englert, C. Kurtsiefer, and H. Weinfurter, “Universal unitary gate for single-photon two-qubit states,” Phys. Rev. A 63, 032303 (2001).
[CrossRef]

Georgieva, E.

S. Başkal, E. Georgieva, Y. S. Kim, and M. E. Noz, “Lorentz group in classical ray optics,” J. Opt. B 6, S455–S472 (2004).
[CrossRef]

Kagalwala, K. H.

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nat. Photonics 7, 72–78 (2013).
[CrossRef]

Kim, Y. S.

S. Başkal, E. Georgieva, Y. S. Kim, and M. E. Noz, “Lorentz group in classical ray optics,” J. Opt. B 6, S455–S472 (2004).
[CrossRef]

Korotkova, O.

T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A 7, 232–237 (2005).
[CrossRef]

Kurtsiefer, C.

B.-G. Englert, C. Kurtsiefer, and H. Weinfurter, “Universal unitary gate for single-photon two-qubit states,” Phys. Rev. A 63, 032303 (2001).
[CrossRef]

Lu, S.-Y.

S.-Y. Lu and R. A. Chipman, “Mueller matrices and the degree of polarization,” Opt. Commun. 146, 11–14 (1998).
[CrossRef]

Martínez-Niconoff, G.

A. S. Ostrovsky, M. A. Olvera, C. Rickenstorff, G. Martínez-Niconoff, and V. Arrizón, “Generation of a secondary electromagnetic source with desired statistical properties,” Opt. Commun. 283, 4490–4493 (2010).
[CrossRef]

Meneses-Fabián, C.

Mukunda, N.

R. Simon, S. Chaturvedi, V. Srinivasan, and N. Mukunda, “Hamilton’s turns for the Lorentz group,” Int. J. Theor. Phys. 45, 2051–2070 (2006).
[CrossRef]

Noz, M. E.

S. Başkal, E. Georgieva, Y. S. Kim, and M. E. Noz, “Lorentz group in classical ray optics,” J. Opt. B 6, S455–S472 (2004).
[CrossRef]

Olvera, M. A.

A. S. Ostrovsky, M. A. Olvera, C. Rickenstorff, G. Martínez-Niconoff, and V. Arrizón, “Generation of a secondary electromagnetic source with desired statistical properties,” Opt. Commun. 283, 4490–4493 (2010).
[CrossRef]

Olvera-Santamaría, M. A.

Ostrovsky, A. S.

A. S. Ostrovsky, G. Rodríguez-Zurita, C. Meneses-Fabián, M. A. Olvera-Santamaría, and C. Rickenstorff-Parrao, “Experimental generating the partially coherent and partially polarized electromagnetic source,” Opt. Express 18, 12864–12871 (2010).
[CrossRef]

A. S. Ostrovsky, M. A. Olvera, C. Rickenstorff, G. Martínez-Niconoff, and V. Arrizón, “Generation of a secondary electromagnetic source with desired statistical properties,” Opt. Commun. 283, 4490–4493 (2010).
[CrossRef]

Rickenstorff, C.

A. S. Ostrovsky, M. A. Olvera, C. Rickenstorff, G. Martínez-Niconoff, and V. Arrizón, “Generation of a secondary electromagnetic source with desired statistical properties,” Opt. Commun. 283, 4490–4493 (2010).
[CrossRef]

Rickenstorff-Parrao, C.

Rodríguez-Zurita, G.

Saleh, B. E. A.

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nat. Photonics 7, 72–78 (2013).
[CrossRef]

Shirai, T.

Simon, R.

R. Simon, S. Chaturvedi, V. Srinivasan, and N. Mukunda, “Hamilton’s turns for the Lorentz group,” Int. J. Theor. Phys. 45, 2051–2070 (2006).
[CrossRef]

Srinivasan, V.

R. Simon, S. Chaturvedi, V. Srinivasan, and N. Mukunda, “Hamilton’s turns for the Lorentz group,” Int. J. Theor. Phys. 45, 2051–2070 (2006).
[CrossRef]

Weinfurter, H.

B.-G. Englert, C. Kurtsiefer, and H. Weinfurter, “Universal unitary gate for single-photon two-qubit states,” Phys. Rev. A 63, 032303 (2001).
[CrossRef]

Wolf, E.

