Abstract

We report the experimental observation of spectral interference in a Michelson interferometer, regardless of the relationship between the temporal path difference introduced between the arms of the interferometer and the spectral width of the input pulse. This observation is possible by introducing the polarization degree of freedom into a Michelson interferometer using a typical weak value amplification scenario.

© 2014 Optical Society of America

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  1. M. P. Givens, J. Opt. Soc. Am. 51, 1030 (1961).
    [CrossRef]
  2. L. Mandel, J. Opt. Soc. Am. 52, 1335 (1962).
    [CrossRef]
  3. W. P. Alford and A. Gold, Am. J. Phys. 26, 481 (1958).
    [CrossRef]
  4. X. Y. Zou, T. P. Grayson, and L. Mandel, Phys. Rev. Lett. 69, 3041 (1992).
    [CrossRef]
  5. Y. Aharonov, D. Z. Albert, and L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988).
    [CrossRef]
  6. I. M. Duck, P. M. Stevenson, and E. C. G. Sudarhshan, Phys. Rev. D 40, 2112 (1989).
    [CrossRef]
  7. J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, Rev. Mod. Phys. 86, 307 (2014).
    [CrossRef]
  8. J. C. Howell, D. J. Starling, P. Ben Dixon, P. K. Vudyasetu, and A. N. Jordan, Phys. Rev. A 81, 033813 (2010).
    [CrossRef]
  9. N. Brunner and C. Simon, Phys. Rev. Lett. 105, 010405 (2010).
    [CrossRef]
  10. C.-F. Li, X.-Y. Xu, J.-S. Tang, J.-S. Xu, and G.-C. Guo, Phys. Rev. A 83, 044102 (2011).
    [CrossRef]
  11. X.-Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C.-F. Li, and G.-C. Guo, Phys. Rev. Lett. 111, 033604 (2013).
    [CrossRef]
  12. G. I. Viza, J. Martinez-Rincon, G. A. Howland, H. Frostig, I. Shomroni, B. Dayan, and J. C. Howell, Opt. Lett. 38, 2949 (2013).
    [CrossRef]
  13. L. J. Salazar-Serrano, D. Janner, N. Brunner, V. Pruneri, and J. P. Torres, Phys. Rev. A 89, 012126 (2014).
    [CrossRef]
  14. J. Dressel, K. Lyons, A. N. Jordan, T. M. Graham, and P. G. Kwiat, Phys. Rev. A 88, 023821 (2013).
    [CrossRef]
  15. C. V. S. Borges, M. Hor-Meyll, J. A. O. Huguenin, and A. Z. Khoury, Phys. Rev. A 82, 033833 (2010).
    [CrossRef]
  16. K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, Nat. Photonics 7, 72 (2013).
    [CrossRef]
  17. B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, Phys. Rev. Lett. 104, 023901 (2010).
    [CrossRef]
  18. X. F. Qian and J. H. Eberly, Opt. Lett. 36, 4110 (2011).
    [CrossRef]

2014 (2)

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, Rev. Mod. Phys. 86, 307 (2014).
[CrossRef]

L. J. Salazar-Serrano, D. Janner, N. Brunner, V. Pruneri, and J. P. Torres, Phys. Rev. A 89, 012126 (2014).
[CrossRef]

2013 (4)

J. Dressel, K. Lyons, A. N. Jordan, T. M. Graham, and P. G. Kwiat, Phys. Rev. A 88, 023821 (2013).
[CrossRef]

X.-Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C.-F. Li, and G.-C. Guo, Phys. Rev. Lett. 111, 033604 (2013).
[CrossRef]

G. I. Viza, J. Martinez-Rincon, G. A. Howland, H. Frostig, I. Shomroni, B. Dayan, and J. C. Howell, Opt. Lett. 38, 2949 (2013).
[CrossRef]

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, Nat. Photonics 7, 72 (2013).
[CrossRef]

2011 (2)

C.-F. Li, X.-Y. Xu, J.-S. Tang, J.-S. Xu, and G.-C. Guo, Phys. Rev. A 83, 044102 (2011).
[CrossRef]

X. F. Qian and J. H. Eberly, Opt. Lett. 36, 4110 (2011).
[CrossRef]

2010 (4)

