Modes in optical fibers I am trying to understand the modes in step-index optical fibers and I saw that they say the electric field distribution in the core and cladding is as bellow. my question is that which component of electric field is this?

 A: "TE" means "Transverse Electrical". That means these modes have E-field perpendicular to the axis of the fiber. Because the fiber is circularly symmetric, the E field could point in any direction perpendicular to the axis (we say that the modes in different polarizations are degenerate).
However, circular dielectric waveguide like step-index optical fiber does not actually have TE modes. The actual modes in optical fiber are called LP (linearly polarized), HE, and HM (hybrid electric or magnetic) modes. These modes have E-field that is not exactly perpendicular to the fiber axis. They will behave approximately like TE modes, but not exactly. The approximation will be better, the stronger the index contrast between core and cladding.
A: As The Photon already pointed out, "TE" means "Transverse Electrical", which is just telling you that there is no component along the direction of propagation - $z$, in this case. See here for the distinction.
Now, if you want to find the functional form of your electric field, you have to solve the wave equation. 
Since your problem is cylindrically symmetric around $z$, the direction of propagation, your solution will exhibit the same symmetry.
These solutions have a name, the Laguerre-Gassian modes, which look like this:
$$ E(r, \phi, z) \propto e^{-\frac{r^2}{w^2(z)}}\cdot e^{-il\phi}\cdot e^{-ikz}. $$ 
You can see that the $\phi$ dependence is in a pure phase factor.
What you actually see on a camera is the intenstiy $I \propto E^{\dagger}E$ so $$ I \propto e^{-2\frac{r^2}{w^2(z)}}.$$
So only the radial part remains, and you can drop the $\phi $ depdendence from $E(r, \phi, z) \propto e^{-\frac{r^2}{w^2(z)}}$. Which is exactly what is plotted in your drawings. The $y$ axis is $r$.
(I have just written the fundamental mode, which is a gaussian, like your $TE_0$, on the Wiki link you can see that there is an $l$ dependent spatial part, which is what gives you the different shape of the other $TE$ modes: for details look at the Mathematica script below:
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