• 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
    Illustration of Michelson’s interferometer. An incident beam is split into arms 1 and 2 by a BS. The fields reflect back from the mirrors (M) and propagate to the output via the BS again. The length of arm 2 can be adjusted by translating the mirror, yielding to a time delay τ between the fields from the two arms.
    Fig. 1. Illustration of Michelson’s interferometer. An incident beam is split into arms 1 and 2 by a BS. The fields reflect back from the mirrors (M) and propagate to the output via the BS again. The length of arm 2 can be adjusted by translating the mirror, yielding to a time delay τ between the fields from the two arms.
    Illustration of the used measurement setup. Collimating optics render the light from the source beam-like. The beam is split into arms 1 and 2 with a nonpolarizing BS. The mirror (M) in arm 2 is translated by a piezo element, yielding a controllable time difference τ between the fields from the two arms, and their interference is observed with a CMOS camera. To transform the variations of the polarization Stokes parameters into intensity modulation, suitable quarter-wave plates Q(θ), where θ is the angle the fast axis of the wave plate created with the x axis, are placed into the two arms.
    Fig. 2. Illustration of the used measurement setup. Collimating optics render the light from the source beam-like. The beam is split into arms 1 and 2 with a nonpolarizing BS. The mirror (M) in arm 2 is translated by a piezo element, yielding a controllable time difference τ between the fields from the two arms, and their interference is observed with a CMOS camera. To transform the variations of the polarization Stokes parameters into intensity modulation, suitable quarter-wave plates Q(θ), where θ is the angle the fast axis of the wave plate created with the x axis, are placed into the two arms.
    Measured spectra of the considered light sources: an LED with the center wavelength of 633.8 nm (solid red line), filtered light from a halogen lamp (dashed blue line) with the bandwidth of 10 nm and center wavelength of 634.5 nm, and a He–Ne laser of the wavelength 632.8 nm (yellow vertical line).
    Fig. 3. Measured spectra of the considered light sources: an LED with the center wavelength of 633.8 nm (solid red line), filtered light from a halogen lamp (dashed blue line) with the bandwidth of 10 nm and center wavelength of 634.5 nm, and a He–Ne laser of the wavelength 632.8 nm (yellow vertical line).
    Intensity, S0, of the LED source as a function of τ at the output of Michelson’s interferometer. Inset shows a magnified section over a short τ range demonstrating the oscillatory behavior of S0(τ).
    Fig. 4. Intensity, S0, of the LED source as a function of τ at the output of Michelson’s interferometer. Inset shows a magnified section over a short τ range demonstrating the oscillatory behavior of S0(τ).
    Illustration of the temporal coherence properties of an LED source. (a) Visibilities of the Stokes-parameter modulations for unpolarized LED light. (b) Temporal electromagnetic degree of coherence obtained from the visibilities (blue curve, maximum value γ(0)=0.68, coherence time τc=24 fs) and by Fourier transforming the spectrum (red crosses). Panels (c) and (d) are as in (a) and (b), respectively, but for polarized LED light. In (d) the maximum value is γ(0)=0.9 and τc=22 fs.
    Fig. 5. Illustration of the temporal coherence properties of an LED source. (a) Visibilities of the Stokes-parameter modulations for unpolarized LED light. (b) Temporal electromagnetic degree of coherence obtained from the visibilities (blue curve, maximum value γ(0)=0.68, coherence time τc=24  fs) and by Fourier transforming the spectrum (red crosses). Panels (c) and (d) are as in (a) and (b), respectively, but for polarized LED light. In (d) the maximum value is γ(0)=0.9 and τc=22  fs.
    Temporal coherence properties of filtered light from a halogen lamp. (a) Visibilities of the Stokes-parameter modulations for unpolarized light. (b) Temporal electromagnetic degree of coherence obtained from the visibilities (blue curve, maximum value γ(0)=0.66, coherence time τc=53 fs) and by Fourier transforming the spectrum of the light (red crosses). Panels (c) and (d) are as in (a) and (b), respectively, but for polarized lamp light. In (d) the maximum value is γ(0)=0.94 and τc=57 fs.
    Fig. 6. Temporal coherence properties of filtered light from a halogen lamp. (a) Visibilities of the Stokes-parameter modulations for unpolarized light. (b) Temporal electromagnetic degree of coherence obtained from the visibilities (blue curve, maximum value γ(0)=0.66, coherence time τc=53  fs) and by Fourier transforming the spectrum of the light (red crosses). Panels (c) and (d) are as in (a) and (b), respectively, but for polarized lamp light. In (d) the maximum value is γ(0)=0.94 and τc=57  fs.
    Temporal coherence properties of a He–Ne laser source. (a) Visibilities of the Stokes-parameter modulations when the beam is unpolarized. (b) Temporal electromagnetic degree of coherence (maximum value γ(0)=0.66, coherence time τc=0.71 ns). Panels (c) and (d) are as in (a) and (b), respectively, but for a polarized laser beam. In (d) the maximum value is γ(0)=0.88 and τc=0.63 ns.
    Fig. 7. Temporal coherence properties of a He–Ne laser source. (a) Visibilities of the Stokes-parameter modulations when the beam is unpolarized. (b) Temporal electromagnetic degree of coherence (maximum value γ(0)=0.66, coherence time τc=0.71  ns). Panels (c) and (d) are as in (a) and (b), respectively, but for a polarized laser beam. In (d) the maximum value is γ(0)=0.88 and τc=0.63  ns.
    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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