Abstract

We propose a simple and fast procedure to retrieve the phase profile of arbitrary light pulses. It combines a first experimental stage, followed by a one-step numerical stage. To this end, it is necessary to perform a Fresnel transform, which is obtained just by propagating the light pulses through an optical fiber. We experimentally test this proposal recovering the phase profile in the light pulses provided by a passively mode-locked laser. The proposal is then compared with a temporal variation of the Gerchberg–Saxton recursive algorithm, which is specially modified for this purpose.

© 2014 Optical Society of America

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References

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  1. R. W. Gerchberg and W. O. Saxton, Optik 35, 237 (1972).
  2. Z. Zalevsky, D. Mendlovic, and R. G. Dorsch, Opt. Lett. 21, 842 (1996).
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  6. T. Alieva and M. J. Bastiaans, IEEE Signal Process. Lett. 7, 320 (2000).
    [CrossRef]
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  8. C. Dorrer, Opt. Lett. 30, 3237 (2005).
    [CrossRef]
  9. F. Li, Y. Park, and J. Azaña, Opt. Lett. 32, 3364 (2007).
    [CrossRef]
  10. M. H. Asghari and J. Azaña, Opt. Lett. 37, 3582 (2012).
    [CrossRef]
  11. M. H. Asghari and B. Jalali, IEEE Photon. J. 4, 1693 (2012).
    [CrossRef]
  12. K. Goda and B. Jalali, Nat. Photonics 7, 102 (2013).
    [CrossRef]
  13. D. R. Solli, S. Gupta, and B. Jalali, Appl. Phys. Lett. 95, 231108 (2009).
    [CrossRef]
  14. M. A. Muriel, J. Azaña, and A. Carballar, Opt. Lett. 24, 1 (1999).
    [CrossRef]

2013 (1)

K. Goda and B. Jalali, Nat. Photonics 7, 102 (2013).
[CrossRef]

2012 (2)

M. H. Asghari and B. Jalali, IEEE Photon. J. 4, 1693 (2012).
[CrossRef]

M. H. Asghari and J. Azaña, Opt. Lett. 37, 3582 (2012).
[CrossRef]

2009 (1)

D. R. Solli, S. Gupta, and B. Jalali, Appl. Phys. Lett. 95, 231108 (2009).
[CrossRef]

2007 (1)

2005 (1)

2003 (1)

2000 (1)

T. Alieva and M. J. Bastiaans, IEEE Signal Process. Lett. 7, 320 (2000).
[CrossRef]

1999 (1)

1996 (1)

1988 (1)

1984 (1)

N. Streibl, Opt. Commun. 49, 6 (1984).
[CrossRef]

1983 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, Optik 35, 237 (1972).

Alieva, T.

T. Alieva and M. J. Bastiaans, IEEE Signal Process. Lett. 7, 320 (2000).
[CrossRef]

Asghari, M. H.

M. H. Asghari and B. Jalali, IEEE Photon. J. 4, 1693 (2012).
[CrossRef]

M. H. Asghari and J. Azaña, Opt. Lett. 37, 3582 (2012).
[CrossRef]

Azaña, J.

Bastiaans, M. J.

M. J. Bastiaans and K. B. Wolf, J. Opt. Soc. Am. A 20, 1046 (2003).
[CrossRef]

T. Alieva and M. J. Bastiaans, IEEE Signal Process. Lett. 7, 320 (2000).
[CrossRef]

Carballar, A.

Dorrer, C.

Dorsch, R. G.

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, Optik 35, 237 (1972).

Goda, K.

K. Goda and B. Jalali, Nat. Photonics 7, 102 (2013).
[CrossRef]

Gupta, S.

D. R. Solli, S. Gupta, and B. Jalali, Appl. Phys. Lett. 95, 231108 (2009).
[CrossRef]

Ichikawa, K.

Jalali, B.

K. Goda and B. Jalali, Nat. Photonics 7, 102 (2013).
[CrossRef]

M. H. Asghari and B. Jalali, IEEE Photon. J. 4, 1693 (2012).
[CrossRef]

D. R. Solli, S. Gupta, and B. Jalali, Appl. Phys. Lett. 95, 231108 (2009).
[CrossRef]

Li, F.

Lohmann, A. W.

Mendlovic, D.

Muriel, M. A.

Park, Y.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, Optik 35, 237 (1972).

Solli, D. R.

D. R. Solli, S. Gupta, and B. Jalali, Appl. Phys. Lett. 95, 231108 (2009).
[CrossRef]

Streibl, N.

N. Streibl, Opt. Commun. 49, 6 (1984).
[CrossRef]

Takeda, M.

Teague, M. R.

Wolf, K. B.

Zalevsky, Z.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

D. R. Solli, S. Gupta, and B. Jalali, Appl. Phys. Lett. 95, 231108 (2009).
[CrossRef]

IEEE Photon. J. (1)

M. H. Asghari and B. Jalali, IEEE Photon. J. 4, 1693 (2012).
[CrossRef]

IEEE Signal Process. Lett. (1)

T. Alieva and M. J. Bastiaans, IEEE Signal Process. Lett. 7, 320 (2000).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Nat. Photonics (1)

K. Goda and B. Jalali, Nat. Photonics 7, 102 (2013).
[CrossRef]

Opt. Commun. (1)

N. Streibl, Opt. Commun. 49, 6 (1984).
[CrossRef]

Opt. Lett. (5)

Optik (1)

R. W. Gerchberg and W. O. Saxton, Optik 35, 237 (1972).

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Figures (5)

Fig. 1.
Fig. 1.

GSA for temporal phase retrieval at the input by FrT.

Fig. 2.
Fig. 2.

Experimental setup.

Fig. 3.
Fig. 3.

(a) Measured temporal profiles at the input (plus the corresponding fitting) and output of a fiber length of 315 m, the TPD is also shown. (b) Phase recovered by the proposed FrT technique, experimentally and numerically (Exp. FrT and Sim. FrT, respectively), as compared with the phase experimentally recovered by the modified GSA, a theoretical parabolic phase profile with C=11 is also shown.

Fig. 4.
Fig. 4.

Same as in Fig. 3(b), but for a fiber length of 214 m (a) and 101 m (b).

Fig. 5.
Fig. 5.

(a) Simulated phase recovered by the FrT technique in the presence of noise with SNR=20dB, as compared with the theoretical phase. The inset shows the TPD. (b) Phase profiles numerically recovered by the FrT technique and GSA for a super-Gaussian pulse with a SNR=20dB; the theoretical phase profile is also shown. The inset shows the TPD.

Tables (1)

Tables Icon

Table 1. Procedure for Phase Recovery by FrT Technique

Equations (5)

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fα(t)=(2πjα)1/2dτf(τ)exp[j12(tτ)2/α],
φ(t)=φ0+tdt[1|f(t)|2dτ|fα(τ)|2α|α=0H(tτ)],
S(ω)=exp[j12Φ20ω2]FT1s(t)exp[jt2/2Φ20],
|fα(t)|2/α|α=0[|fα(t)|2|f(t)|2]/α|α0.
LΔt2/2πβ20.

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