## Abstract

A segmented-cladding fiber consists of a uniform core of high refractive index and a cladding with regions of high and low refractive index alternating angularly. This type of fiber provides an effective approach for achieving widely extended single-mode operation with a large core size. We analyze the fiber in detail by the radial-effective-index method, which replaces the fiber with an effective circular fiber. The accuracy of the method is confirmed by comparison with results obtained from the finite-element method. By applying the transverse-matrix method to the effective fiber, the leakage losses of the first two modes of the fiber are calculated. These then form the basis for discussion of the single-mode operation of the fiber. The analysis elucidates not only the physics of the fiber, but also the dependence of the performance of the fiber on various fiber parameters. With illustrations, we demonstrate the possibility of designing an ultralarge-core, segmented-cladding fiber that is single moded over the entire $\mathrm{S}+\mathrm{C}+\mathrm{L}$ band. The fiber should be able to suppress nonlinear optical effects and therefore prove useful for broadband optical communication employing dense-wavelength-division multiplexing.

© 2004 Optical Society of America

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### Equations (12)

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(1)
$$\frac{{\partial}^{2}\varphi}{\partial {r}^{2}}+\frac{1}{r}\frac{\partial \varphi}{\partial r}+\frac{1}{{r}^{2}}\frac{{\partial}^{2}\varphi}{\partial {\theta}^{2}}+{k}^{2}[{n}^{2}(r,\theta )-{n}_{\mathrm{eff}}^{2}]\varphi =0,$$
(2)
$$\varphi (r,\theta )={\varphi}_{r}(r){\varphi}_{r\theta}(r,\theta ).$$
(3)
$${\varphi}_{r\theta}\frac{{\mathrm{d}}^{2}{\varphi}_{r}}{\mathrm{d}{r}^{2}}+\frac{{\varphi}_{r\theta}}{r}\frac{\mathrm{d}{\varphi}_{r}}{\mathrm{d}r}+\frac{{\varphi}_{r}}{{r}^{2}}\frac{{\partial}^{2}{\varphi}_{r\theta}}{\partial {\theta}^{2}}$$
(4)
$$+{k}^{2}[{n}^{2}(r,\theta )-{n}_{\mathrm{eff}}^{2}]{\varphi}_{r}{\varphi}_{r\theta}=0.$$
(5)
$$\frac{{\partial}^{2}{\varphi}_{r\theta}}{\partial {\theta}^{2}}+{k}^{2}[{n}^{2}(r,\theta )-{n}_{\mathrm{effr}}^{2}(r)]{r}^{2}{\varphi}_{r\theta}=0.$$
(6)
$$\frac{{\mathrm{d}}^{2}{\varphi}_{r}}{\mathrm{d}{r}^{2}}+\frac{1}{r}\frac{\mathrm{d}{\varphi}_{r}}{\mathrm{d}r}+{k}^{2}\left[{\tilde{n}}_{\mathrm{effr}}^{2}(r)-\frac{{l}^{2}}{{k}^{2}{r}^{2}}-{n}_{\mathrm{eff}}^{2}\right]{\varphi}_{r}=0,$$
(7)
$${\tilde{n}}_{\mathrm{effr}}^{2}(r)={n}_{\mathrm{effr}}^{2}(r)+\frac{{l}^{2}}{{k}^{2}{r}^{2}}\hspace{1em}\hspace{1em}l=0,1,2,\dots .$$
(8)
$${n}_{\mathrm{effr}}^{2}(r)={n}^{2}(r)-\frac{{l}^{2}}{{k}^{2}{r}^{2}}.$$
(9)
$$\frac{{\partial}^{2}{\varphi}_{r\theta}({r}_{i},\theta )}{\partial {\theta}^{2}}+{k}^{2}[{n}^{2}({r}_{i},\theta )-{n}_{\mathrm{effr}}^{2}({r}_{i})]{r}_{i}^{2}{\varphi}_{r\theta}({r}_{i},\theta )=0.$$
(10)
$$\tilde{u}tan\tilde{u}=\tilde{w}tanh\left(\tilde{w}\frac{{\theta}_{2}}{{\theta}_{1}}\right)$$
(11)
$$cosh\left(2\tilde{w}\frac{{\theta}_{2}}{{\theta}_{1}}\right)cos2\tilde{u}+\frac{{\tilde{w}}^{2}-{\tilde{u}}^{2}}{2\tilde{u}\tilde{w}}sinh\left(2\tilde{w}\frac{{\theta}_{2}}{{\theta}_{1}}\right)sin2\tilde{u}$$
(12)
$$=cos\frac{2\pi}{N}$$