  In recent work [P. Grohs and M. Rathmair. Stable Gabor Phase Retrieval and
Spectral Clustering. Communications on Pure and Applied Mathematics (2018)] and
[P. Grohs and M. Rathmair. Stable Gabor phase retrieval for multivariate
functions. Journal of the European Mathematical Society (2021)] the
instabilities of Gabor phase retrieval problem, i.e. reconstructing $ f\in
L^2(\mathbb{R})$ from its spectrogram $|\mathcal{V}_g f|$ where $$\mathcal{V}_g
f(x,\xi) = \int_{\mathbb{R}} f(t)\overline{g(t-x)}e^{-2\pi i \xi
t}\,\mbox{d}t,$$ have been classified in terms of the connectivity of the
measurements. These findings were however crucially restricted to the case
where the window $g(t)=e^{-\pi t^2}$ is Gaussian. In this work we establish a
corresponding result for a number of other window functions including the
one-sided exponential $g(t)=e^{-t}\mathbb{1}_{[0,\infty)}(t)$ and
$g(t)=\exp(t-e^t)$. As a by-product we establish a modified version of
Poincar\'e's inequality which can be applied to non-differentiable functions
and may be of independent interest.
