Abstract

The novel spatiotemporal optical coherence manipulation technique, which allows one to tailor the second-order coherence properties of a light beam, is introduced. With the use of an interferometric setup we show that the basic measure of the contrast of interference fringes, i.e., Michelson’s visibility, can be controlled across the interference pattern by modulating the phase of the spectral degree of coherence.

© 2013 Optical Society of America

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References

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  1. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
  2. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
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    [CrossRef]
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    [CrossRef]
  6. G. J. Tearney, M. Shishkov, and B. E. Bouma, Opt. Lett. 27, 412 (2002).
    [CrossRef]
  7. M. J. Góra, J. S. Sauk, R. W. Carruth, K. A. Gallagher, M. J. Suter, N. S. Nishioka, L. E. Kava, M. Rosenberg, B. E. Bouma, and G. J. Tearney, Nat. Med. 19, 238 (2013).
    [CrossRef]
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    [CrossRef]
  9. P. D. Maker and R. W. Terhune, Phys. Rev. 137, A801 (1965).
    [CrossRef]
  10. G. Eckhardt, R. W. Hellwarth, F. J. McClung, S. E. Schwarz, D. Weiner, and E. J. Woodbury, Phys. Rev. Lett. 9, 455 (1962).
    [CrossRef]
  11. W. Martienssen and E. Spiller, Am. J. Phys. 32, 919 (1964).
    [CrossRef]
  12. F. Scudieri, M. Bertolotti, and R. Bartolino, Appl. Opt. 13, 181 (1974).
    [CrossRef]
  13. Y. Ohtsuka, J. Opt. Soc. Am. A 3, 1247 (1986).
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    [CrossRef]
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  16. E. Baleine and A. Dogariu, Opt. Lett. 29, 1233 (2004).
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  17. E. Baleine and A. Dogariu, Phys. Rev. Lett. 95, 193904 (2005).
    [CrossRef]
  18. A. S. Ostrovsky, G. Martínez-Niconoff, V. Arrizón, P. Martínez-Vara, M. A. Olvera-Santamaría, and C. Rickenstorff-Parrao, Opt. Express 17, 5257 (2009).
    [CrossRef]
  19. O. G. Rodriguez-Herrera and J. S. Tyo, J. Opt. Soc. Am. A 29, 1939 (2012).
    [CrossRef]
  20. J. C. Dainty, ed., Laser Speckles and Related Phenomena, 2nd ed. (Springer-Verlag, 1984).
  21. J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2004).
  22. L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).
    [CrossRef]
  23. D. Malacara, ed., Optical Shop Testing (Wiley, 2007).
  24. S. Osten, S. Krüger, and A. Hermeschmidt, in Adaptive Optics for Industry and Medicine, C. Dainty, ed. (Imperial College, 2007), pp. 124–129.
  25. E. G. van Putten, I. M. Vellekoop, and A. P. Mosk, Appl. Opt. 47, 2076 (2008).
    [CrossRef]
  26. A. A. Michelson, J. Phil. Mag. 30(182), 1 (1890).
    [CrossRef]
  27. R. K. Mali, T. G. Bifano, N. Vandelli, and M. N. Horenstein, Opt. Eng. 36, 542 (1997).
    [CrossRef]

2013 (1)

M. J. Góra, J. S. Sauk, R. W. Carruth, K. A. Gallagher, M. J. Suter, N. S. Nishioka, L. E. Kava, M. Rosenberg, B. E. Bouma, and G. J. Tearney, Nat. Med. 19, 238 (2013).
[CrossRef]

2012 (1)

2009 (1)

2008 (1)

2005 (1)

E. Baleine and A. Dogariu, Phys. Rev. Lett. 95, 193904 (2005).
[CrossRef]

2004 (2)

2003 (1)

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, Rep. Prog. Phys. 66, 239 (2003).
[CrossRef]

2002 (1)

1997 (1)

R. K. Mali, T. G. Bifano, N. Vandelli, and M. N. Horenstein, Opt. Eng. 36, 542 (1997).
[CrossRef]

1991 (1)

