## Abstract

The boundary conditions in Eq. (2) were used incorrectly, which influenced the numerical results in Fig. 3(a) correspondingly. The corrected calculated mode intensity profile matches better with the measured one.

©2008 Optical Society of America

Equation (2) in Ref. [1] should be written as follows:

(2)$$\frac{\partial {C}_{A}}{\partial t}=D\left(\frac{{\partial}^{2}{C}_{A}}{\partial {x}^{2}}+\frac{{\partial}^{2}{C}_{A}}{\partial {y}^{2}}\right),$$$$\{\begin{array}{c}{C}_{A}\left(x,0,t>0\right)={C}_{0}\phantom{\rule{2.em}{0ex}}\mathit{for}\mid x\mid \le \frac{w}{2},\\ \frac{\partial {C}_{A}\left(x,0,t>0\right)}{\partial y}=0\phantom{\rule{3.em}{0ex}}\mathit{for}\mid x\mid >\frac{w}{2},\\ \frac{\partial {C}_{A}\left(x,-h,t>0\right)}{\partial y}=0\phantom{\rule{2.em}{0ex}}\mathit{for}-\infty <x<+\infty ,\phantom{\rule{.2em}{0ex}}\end{array}$$$${C}_{A}\left(x,y,t=0\right)=0\phantom{\rule{1.em}{0ex}}\mathit{for}-\infty <x<+\infty ,y<0.$$ where *h*=11 μm is the thickness of a Li^{+} ions-containing ion-exchangeable layer.

The corresponding contour of the numerical simulation of mode intensity profile (red dashed lines) in Fig. 3(a) in Ref. [1] should be corrected as follows. Corrected calculated mode intensity profile matches better with the measured one.

## References and links

**1. **Z. He, Y. Li, Y. Li, Y. Zhang, L. Liu, and Lei Xu, “Low-loss channel waveguides and Y-splitter formed by ion-exchange in silica-on-silicon,” Opt. Express **16**, 3172–3177 (2008). [CrossRef] [PubMed]

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### Equations (3)

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(2)
$$\frac{\partial {C}_{A}}{\partial t}=D\left(\frac{{\partial}^{2}{C}_{A}}{\partial {x}^{2}}+\frac{{\partial}^{2}{C}_{A}}{\partial {y}^{2}}\right),$$
(2)
$$\{\begin{array}{c}{C}_{A}\left(x,0,t>0\right)={C}_{0}\phantom{\rule{2.em}{0ex}}\mathit{for}\mid x\mid \le \frac{w}{2},\\ \frac{\partial {C}_{A}\left(x,0,t>0\right)}{\partial y}=0\phantom{\rule{3.em}{0ex}}\mathit{for}\mid x\mid >\frac{w}{2},\\ \frac{\partial {C}_{A}\left(x,-h,t>0\right)}{\partial y}=0\phantom{\rule{2.em}{0ex}}\mathit{for}-\infty <x<+\infty ,\phantom{\rule{.2em}{0ex}}\end{array}$$
(2)
$${C}_{A}\left(x,y,t=0\right)=0\phantom{\rule{1.em}{0ex}}\mathit{for}-\infty <x<+\infty ,y<0.$$