Spatio-temporal pulse propagation in nonlinear dispersive optical media

We discuss state-of-art approaches to modeling of propagation of ultrashort optical pulses in one and three spatial dimensions. We operate with the analytic signal formulation for the electric field rather than using the slowly varying envelope approximation, because the latter becomes questionable for few-cycle pulses. Suitable propagation models are naturally derived in terms of unidirectional approximation.     

Regularities of radio-pulse propagation in transparent dispersive media

The distortions of pulsed radio signals in passage through a dispersive medium with a quadratic phase function are examined. These distortions are determined quantitatively by the relative pulse broadening. Analysis shows that the degree of envelope distortion is determined by a single dimensionless parameter and is practically independent of the signal spectrum. This parameter, which is called dispersion disphasing over the spectral interval, is easily calculated and is very useful for estimation of the degree of radio-pulse broadening. An example of its use for the simple case of pulse propagation through a parabolic ionospheric layer is provided.Moscow Physicotechnical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 9, pp. 943–951, September, 1993.     

Energy propagation for dispersive waves in dissipative media

University of Bologna, Italy. Published in Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 7, pp. 650–664, July, 1993.     

Diffraction-free and dispersion-free pulsed beam propagation in dispersive media

The diffraction of pulsed beams of light is formulated as an anomalously dispersive phenomenon. In a dispersive material, the effects of material group-velocity dispersion and diffraction on pulsed beam propagation can mutually cancel if the transverse profile of the pulse is suitably chosen.     

固体介质中光速减慢研究的若干进展

首先介绍了光速减慢的物理理论基础与实现方法以及国内外光速减慢研究的进展概况．主要阐述了均匀加宽介质中的光谱烧孔理论以及借助光谱烧孔技术在红宝石晶体中实现光速减慢的实验．最后，就极慢光速研究的前景及研究意义进行了讨论．     

Coherent pulse propagation through resonant media

Hyperfine Interactions - Resonant pulse propagation (RPP) is reviewed with special emphasis on the propagation of synchrotron radiation (SR) pulses through nuclear single-resonance media. The most...     

Chirped optical pulse propagation in saturating nonlinear media

Using a variational method, we have investigated the propagation characteristics of a chirped optical pulse in anomalously dispersive media possessing saturating nonlinearity. For the special case of uniform loss less media, the dynamics of the temporal width of the pulse is shown to be equivalent to an oscillator of unit mass which is executing its motion under some effective potential well. The potential is examined and four different types of behavior of the pulse width are noticed. The role of saturation parameter and the initial chirp in determining the propagation characteristics have been examined. It is found that, both high value of chirp and saturation are detrimental to stable pulse propagation. Particularly, the effect of chirp becomes severe with the increase in the value of saturation. We have shown that incorporation of saturation in the nonlinearity leads to the existence of bistable soliton. For the case of a lossy medium, net broadening of width takes place over many cycles of oscillation. The net broadening decreases with the increase in the value of saturation.     

Nonlocal control of pulse propagation in excitable media

We study the effects of nonlocal control of pulse propagation in excitable media. As ageneric example for an excitable medium the FitzHugh-Nagumo model with diffusion in theactivator variable is considered. Nonlocal coupling in form of an integral term with aspatial kernel is added. We find that the nonlocal coupling modifies the propagatingpulses of the reaction-diffusion system such that a variety of spatio-temporal patternsare generated including acceleration, deceleration, suppression, or generation of pulses,multiple pulses, and blinking pulse trains. It is shown that one can observe these effectsfor various choices of the integral kernel and the coupling scheme, provided that thecontrol strength and spatial extension of the integral kernel is appropriate. In addition,an analytical procedure is developed to describe the stability borders of the spatiallyhomogeneous steady state in control parameter space in dependence on the parameters of thenonlocal coupling.     

Description of pulse propagation in a dispersive medium by use of a pulse quality factor

We investigated how the duration of short laser pulses evolves in a dispersive material, using rms widths and a propagation law based on a pulse quality factor. Experiments were carried out with femtosecond pulses (10 to 25fs at the temporal waist) propagating in bulk fused silica. Excellent agreement was found between theory and experiment. This approach does not require complete characterization of laser pulses and eliminates the need for any assumption regarding the interpretation of autocorrelation traces. The method is of general validity, and it can be applied to pulses of arbitrary shape.     

