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Applied Physics Letters

Paraxial energy transport of a focused Gaussian beam in ruby with nondegenerate two-wave couplinglike mechanism

Feng Gao, Jingjun Xu, Guoquan Zhang, Fang Bo, Haixu Liu

Published Jan 14, 2008• 15 citations
Publisher

Abstract

Paraxial energy transport of an intensity-modulated and focused Gaussian beam is studied in ruby. Deformations of the temporal profiles are observed under different conditions and explained by the interplay among a nondegenerate two-wave couplinglike mechanism, the population oscillations, and the Fraunhofer diffraction. Experimental evidence is provided for the existence of a nondegenerate two-wave couplinglike mechanism. The self-superluminal can be observed under proper conditions. A group velocity of −83m∕s is achieved with a Gaussian-like-modulated pulse of 30ms with background illumination. Based on these results, a method to control the group velocity of a single beam in such media is proposed.

DOI
10.1063/1.2827568

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Paraxial energy transport of an intensity-modulated and focused Gaussian beam is studied in ruby. Deformations of the temporal profiles are observed under different conditions and explained by the interplay among a nondegenerate two-wave couplinglike mechanism, the population oscillations, and the Fraunhofer diffraction. Experimental evidence is provided for the existence of a nondegenerate two-wave couplinglike mechanism. The self-superluminal can be observed under proper conditions. A group velocity of −83m∕s is achieved with a Gaussian-like-modulated pulse of 30ms with background illumination. Based on these results, a method to control the group velocity of a single beam in such media is proposed.
Nondegenerate two-wave coupling process and group velocity change in the paraxial part of an intensity-modulated and focused transverse electromagnetic beam (TEM00 beam in the article) was observed in the rhodamine 6G(R6G)-doped polymethyl methacrylate (PMMA) but not in the pure PMMA. The typical superluminal result was −5.1 m/s and the subluminal result was 9.19 m/s, respectively. Furthermore, the results provide a support to our former conclusion that nondegenerate two-wave couplinglike mechanism could be used to change the group velocity of the paraxial part of a focused TEM00 beam in materials with nondegenerate two-wave coupling process.
In this review article,we summarized the study of the weak light nonlinear properties associated with group velocity change in the ruby.The ruby could be reduced to a two-level system,in which population oscillations could lead to a subluminal result.With the modulated TEM00 beam introduced into the ruby,self-phase modulation together with Fraunhofer diffractions and nondegenerate two-wave coupling between different spatial frequency components of the beam occurs at the same time.Population oscillations,self-phase modulation together with Fraunhofer diffractions and nondegenerate two-wave coupling mechanism competes with each other,which brings a new phenomenon of self-superluminal group velocity propagation in the ruby.
The mechanism by which light is slowed through ruby has been the subject of great debate. To distinguish between the two main proposed mechanisms, we investigate the problem in the time domain by modulating a laser beam with a chopper to create a clean square wave. By exploring the trailing edge of the pulsed laser beam propagating through ruby, we can determine whether energy is delayed beyond the input pulse. The effects of a time-varying absorber alone cannot delay energy into the trailing edge of the pulse, as a time-varying absorber can only attenuate a coherent pulse. Therefore, our observation of an increase in intensity at the trailing edge of the pulse provides evidence for a complicated model of slow light in ruby that requires more than just pulse reshaping. In addition, investigating the Fourier components of the modulated square wave shows that harmonic components with different frequencies are delayed by different amounts, regardless of the intensity of the component itself. Understanding the difference in delays of the individual Fourier components of the modulated beam reveals the cause of the distortion the pulse undergoes as it propagates through the ruby.
Evolution under two-photon near-resonance conditions of an adiabatic Gaussian pulse is considered in Rb vapour. Theoretical results show strong self-phase modulation and pulse deformation with increasing distance of propagation and intensity at a fixed detuning. At sufficiently large distances of propagation and/or input intensity pulse deformation is seen to develop into (two-photon) optical shocks. At a higher intensity double shock fronts are predicted to occur. The previously anticipated existence of an upper bound for the output maximum and of the vanishing of the self-phase modulation at the 'interaction time' between the output and the input profiles are shown explicitly to hold for the cases considered. A quasi free-wave like evolution occurs at asymptotically higher intensities.
We have observed slow light propagation with a group velocity as slow as 27.52±0.05m/s in a ruby crystal at room temperature. The Gaussian-like pulse signal, which was gained by modulating beam at 514.5nm, was injected into a ruby crystal. The spectral hole effect, attributed to high laser power density, leads to the induced refractive index steep rising. According as this rising, the group velocity of pulse propagation in the ruby becomes very slowly. The experiment result shows that the velocity of pulse propagation depends on the modulation frequency, laser power, the position of crystal and the profile of signal waveform. At the same condition the Gaussian-like pulse obtains much slower velocity than sinusoidal signal.
An analytic model based on a single encoding–diffraction sequence is developed to describe the first main region of focusing that occurs when a cw off-resonant monochromatic Gaussian beam enters a medium of two-state atoms. A quantitative definition of the dispersive regime for self-focusing is given, and an explicit form is obtained for the field encoding produced by the initial propagation. The phase profile of this encoded field incorporates the effects of both the medium and diffraction, and we find a simple expression for the fundamental length scale, which determines where diffractive effects become dominant. An analytic expression is obtained for the on-axis field, which results once the encoded field begins to diffract freely, and simple expressions for the position and size of the main enhancement are given. We give a simple interpretation of the focusing and the two parameters required for its characterization. The model gives excellent agreement to the full numeric solution over a wide parameter range and, in particular, explains the rapid on-axis oscillations at the outset of focusing.