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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 12, Iss. 5 — Mar. 8, 2004
  • pp: 847–852
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Structure and propagation of modes of large mode area holey fibers

J.C. Gates, C.W.J. Hillman, Joanne C. Baggett, K. Furusawa, Tanya M. Monro, and W.S. Brocklesby  »View Author Affiliations


Optics Express, Vol. 12, Issue 5, pp. 847-852 (2004)
http://dx.doi.org/10.1364/OPEX.12.000847


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Abstract

We report cross-section measurement and propagation measurement of modes of large mode area holey fibers using near-field scanning optical microscopy (NSOM). Mode profiles are measured at the fiber end face using a scanning optical fiber tip held 10 nm from the surface, and compared to theoretical models. Both amplitude and phase of the electric field of the propagating light is measured using NSOM techniques as a function of distance from the fiber end, from 10 nm to 150 µm. Good agreement is found between the data and simple scalar paraxial beam propagation simulations of theoretical mode profiles.

© 2004 Optical Society of America

1. Introduction

Holey fibers have proved to be one of the most innovative areas of optical waveguide development in the recent past. Their guiding properties can be varied using geometrical rather than material parameters, and they can demonstrate some extreme variation of mode area [1

1. J.C. Baggett, T.M. Monro, K. Furusawa, and D.J. Richardson, “Comparative study of large mode holey and conventional fibers,” Opt. Lett. 261045–1047 (2001). [CrossRef]

], nonlinearity [2

2. N. G. R. Broderick, T. M. Monro, P. J. Bennett, and D. J. Richardson. “Nonlinearity in holey optical fibers: measurement and future opportunities,” Opt. Lett. 24, 1395–1397 (1999). [CrossRef]

], and dispersion [3

3. T. A. Birks, D. Mogilevtsev, J. C. Knight, and P. S. Russell, “Dispersion compensation using single-material fibers,” IEEE Photonics Technol. Lett. 11, 674–676 (1999). [CrossRef]

]. They are typically formed by drawing from a perform consisting of a large number of small capillaries, and the resultant structure can be very complex [4

4. T. M. Monro and D. J. Richardson, “Holey optical fibres: Fundamental properties and device applications,” Comptes Rendus Physique 4, 175–186 (2003). [CrossRef]

]. The electromagnetic modes which propagate in these structures are similarly much more complex than the modes of a traditional step-index fiber. As with other complex fiber structures, calculation of the form of holey fiber (HF) modes is typically done by numerical simulation [5

5. T. M. Monro, D. J. Richardson, N. G. R. Broderick, and P. J. Bennett, “Modeling large air fraction holey optical fibers,” J. Lightwave Technol. 18, 50–56 (2000). [CrossRef]

].

In this paper we report the detailed measurement of HF modes at the end faces of the fibers using near-field scanning optical microscopy (NSOM). NSOM has several advantages over other mode measurement techniques. It allows resolution that is tip-aperture-limited for any evanescent fields at the end face, and diffraction-limited for propagating fields. It allows very accurate control of distance from the end face, via the piezoelectric scanning system used to control tip position, and can also measure the surface contour of the end face if the tip is locked to the surface via shear-force control [6

6. K. Karrai and R. D. Grober, “Piezoelectric Tip-Sample Distance Control for Near-Field Optical Microscopes,” Appl. Phys. Lett. 66, 1842–1844 (1995). [CrossRef]

]. These advantages make it an ideal tool for study of complex HF modes. In addition, because the tip measures the electric field at a particular position in space, cross-sectional profiles in any direction through the beam propagating away from the fiber end can be measured. Addition of an interferometer to the NSOM system [7

7. M. L. M. Balistreri, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Local observations of phase singularities in optical fields in waveguide structures,” Phys. Rev. Lett. 85, 294–297 (2000). [CrossRef] [PubMed]

] allows direct measurement of amplitude and phase of the electric field of the beam, instead of just intensity. This allows more direct comparison with propagation models of the beam from the end of the HF.

The combination of NSOM with interferometry allows us to characterize the mode profile of our fibers from the fiber end out through the Rayleigh region with high accuracy. In this letter we will present detailed measurements of the mode profiles as the beam propagates away from the end face of the fiber, and show that the propagation is modeled very well by a simple scalar beam propagation calculation, despite the complex nature of the HF mode.