B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, Phys. Rev. Lett. 104, 023901 (2010).
[CrossRef]

C. V. S. Borges, M. Hor-Meyll, J. A. O. Huguenin, and A. Z. Khoury, Phys. Rev. A 82, 033833 (2010).
[CrossRef]

J. C. Howell, D. J. Starling, P. Ben Dixon, P. K. Vudyasetu, and A. N. Jordan, Phys. Rev. A 81, 033813 (2010).
[CrossRef]

N. Brunner and C. Simon, Phys. Rev. Lett. 105, 010405 (2010).
[CrossRef]

1992 (1)

X. Y. Zou, T. P. Grayson, and L. Mandel, Phys. Rev. Lett. 69, 3041 (1992).
[CrossRef]

1989 (1)

I. M. Duck, P. M. Stevenson, and E. C. G. Sudarhshan, Phys. Rev. D 40, 2112 (1989).
[CrossRef]

1988 (1)

Y. Aharonov, D. Z. Albert, and L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988).
[CrossRef]

1962 (1)

1961 (1)

1958 (1)

W. P. Alford and A. Gold, Am. J. Phys. 26, 481 (1958).
[CrossRef]

Abouraddy, A. F.

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, Nat. Photonics 7, 72 (2013).
[CrossRef]

Aharonov, Y.

Y. Aharonov, D. Z. Albert, and L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988).
[CrossRef]

Albert, D. Z.

Y. Aharonov, D. Z. Albert, and L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988).
[CrossRef]

Alford, W. P.

W. P. Alford and A. Gold, Am. J. Phys. 26, 481 (1958).
[CrossRef]

Ben Dixon, P.

J. C. Howell, D. J. Starling, P. Ben Dixon, P. K. Vudyasetu, and A. N. Jordan, Phys. Rev. A 81, 033813 (2010).
[CrossRef]

Borges, C. V. S.

C. V. S. Borges, M. Hor-Meyll, J. A. O. Huguenin, and A. Z. Khoury, Phys. Rev. A 82, 033833 (2010).
[CrossRef]

Borghi, R.

B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, Phys. Rev. Lett. 104, 023901 (2010).
[CrossRef]

Boyd, R. W.

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, Rev. Mod. Phys. 86, 307 (2014).
[CrossRef]

Brunner, N.

L. J. Salazar-Serrano, D. Janner, N. Brunner, V. Pruneri, and J. P. Torres, Phys. Rev. A 89, 012126 (2014).
[CrossRef]

N. Brunner and C. Simon, Phys. Rev. Lett. 105, 010405 (2010).
[CrossRef]

Dayan, B.

Di Giuseppe, G.

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, Nat. Photonics 7, 72 (2013).
[CrossRef]

Dressel, J.

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, Rev. Mod. Phys. 86, 307 (2014).
[CrossRef]

J. Dressel, K. Lyons, A. N. Jordan, T. M. Graham, and P. G. Kwiat, Phys. Rev. A 88, 023821 (2013).
[CrossRef]

Duck, I. M.

I. M. Duck, P. M. Stevenson, and E. C. G. Sudarhshan, Phys. Rev. D 40, 2112 (1989).
[CrossRef]

Eberly, J. H.

Frostig, H.

Givens, M. P.

Gold, A.

W. P. Alford and A. Gold, Am. J. Phys. 26, 481 (1958).
[CrossRef]

Gori, F.

B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, Phys. Rev. Lett. 104, 023901 (2010).
[CrossRef]

Graham, T. M.

J. Dressel, K. Lyons, A. N. Jordan, T. M. Graham, and P. G. Kwiat, Phys. Rev. A 88, 023821 (2013).
[CrossRef]

Grayson, T. P.

X. Y. Zou, T. P. Grayson, and L. Mandel, Phys. Rev. Lett. 69, 3041 (1992).
[CrossRef]

Guo, G.-C.

X.-Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C.-F. Li, and G.-C. Guo, Phys. Rev. Lett. 111, 033604 (2013).
[CrossRef]

C.-F. Li, X.-Y. Xu, J.-S. Tang, J.-S. Xu, and G.-C. Guo, Phys. Rev. A 83, 044102 (2011).
[CrossRef]

Hor-Meyll, M.

