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Using Maxwell-Bloch equations, we analyze the response of a two-component medium of two-level atoms driven by a two-cycle optical pulse beyond the traditional approach of slowly varying amplitudes and phases. We show that the notions of carrier, envelope, phase, and group velocities can be generalized to this situation. For optical pulses of a given duration, we show that the optical field can form a temporal soliton.

The wave-particle duality of light is a controversial topic in modern physics. In this context, this work highlights the ability of the wave-nature of light on its own to account for the conservation of energy in light-matter interaction. Two simple fundamental properties of light as wave are involved: its period and its power P. The power P depends only on the amplitude of the wave's electric and magnetic fields (Poynting's vector), and can easily be measured with a power sensor for visible and infrared lasers. The advantage of such a wave-based approach is that it unveils unexpected effects of light's power P capable of explaining numerous results published in current scientific literature, of correlating phenomena otherwise considered as disjointed, and of making predictions on ways to employ the electromagnetic (EM) waves which so far are unexplored. In this framework, this work focuses on determining the magnitude of the time interval that, coupled with light's power P, establishes the energy conserved in the exchange of energy between light and matter. To reach this goal, capacitors were excited with visible and IR lasers at variable average power P. As the result of combining experimental measurements and simulations based on the law of conservation of energy, it was found that the product of the period of the light by its power P fixes the magnitude of the energy conserved in light's interaction with the capacitors. This finding highlights that the energy exchanged is defined in the time interval equal to the period of the light's wave. The validity of the finding is shown to hold in light's interaction with matter in general, e.g.

By using the exact four-soliton solutions of the modified Korteweg-de Vries-sine Gordon equation describing the propagation of few-optical-cycle pulses in transparent media with instantaneous cubic nonlinearity, the interaction of two such initially well-separated pulses is studied. The shapes of soliton envelopes, the shifts in the location of envelope maxima, and the corresponding phase shifts are explicitly calculated.

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