Under investigation is the nonlocal (2+1)-dimensional Hirota–Maxwell–Bloch system, which governs optical wave propagation in erbium-doped fibers. Different from previously studied local and reverse-space counterparts, this model features a unique partial reverse space-time symmetry. Based on the Lax integrability, we construct an explicit N-fold Darboux transformation that admits special eigenfunctions containing arbitrary functions \(F(\xi _j)\) and \(G(\xi _j)\) , and further derive the generalized Darboux transformation via Taylor expansion to generate exact solutions. It yields a unified construction of distinct exact waveforms from nonzero seed solutions, including linear waves, parabolic breathers, parabolic periodic line waves, and higher-order parabolic rational solutions with tunable geometry. The resulting dynamics reveal (i) periodic energy accumulation and dissipation in parabolic breathers, (ii) collision-induced energy focusing indicative of strong nonlinear interactions, (iii) parameter-controlled modulation of amplitude and spatiotemporal profiles. These findings elucidate how nonlocality in higher dimensions organizes and controls coherent structures in doped optical media, offering analytical tools for waveform design and manipulation. These results provide analytical tools for manipulating complex wave phenomena in doped optical media.