C. V. S. Borges, M. Hor-Meyll, J. A. O. Huguenin, and A. Z. Khoury, Phys. Rev. A 82, 033833 (2010).
[CrossRef]

Howell, J. C.

G. I. Viza, J. Martinez-Rincon, G. A. Howland, H. Frostig, I. Shomroni, B. Dayan, and J. C. Howell, Opt. Lett. 38, 2949 (2013).
[CrossRef]

J. C. Howell, D. J. Starling, P. Ben Dixon, P. K. Vudyasetu, and A. N. Jordan, Phys. Rev. A 81, 033813 (2010).
[CrossRef]

Howland, G. A.

Huguenin, J. A. O.

C. V. S. Borges, M. Hor-Meyll, J. A. O. Huguenin, and A. Z. Khoury, Phys. Rev. A 82, 033833 (2010).
[CrossRef]

Janner, D.

L. J. Salazar-Serrano, D. Janner, N. Brunner, V. Pruneri, and J. P. Torres, Phys. Rev. A 89, 012126 (2014).
[CrossRef]

Jordan, A. N.

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, Rev. Mod. Phys. 86, 307 (2014).
[CrossRef]

J. Dressel, K. Lyons, A. N. Jordan, T. M. Graham, and P. G. Kwiat, Phys. Rev. A 88, 023821 (2013).
[CrossRef]

J. C. Howell, D. J. Starling, P. Ben Dixon, P. K. Vudyasetu, and A. N. Jordan, Phys. Rev. A 81, 033813 (2010).
[CrossRef]

Kagalwala, K. H.

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, Nat. Photonics 7, 72 (2013).
[CrossRef]

Kedem, Y.

X.-Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C.-F. Li, and G.-C. Guo, Phys. Rev. Lett. 111, 033604 (2013).
[CrossRef]

Khoury, A. Z.

C. V. S. Borges, M. Hor-Meyll, J. A. O. Huguenin, and A. Z. Khoury, Phys. Rev. A 82, 033833 (2010).
[CrossRef]

Kwiat, P. G.

J. Dressel, K. Lyons, A. N. Jordan, T. M. Graham, and P. G. Kwiat, Phys. Rev. A 88, 023821 (2013).
[CrossRef]

Li, C.-F.

X.-Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C.-F. Li, and G.-C. Guo, Phys. Rev. Lett. 111, 033604 (2013).
[CrossRef]

C.-F. Li, X.-Y. Xu, J.-S. Tang, J.-S. Xu, and G.-C. Guo, Phys. Rev. A 83, 044102 (2011).
[CrossRef]

Lyons, K.

J. Dressel, K. Lyons, A. N. Jordan, T. M. Graham, and P. G. Kwiat, Phys. Rev. A 88, 023821 (2013).
[CrossRef]

Malik, M.

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, Rev. Mod. Phys. 86, 307 (2014).
[CrossRef]

Mandel, L.

X. Y. Zou, T. P. Grayson, and L. Mandel, Phys. Rev. Lett. 69, 3041 (1992).
[CrossRef]

L. Mandel, J. Opt. Soc. Am. 52, 1335 (1962).
[CrossRef]

Martinez-Rincon, J.

Miatto, F. M.

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, Rev. Mod. Phys. 86, 307 (2014).
[CrossRef]

Mukunda, N.

B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, Phys. Rev. Lett. 104, 023901 (2010).
[CrossRef]

Pruneri, V.

L. J. Salazar-Serrano, D. Janner, N. Brunner, V. Pruneri, and J. P. Torres, Phys. Rev. A 89, 012126 (2014).
[CrossRef]

Qian, X. F.

Salazar-Serrano, L. J.

L. J. Salazar-Serrano, D. Janner, N. Brunner, V. Pruneri, and J. P. Torres, Phys. Rev. A 89, 012126 (2014).
[CrossRef]

Saleh, B. E. A.

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, Nat. Photonics 7, 72 (2013).
[CrossRef]

Santarsiero, M.

B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, Phys. Rev. Lett. 104, 023901 (2010).
[CrossRef]

Shomroni, I.

