## Abstract

We investigate numerically the optical field in the region immediately behind the input facets of dielectric step-index single-mode slab and fiber waveguides. Visualization of the intensity distributions gives insight into the formation of the fundamental mode and of radiation modes. For a more quantitative characterization we determine the amount of optical power and mode purity of the field in core vicinity as a function of propagation distance. The investigation assists in designing and optimizing waveguides being employed as modal filters, e.g. for astronomical interferometers.

© 2007 Optical Society of America

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### Equations (9)

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(1)
$$f\left(x\text{'}\right)=\frac{\mathrm{sin}\left(\pi \frac{x\text{'}}{w}\right)}{x\text{'}}$$
(2)
$$f\left(r\right)=\frac{{J}_{1}\left(1.22\pi \frac{r}{w}\right)}{r}\phantom{\rule{.2em}{0ex}}\mathrm{with}\phantom{\rule{.2em}{0ex}}r=\sqrt{{x}^{2}+{y}^{2}},$$
(3)
$$p\left(z\right)=\frac{{P}_{\mathrm{DC}}\left(z\right)}{{P}_{\mathrm{in}}}$$
(4)
$$\eta =\frac{{P}_{\mathrm{DC},z\to \infty}}{{P}_{\mathrm{in}}}$$
(5)
$${P}_{\mathrm{slab}\pm}\propto {\int}_{-\frac{{D}_{B}}{2}}^{\frac{{D}_{B}}{2}}{I}_{\mathrm{slab}\pm}\left(x\right)\mathrm{dx}\phantom{\rule{2em}{0ex}}\mathrm{and}\phantom{\rule{2em}{0ex}}{P}_{\mathrm{fiber}\pm}\propto {\int}_{0}^{2\pi}{\int}_{0}^{\frac{{D}_{B}}{2}}{I}_{\mathrm{fiber}\pm}(r,\phi )\mathrm{rdrd}\phi $$
(6)
$${I}_{\mathrm{slab}\phantom{\rule{.2em}{0ex}}\pm}\propto {\mid {A}_{w}\left(x,z=L\right)\mathrm{exp}\left[j{\phi}_{w}\left(x,z=L\right)\right]\pm {A}_{f}\left(x\right)\frac{{A}_{w}\left(x=0\right)}{{A}_{f}\left(x=0\right)}\mathrm{exp}\left[j{\phi}_{w}(x=0,z=L)\right]\mid}^{2},$$
(7)
$$\mathrm{MP}=\frac{{P}_{+}}{{P}_{-}}$$
(8)
$$E(x,y,z)={S}_{m}(x,y){e}^{j{b}_{m}z}$$
(9)
$${E}^{1}(x,z)=\sum _{m=-M}^{M}\left[\left({A}_{m}^{1}\mathrm{exp}\left(j{b}_{m}^{1}z\right)+{B}_{m}^{1}\mathrm{exp}(-j{b}_{m}^{1}z)\right)\sum _{p=-P}^{P}\sum _{q=-Q}^{Q}{S}_{\mathrm{pqm}}^{1}\mathrm{exp}\left(\mathrm{jKpx}\right)\mathrm{exp}\left(\mathrm{jKqy}\right)\right]$$