• Photonics Research
  • Vol. 5, Issue 3, 156 (2017)
Lasse-Petteri Leppänen*, Kimmo Saastamoinen, Ari T. Friberg, and Tero Setälä
Author Affiliations
  • Institute of Photonics, University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu, Finland
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    DOI: 10.1364/PRJ.5.000156 Cite this Article Set citation alerts
    Lasse-Petteri Leppänen, Kimmo Saastamoinen, Ari T. Friberg, Tero Setälä. Measurement of the degree of temporal coherence of unpolarized light beams[J]. Photonics Research, 2017, 5(3): 156 Copy Citation Text show less

    Abstract

    We measure the electromagnetic degree of temporal coherence and the associated coherence time for quasi-monochromatic unpolarized light beams emitted by an LED, a filtered halogen lamp, and a multimode He–Ne laser. The method is based on observing at the output of a Michelson interferometer the visibilities (contrasts) of the intensity and polarization-state modulations expressed in terms of the Stokes parameters. The results are in good agreement with those deduced directly from the source spectra. The measurements are repeated after passing the beams through a linear polarizer so as to elucidate the role of polarization in electromagnetic coherence. While the polarizer varies the equal-time degree of coherence consistently with the theoretical predictions and alters the inner structure of the coherence matrix, the coherence time remains almost unchanged when the light varies from unpolarized to polarized. The results are important in the areas of applications dealing with physical optics and electromagnetic interference.
    γ2(τ)=tr[Γ(τ)Γ(τ)]tr2[Γ(0)],(1)

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    S0(τ)=Γxx(τ)+Γyy(τ),(2)

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    S1(τ)=Γxx(τ)Γyy(τ),(3)

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    S2(τ)=Γxy(τ)+Γyx(τ),(4)

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    S3(τ)=i[Γyx(τ)Γxy(τ)],(5)

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    Γ(τ)=12n=03Sn(τ)σn,(6)

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    σ0=[1001],σ1=[1001],σ2=[0110],σ3=[0ii0].(7)

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    S0=Jxx+Jyy,(8)

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    S1=JxxJyy,(9)

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    S2=Jxy+Jyx,(10)

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    S3=i(JyxJxy),(11)

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    γ2(τ)=12n=03|γn(τ)|2,(12)

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    Sn(τ)=12Sn(i)+12S0(i)|γn(i)(τ)|cos[αn(τ)+Δϕω0τ],(13)

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    Vn(τ)=max[Sn(τ)]min[Sn(τ)]max[S0(τ)]+min[S0(τ)]=|γn(i)(τ)|,(14)

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    γ(i)(τ)=[12n=03Vn2(τ)]1/2.(15)

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    n=13Vn2(τ)=V02(τ)=|γs(τ)|2,(16)

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    τc2=τ2γ2(τ)dτγ2(τ)dτ,(17)

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    γ2(0)=12(P2+1),(18)

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    Lasse-Petteri Leppänen, Kimmo Saastamoinen, Ari T. Friberg, Tero Setälä. Measurement of the degree of temporal coherence of unpolarized light beams[J]. Photonics Research, 2017, 5(3): 156
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