Analysis and Discussion

Table 2. Near field 1/e2 diameter spot size from near field and far field data.

The far field data were analyzed to provide the Petermann II MFD [1], the 1/e2 diameter from a diffraction-limited Gaussian approximation using the ISO/DIS 13694 laser standard fit [2], and the 1/e2 diameter of the near field obtained from 2D Fourier analysis with phase retrieval [3-5]. The near field profile data were analyzed to provide the 1/e2 diameter, using the equivalent scanning slit method. The profile diameters obtained with the 40X lens were corrected for the spread function width.

The MFD for the lensed/tapered fibers depends significantly on the angular integration limit of the Petermann II integral, due to the wide angular extent of the far field. The MFD stabilizes for most of the fibers in the range from 40°to 60°. For the elliptical fiber #6 the integration needs to extend beyond 70°. However, the Petermann II formulation has radial symmetry as an underlying assumption. Therefore, strictly speaking, it is inappropriate to use this MFD measure for elliptical fibers. Table 1 summarizes the MFD results over the integral limit ranging from 40° to 60°. The fractional percent variation from the average value for fibers #1-5 is well within acceptable limits, and errors associated with the elliptical fiber are quite significant.

The 1/e2 diameter spot sizes obtained from the far and near field analyses are summarized in Table 2. For any fiber, the diameter reported using the different methods varies significantly, on the order of ±15-20%. This result is not surprising for these sources. The extremely non- Gaussian shape of the far field makes the Gaussian approximation highly questionable. Similarly, the very small spot size of the lensed/tapered fibers is at or beyond the performance limits of the optical near-field imaging techniques, and the measured values must undergo significant corrections that increase uncertainty and error. The most accurate method here may be that of the 2D Fourier transform with phase retrieval. It is also observed that these values are overall the most consistent with the MFD values.


Figure 2. Near field profiles of fiber #6, the elliptical lensed/tapered fiber, obtained with a.) 40X lens and b.) 100X lens. The horizontal scale in the profile cross sections is 1 μm/division.

Lensed and tapered specialty fibers exhibit wide angular divergence and corresponding small spot sizes. These characteristics pose significant challenges to measurement of MFD and spot size. The results presented highlight the limitations of standard near-field optical techniques, and the necessity for far-field measurements to include very wide angles. Specifically, for some of the fibers measured here, far-field measurement instruments must acquire data at angles extending to ±60° or greater for accurate determination of the MFD. For near-field measurements using conventional optical techniques, the small spot sizes of these fibers push the limits of resolution and can lead to significant errors. Also, the typically non-Gaussian profiles of lensed and tapered fibers also lend doubts as to the accuracy of Gaussian approximations used to determine spot size. Estimation of spot size using these methods shows considerable variation. Due to this, and also to ease of measurement, far-field transform techniques are the preferred method of characterization.

For radially symmetric fibers, specification of the Petermann II MFD to characterize the focused beam yields consistent results and appears to be fine, but due to variation in the integral with angular limit and to avoid ambiguity, the actual limit used in the calculation should be specified as well as the MFD value. For non-radially symmetric fibers, use of the Petermann II MFD, although it does provide a measure, is problematic and highly questionable based on the underlying assumptions of radial symmetry in the Petermann II integral. For such non-radially symmetric fibers, the development of new metrics using 2D Fourier transform methods may provide more accurate and consistent specifications.

This article was written by Jeffrey L. Guttman, Ph.D., Director of Engineering, Ophir-Spiricon (North Logan, UT). For more information, contact Mr. Guttman at jeff.guttman@us. ophiropt.com, or visit http://info.hotims.com/40431-200.


The author is grateful to David Pikey for his efforts in the implementation of the algorithm for the 2D Fourier transform with phase retrieval.


  1. “Measurement of Mode-Field Diameter of Single-Mode Optical Fiber”, Fiberoptic Test Procedure FOTP-191, Telecommunications Industry Association, Standards and Technology Department, 2500 Wilson Blvd., Suite 300, Arlington, VA, 22201 (1998).
  2. ISO/DIS Standard 13694, “Test methods for laser beam power (energy) density distribution”, International Organization for Standardization, September 1998.
  3. J.R.Fienup, “Reconstruction of an Object from the modulus of its Fourier transform”, Optics Letters, Vol. 3, No. 1, pp 27-29, July 1978.
  4. J.R.Fienup, “Phase retrieval algorithms: a comparison”, Applied Optics, Vol. 21, No. 15, pp. 2758-2769, August 1982.
  5. J.R.Fienup and C.C.Wackermann, “Phase retrieval stagnation problems and solutions”, J. Opt. Soc. Am. A, Vol. 3, No.11, pp. 1897-1907, November 1986.
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