Near-field and far-field propagation of beams and pulses in dispersive media

We formulate an efficient exact method of propagating optical wave packets (and cw beams) in isotropic and nonisotropic dispersive media. The method does not make the slowly varying envelope approximation in time or space and treats dispersion and diffraction exactly to all orders, even in the near field. It can also be used to determine the partial differential wave equation for pulses (and beams) to any order as a power series in the partial derivatives with respect to time and space. The method can treat extremely focused pulses and beams, e.g., from near-field scanning optical microscopy sources whose transverse spatial extent in smaller than a wavelength.     

Linear approximation in pulse propagation problems in nonlinear media

It seems obvious that the manifestation of nonlinear effects (such as shock wave and soliton formation) is possible only at comparatively high levels of nonlinearity. Nevertheless, there are well-known examples where a disturbance which is as small as one pleases ceases in time to be linear, and must be described in nonlinear terms. This, e.g., is the situation for the well-known Korteweg-de Vries (KdV) equations, which for an impulsive initial condition of definite sign has an asymptotic solution described by a set of solitons and by a rapidly oscillating wave packet. There will in fact always be at least one soliton asymptotically, no matter how small the initial pulse amplitude [1]. Another example is shock wave (triangular pulse) attenuation at large distances (or times) within the framework of the Burgers equation; the wave remains a shock wave even though its amplitude decreases to zero [1]. It is thus necessary to indicate a criterion which might be used to establish the nature of the asymptotic solution. The aim of the present note is the definition of such a criterion; that is, a relation between nonlinearity and dispersion (dissipation) in which nonlinear effects are manifested only above some threshold level.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 21, No. 11, pp. 1706–1708, November, 1978.     

Polarization instability of femtosecond pulse splitting in normally dispersive self-focusing media

We investigate the propagation of elliptically polarized intense femtosecond pulses through third-order media. Self-focusing and pulse splitting can be controlled by alternation of the polarization state.     

Velocity of pulse propagation in media with amplitude nonlinearity

The propagation velocity of optical wave fronts can be accelerated by the influence of gain saturation. We report systematic measurements for the specific case of Brillouin gain in optical fibers. A simplified analytic rate equation approach permits a qualitative understanding of the observations in terms of a pure amplitude nonlinearity. We point out that there is a close analogy to a mode-locked laser with gain saturation. Pursuing this analogy, we can explain why the changes in propagation velocity are hardly measurable for synchronously pumped lasers, but easily amount to several percent for amplifiers or lasers based on stimulated Brillouin scattering.     

Slow light with integrated gain and large pulse delay

We demonstrate slow and stored light in Rb vapor with a combination of desirable features: minimal loss and distortion of the pulse shape, and large fractional delay (>10). This behavior is enabled by (i) a group index that can be controllably varied during light pulse propagation, and (ii) controllable gain integrated into the medium to compensate for pulse loss. Any medium with the above two characteristics should be able to realize similarly high-performance slow light.     

Slow light and superluminality in Kerr media without a pump

Subluminal and superluminal propagation of a light pulse in Kerr materials has been investigated. Group velocities as slow as much less than 1 mm per second to as fast as negative several thousands meters per second can easily be obtained in the Kerr medium, which possesses a large nonlinear refractive index and long relaxation time, such as Cr3+-doped alexandrite, ruby, and GdAlO3. The physical mechanism is the strong highly dispersive coupling between different frequency components of the pulse.     

Amplitude and phase measurements of femtosecond pulse splitting in nonlinear dispersive media

Frequency-resolved optical gating is used to characterize the propagation of intense femtosecond pulses in a nonlinear, dispersive medium. The combined effects of diffraction, normal dispersion, and cubic nonlinearity lead to pulse splitting. The role of the phase of the input pulse is studied. The results are compared with the predictions of a three-dimensional nonlinear Schr?dinger equation.