Simon, B. N.

B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, Phys. Rev. Lett. 104, 023901 (2010).
[CrossRef]

Simon, C.

N. Brunner and C. Simon, Phys. Rev. Lett. 105, 010405 (2010).
[CrossRef]

Simon, R.

B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, Phys. Rev. Lett. 104, 023901 (2010).
[CrossRef]

Simon, S.

B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, Phys. Rev. Lett. 104, 023901 (2010).
[CrossRef]

Starling, D. J.

J. C. Howell, D. J. Starling, P. Ben Dixon, P. K. Vudyasetu, and A. N. Jordan, Phys. Rev. A 81, 033813 (2010).
[CrossRef]

Stevenson, P. M.

I. M. Duck, P. M. Stevenson, and E. C. G. Sudarhshan, Phys. Rev. D 40, 2112 (1989).
[CrossRef]

Sudarhshan, E. C. G.

I. M. Duck, P. M. Stevenson, and E. C. G. Sudarhshan, Phys. Rev. D 40, 2112 (1989).
[CrossRef]

Sun, K.

X.-Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C.-F. Li, and G.-C. Guo, Phys. Rev. Lett. 111, 033604 (2013).
[CrossRef]

Tang, J.-S.

C.-F. Li, X.-Y. Xu, J.-S. Tang, J.-S. Xu, and G.-C. Guo, Phys. Rev. A 83, 044102 (2011).
[CrossRef]

Torres, J. P.

L. J. Salazar-Serrano, D. Janner, N. Brunner, V. Pruneri, and J. P. Torres, Phys. Rev. A 89, 012126 (2014).
[CrossRef]

Vaidman, L.

X.-Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C.-F. Li, and G.-C. Guo, Phys. Rev. Lett. 111, 033604 (2013).
[CrossRef]

Y. Aharonov, D. Z. Albert, and L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988).
[CrossRef]

Viza, G. I.

Vudyasetu, P. K.

J. C. Howell, D. J. Starling, P. Ben Dixon, P. K. Vudyasetu, and A. N. Jordan, Phys. Rev. A 81, 033813 (2010).
[CrossRef]

Xu, J.-S.

C.-F. Li, X.-Y. Xu, J.-S. Tang, J.-S. Xu, and G.-C. Guo, Phys. Rev. A 83, 044102 (2011).
[CrossRef]

Xu, X.-Y.

X.-Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C.-F. Li, and G.-C. Guo, Phys. Rev. Lett. 111, 033604 (2013).
[CrossRef]

C.-F. Li, X.-Y. Xu, J.-S. Tang, J.-S. Xu, and G.-C. Guo, Phys. Rev. A 83, 044102 (2011).
[CrossRef]

Zou, X. Y.

X. Y. Zou, T. P. Grayson, and L. Mandel, Phys. Rev. Lett. 69, 3041 (1992).
[CrossRef]

Am. J. Phys. (1)

W. P. Alford and A. Gold, Am. J. Phys. 26, 481 (1958).
[CrossRef]

J. Opt. Soc. Am. (2)

Nat. Photonics (1)

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, Nat. Photonics 7, 72 (2013).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (5)

L. J. Salazar-Serrano, D. Janner, N. Brunner, V. Pruneri, and J. P. Torres, Phys. Rev. A 89, 012126 (2014).
[CrossRef]

J. Dressel, K. Lyons, A. N. Jordan, T. M. Graham, and P. G. Kwiat, Phys. Rev. A 88, 023821 (2013).
[CrossRef]

C. V. S. Borges, M. Hor-Meyll, J. A. O. Huguenin, and A. Z. Khoury, Phys. Rev. A 82, 033833 (2010).
[CrossRef]

C.-F. Li, X.-Y. Xu, J.-S. Tang, J.-S. Xu, and G.-C. Guo, Phys. Rev. A 83, 044102 (2011).
[CrossRef]

J. C. Howell, D. J. Starling, P. Ben Dixon, P. K. Vudyasetu, and A. N. Jordan, Phys. Rev. A 81, 033813 (2010).
[CrossRef]

Phys. Rev. D (1)

