We know examples of buried Julia components (Definition: A Julia component is called buried if it is not contained in the boundary of any Fatou component) for rational functions. In 1998, McMullen gave the following example of a family of rational maps having buried Julia components: $f_{c,\lambda}(z)=z^m+c+\frac{\lambda}{z^l}$ where $m,l\geq 2$ and $c,\lambda\in\mathbb{C}$.
But in the literature I didn't find any example of a transcendental meromorphic function having buried Julia component, even in the simplest case when the Julia component is singleton. Is there any such example? If so, how to construct those functions? Any direction or suggestion will be appreciated. Thank you.