We perform phase-space tomography of semiconductor laser dynamics by simultaneous experimental determination of optical intensity, frequency, and population inversion with high temporal resolution. We apply this technique to a laser with delayed feedback, serving as prominent example for high-dimensional chaotic dynamics and as model system for fundamental investigations of complex systems. Our approach allows us to explore so far unidentified trajectories in phase space and identify the underlying physical mechanism. DOI: 10.1103/PhysRevLett.115.053901 PACS numbers: 42.55.Px, 05.45.Jn, 42.60.Mi, 42.65.Sf Shortly after the initial demonstration of semiconductor lasers in the 1960s, it was discovered that these devices are extremely sensitive to time-delayed back reflections of their own emission [1]: in a range from very weak (40 dB attenuated) to strong delayed feedback, one can observe dramatic modifications of their dynamical behavior [2]. While initially the resulting dynamics was mainly considered to be a major nuisance, soon, fundamental aspects of the observed behavior received increasing interest [3]. Delayed-feedback semiconductor lasers became a prime test bed for the scientific study of nonlinear and highdimensional systems exhibiting chaotic behavior. The dramatic modification to the laser's properties manifests itself in the collapse of the laser's coherence, with an increase of the optical emission linewidth from ∼MHz to easily tens of GHz [4]. This reduction of coherence by up to 5 orders of magnitude is accompanied by corresponding picosecond intensity pulsations [5]. As such, the impact of delayed feedback has to be considered as nontrivial.The state of a free running, single mode semiconductor laser diode biased above threshold is characterized by its carrier inversion (N 0 ), frequency (ν 0 ), and intensity (I 0 ). This solitary laser mode (SLM) usually is a stable fixed point. Delayed feedback strongly modifies the laser's phase-space structure, resulting in a large variety of delay-induced complex phenomena, including narrow linewidth emission or dynamics in the form of limit cycles, quasiperiodic behavior, and deterministic chaos [6,7]. Each of these regimes is characterized by its corresponding phase-space trajectory [8]. Full-bandwidth and realtime measurements of feedback laser intensity [IðtÞ] [5] and frequency [νðtÞ] [9] dynamics already revealed significant new insight; however, this lacked the additional information on the carrier dynamics. Though highly successful, reconstructing complete phase space trajectories from scalar or few-variable via Takens' approach does not allow for the association of different phase-space directions to variables of the physical system [10]. Therefore, it is difficult to identify physical mechanisms from such a reconstructed phase space.Here, we report on the simultaneous experimental determination of the three aforementioned physical phase-space variables with high temporal resolution. Our phase-space tomography therefore allows us to experiment...