I. M. Duck, P. M. Stevenson, and E. C. G. Sudarhshan, Phys. Rev. D 40, 2112 (1989).
[CrossRef]

Phys. Rev. Lett. (5)

N. Brunner and C. Simon, Phys. Rev. Lett. 105, 010405 (2010).
[CrossRef]

X. Y. Zou, T. P. Grayson, and L. Mandel, Phys. Rev. Lett. 69, 3041 (1992).
[CrossRef]

Y. Aharonov, D. Z. Albert, and L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988).
[CrossRef]

X.-Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C.-F. Li, and G.-C. Guo, Phys. Rev. Lett. 111, 033604 (2013).
[CrossRef]

B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, Phys. Rev. Lett. 104, 023901 (2010).
[CrossRef]

Rev. Mod. Phys. (1)

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, Rev. Mod. Phys. 86, 307 (2014).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Typical interference patterns that can be observed in a Michelson interferometer in the time and frequency domains. (a) depicts the interferometric configuration considered. BS: beam splitter, PD: photodetector. Panels (b) and (d) show the intensity measured as a function of a temporal delay T. Panels (c) and (e) show the intensity as a function of frequency for a given value of T. Panels (b) and (c) correspond to the case Tτ, while (d) and (e) correspond to the case Tτ.

Fig. 2.
Fig. 2.

Experimental setup: a fiber-coupled laser generates pulses of duration τ=320fs, centered in 1550 nm (ν0=193.5THz). The input pulse polarization state is selected to be left-circular by using a polarizer, a quarter-wave plate (QWP) and a half-wave plate (HWP). A polarizing beam splitter (PBS) splits the input into two orthogonal linear polarizations that propagate along different arms of the interferometer. An additional QWP is introduced in each arm to rotate the beam polarization by 90° to allow the recombination of both beams in a single beam by the same PBS. After the PBS, the output polarization state is selected with a liquid crystal variable retarder (LCVR) followed by a polarizer at 45°. Finally, the output beam is coupled to a single-mode (SM) fiber, and its spectrum is measured using an optical spectrum analyzer (OSA).

Fig. 3.
Fig. 3.

Spectral interference in the regime Tτ. The first column depicts the experimental input spectrum, Sin(ν), of a pulsed laser with a temporal duration τ=320fs centered in ν0=193.5THz (solid line) and the theoretical transfer function, H(ν) (dashed line). As a reference, the vertical dashed line indicates the central frequency, v0, of the input spectrum. The second column shows the experimental output spectrum that can be obtained by evaluating Sout(ν)=H(ν)Sin(ν). (a) and (b) Time delay T=1453fs, (c) and (d) T=2120fs, (e) and (f) T=2786fs, and (g) and (h) T=4120fs. In all cases Γ=26.55°.

Fig. 4.
Fig. 4.

Spectral interference in the regime Tτ. The first column depicts the experimental input spectrum, Sin(ν), of a pulsed laser with a temporal duration τ=320fs centered in ν0=193.5THz (solid line) and the theoretical transfer function, H(ν), (dashed line) for a fixed delay of T=53.7fs. The vertical dashed line in the first column indicates the central frequency of the input spectrum. The second column shows the experimental output spectrum that can be obtained by evaluating Sout(ν)=H(ν)Sin(ν). (a) and (b) Γ=98.5°, (c) and (d) Γ=273.1°, (e) and (f) Γ=231.2°, and (g) and (h) Γ=198.9°. Notice that the vertical axis in the right column has been rescaled, since the output intensity changes dramatically with different values of Γ.

Equations (8)

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

Ein(t)=E0exp[(2ln2/τ2)t2+i2πν0t]ein,
I(T)=I02[1+exp(ln2T2/τ2)cos(2πν0T)],
ITτ(T)=I02[1+cos(2πν0T)],
ITτ(T)=I02.
S(ν)=Sin(ν)2[1+cos(2πνT)],
Sin(ν)=S0exp[(π2τ2/ln2)(νν0)2]
Eout(ν)=E0πτ28ln2exp{[π2τ2/(2ln2)](νν0)2}×{exp(i2πνT)+exp[i(Γ+π/2)]}(x+y).
Sout(ν)=Sin(ν)2[1+cos(2πνTΓπ/2)].

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