1990 (1)

E. T. J. Turunen and A. T. Friberg, J. Appl. Phys. 67, 49 (1990).
[CrossRef]

1986 (1)

1974 (1)

1965 (2)

L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).
[CrossRef]

P. D. Maker and R. W. Terhune, Phys. Rev. 137, A801 (1965).
[CrossRef]

1964 (1)

W. Martienssen and E. Spiller, Am. J. Phys. 32, 919 (1964).
[CrossRef]

1962 (1)

G. Eckhardt, R. W. Hellwarth, F. J. McClung, S. E. Schwarz, D. Weiner, and E. J. Woodbury, Phys. Rev. Lett. 9, 455 (1962).
[CrossRef]

1928 (1)

C. V. Raman and K. S. Krishnan, Nature 121, 501 (1928).
[CrossRef]

1890 (1)

A. A. Michelson, J. Phil. Mag. 30(182), 1 (1890).
[CrossRef]

Arrizón, V.

Baleine, E.

E. Baleine and A. Dogariu, Phys. Rev. Lett. 95, 193904 (2005).
[CrossRef]

E. Baleine and A. Dogariu, Opt. Lett. 29, 1233 (2004).
[CrossRef]

Bartolino, R.

Bertolotti, M.

Bifano, T. G.

R. K. Mali, T. G. Bifano, N. Vandelli, and M. N. Horenstein, Opt. Eng. 36, 542 (1997).
[CrossRef]

Born, M.

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

Bouma, B. E.

M. J. Góra, J. S. Sauk, R. W. Carruth, K. A. Gallagher, M. J. Suter, N. S. Nishioka, L. E. Kava, M. Rosenberg, B. E. Bouma, and G. J. Tearney, Nat. Med. 19, 238 (2013).
[CrossRef]

G. J. Tearney, M. Shishkov, and B. E. Bouma, Opt. Lett. 27, 412 (2002).
[CrossRef]

Carruth, R. W.

M. J. Góra, J. S. Sauk, R. W. Carruth, K. A. Gallagher, M. J. Suter, N. S. Nishioka, L. E. Kava, M. Rosenberg, B. E. Bouma, and G. J. Tearney, Nat. Med. 19, 238 (2013).
[CrossRef]

Dogariu, A.

E. Baleine and A. Dogariu, Phys. Rev. Lett. 95, 193904 (2005).
[CrossRef]

E. Baleine and A. Dogariu, Opt. Lett. 29, 1233 (2004).
[CrossRef]

Drexler, W.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, Rep. Prog. Phys. 66, 239 (2003).
[CrossRef]

Eckhardt, G.

G. Eckhardt, R. W. Hellwarth, F. J. McClung, S. E. Schwarz, D. Weiner, and E. J. Woodbury, Phys. Rev. Lett. 9, 455 (1962).
[CrossRef]

Fercher, A. F.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, Rep. Prog. Phys. 66, 239 (2003).
[CrossRef]

Friberg, A. T.

E. T. J. Turunen and A. T. Friberg, J. Appl. Phys. 67, 49 (1990).
[CrossRef]

Gallagher, K. A.

M. J. Góra, J. S. Sauk, R. W. Carruth, K. A. Gallagher, M. J. Suter, N. S. Nishioka, L. E. Kava, M. Rosenberg, B. E. Bouma, and G. J. Tearney, Nat. Med. 19, 238 (2013).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2004).

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

Góra, M. J.

M. J. Góra, J. S. Sauk, R. W. Carruth, K. A. Gallagher, M. J. Suter, N. S. Nishioka, L. E. Kava, M. Rosenberg, B. E. Bouma, and G. J. Tearney, Nat. Med. 19, 238 (2013).
[CrossRef]

Hellwarth, R. W.

G. Eckhardt, R. W. Hellwarth, F. J. McClung, S. E. Schwarz, D. Weiner, and E. J. Woodbury, Phys. Rev. Lett. 9, 455 (1962).
[CrossRef]

Hermeschmidt, A.

