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\begin{tikzpicture}[>=stealth', auto, node distance=2cm, scale=1.2]
\tikzstyle{zero} = [draw, circle, inner sep =0, minimum height=0.15cm]
\tikzset{pole/.style={cross out, draw=black, minimum size=(0.15cm-\pgflinewidth), inner sep=0pt, outer sep=0pt}}
\begin{scope}[xscale=2, yscale=2]
\fill[ gray!20] (0,0) rectangle (1,0.707);
\draw[gray, ->] (0,-0.25) -- (0,1.25) node[anchor=south]{$|H(\Omega)|$};
\draw[gray, ->] (-0.25,0) -- (3,0) node[anchor=west]{$\Omega$};
\draw[fill = gray!20] (0,0.707) node[left] {$\sqrt{\frac{1}{1+\varepsilon^2}}$} -| (1,0) node[below] {$\Omega_p$};
\draw[fill = gray!20] (0,0.707) node[left] {$\sqrt{\frac{1}{1+\varepsilon^2}}$} -| (1,0) node[below] {$\Omega_p$};
\begin{scope}[]
\draw[thick, domain=0:2.5, variable=\x, smooth, samples=200] plot
({\x}, {sqrt(abs(1/ (1 + \x^10)))});
\end{scope}
\end{scope}
\end{tikzpicture}
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