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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 4 — Feb. 13, 2012
  • pp: 4074–4084
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Complete measurement of fiber modal content by wavefront analysis

Mathieu Paurisse, Louis Lévèque, Marc Hanna, Frédéric Druon, and Patrick Georges  »View Author Affiliations


Optics Express, Vol. 20, Issue 4, pp. 4074-4084 (2012)
http://dx.doi.org/10.1364/OE.20.004074


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Abstract

We propose and demonstrate the use of a wavefront analyzer based on lateral shearing interferometry to characterize the modal content of multimode fibers. This wavefront measurement technique is applied to large mode area fibers, and allows us to recover both the intensity and relative phase of each guided mode. This constitutes an innovative complete characterization of the beam, and might be used as a probe in deterministic active wavefront correction techniques.

© 2012 OSA

1. Introduction

2. Experimental setup and procedures

2.1 Experimental setup

The wavefront analyzer we used is a SID4-HR manufactured by Phasics. This analyzer relies upon the use of lateral shearing interferometry [13

13. J. C. Chanteloup, “Multiple-wave lateral shearing interferometry for wave-front sensing,” Appl. Opt. 44(9), 1559–1571 (2005). [CrossRef] [PubMed]

]. The incident beam is split into four identical replicas which propagate with a different angle. After few millimeters of propagation, the interference pattern between these four replicas is recorded on a CCD camera and leads to the spatial phase gradient of the incident beam. The provided software integrates this gradient map and allows accessing the wavefront of the beam. The device allows a measurement of the wavefront on a 300x400 grid with a total aperture of 8.9x11.8 mm2.

The fiber is placed on a 3 axis positioning stage and an additional mirror is used before injection to adjust the angle of the beam coupled to the fiber. In the geometrical approach, one can consider that each mode corresponds to a specific propagation angle. Therefore, by adjusting the position of the input mirror, it is possible to excite a limited combination and even a single mode of the fiber.

The wavefront analyzer used in this experiment allows measuring the intensity Imes(x,y) and the phase Φmes(x,y) of the multimode beam coming out of the fiber. The measured electric field can therefore be retrieved as:

Emes(x,y)=Imes(x,y).exp(iΦmes(x,y)).
(1)

This measured field is decomposed on the theoretical LP modes ELPjk supported by the fiber. The calculation of these theoretical modes requires the knowledge or the measurement of the refractive index profile of the fiber under test. Since this actual profile is difficult to obtain, we considered in this proof of principle demonstration that the fiber is an ideal step-index one. The decomposition is obtained by simply projecting the measured field on the modes. The projection coefficients are given by:

cjk=Emes(x,y).ELPjk*(x,y)dxdy(|Emes(x,y)|2dxdy)(|ELPjk(x,y)|2dxdy).
(2)

Er(x,y)=1Ncjk.ELPjk(x,y).
(4)

In theory, the reconstructed field Er and the measured field Emes are equal. In practice, they can differ due several reasons:

  • - there is noise on the measured intensity and phase maps and imperfections in the experimental setup
  • - the theoretical modes used for the decomposition can differ from the actual modes supported by the fiber, due to uncertainties on the knowledge of the actual opto-geometric parameters of the fiber

Therefore, the comparison of the reconstructed field and the measured one gives direct information on the validity of the intensity and phase measurement. To estimate the accuracy of the reconstruction, we define the error between the measured and the reconstructed fields by:

Δ=1NpixelsNpixels|EmesEr|2.
(5)

Such a definition has the advantage of being very sensitive to small reconstruction errors. It can be used directly during the calibration step to adjust the centering of the device (see section 2.2). However, the error values obtained are not bounded. Therefore it can be useful to define another bounded error coefficient, in terms of a correlation coefficient between the measured and the reconstructed field:

C=maxr|Emes(r'r).Er*(r')dr'|.
(6)

This coefficient is normalized to one when both fields are. Both errors will be mentioned in the experimental results presented in section 3.

2.2 Calibration procedure

The choice of a proper reference beam is also an important issue. Indeed, an absolute wavefront measurement on the multimode beam is difficult to perform as the optical magnification system we use suffers from aberrations with amplitudes stronger than the weak phase defects due to the multimode structure we want to measure. To overcome this, a reference beam with a plane wavefront is needed. In our case, we used the same fiber in which we excited selectively a mode close to the fundamental one with the help of the input mirror and the positioning stage (Fig. 2 right). Therefore, the accuracy of the measurement is limited in our case to our ability to selectively excite the fundamental mode. Such a method can be very difficult to implement on a highly multimode fiber. In such cases, an alternative phase calibration method could be applied for example by illuminating the whole optical system and wavefront analyzer with a beam coming out of a single-mode fiber placed on the same micro-positioning stage than the multimode fiber under analysis, prior to the multimode measurement, or to put a cleaning pinhole at the output of the multimode fiber to generate a quasi plane reference wave.