S. Osten, S. Krüger, and A. Hermeschmidt, in Adaptive Optics for Industry and Medicine, C. Dainty, ed. (Imperial College, 2007), pp. 124–129.

Hitzenberger, C. K.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, Rep. Prog. Phys. 66, 239 (2003).
[CrossRef]

Horenstein, M. N.

R. K. Mali, T. G. Bifano, N. Vandelli, and M. N. Horenstein, Opt. Eng. 36, 542 (1997).
[CrossRef]

Kava, L. E.

M. J. Góra, J. S. Sauk, R. W. Carruth, K. A. Gallagher, M. J. Suter, N. S. Nishioka, L. E. Kava, M. Rosenberg, B. E. Bouma, and G. J. Tearney, Nat. Med. 19, 238 (2013).
[CrossRef]

Krishnan, K. S.

C. V. Raman and K. S. Krishnan, Nature 121, 501 (1928).
[CrossRef]

Krüger, S.

S. Osten, S. Krüger, and A. Hermeschmidt, in Adaptive Optics for Industry and Medicine, C. Dainty, ed. (Imperial College, 2007), pp. 124–129.

Lasser, T.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, Rep. Prog. Phys. 66, 239 (2003).
[CrossRef]

Maker, P. D.

P. D. Maker and R. W. Terhune, Phys. Rev. 137, A801 (1965).
[CrossRef]

Mali, R. K.

R. K. Mali, T. G. Bifano, N. Vandelli, and M. N. Horenstein, Opt. Eng. 36, 542 (1997).
[CrossRef]

Mandel, L.

L. Mandel, Opt. Lett. 16, 1882 (1991).
[CrossRef]

L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).
[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Martienssen, W.

W. Martienssen and E. Spiller, Am. J. Phys. 32, 919 (1964).
[CrossRef]

Martínez-Niconoff, G.

Martínez-Vara, P.

McClung, F. J.

G. Eckhardt, R. W. Hellwarth, F. J. McClung, S. E. Schwarz, D. Weiner, and E. J. Woodbury, Phys. Rev. Lett. 9, 455 (1962).
[CrossRef]

Michelson, A. A.

A. A. Michelson, J. Phil. Mag. 30(182), 1 (1890).
[CrossRef]

Mosk, A. P.

Nishioka, N. S.

M. J. Góra, J. S. Sauk, R. W. Carruth, K. A. Gallagher, M. J. Suter, N. S. Nishioka, L. E. Kava, M. Rosenberg, B. E. Bouma, and G. J. Tearney, Nat. Med. 19, 238 (2013).
[CrossRef]

Ohtsuka, Y.

Olvera-Santamaría, M. A.

Osten, S.

S. Osten, S. Krüger, and A. Hermeschmidt, in Adaptive Optics for Industry and Medicine, C. Dainty, ed. (Imperial College, 2007), pp. 124–129.

Ostrovsky, A. S.

Raman, C. V.

C. V. Raman and K. S. Krishnan, Nature 121, 501 (1928).
[CrossRef]

Rickenstorff-Parrao, C.

Rodriguez-Herrera, O. G.

Rosenberg, M.

M. J. Góra, J. S. Sauk, R. W. Carruth, K. A. Gallagher, M. J. Suter, N. S. Nishioka, L. E. Kava, M. Rosenberg, B. E. Bouma, and G. J. Tearney, Nat. Med. 19, 238 (2013).
[CrossRef]

Sauk, J. S.

M. J. Góra, J. S. Sauk, R. W. Carruth, K. A. Gallagher, M. J. Suter, N. S. Nishioka, L. E. Kava, M. Rosenberg, B. E. Bouma, and G. J. Tearney, Nat. Med. 19, 238 (2013).
[CrossRef]

Schwarz, S. E.

