Normalization of single-mode fibers having an arbitrary index profile

H. Matsumura; T. Suganuma

doi:10.1364/AO.19.003151

Applied Optics
Vol. 19,
Issue 18,
pp. 3151-3158
(1980)
•https://doi.org/10.1364/AO.19.003151

Normalization of single-mode fibers having an arbitrary index profile

H. Matsumura and T. Suganuma

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H. Matsumura and T. Suganuma, "Normalization of single-mode fibers having an arbitrary index profile," Appl. Opt. 19, 3151-3158 (1980)

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Abstract

A method is proposed whereby the propagation characteristics of a single-mode fiber having an arbitrary refractive-index profile may be expressed in terms of a newly defined equivalent step-index profile. The theory is based on the fact that the field distribution of the HE₁₁ mode of a fiber closely resembles the Gaussian profile. The method makes it possible to characterize a fiber from a simple measurement of the HE₁₁ mode spot size without making difficult index profile and core radius measurements. It is also found that the step-index distribution is suitable for single-mode fibers.

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Graded index	Step index with the central dip		W type index
$n^{2} = {\begin{array}{l} {n_{1}}^{2} {1 - 2 Δ {(r / a)}^{g}} & (r \leq a) \\ {n_{1}}^{2} (1 - 2 Δ) = {n_{2}}^{2} & (r > a) \end{array}$	$n^{2} = {\begin{array}{l} {n_{1}}^{2} {1 - 2 d {(1 - r / a)}^{g}} & (r \leq a) \\ {n_{1}}^{2} (1 - 2 Δ) = {n_{2}}^{2} & (r > a) \end{array}$		$n^{2} = {\begin{array}{l} {n_{1}}^{2} & (r \leq a) \\ {n_{2}}^{2} & (a \leq r \leq ca) \\ {n_{3}}^{2} & (ca \leq r) \end{array}$
n_1,2 ; Maximum refractive index of the core and the index of the cladding, respectively n₃ ; Refractive index of the third layer of the W type index Λ ; Relative index difference between core and cladding = (n₁² − n₂²)/2n₁²		g ; Coefficient of the index gradient a ; Radius of the core d ; Depth of the central dip D ; Normalized depth of the central dip = d/Δ c ; Width coefficient of the cladding of the W type fibre

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Applied Optics