Researching | Spectral measurement of coherence Stokes parameters of random broadband light beams

Journals >Photonics Research >Volume 7 >Issue 6 >Page 669 > Article

Photonics Research
Vol. 7, Issue 6, 669 (2019)

Spectral measurement of coherence Stokes parameters of random broadband light beams | On the Cover

Henri Partanen^*, Ari T. Friberg, Tero Set?l?, and Jari Turunen

Author Affiliations

Institute of Photonics, University of Eastern Finland, FI-80101 Joensuu, Finland

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DOI: 10.1364/PRJ.7.000669 Cite this Article Set citation alerts

Henri Partanen, Ari T. Friberg, Tero Set?l?, Jari Turunen. Spectral measurement of coherence Stokes parameters of random broadband light beams[J]. Photonics Research, 2019, 7(6): 669 Copy Citation Text

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Abstract

We introduce a spectrally resolved Young’s interferometer based on a digital micromirror device, a grating spectrometer, and a set of polarization-modulation elements to measure the spectral coherence (two-point) Stokes parameters of random light beams. An experimental demonstration is provided with a spatially partially coherent superluminescent diode amounting to a complex structure of spatio-spectral coherence induced by a quartz-wedge depolarizer. We also show that the polarization and spatial coherence of light can vary with wavelength on a subnanometer scale. The technique is simple and robust and applies to light beams with any spectral bandwidth.

W (r_{1}, r_{2}, λ) = ⟨ E^{*} (r_{1}, λ) E^{T} (r_{2}, λ) ⟩,

(1)

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S_{0} (r_{1}, r_{2}, λ) = W_{x x} (r_{1}, r_{2}, λ) + W_{y y} (r_{1}, r_{2}, λ),

(2)

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S_{1} (r_{1}, r_{2}, λ) = W_{x x} (r_{1}, r_{2}, λ) - W_{y y} (r_{1}, r_{2}, λ),

(3)

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S_{2} (r_{1}, r_{2}, λ) = W_{x y} (r_{1}, r_{2}, λ) + W_{y x} (r_{1}, r_{2}, λ),

(4)

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S_{3} (r_{1}, r_{2}, λ) = i [W_{y x} (r_{1}, r_{2}, λ) - W_{x y} (r_{1}, r_{2}, λ)],

(5)

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S_{n} (r, λ) = S_{n} (r, r, λ), n \in {0, \dots, 3} .

(6)

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μ_{n} (r_{1}, r_{2}, λ) = \frac{S_{n} (r_{1}, r_{2}, λ)}{{[S_{0} (r_{1}, λ) S_{0} (r_{2}, λ)]}^{1 / 2}}, n \in {0, \dots, 3},

(7)

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μ (r_{1}, r_{2}, λ) = {[\frac{1}{2} \sum_{n = 0}^{3} {| μ_{n} (r_{1}, r_{2}, λ) |}^{2}]}^{1 / 2} .

(8)

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W_{0} (x_{1}, x_{2}, λ) = \sum_{j = 0}^{J} α_{j} ψ_{j, 0}^{*} (x_{1}, λ) ψ_{j, 0}^{T} (x_{2}, λ),

(9)

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ψ_{j, 0} (x, λ) = {(\frac{2}{π})}^{1 / 4} \frac{1}{\sqrt{2^{j} j! w_{c}}} H_{j} (\frac{\sqrt{2} x}{w_{c}}) \exp (- \frac{x^{2}}{w_{c}^{2}}),

(10)

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α_{j} = α_{0} {(\frac{1 - β}{1 + β})}^{j} .

(11)

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J (r) = \int_{0}^{\infty} ϕ (r, ω) d ω,

(12)

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S_{0} (r) = I_{1} (r) + I_{2} (r),

(13)

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S_{1} (r) = I_{1} (r) - I_{2} (r),

(14)

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S_{2} (r) = 2 I_{3} (r) - I_{1} (r) - I_{2} (r),

(15)

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S_{3} (r) = 2 I_{4} (r) - I_{1} (r) - I_{2} (r) .

(16)

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S_{n} (x^{'}, λ) = S_{n}^{(1)} (x^{'}, λ) + S_{n}^{(2)} (x^{'}, λ) + 2 {[S_{0}^{(1)} (x^{'}, λ) S_{0}^{(2)} (x^{'}, λ)]}^{1 / 2} \times | μ_{n} (x_{1}, x_{2}, λ) | \cos [ϕ_{n} (x_{1}, x_{2}, λ) + A (λ) x^{'}],

(17)

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C_{n} (x^{'}, λ) = \frac{S_{n} (x^{'}, λ) - S_{n}^{(1)} (x^{'}, λ) - S_{n}^{(2)} (x^{'}, λ)}{2 {[S_{0}^{(1)} (x^{'}, λ) S_{0}^{(2)} (x^{'}, λ)]}^{1 / 2}},

(18)

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C_{n} (x^{'}, λ) = | μ_{n} (x_{1}, x_{2}, λ) | \cos [ϕ_{n} (x_{1}, x_{2}, λ) + A (λ) x^{'}],

(19)

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Henri Partanen, Ari T. Friberg, Tero Set?l?, Jari Turunen. Spectral measurement of coherence Stokes parameters of random broadband light beams[J]. Photonics Research, 2019, 7(6): 669

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