G. Eckhardt, R. W. Hellwarth, F. J. McClung, S. E. Schwarz, D. Weiner, and E. J. Woodbury, Phys. Rev. Lett. 9, 455 (1962).
[CrossRef]

Scudieri, F.

Shirai, T.

Shishkov, M.

Spiller, E.

W. Martienssen and E. Spiller, Am. J. Phys. 32, 919 (1964).
[CrossRef]

Suter, M. J.

M. J. Góra, J. S. Sauk, R. W. Carruth, K. A. Gallagher, M. J. Suter, N. S. Nishioka, L. E. Kava, M. Rosenberg, B. E. Bouma, and G. J. Tearney, Nat. Med. 19, 238 (2013).
[CrossRef]

Tearney, G. J.

M. J. Góra, J. S. Sauk, R. W. Carruth, K. A. Gallagher, M. J. Suter, N. S. Nishioka, L. E. Kava, M. Rosenberg, B. E. Bouma, and G. J. Tearney, Nat. Med. 19, 238 (2013).
[CrossRef]

G. J. Tearney, M. Shishkov, and B. E. Bouma, Opt. Lett. 27, 412 (2002).
[CrossRef]

Terhune, R. W.

P. D. Maker and R. W. Terhune, Phys. Rev. 137, A801 (1965).
[CrossRef]

Turunen, E. T. J.

E. T. J. Turunen and A. T. Friberg, J. Appl. Phys. 67, 49 (1990).
[CrossRef]

Tyo, J. S.

van Putten, E. G.

Vandelli, N.

R. K. Mali, T. G. Bifano, N. Vandelli, and M. N. Horenstein, Opt. Eng. 36, 542 (1997).
[CrossRef]

Vellekoop, I. M.

Weiner, D.

G. Eckhardt, R. W. Hellwarth, F. J. McClung, S. E. Schwarz, D. Weiner, and E. J. Woodbury, Phys. Rev. Lett. 9, 455 (1962).
[CrossRef]

Wolf, E.

T. Shirai and E. Wolf, J. Opt. Soc. Am. A 21, 1907 (2004).
[CrossRef]

L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).
[CrossRef]

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

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Woodbury, E. J.

G. Eckhardt, R. W. Hellwarth, F. J. McClung, S. E. Schwarz, D. Weiner, and E. J. Woodbury, Phys. Rev. Lett. 9, 455 (1962).
[CrossRef]

Am. J. Phys. (1)

W. Martienssen and E. Spiller, Am. J. Phys. 32, 919 (1964).
[CrossRef]

Appl. Opt. (2)

J. Appl. Phys. (1)

E. T. J. Turunen and A. T. Friberg, J. Appl. Phys. 67, 49 (1990).
[CrossRef]

J. Opt. Soc. Am. A (3)

J. Phil. Mag. (1)

A. A. Michelson, J. Phil. Mag. 30(182), 1 (1890).
[CrossRef]

Nat. Med. (1)

M. J. Góra, J. S. Sauk, R. W. Carruth, K. A. Gallagher, M. J. Suter, N. S. Nishioka, L. E. Kava, M. Rosenberg, B. E. Bouma, and G. J. Tearney, Nat. Med. 19, 238 (2013).
[CrossRef]

Nature (1)

C. V. Raman and K. S. Krishnan, Nature 121, 501 (1928).
[CrossRef]

Opt. Eng. (1)

R. K. Mali, T. G. Bifano, N. Vandelli, and M. N. Horenstein, Opt. Eng. 36, 542 (1997).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. (1)

P. D. Maker and R. W. Terhune, Phys. Rev. 137, A801 (1965).
[CrossRef]

Phys. Rev. Lett. (2)

G. Eckhardt, R. W. Hellwarth, F. J. McClung, S. E. Schwarz, D. Weiner, and E. J. Woodbury, Phys. Rev. Lett. 9, 455 (1962).
[CrossRef]

E. Baleine and A. Dogariu, Phys. Rev. Lett. 95, 193904 (2005).
[CrossRef]

Rep. Prog. Phys. (1)

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, Rep. Prog. Phys. 66, 239 (2003).
[CrossRef]

Rev. Mod. Phys. (1)

L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).
[CrossRef]

Other (7)

D. Malacara, ed., Optical Shop Testing (Wiley, 2007).

S. Osten, S. Krüger, and A. Hermeschmidt, in Adaptive Optics for Industry and Medicine, C. Dainty, ed. (Imperial College, 2007), pp. 124–129.

