Pulse propagation in a resonant medium: Application to sound waves in superfluid 3He-B

Unified asymptotic description of Gaussian pulse propagation of arbitrary initial pulse width in a Lorentz-type gain medium

An asymptotic approach is utilized in order to obtain a unified description of the propagated field dynamics due to an input Gaussian-modulated harmonic wave of arbitrary initial pulse width in a linear, causally dispersive gain medium, described by the single resonance Lorentz model. The asymptotic method of analysis is applied on the unified, exact integral representation of the propagated field, which is characterized by a unified complex phase function that depends upon the input field and gain medium parameters as well as upon the propagation distance in the medium. In order to apply the asymptotic method, an analysis of the evolution of the saddle point locations, which depend upon the dispersive properties of the gain medium, the temporal width, and the carrier frequency of the input Gaussian pulse as well as upon the propagation distance and of the topography of the real part of the unified phase function in the complex ω plane, must be performed. Upon the subsequent numerical application of the asymptotic method, the predictions of the unified asymptotic approach are found to be in exceptional agreement with the respective results of a purely numerical experiment for all considered initial pulse widths and lead to a unified model of Gaussian pulse propagation in a gain Lorentzian medium. According to this model, the propagated field is composed of pulse components, each being due to the asymptotic contribution of a respective relevant saddle point of the unified phase function. The instantaneous angular frequency of oscillation and the stationary point(s) of the envelope of each such pulse component are then obtained from the real and imaginary parts, respectively, of the corresponding relevant saddle point as it evolves in the complex ω plane. This theoretical approach may then yield particularly useful physical insights into attosecond pulse propagation.

Stacked optical precursors from amplitude and phase modulations

We report the generation of stacked optical precursors from a laser beam whose amplitude or phase is modulated by sequenced on-off step waveforms. Making use of the constructive interference between the precursors produced from different steps, as well as the main field, we generate optical transient pulses having peak powers of eight times the input power with electromagnetically induced transparency in laser-cooled atoms.

Slow-light-induced interference with stacked optical precursors for square input pulses

We theoretically study the stacked optical transients generated from a series of square pulses passing through a cold atomic ensemble. Using the hybrid analysis and fast Fourier transform, we identify the stacked coherent transients [Europhys. Lett. 4, 47 (1987)] as optical precursors. With slow-light and electromagnetically induced transparency, we obtain nearly 700% transmitted intensity at the transient spikes resulting from the interference between the delayed main field and the stacked optical precursors.

Optical precursors with electromagnetically induced transparency in cold atoms

We report the observation of Sommerfeld-Brillouin optical precursors generated from a long square-modulated laser pulse propagating through a cold atomic ensemble with electromagnetically induced transparency. The optical depth (alpha(0)L) of the medium can be varied from 0 up to 50. We demonstrated that the step-on rising and step-off falling edges propagate with the speed of light in vacuum without a slow light effect. At high alpha(0)L, the precursor is separated from the delayed main pulse at the rising edge, while at the falling edge, we observe damped oscillatory structures resulting from the interference between the precursor and main field.

Direct observation of optical precursors in a region of anomalous dispersion

We create optical precursors by propagating a step-modulated optical pulse through a linear resonant dielectric absorber. The field emerging from the dielectric consists of a several-nanosecond-long spike with near 100% transmission, which decays to a constant value expected from Beer's law. This high-transmission spike might be useful for imaging applications requiring penetrating optical radiation. We compare our observations to two different theories, revealing that the spike consists of both the Sommerfeld and Brillouin precursors.

Observation of Sommerfeld precursors on a fluid surface

We report the observation of two types of Sommerfeld precursors (or forerunners) on the surface of a layer of mercury. When the fluid depth increases, we observe a transition between these two precursor surface waves in good agreement with the predictions of asymptotic analysis. At depths thin enough compared to the capillary length, high frequency precursors propagate ahead of the "main signal" and their period and amplitude, measured at a fixed point, increase in time. For larger depths, low frequency "precursors" follow the main signal with a decreasing period and amplitude. These behaviors are understood in the framework of the analysis first introduced for linear transient electromagnetic waves in a dielectric medium by Sommerfeld [Ann. Phys. (Leipzig) 44, 177 (1914)]] and Brillouin [Ann. Phys. (Leipzig) 44, 203 (1914)]].