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Results tagged with fiber-optics
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user 42377
Fiber optics is the study of optical fibers, which are thin pieces of high quality optical materials which are able to act as a waveguide for some frequencies of light. This waveguide or 'light pipe' feature of optical fibers allows them to transmit light with very low loss from one end of the fiber to the other.
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Radial field dependence in optical fibers cladding
Consider an optical fiber whose axis is the $z$-axis. Assume that the electric field $e_z$ along this direction can be written (in cylindrical coordinates) as
$$e_z(r,\phi) = A(\phi)B(r)$$
$k_c$ is …
- 777
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Optical fibers field analysis, $\phi$ dependence not considered
In optical fibers, the core (with $\varepsilon = \varepsilon_1$) is usually represented by a cylinder of radius $a$, whose axis coincides with the $z$-axis in cylindrical coordinates. The cladding is …
- 777
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Optical fibers eigenvalue equation considering $\phi$ dependency
Consider the system of equations formulated in a previous question (optical fibers continuity of tangent field components across the core-cladding interface):
$$
\left\{
\begin{array}{c}
e_z^{(1)}(r, …
- 777
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Accepted
Optical fibers eigenvalue equation considering $\phi$ dependency
It would be too long to copy the whole procedure here. If I did not make mistakes, the result should be:
$$\left[ \displaystyle \frac{n_1^2}{n_2^2} \frac{1}{a k_{c_1}} \frac{J'_{\nu} (a k_{c_1})}{J_{ …
- 777
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Plot the eigenvalue equation for optical fibers LP modes
The choice about the quantities represented by the $x$ and $y$ axes is arbitrary. A convenient choice is the following one.
Rewrite the eigenvalue equation as
$$u \frac{J_{\ell - 1}(u)}{J_{\ell}(u)} = …
- 777
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2
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Plot the eigenvalue equation for optical fibers LP modes
The eigenvalue equation for LP modes in Optical Fibers is:
$$\frac{J_{\ell - 1}(u)}{J_{\ell}(u)} = -\frac{w}{u} \frac{K_{\ell - 1}(w)}{K_{\ell}(w)}$$
where:
$J_{\ell}(u)$ is the Bessel function of th …
- 777
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Existence of $\mathrm{HE}_{11}$ mode in optical fibers for $v \to 0$
In a step-index optical fiber, the eigenvalue equation for the $\mathrm{HE}_{11}$ fundamental mode, under the weak guidance approximation, can be written as
$$\frac{J'_n (u)}{u J_n (u)} = - \frac{K'_n …
- 777