J. C. Dainty, ed., Laser Speckles and Related Phenomena, 2nd ed. (Springer-Verlag, 1984).

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2004).

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

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

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

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Figures (3)

Fig. 1.
Fig. 1.

Sketch of the experimental setup. MOb, microscope objective; L1, lens, f=150mm; L2, lens, f=50mm; M1 and M2, flat mirrors; P, polarizer; A, analyzer; BS, nonpolarizing beam splitter; L3, lens, f=300mm; L4, lens, f=300mm; SLM, spatial light modulator; λ/4, quarter-wave plate; ND, neutral density filter; L5, lens, f=200mm; L6, lens, f=50mm; D, diaphragm; L7, lens, f=100mm.

Fig. 2.
Fig. 2.

STOC manipulation effect on the interference fringe pattern for φ(2)=[0,π]. (a)–(f) Averaged light intensity registered by the CMOS detector for the PM geometries (r=160μm) (a) F(1)(ξ,η,0), (b) F(1)(ξ,η,π) with ξ0=η0=0, and (c) F(2)(ξ,η,π), together with their central horizontal profiles (d)–(f). (g)–(i) Michelson’s visibility V(r) of interference fringe patterns (a)–(c), respectively.

Fig. 3.
Fig. 3.

STOC manipulation effect on the interference fringe pattern (upper panel) and Michelson’s visibility (bottom panel). Results were obtained for φ(2)=[0,π], t1=t2=100ms and the geometry of the PMs imprinted on the SLM surface according to the function F(1)(ξ,η,π) with r=32μm and the following parameters: (b), (f) ξ0=η0=0μm, (c), (g) ξ0=0μm and η0=64μm, and (d), (h) ξ0=64μm and η0=0μm. Dashed circles indicate the boundary of the fringes’ visibility region corresponding to unmodulated light (a), (e).

Equations (10)

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

V(r,t)=0V˜(r,ν)exp[2πiνt]dν.
μ(r1,r2,ν)=W(r1,r2,ν)S(r1,ν)S(r2,ν),
W(r1,r2,ν)δ(νν)=V˜*(r1,ν)V˜(r2,ν)
W(r1,r2,ν)=Γ(r1,r2,τ)exp[2πiντ]dτ
Γ(r1,r2,τ)=V*(r1,t)V(r2,t+τ)=limT12TTTV*(r1,t)V(r2,t+τ)dt,
Wm(r1,r2,ν,φ)δ(νν)=V˜*(r1,ν)V˜(r2,ν)H(1,φ).
S(rd,ν,φ)=S1(rd,ν)+S2(rd,ν)+2S1(rd,ν)S2(rd,ν)×Re{μ(r1,r2,ν)exp[i(2πντφ)]}.
μeff(r1,r2,ν,φ(N))=Weff(r1,r2,ν,φ(N))S(r1,ν)S(r2,ν)=1φNφ1φ1φNWm(i)(r1,r2,ν,φ)S(r1,ν)S(r2,ν)dφ=limN1Ni=1NWm(i)(r1,r2,ν,φi)S(r1,ν)S(r2,ν)=limN1Ni=1Nμm(i)(r1,r2,ν,φi),
I(rd,t)=I1(rd,t)+I2(rd,t)+2I1(rd,t)I2(rd,t)Re[γeff(r1,r2,τ,φ(2))],
FPM(1)(ξ,η,φi)={0,for(ξξ0)2+(ηη0)2rφi,otherwise,FPM(2)(ξ,η,φi)={0,for|ξ|,|η|rφi,otherwise..

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