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The spectral singularity (SS) from a non-Hermitian potential is one of themost remarkable scattering feature of non-Hermitian quantum mechanics. At thespectral singular point, the scattering amplitudes diverge to infinite. Thisphenomena have been extensively studied over the last two decades. The previousstudies have suggested the need of extremely fine control of the various systemparameters for practical applications of SS. However no study have been carriedout to understand the behavior of the scattering amplitude in the vicinity ofSS. Such study would be important towards the practical application of SS whereit is desired to maintain outgoing scattering amplitude to a specific value.The behavior of the loci of constant scattering amplitude in the neighborhoodof SS are studied for a pure imaginary barrier potential $iV$, $V \in R^{+}$.We show that these loci are elliptical and self-similar to each other in $E-V$plane where $E$ is energy of the wave. The orientations of these ellipses forreflection ($R$) and transmission ($T$) amplitude around a given SS are same.This is surprising due to the different mathematical forms of $R$ and $T$. Inthe vicinity of SS, $R \approx T$.

Self-similar features around spectral singularity in complex barrier potential