Abstract

We introduce and numerically demonstrate a simple and general concept for direct reconstruction of the temporal phase profile of an optical signal from temporal intensity measurements at the input and output of an arbitrary linear optical filter. The concept is based on exploiting the linearity and causality properties of any physical filter. Very few restrictions need to be imposed on the optical filter response to ensure an unambiguous phase reconstruction. The filter can be specifically designed to minimize the noise influence on the measurement process.

© 2012 Optical Society of America

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References

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  1. I. Walmsley and C. Dorrer, Adv. Opt. Photon. 1, 308 (2009).
    [CrossRef]
  2. M. E. Anderson, A. Monmayrant, S. P. Gorza, P. Wasylczyk, and I. A. Walmsley, Laser Phys. Lett. 5, 259 (2008).
    [CrossRef]
  3. D. J. Kane and R. Trebino, Opt. Lett. 18, 823 (1993).
    [CrossRef]
  4. C. Dorrer, D. C. Kilper, H. R. Stuart, G. Raybon, and M. G. Raymer, IEEE Photonics Technol. Lett. 15, 1746 (2003).
    [CrossRef]
  5. N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, Nat. Photon. 4, 248 (2010).
    [CrossRef]
  6. R. Saunders, J. King, and I. Hardcastle, Electron. Lett. 30, 1336 (1994).
    [CrossRef]
  7. K. Sato, S. Kuwahara, and Y. Miyamoto, J. Lightwave Technol. 23, 3790 (2005).
    [CrossRef]
  8. F. Li, Y. Park, and J. Azaña, J. Lightwave Technol. 27, 4623 (2009).
    [CrossRef]
  9. F. Li, Y. Park, and J. Azaña, Opt. Lett. 34, 2742 (2009).
    [CrossRef]
  10. A. V. Oppenheim, A. S. Willsky, S. N. Nawab, and S. H. Nawab, Signals and Systems, 2nd ed. (Prentice Hall, 1996).

2010

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, Nat. Photon. 4, 248 (2010).
[CrossRef]

2009

2008

M. E. Anderson, A. Monmayrant, S. P. Gorza, P. Wasylczyk, and I. A. Walmsley, Laser Phys. Lett. 5, 259 (2008).
[CrossRef]

2005

2003

C. Dorrer, D. C. Kilper, H. R. Stuart, G. Raybon, and M. G. Raymer, IEEE Photonics Technol. Lett. 15, 1746 (2003).
[CrossRef]

1994

R. Saunders, J. King, and I. Hardcastle, Electron. Lett. 30, 1336 (1994).
[CrossRef]

1993

Anderson, M. E.

M. E. Anderson, A. Monmayrant, S. P. Gorza, P. Wasylczyk, and I. A. Walmsley, Laser Phys. Lett. 5, 259 (2008).
[CrossRef]

Azaña, J.

Dorrer, C.

I. Walmsley and C. Dorrer, Adv. Opt. Photon. 1, 308 (2009).
[CrossRef]

C. Dorrer, D. C. Kilper, H. R. Stuart, G. Raybon, and M. G. Raymer, IEEE Photonics Technol. Lett. 15, 1746 (2003).
[CrossRef]

Fontaine, N. K.

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, Nat. Photon. 4, 248 (2010).
[CrossRef]

Gorza, S. P.

M. E. Anderson, A. Monmayrant, S. P. Gorza, P. Wasylczyk, and I. A. Walmsley, Laser Phys. Lett. 5, 259 (2008).
[CrossRef]

Hardcastle, I.

R. Saunders, J. King, and I. Hardcastle, Electron. Lett. 30, 1336 (1994).
[CrossRef]

Heritage, J. P.

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, Nat. Photon. 4, 248 (2010).
[CrossRef]

Kane, D. J.

Kilper, D. C.

C. Dorrer, D. C. Kilper, H. R. Stuart, G. Raybon, and M. G. Raymer, IEEE Photonics Technol. Lett. 15, 1746 (2003).
[CrossRef]

King, J.

R. Saunders, J. King, and I. Hardcastle, Electron. Lett. 30, 1336 (1994).
[CrossRef]

Kuwahara, S.

Li, F.

Miyamoto, Y.

Monmayrant, A.

M. E. Anderson, A. Monmayrant, S. P. Gorza, P. Wasylczyk, and I. A. Walmsley, Laser Phys. Lett. 5, 259 (2008).
[CrossRef]

Nawab, S. H.

A. V. Oppenheim, A. S. Willsky, S. N. Nawab, and S. H. Nawab, Signals and Systems, 2nd ed. (Prentice Hall, 1996).

Nawab, S. N.