2. Holey fibers

The fibers used in this work are silica, and the typical structure is shown in Fig. 1, with a hexagonal lattice of small holes except for one lattice point in the center, where the hole is missing. These fibers have the important properties that they can be single mode over large wavelength regimes, and their mode area is much larger than that of typical single mode step index fiber [8

8. J.C. Knight, T.A. Birks, R.F. Cregan, P.S. Russell, and J.P. de Sandro, “Large mode area photonic crystal fibre,” Electron. Lett. 4, 1347–13 (1998). [CrossRef]

], making them ideally suitable for applications such as high-power low nonlinearity transmission. Although the holes shown in Fig. 1 have a regular hexagonal structure, the fiber guides via effective index rather than photonic crystal effects. In this paper the propagating modes of these fibers have been calculated using a hybrid orthogonal function method [5

5. T. M. Monro, D. J. Richardson, N. G. R. Broderick, and P. J. Bennett, “Modeling large air fraction holey optical fibers,” J. Lightwave Technol. 18, 50–56 (2000). [CrossRef]

], which uses sums of Hermite polynomials to construct the field distribution, starting from the known refractive index profile of the fiber itself.

Fig 1. SEM image of end face of large mode area fiber

3. NSOM detection systems

4. Experimental results

Fig. 2. Experimental (a) and theoretical (b) contour plots of the optical field amplitude 100nm above the fiber end face. Contours are linearly spaced, with spacing of 0.1. Maximum amplitude is scaled to 1. The rotation of the field in (a) is an experimental artifact.

Figure 2(a) shows the electric field amplitude measured in a plane 100 nm away from the end face of the large mode area fiber at 1550 nm. The contours are linearly spaced, with spacing of 0.1, and the maximum amplitude is scaled to 1. The confinement of the mode around the holes is clearly visible. Figure 2(b) shows the theoretically calculated mode, based on knowledge of the glass structure, with equivalent contour lines. The mode shapes correlate well, although the mode field area is overestimated by the theoretical calculations. Cross-sections across the mode profiles are shown in Fig. 3. The form of the cross-sections agrees well, but the widths from measured and theoretical mode field profiles differ by ~5–10%. The glass used to fabricate this fiber has been observed to have inhomogeneities in its refractive index in the vicinity of the core, and this index variation, which is not included in the modeling, is likely to be responsible for the discrepancy.

Fig. 3. Cross-sections across the optical field amplitude at the end face of the fiber. Red line is a cross-section of the theoretical mode across one of the inner ring of holes, and the red open circles are the equivalent data. Black line is a cross-section in an orthogonal direction, between the holes, and the black open squares are the equivalent data.

Figures 4 and 5 show cross-sections of the 1550 nm beam emerging from the end face of the LMA fiber. The cross-sections are measured by first mapping the position of the end face of the fiber using shear force measurement, and then moving the tip in a plane perpendicular to the fiber end face. Distance from the centre of the fiber is shown on the x-axis of the figures. Figure 4 shows the intensity variation in a plane that crosses one of the innermost holes in the fiber, with the centre of the mode at 0 on the x axis. The scale is logarithmic to show detail of the low-intensity components. The intensity minimum at the hole is clearly visible. The high spatial frequencies in the beam cause diffraction at much higher angles than would be expected for a similar-area Gaussian mode.

Figure 5 shows a smaller-scale scan of the phase variation in a similar plane. In this figure the π phase shift between adjacent mode antinodes within the fiber gradually disappears as the mode propagates in free space. In both figures, the lower plot is a numerical simulation of the fields using a simple split-step beam propagation technique [9

9. G.P. Agrawal, Nonlinear Fiber Optics (Academic Press, 1989).

], which was used to simulate the propagation out of the end of the fiber, starting with the theoretically calculated modes. The agreement between the simulated and measured spatial variation is very good in both cases.

Fig. 4. Cross-section of the intensity of the mode as it propagates away from the end face of the fiber. The center of the mode is at the left end of the x-axis. The colormap scale is logarithmic, to show detail in the patterns. The top figure shows the square of the measured field amplitude, and the bottom figure shows the intensity distribution calculated by numerically propagating the theoretical mode.
Fig 5. Cross-section of the phase of the mode as it propagates away from the end face of the fiber. The center of the mode is at the left end of the x-axis. The colormap scale shows the cosine of the phase. The top figure shows the measured phase, and the bottom figure shows the phase variation calculated by numerically propagating the theoretical mode. The phase offset is arbitrary.

As well as cross-sections along the propagation direction, it is possible to take cross-sections across the mode at different distances from the fiber end. Figure 6 shows the variation of the intensity of the mode as a function of distance out to 163 µm from the end face, equivalent to several Rayleigh lengths for a similar area Gaussian beam. The intensity scale is logarithmic, to show the low-intensity detail in the images. The wavelength in this case is 633 nm. Because of the large size of the mode compared to the travel on the stages used to control the tip, only about a quarter of the beam is shown in the figures. As the mode propagates away from the fiber end, the lobes appear to rotate by π/6 by a distance of 73 µm from the end face, and then rotate again by π/6 by the last frame, at 163 µm.

Fig. 6. Measured cross-sections of the intensity of the mode at longer distances from the fiber end face. Heights above the end face are shown on the figure. The top left frame is measured in contact with the end face, The intensity colormap scale is logarithmic to show low-intensity detail. The center of the mode is in the bottom left corner of each frame.

