Abstract

An image-shearing interferometer of Mach–Zehnder type with corner cubes is introduced for the purpose of measuring spatial coherence at the output of inhomogeneous optical sources, such as multimode fibers (MMFs). One arm of the interferometer is modulated in optical delay to produce dynamic interference fringes. Fringe visibility and the two individual intensities are measured nearly simultaneously to allow direct calculation of the modulus of the complex degree of coherence as a function of the lateral shear between the two interferometer arms. Spatial degree of coherence is measured for a step-index MMF pumped with monochromatic and broadband optical sources.

© 2013 Optical Society of America

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References

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J. Kim, D. T. Miller, E. Kim, S. Oh, J. Oh, and T. E. Milner, J. Biomed. Opt. 10, 064034 (2005).
[CrossRef]

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[CrossRef]

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Borghi, R.

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Feuermann, D.

Goldstein, A.

Goodman, J. W.

Gordon, J. M.

Iaconis, C.

Kanabe, T.

H. Nakano, N. Miyanaga, K. Yagi, K. Tsubakimoto, T. Kanabe, M. Nakatsuka, and S. Nakai, Appl. Phys. Lett. 63, 580 (1993).
[CrossRef]

Kim, E.

J. Kim, D. T. Miller, E. Kim, S. Oh, J. Oh, and T. E. Milner, J. Biomed. Opt. 10, 064034 (2005).
[CrossRef]

Kim, J.

J. Kim, D. T. Miller, E. Kim, S. Oh, J. Oh, and T. E. Milner, J. Biomed. Opt. 10, 064034 (2005).
[CrossRef]

Kumar, A.

Mashaal, H.

Miller, D. T.

J. Kim, D. T. Miller, E. Kim, S. Oh, J. Oh, and T. E. Milner, J. Biomed. Opt. 10, 064034 (2005).
[CrossRef]

Milner, T. E.

J. Kim, D. T. Miller, E. Kim, S. Oh, J. Oh, and T. E. Milner, J. Biomed. Opt. 10, 064034 (2005).
[CrossRef]

Miyanaga, N.

H. Nakano, N. Miyanaga, K. Yagi, K. Tsubakimoto, T. Kanabe, M. Nakatsuka, and S. Nakai, Appl. Phys. Lett. 63, 580 (1993).
[CrossRef]

Nakai, S.

H. Nakano, N. Miyanaga, K. Yagi, K. Tsubakimoto, T. Kanabe, M. Nakatsuka, and S. Nakai, Appl. Phys. Lett. 63, 580 (1993).
[CrossRef]

Nakano, H.

H. Nakano, N. Miyanaga, K. Yagi, K. Tsubakimoto, T. Kanabe, M. Nakatsuka, and S. Nakai, Appl. Phys. Lett. 63, 580 (1993).
[CrossRef]

Nakatsuka, M.

H. Nakano, N. Miyanaga, K. Yagi, K. Tsubakimoto, T. Kanabe, M. Nakatsuka, and S. Nakai, Appl. Phys. Lett. 63, 580 (1993).
[CrossRef]

Norton, R. E.

Oh, J.

J. Kim, D. T. Miller, E. Kim, S. Oh, J. Oh, and T. E. Milner, J. Biomed. Opt. 10, 064034 (2005).
[CrossRef]

Oh, S.

J. Kim, D. T. Miller, E. Kim, S. Oh, J. Oh, and T. E. Milner, J. Biomed. Opt. 10, 064034 (2005).
[CrossRef]

Prabhakar, S.

Rawson, E. G.

Santarsiero, M.

Singh, R. P.

Tsubakimoto, K.

H. Nakano, N. Miyanaga, K. Yagi, K. Tsubakimoto, T. Kanabe, M. Nakatsuka, and S. Nakai, Appl. Phys. Lett. 63, 580 (1993).
[CrossRef]

Vaity, P.

Walmsley, I. A.

Wolf, E.

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

Yagi, K.

H. Nakano, N. Miyanaga, K. Yagi, K. Tsubakimoto, T. Kanabe, M. Nakatsuka, and S. Nakai, Appl. Phys. Lett. 63, 580 (1993).
[CrossRef]

Appl. Phys. Lett.

H. Nakano, N. Miyanaga, K. Yagi, K. Tsubakimoto, T. Kanabe, M. Nakatsuka, and S. Nakai, Appl. Phys. Lett. 63, 580 (1993).
[CrossRef]

J. Biomed. Opt.

J. Kim, D. T. Miller, E. Kim, S. Oh, J. Oh, and T. E. Milner, J. Biomed. Opt. 10, 064034 (2005).
[CrossRef]

J. Opt. Soc. Am.

Opt. Lett.

Other

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

J. W. Goodman, Statistical Optics (Wiley, 2000).

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Figures (4)

Fig. 1.
Fig. 1.

Schematic of the shearing Mach–Zehnder interferometer.

Fig. 2.
Fig. 2.

Illustration of the overlap of the points P1 and P2 by shearing.

Fig. 3.
Fig. 3.

Four windows modulating the detected signal by the two phase-locked, 90° out-of-phase chopper wheels (left) and an example of the actual signal (right).

Fig. 4.
Fig. 4.

(a) Intensity profiles in the shearing arm of the interferometer S2 and (b) modulus of the complex degree of coherence |γ12(0)|, at the output of a step-index MMF pumped with a monochromatic (squares) and broadband (circles) sources.

Equations (3)

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

S(τ)=S1+S2+2S1S2Re{γ12(τ)}=S1+S2+2S1S2|γ12|cos(ωτ+α12),
|γ12(0)|=max(S)min(S)4S1S2,
S(ω)=S1(ω)+S2(ω)+2S1(ω)S2(ω)Re{γ12(ω)eiωτ},

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