2.3 Influence of the reference beam

  • - the intensity of the reference beam given in Fig. 3 appears to be clearly off-centered with respect to the core of the fiber. This centering defect can be detected and corrected with our centering method described above
  • - no significant change is observed in the intensity and phase profiles in the core region, i.e. in the region where the phase is actually measured by the wavefront analyzer. To quantify this, the reconstruction error as defined in Eq. (5) is 8.6.10−4, which is well below the experimental values presented further.
  • - the most important issue is the error with respect to the actual multimode field coming out of the fiber, before subtraction of the reference field phase. This error is not measurable by experimental means and therefore represents the absolute limitation of our measurement. In this simulation, the value of the error between the reconstructed field and the actual field, due to the non perfect reference beam, is 1.4.10−3, which is still below the typical experimental reconstruction errors presented further, and still allow good modal content analysis.

These results show that the sensitivity of the reconstruction procedure with regard to the reference beam seems to be low when the degradation of the reference beam is limited. When several modes in a high proportion compared to the fundamental one are composing the reference beam, the reconstruction loses its validity; but such cases can be easily detected by looking directly at the intensity profile of the reference beam.

3. Results and discussion

4. Conclusion

The technique reported here is also applicable in the case of less conventional fibers such as rod type or photonic crystal fibers, provided their mode structure is known. Multicore fibers are also of great interest since their effective area can be increased by simply increasing the number of cores and this technique can also be used to determine the phase difference between the cores. However, the wavefront analyzer cannot be directly used for this, and the distance between the diffraction grating and the camera has to be changed in order to observe an interference pattern between adjacent cores [14

14. C. Bellanger, B. Toulon, J. Primot, L. Lombard, J. Bourderionnet, and A. Brignon, “Collective phase measurement of an array of fiber lasers by quadriwave lateral shearing interferometry for coherent beam combining,” Opt. Lett. 35(23), 3931–3933 (2010). [CrossRef] [PubMed]

].

Acknowledgments

This work was supported by the ANR MultiFemto project of the French Agence Nationale de la Recherche. Mathieu Paurisse acknowledges the funding of his Ph. D. by the Délégation Générale de l’Armement.

References and links

1.

J. W. Nicholson, A. D. Yablon, S. Ramachandran, and S. Ghalmi, “Spatially and spectrally resolved imaging of modal content in large-mode-area fibers,” Opt. Express 16(10), 7233–7243 (2008). [CrossRef] [PubMed]

2.

J. W. Nicholson, A. D. Yablon, J. F. Fini, and M. D. Mermelstein, “Measuring the modal content of large-mode-area fibers,” IEEE J. Sel. Top. Quantum Electron. 15(1), 61–70 (2009). [CrossRef]

3.

Y. Z. Ma, Y. Sych, G. Onishchukov, S. Ramachandran, U. Peschel, B. Schmauss, and G. Leuchs, “Fiber –modes and fiber-anisotropy characterization using low-coherence interferometry,” Appl. Phys. B 96(2-3), 345–353 (2009). [CrossRef]

4.

D. B. S. Soh, J. Nilsson, S. Baek, C. Codemard, Y. Jeong, and V. Philippov, “Modal power decomposition of beam intensity profiles into linearly polarized modes of multimode optical fibers,” J. Opt. Soc. Am. A 21(7), 1241–1250 (2004). [CrossRef] [PubMed]

5.

O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett. 94(14), 143902 (2005). [CrossRef] [PubMed]

6.

F. Stutzki, H. J. Otto, F. Jansen, C. Gaida, C. Jauregui, J. Limpert, and A. Tünnermann, “High-speed modal decomposition of mode instabilities in high-power fiber lasers,” Opt. Lett. 36(23), 4572–4574 (2011). [CrossRef] [PubMed]

7.

T. Kaiser, D. Flamm, S. Schröter, and M. Duparré, “Complete modal decomposition for optical fibers using CGH-based correlation filters,” Opt. Express 17(11), 9347–9356 (2009). [CrossRef] [PubMed]

8.

J. Primot, “Three-wave lateral shearing interferometer,” Appl. Opt. 32(31), 6242–6249 (1993). [CrossRef] [PubMed]

9.

J. Primot and N. Guérineau, “Extended hartmann test based on the pseudoguiding property of a hartmann mask completed by a phase chessboard,” Appl. Opt. 39(31), 5715–5720 (2000). [CrossRef] [PubMed]

10.

J. C. Chanteloup, F. Druon, M. Nantel, A. Maksimchuk, and G. Mourou, “Single-shot wave-front measurements of high-intensity ultrashort laser pulses with a three-wave interferometer,” Opt. Lett. 23(8), 621–623 (1998). [CrossRef] [PubMed]

11.

D. Flamm, O. A. Schmidt, C. Schulze, J. Borchardt, T. Kaiser, S. Schröter, and M. Duparré, “Measuring the spatial polarization distribution of multimode beams emerging from passive step-index large-mode-area fibers,” Opt. Lett. 35(20), 3429–3431 (2010). [CrossRef] [PubMed]

12.