5. Conclusions

References and links

1.

J.C. Baggett, T.M. Monro, K. Furusawa, and D.J. Richardson, “Comparative study of large mode holey and conventional fibers,” Opt. Lett. 261045–1047 (2001). [CrossRef]

2.

N. G. R. Broderick, T. M. Monro, P. J. Bennett, and D. J. Richardson. “Nonlinearity in holey optical fibers: measurement and future opportunities,” Opt. Lett. 24, 1395–1397 (1999). [CrossRef]

3.

T. A. Birks, D. Mogilevtsev, J. C. Knight, and P. S. Russell, “Dispersion compensation using single-material fibers,” IEEE Photonics Technol. Lett. 11, 674–676 (1999). [CrossRef]

4.

T. M. Monro and D. J. Richardson, “Holey optical fibres: Fundamental properties and device applications,” Comptes Rendus Physique 4, 175–186 (2003). [CrossRef]

5.

T. M. Monro, D. J. Richardson, N. G. R. Broderick, and P. J. Bennett, “Modeling large air fraction holey optical fibers,” J. Lightwave Technol. 18, 50–56 (2000). [CrossRef]

6.

K. Karrai and R. D. Grober, “Piezoelectric Tip-Sample Distance Control for Near-Field Optical Microscopes,” Appl. Phys. Lett. 66, 1842–1844 (1995). [CrossRef]

7.

M. L. M. Balistreri, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Local observations of phase singularities in optical fields in waveguide structures,” Phys. Rev. Lett. 85, 294–297 (2000). [CrossRef] [PubMed]

8.

J.C. Knight, T.A. Birks, R.F. Cregan, P.S. Russell, and J.P. de Sandro, “Large mode area photonic crystal fibre,” Electron. Lett. 4, 1347–13 (1998). [CrossRef]

9.

G.P. Agrawal, Nonlinear Fiber Optics (Academic Press, 1989).

10.

N.A. Mortensen and J.R. Folkenberg, “Near-field to far-field transition of photonic crystal fibers: symmetries and interference phenomena,” Opt. Express 10475–481 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-11-475 [CrossRef] [PubMed]

OCIS Codes
(060.2270) Fiber optics and optical communications : Fiber characterization
(110.0180) Imaging systems : Microscopy

ToC Category:
Research Papers

History
Original Manuscript: January 27, 2004
Revised Manuscript: February 23, 2004
Published: March 8, 2004

Citation
J. Gates, C. Hillman, Joanne Baggett, K. Furusawa, Tanya Monro, and W. Brocklesby, "Structure and propagation of modes of large mode area holey fibers," Opt. Express 12, 847-852 (2004)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-5-847


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References

  1. J.C.Baggett, T.M.Monro, K.Furusawa, D.J.Richardson, �??Comparative study of large mode holey and conventional fibers,�?? Opt. Lett. 26 1045-1047 (2001). [CrossRef]
  2. N. G. R. Broderick, T. M. Monro, P. J. Bennett & D. J. Richardson. "Nonlinearity in holey optical fibers: measurement and future opportunities," Opt. Lett. 24, 1395-1397 (1999). [CrossRef]
  3. T. A. Birks, D. Mogilevtsev, J. C. Knight & P. S. Russell, "Dispersion compensation using single-material fibers," IEEE Photonics Technol. Lett. 11, 674-676 (1999). [CrossRef]
  4. T. M. Monro & D. J. Richardson, "Holey optical fibres: Fundamental properties and device applications," Comptes Rendus Physique 4, 175-186 (2003). [CrossRef]
  5. T. M. Monro, D. J. Richardson, N. G. R. Broderick & P. J. Bennett, "Modeling large air fraction holey optical fibers," J. Lightwave Technol. 18, 50-56 (2000). [CrossRef]
  6. K. Karrai & R. D. Grober, "Piezoelectric Tip-Sample Distance Control for Near-Field Optical Microscopes," Appl. Phys. Lett. 66, 1842-1844 (1995). [CrossRef]
  7. M. L. M. Balistreri, J. P. Korterik, L. Kuipers & N. F. van Hulst, "Local observations of phase singularities in optical fields in waveguide structures," Phys. Rev. Lett. 85, 294-297 (2000). [CrossRef] [PubMed]
  8. J.C. Knight , T.A. Birks, R.F. Cregan, P.S. Russell, J.P. de Sandro, �??Large mode area photonic crystal fibre,�?? Electron. Lett. 4, 1347-13 (1998). [CrossRef]
  9. G.P. Agrawal, Nonlinear Fiber Optics (Academic Press, 1989).
  10. N.A. Mortensen & J.R. Folkenberg, �??Near-field to far-field transition of photonic crystal fibers: symmetries and interference phenomena,�?? Opt. Express 10 475-481(2002), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-11-475"> http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-11-475</a> [CrossRef] [PubMed]

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