In both scenarios, optical beams can be generally composed of multiple incoherent spatial fields, with variable time delays and with numerous spectral peaks. Encoded information can also be a consequence of natural phenomena such as the nonlinear interaction of light with the gain medium of the laser cavity 5, 6, 7. Information can be encoded in optical beams by design, either in space through sculpted complex wavefronts 1, 2, 3 or, in time, through tailored pulse envelopes 4, with further multiplexing of information channels possible using the spectral and polarisation dimensions. We demonstrate these features by characterising the spatiotemporal and spatiospectral output of a vertical-cavity surface-emitting laser.
Each density matrix slice resolves the spatial complex amplitude of multiple mutually incoherent fields, which over several slices reveals the spectral or temporal evolution of these fields even when fields spectrally or temporally overlap. We harness principles of spatial state tomography to circumvent these limitations and measure a complete description of an unknown beam as a set of spectrally, temporally, and polarisation resolved spatial state density matrices. Deciphering complex wavefronts of multiple co-propagating incoherent fields remains particularly challenging. Non-interferometric methods struggle to distinguish spatial phase, while phase-sensitive approaches necessitate either an auxiliary reference source or a self-reference, neither of which is universally available.
Current characterisation techniques apply in limited contexts. Measuring polarisation, spectrum, temporal dynamics, and spatial complex amplitude of optical beams is essential to studying phenomena in laser dynamics, telecommunications and nonlinear optics.
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