J. A. Buck, Fundamentals of Optical Fibers (Wiley, Hoboken, NJ, 2004).

13.

J. C. Chanteloup, “Multiple-wave lateral shearing interferometry for wave-front sensing,” Appl. Opt. 44(9), 1559–1571 (2005). [CrossRef] [PubMed]

14.

C. Bellanger, B. Toulon, J. Primot, L. Lombard, J. Bourderionnet, and A. Brignon, “Collective phase measurement of an array of fiber lasers by quadriwave lateral shearing interferometry for coherent beam combining,” Opt. Lett. 35(23), 3931–3933 (2010). [CrossRef] [PubMed]

OCIS Codes
(060.2320) Fiber optics and optical communications : Fiber optics amplifiers and oscillators
(140.3510) Lasers and laser optics : Lasers, fiber

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: December 2, 2011
Revised Manuscript: January 13, 2012
Manuscript Accepted: January 26, 2012
Published: February 2, 2012

Citation
Mathieu Paurisse, Louis Lévèque, Marc Hanna, Frédéric Druon, and Patrick Georges, "Complete measurement of fiber modal content by wavefront analysis," Opt. Express 20, 4074-4084 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-4-4074


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References

  1. J. W. Nicholson, A. D. Yablon, S. Ramachandran, and S. Ghalmi, “Spatially and spectrally resolved imaging of modal content in large-mode-area fibers,” Opt. Express16(10), 7233–7243 (2008). [CrossRef] [PubMed]
  2. J. W. Nicholson, A. D. Yablon, J. F. Fini, and M. D. Mermelstein, “Measuring the modal content of large-mode-area fibers,” IEEE J. Sel. Top. Quantum Electron.15(1), 61–70 (2009). [CrossRef]
  3. Y. Z. Ma, Y. Sych, G. Onishchukov, S. Ramachandran, U. Peschel, B. Schmauss, and G. Leuchs, “Fiber –modes and fiber-anisotropy characterization using low-coherence interferometry,” Appl. Phys. B96(2-3), 345–353 (2009). [CrossRef]
  4. D. B. S. Soh, J. Nilsson, S. Baek, C. Codemard, Y. Jeong, and V. Philippov, “Modal power decomposition of beam intensity profiles into linearly polarized modes of multimode optical fibers,” J. Opt. Soc. Am. A21(7), 1241–1250 (2004). [CrossRef] [PubMed]
  5. O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Phys. Rev. Lett.94(14), 143902 (2005). [CrossRef] [PubMed]
  6. F. Stutzki, H. J. Otto, F. Jansen, C. Gaida, C. Jauregui, J. Limpert, and A. Tünnermann, “High-speed modal decomposition of mode instabilities in high-power fiber lasers,” Opt. Lett.36(23), 4572–4574 (2011). [CrossRef] [PubMed]
  7. T. Kaiser, D. Flamm, S. Schröter, and M. Duparré, “Complete modal decomposition for optical fibers using CGH-based correlation filters,” Opt. Express17(11), 9347–9356 (2009). [CrossRef] [PubMed]
  8. J. Primot, “Three-wave lateral shearing interferometer,” Appl. Opt.32(31), 6242–6249 (1993). [CrossRef] [PubMed]
  9. J. Primot and N. Guérineau, “Extended hartmann test based on the pseudoguiding property of a hartmann mask completed by a phase chessboard,” Appl. Opt.39(31), 5715–5720 (2000). [CrossRef] [PubMed]
  10. J. C. Chanteloup, F. Druon, M. Nantel, A. Maksimchuk, and G. Mourou, “Single-shot wave-front measurements of high-intensity ultrashort laser pulses with a three-wave interferometer,” Opt. Lett.23(8), 621–623 (1998). [CrossRef] [PubMed]
  11. D. Flamm, O. A. Schmidt, C. Schulze, J. Borchardt, T. Kaiser, S. Schröter, and M. Duparré, “Measuring the spatial polarization distribution of multimode beams emerging from passive step-index large-mode-area fibers,” Opt. Lett.35(20), 3429–3431 (2010). [CrossRef] [PubMed]
  12. J. A. Buck, Fundamentals of Optical Fibers (Wiley, Hoboken, NJ, 2004).
  13. J. C. Chanteloup, “Multiple-wave lateral shearing interferometry for wave-front sensing,” Appl. Opt.44(9), 1559–1571 (2005). [CrossRef] [PubMed]
  14. C. Bellanger, B. Toulon, J. Primot, L. Lombard, J. Bourderionnet, and A. Brignon, “Collective phase measurement of an array of fiber lasers by quadriwave lateral shearing interferometry for coherent beam combining,” Opt. Lett.35(23), 3931–3933 (2010). [CrossRef] [PubMed]

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