A. V. Oppenheim, A. S. Willsky, S. N. Nawab, and S. H. Nawab, Signals and Systems, 2nd ed. (Prentice Hall, 1996).

Oppenheim, A. V.

A. V. Oppenheim, A. S. Willsky, S. N. Nawab, and S. H. Nawab, Signals and Systems, 2nd ed. (Prentice Hall, 1996).

Park, Y.

Raybon, G.

C. Dorrer, D. C. Kilper, H. R. Stuart, G. Raybon, and M. G. Raymer, IEEE Photonics Technol. Lett. 15, 1746 (2003).
[CrossRef]

Raymer, M. G.

C. Dorrer, D. C. Kilper, H. R. Stuart, G. Raybon, and M. G. Raymer, IEEE Photonics Technol. Lett. 15, 1746 (2003).
[CrossRef]

Sato, K.

Saunders, R.

R. Saunders, J. King, and I. Hardcastle, Electron. Lett. 30, 1336 (1994).
[CrossRef]

Scott, R. P.

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, Nat. Photon. 4, 248 (2010).
[CrossRef]

Soares, F. M.

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, Nat. Photon. 4, 248 (2010).
[CrossRef]

Stuart, H. R.

C. Dorrer, D. C. Kilper, H. R. Stuart, G. Raybon, and M. G. Raymer, IEEE Photonics Technol. Lett. 15, 1746 (2003).
[CrossRef]

Trebino, R.

Walmsley, I.

Walmsley, I. A.

M. E. Anderson, A. Monmayrant, S. P. Gorza, P. Wasylczyk, and I. A. Walmsley, Laser Phys. Lett. 5, 259 (2008).
[CrossRef]

Wasylczyk, P.

M. E. Anderson, A. Monmayrant, S. P. Gorza, P. Wasylczyk, and I. A. Walmsley, Laser Phys. Lett. 5, 259 (2008).
[CrossRef]

Willsky, A. S.

A. V. Oppenheim, A. S. Willsky, S. N. Nawab, and S. H. Nawab, Signals and Systems, 2nd ed. (Prentice Hall, 1996).

Yoo, S. J. B.

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, Nat. Photon. 4, 248 (2010).
[CrossRef]

Zhou, L.

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, Nat. Photon. 4, 248 (2010).
[CrossRef]

Adv. Opt. Photon.

Electron. Lett.

R. Saunders, J. King, and I. Hardcastle, Electron. Lett. 30, 1336 (1994).
[CrossRef]

IEEE Photonics Technol. Lett.

C. Dorrer, D. C. Kilper, H. R. Stuart, G. Raybon, and M. G. Raymer, IEEE Photonics Technol. Lett. 15, 1746 (2003).
[CrossRef]

J. Lightwave Technol.

Laser Phys. Lett.

M. E. Anderson, A. Monmayrant, S. P. Gorza, P. Wasylczyk, and I. A. Walmsley, Laser Phys. Lett. 5, 259 (2008).
[CrossRef]

Nat. Photon.

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, Nat. Photon. 4, 248 (2010).
[CrossRef]

Opt. Lett.

Other

A. V. Oppenheim, A. S. Willsky, S. N. Nawab, and S. H. Nawab, Signals and Systems, 2nd ed. (Prentice Hall, 1996).

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Figures (3)

Fig. 1.
Fig. 1.

(a) Spectral transfer function of a designed photonic FBG filter designed for causality-based temporal phase recovery. The SUT spectral amplitude is also shown with a dashed-blue line. Input and output amplitude profiles and filter temporal impulse response; (b) and input phase profile compared to the reconstructed phase; (c) using the proposed technique. Relative phase difference between the input and filtered signals is shown in the inset of (c).

Fig. 2.
Fig. 2.

(a) Optical data bit stream and the generated modulated signal using a 16-QAM constellation (signal under test); (b) modulated signal phase profile compared to the reconstructed phase using the proposed technique.

Fig. 3.
Fig. 3.

Temporal impulse responses of four optical filters under test and the input signal temporal profile.

Tables (1)

Tables Icon

Table 1. Minimum Required Input and Output SNRs for 5 km SMF Dispersion Factor Characterization Using Optical Filters

Equations (2)

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

y(iT)=n=0ie(nT)h((in)T)y(iT)=e(iT)h(0)+Ai,
ϕe(iT)=cos1(|y(iT)|2|e(iT)|2|h(0)|2|Ai|22|e(iT)||h(0)||Ai|)ϕh(0)+ϕAi.

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