Electromagnetic bubble generation by half-cycle pulses

Abstract

Electromagnetic (EM) bubbles (EMB's), unipolar, super-short, and intense nonoscillating solitary pulses of EM radiation, can be generated in a gas of nonlinear atoms by available half-cycle pulses (HCP's). We investigate how EMB's characteristics (amplitude, length, formation distance, and total number) are controlled by the amplitude and length of originating HCP's. We also predict shocklike wave fronts in the multibubble regime. 6 and would result in the generation of an almost-periodic train of powerful subfemtosecond pulses, while another one is based on the generation of powerful EM bubbles 7 (EMB's), which are unipolar EM solitons propagating in a gas of two-level 7,8 or classically nonlinear atoms. The latter effect would allow one to generate a single EMB or an EMB train (in which EMB's propagate with different velocities and can easily be separated into individual pulses).One of the avenues of EMB generation is to use available HCP's to launch much shorter EMB's in a nonlinear medium. For experiments and applications one needs to know how the properties of EMB's are controlled by an incident HCP. In this Letter we answer a few important questions: Given the amplitude E 0 and length t 0 of an incident HCP, (1) what is leading EMB's amplitude E EMB and (2) length t EMB , (3) how many EMB's (per HCP) can be generated, (4) what are their amplitudes and lengths, and (5) what is the formation distance z EMB at which the first EMB appears? In general, these questions cannot be answered analytically; however, our numerical and analytical efforts allowed us to obtain remarkably simple results, qualitatively summarized as follows: E EMB is proportional to (and larger than) E 0 for an incident HCP, and t EMB~E 21 EMB ; the number of EMB's is proportional to the area of the incident HCP, and z EMB~E 2b 0 , where 2 # b # 3. We show that when many EMB's are generated, they evolve into a shocklike wave front. The good news is that very short EMB's can be generated by a much longer HCP with a large enough amplitude.We consider here a linearly polarized wave with the electric field, E ê x E͑t, z͒, propagating in the z axis in either a two-level system (TLS) characterized by the dipole moment d and the resonant frequency v 0 of its constitutive atoms and their density number N (polarization density is P N dp, where p is polarization per atom) or a gas of anharmonic classical oscillators (atoms). For TLS, we use the Bloch equations, with no rotating wave approximation:wheret tv 0 , the overdot designates ≠͞≠t, f ϵ 2dE͞hv 0 is a dimensionless field, and h is the population difference per atom. Relaxation is not included in Eqs.(1) since all the pulses are much shorter than TLS relaxation times. The TLS approximation is valid if the instantaneous Rabi frequency is relatively small, dE͞hv 0 f ͞2 , , 1, which is the case throughout this Letter. 9Indeed, in noble gasses,hv 0 ϳ 8-20 eV, so that even with the still unachievable value E 2 Mv͞cm (see below), f ͞2 ϳ 10 22 . In the opposite limit, f . . 1, an atom can be modeled by...

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