We investigate strongly asymmetric self-assembled nanostructures with one of dimensions reaching hundreds of nanometers. Close to the nanowire-like type of confinement, such objects are sometimes assigned as one-dimensional in nature. Here, we directly observe the spectrum of exciton excited states corresponding to longitudinal quantization. This is based on probing the optical transitions via polarization-resolved microphotoluminescence excitation ($mu$PLE) measurement performed on single nanostructures combined with theoretical calculation of neutral and charged exciton optical properties. We successfully probe absorption-like spectra for individual bright states forming the exciton ground-state fine structure, as well as for the negatively charged exciton. Confronting the calculated spectrum of excitonic absorption with $mu$PLE traces, we identify optical transitions involving states that contain carriers at various excited levels related to the longest dimension. Based on cross-polarized excitation-detection scheme, we show very well conserved spin configuration during orbital relaxation of the exciton from a number of excited states comparable to the quasi-resonant pumping via the optical phonon, and no polarization memory for the trion, as theoretically expected.
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