T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A 7, 232–237 (2005).
[CrossRef]

T. Shirai and E. Wolf, “Coherence and polarization of electromagnetic beams modulated by random phase screens and their changes on propagation in free space,” J. Opt. Soc. Am. A 21, 1907–1916 (2004).
[CrossRef]

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

Int. J. Theor. Phys. (1)

R. Simon, S. Chaturvedi, V. Srinivasan, and N. Mukunda, “Hamilton’s turns for the Lorentz group,” Int. J. Theor. Phys. 45, 2051–2070 (2006).
[CrossRef]

J. Opt. A (1)

T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A 7, 232–237 (2005).
[CrossRef]

J. Opt. B (1)

S. Başkal, E. Georgieva, Y. S. Kim, and M. E. Noz, “Lorentz group in classical ray optics,” J. Opt. B 6, S455–S472 (2004).
[CrossRef]

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

Nat. Photonics (1)

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nat. Photonics 7, 72–78 (2013).
[CrossRef]

Opt. Commun. (2)

S.-Y. Lu and R. A. Chipman, “Mueller matrices and the degree of polarization,” Opt. Commun. 146, 11–14 (1998).
[CrossRef]

A. S. Ostrovsky, M. A. Olvera, C. Rickenstorff, G. Martínez-Niconoff, and V. Arrizón, “Generation of a secondary electromagnetic source with desired statistical properties,” Opt. Commun. 283, 4490–4493 (2010).
[CrossRef]

Opt. Express (1)

Phys. Lett. A (1)

F. De Zela, “Two-component gadget for transforming any two nonorthogonal polarization states into one another,” Phys. Lett. A 376, 1664–1668 (2012).
[CrossRef]

Phys. Rev. A (1)

B.-G. Englert, C. Kurtsiefer, and H. Weinfurter, “Universal unitary gate for single-photon two-qubit states,” Phys. Rev. A 63, 032303 (2001).
[CrossRef]

Other (2)

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

J. Audretsch, Entangled Systems: New Directions in Quantum Physics (Wiley-VCH, 2007).

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Figures (1)

Fig. 1.
Fig. 1.

Mach–Zehnder array. BS, beam splitter; M, mirror; Q, quarter-wave plate; and DxDy, detectors. The input state |Xv is a vertically polarized light-beam that propagates along the X direction. The array produces an output state carrying the desired characteristics of partial polarization. To extract them from the pure path-polarization product-state, one must trace over the path degree of freedom, thereby obtaining a mixed, i.e., partially polarized state. This can be done, e.g., by summing up the counts—or the registered intensities—of the two detectors.

Equations (18)

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J^=12(s01+s·σ).
ρ^=12(1+Pn·σ),
P=(14Detρ^)1/2=(14DetJ^(TrJ^)2)1/2.
|n±n±|=12(1±n·σ).
|Φλ+|X,n++λ|Y,n.
Tra(|ΦΦ|)=(λ++λ2)1+(λ+λ2)n·σ=12(1+Pn·σ).
UMZ=UXX|XX|+UXY|XY|+UYX|YX|+UYY|YY|,
Tra|ΨfΨf|=UXX|vv|UXX+UYX|vv|UYX.
VX=eiϕX(|tXh|+|sXv|),VY=eiϕY(|tYh|+|sYv|),
Tra|ΨfΨf|=12(VX|vv|VX+VY|vv|VY)=12(|sXsX|+|sYsY|).
|tX=λ+|n+iλ|n+,|sX=λ|n+iλ+|n+,|tY=λ+|niλ|n+,|sY=λ|niλ+|n+.
Tra|ΨfΨf|=λ+|n+n+|+λ|nn|=12(1+Pn·σ),
sf=(Pcos2χ,1P2sinϕPcosϕsin2χ,1P2cosϕPsinϕsin2χ)
(xc3+t3)2[1+(xc3+t3)2]=(xc1+t1)2+(xc2+t2)2.
Ii(θ,ϵ)=Trp(PθQερiQεPθ),
Pθ=(cos2θcosθsinθcosθsinθsin2θ)
Qπ/2=(eiπ/400eiπ/4)
J^=12((1+Pcos2χ)Peiϕsin2χPeiϕsin2χ(1Pcos2χ)),

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