Abstract

We demonstrate a novel interferometric characterization scheme that allows the complete reconstruction of two interfering electric fields. The phase profiles of both beams, and their relative phase, can be retrieved simultaneously as a function of any degree of freedom in which it is possible to shear one of the beams. The method has applications in wavefront sensing or ultrashort-pulse measurement, especially also in the domain of extreme light sources where it is difficult to generate a reference field or to replicate the beam in order to perform a self-referencing measurement. We demonstrate the technique experimentally by measuring simultaneously two ultrashort pulses in a single laser shot.

© 2013 Optical Society of America

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References

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2010 (1)

2009 (3)

2007 (1)

2005 (1)

1998 (1)

1997 (1)

1982 (1)

1974 (1)

1973 (1)

C. Froehly, A. Lacourt, and J. C. Vienot, J. Opt. 4, 183 (1973).

Austin, D. R.

Bunk, O.

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, Ultramicroscopy 109, 338 (2009).
[CrossRef]

Clement, T. S.

Cohen, M.

Dierolf, M.

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, Ultramicroscopy 109, 338 (2009).
[CrossRef]

Froehly, C.

C. Froehly, A. Lacourt, and J. C. Vienot, J. Opt. 4, 183 (1973).

Gorza, S.-P.

Guérineau, N.

Iaconis, C.

Ina, H.

Kane, D. J.

Kobayashi, S.

Lacourt, A.

C. Froehly, A. Lacourt, and J. C. Vienot, J. Opt. 4, 183 (1973).

Menzel, A.

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, Ultramicroscopy 109, 338 (2009).
[CrossRef]

Pfeiffer, F.

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, Ultramicroscopy 109, 338 (2009).
[CrossRef]

Primot, J.

Rimmer, M. P.

Rodriguez, G.

Takeda, M.

Taylor, A. J.

Thibault, P.

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, Ultramicroscopy 109, 338 (2009).
[CrossRef]

Velghe, S.

Vienot, J. C.

C. Froehly, A. Lacourt, and J. C. Vienot, J. Opt. 4, 183 (1973).

Walmsley, I. A.

Wasylczyk, P.

Wattellier, B.

Witting, T.

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Figures (4)

Fig. 1.
Fig. 1.

Two complex fields can be retrieved from their interferogram obtained for multiple shears.

Fig. 2.
Fig. 2.

(a) Interferograms for three different shears. The white dots represent the locations of the different spatial shears used for the reconstruction. The interferogram in the right panel represents the high noise case. (b) Simulated and reconstructed wavefronts of both fields. Insets: Spatial intensity profiles of the two fields. The linear term in the wavefront of Field 2 has been removed for clarity.

Fig. 3.
Fig. 3.

(a) MICE interferogram of two pulses; the dashed blue line and the red line stand for the axes Ω1,2(x), along which the pulses are spectrally sheared. The black dotted line indicates the shear used for the SPIDER reconstruction. (b) Moduli of the original (inset) and retrieved (main figure) interferometric products associated to the interferogram in (a) after 10 iterations of Eqs. (5)–(7). (c) Evolution of the error between the original and retrieved interferometric products.

Fig. 4.
Fig. 4.

(a) Fields E1 (dashed blue line), E2 (red line), and (b) A retrieved for 10 single-shot measurements. (c) Single-shot pulse profiles of the fields E1 (dashed blue line) and E2 (red line) reconstructed from Figs. 3(a) and 3(b). The black dotted lines stand for the spectral phase (a) and pulse profile (c) retrieved with SPIDER.

Equations (7)

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Ij,k=|E1(γj)|2+|E2(γjΓk)|2+2Re[E1(γj)E2*(γjΓk)].
ϵ=j,kJ,K|ACj,jkmeasE1(γj)E2*(γjΓk)|2.
E1(γj)=kACj,jkmeas·E2(γjΓk)k|E2(γjΓk)|2,
E2*(γj)=kACj+k,jmeas·E1*(γj+Γk)k|E1(γj+Γk)|2.
E1(ωj)=kACj,jkmeas·E2(ωjΩk)·A*(Ωk)k|E2(ωjΩk)·A(Ωk)|2,
E2*(ωj)=kACj+k,jmeas·E1*(ωj+Ωk)·A*(Ωk)Σk|E1(ωj+Ωk)·A(Ωk)|2,
A(Ωk)=jACj,jkmeas·E1*(ωj)E2(ωjΩk)j|E1(ωj)E2(ωjΩk)|2.

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