Mode field diameter gets redefined
By WILLIAM B. GARDNER
Standards bodies have recovered from conceptual errors in determining the mode field diameter (MFD) of singlemode fibers. In 1983, Klaus Petermann proposed what would become the popular MFD definition "Petermann II" (to distinguish it from the 1976 definition known as "Petermann I").
In 1983, some test sets measured the MFD in the near field (near the fiber`s exit face). Other test sets measured the far field (several centimeters from the exit face) and used a Hankel Transform to convert the far field to the near field. Accurate measurement of the far-field pattern is easier because it is much larger than the near field. In 1989, the International Telecommunication Union (ITU) selected the far field as its Reference Test Method for MFD, putting the spotlight on the far-field/near-field conversion, because the Petermann II definition was made in the near field.
In 1989, another paper used the Petermann II definition to derive a formula for MFD in terms of integrals in the far field. This formula is now used in virtually all far-field determinations of the MFD.
Confidence in this equation was challenged, though, when Andy Hallam of PK Technology (UK) raised a question about the equation to Matt Young of the National Institute of Standards and Technology (NIST) in Boulder, CO. Young discussed the equation with Ron Wittmann of NIST`s Radio Frequency Technology Div. Wittmann is an electromagnetic-field theorist who recognized similarities between this problem and microwave antenna theory. The fiber under test can be viewed as a radiating optical antenna. The mode field that exists inside the fiber core becomes the aperture field at the fiber`s exit face. Optical physicists had been taking these two fields to be identical, but Wittmann pointed out that the discontinuity at the end of the fiber excites a radiative wave that slightly but significantly alters the aperture field. In fact, Petermann II does not exist for aperture fields.
Wittmann and Young also discovered that the "obliquity factor" was ignored in the popular 1989 formula for deriving MFD from the far field. When the formula incorporates the correct obliquity factor, the integrals in both the numerator and denominator diverge. Correcting the MFD formula that has enjoyed nearly universal acceptance since 1989 would render it useless.
So what to do? Since nearly everyone prefers the far field to the near field for measuring MFD, why not use the accepted far-field formula to define the MFD? Standards bodies have now declared the 1989 formula to be the definition of MFD. It appears as Eq. (1-1) in Clause 1.3.2 of ITU`s Recommendation G.650.
Tom Hanson of Corning Inc. (Corning, NY) recently authored and balloted the Telecommunications Industry Association`s (TIA`s) FOTP-191 "Measurement of MFD of singlemode optical fiber." The 1989 far-field formula (which now becomes TIA`s definition of MFD) appears as Eq. (1), Clause 6.1 in FOTP-191. The old TIA near-field formula must be discarded or corrected. The small systematic differences between the new MFD definition and original Petermann II definition are believed to be negligible for fibers of current interest. This difference increases with decreasing core size and increasing core-cladding index difference. q