Abstract
After detailed reviews of the exact mode field distribution of Single Mode Step-Index (SMSI) fibers and relevant definitions of Mode Field Diameter (MFD) and a careful comparison between them, a new approximate equation to calculate the mode field diameter is presented in this study. This equation is more accurate and flexible to determine MFD of Peterman I than Gaussian spot size with that of 1/e and Marcuse empirical equation, and what's more, have a analytic solution of its inverse problem that can be used to directly calculate normalized frequency, Numerical Aperture (NA) and the cut-off wavelength. In order to evaluate the new equation, a beam propagation method that simulates the distribution of fundamental mode field is adopted. Numerical simulation results indicate that the new equation is in good agreement with the theoretical predictions. The new approximation function of MFD is a high level functional equation for the theoretical study of the characteristics of the single-mode fibers and construction of new special fibers.
Highlights
The Mode Field Diameter (MFD) is an important transmission characteristic of single-mode step-index optical fibers, which controls substantial splice loss, disperses loss, and micro bending loss that is sensitive to fiber bend (Li et al, 2009; Chen, 2007; Artiglia et al, 1989)
Marcuse (1977) proposed an empirical equation to evaluate the mode field diameter as the Gaussian beam waist size based on numerical results by Eq(3), so the Marcuse diameter wm is still an approximation of wg
Using Eq (16) and Eq (1), Numerical Aperture is rewritten in an analytic form as: In order to verify Eq (15), we used the Finite Difference Beam Propagation Method (FDBPM) to simulate mode field distribution of single-mode stepindex fibers, which is a well-known parabolic or paraxial approximation of Helmholtz equation with transparent boundary condition and widely used for propagation simulation of modeling fiber-optic devices
Summary
The MFD is an important transmission characteristic of single-mode step-index optical fibers, which controls substantial splice loss, disperses loss, and micro bending loss that is sensitive to fiber bend (Li et al, 2009; Chen, 2007; Artiglia et al, 1989). An empirical equation of calculating MFD of single mode fibers, proposed by Marcuse (1977), was ever used to calculate Gaussian beam waist and to determine NA and cut-off wavelength (Gambling and Matsμmura, 1977).
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