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Journal of Modern Optics

Can precursors improve the transmission of energy at optical frequencies?

David Lukofsky, Jonathan T. Bessette, Heejeong Jeong, E. Garmire, Ulf L. Österberg

Published May 15, 2009• 9 citations

Abstract

The recent interest in precursors has been fuelled by the possibility of using them for the efficient transmission of information through absorbing media at radio or optical frequencies. Here we demonstrate that the low attenuation experienced by the Brillouin precursor is attributed to the inherently low absorption of dispersive media near DC, a characteristic already exploited with communications systems using the extremely low frequency (ELF) band. Pulses, regardless of their temporal width and carrier frequency, always obey Beer's law as long as they propagate in the linear time invariant regime. We conclude with an FDTD simulation of the Maxwell-Bloch equations that shows how optical coherent bleaching effects, which take place in the linear time variant regime of the Lorentz oscillator model, can cause sustained deviations from Beer's law over relatively long distances of water.

DOI: 10.1080/09500340902947023

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The propagation of short pulses in a dispersive medium can be described in simple physical terms by employing the concept of the group velocity provided the medium is lossless. When the medium is absorbing, the group velocity description breaks down. In a previous paper,1 we presented a similar description employing the velocity of energy of monochromatic waves in place of the group velocity which is valid for a particular dispersive medium with absorption known as the Lorentz medium. That model describes the entire dynamics of the pulse as it propagates with the exception of the early stages of the evolution of the second precursor (otherwise known as the Brillouin precursor). Since that region contains the peak values of the pulse, it is important to include it in the model. The present paper describes the arrival of the Brillouin precursor in terms of the group velocity of a propagating field of the form exp [ωttω z] where ω and kω are real and positive.

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The recent interest in precursors has been fuelled by the possibility of using them for the efficient transmission of information through absorbing media at radio or optical frequencies. Here we demonstrate that the low attenuation experienced by the Brillouin precursor is attributed to the inherently low absorption of dispersive media near DC, a characteristic already exploited with communications systems using the extremely low frequency (ELF) band. Pulses, regardless of their temporal width and carrier frequency, always obey Beer's law as long as they propagate in the linear time invariant regime. We conclude with an FDTD simulation of the Maxwell-Bloch equations that shows how optical coherent bleaching effects, which take place in the linear time variant regime of the Lorentz oscillator model, can cause sustained deviations from Beer's law over relatively long distances of water.

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.

Recent interest in Sommerfeld-Brillouin optical precursors has brought attention to the possibility of optical precursor observation in bulk matter. We investigate the possible formation of optical precursors in an organic dye solution with a sharp absorption band and anomalous dispersion at a wavelength of approximately 800 nm. We explore this regime experimentally with sub-10-fs pulses with a central wavelength of approximately 800 nm from a Ti : sapphire oscillator. The pulses are passed through a thin layer of the dye solution and characterized by interferometric autocorrelation. The obtained autocorrelation traces are compared with simulations, and we observe important dispersion effects on the shape of the propagated pulses, including precursorlike behavior in their time evolution.

This article mainly deals with the propagation of step-modulated light pulses in a dense Lorentz medium at distances such that the medium is opaque in a broad spectral region including the carrier frequency. The transmitted field is then reduced to the celebrated precursors of Sommerfeld and Brillouin, far apart from each other. We obtain simple analytical expressions of the first (Sommerfeld) precursor, whose shape only depends on the order of the initial discontinuity of the incident field and whose amplitude rapidly decreases with this order (rise-time effects). We show that, in a strictly asymptotic limit, the second (Brillouin) precursor is entirely determined by the frequency dependence of the medium attenuation and has a Gaussian or Gaussian-derivative shape. We point out that this result applies to the precursor directly observed in a Debye medium at decimetric wavelengths. When attenuation and group-delay dispersion both contribute to its formation, we establish a more general expression of the Brillouin precursor, containing the previous one (dominant-attenuation limit) and that obtained by Brillouin (dominant-dispersion limit) as particular cases. We finally study the propagation of square or Gaussian pulses, and we determine the pulse parameters optimizing the Brillouin precursor. Obtained by standard Laplace-Fourier procedures, our results are explicit and contrast in their simplicity those derived by the uniform saddle-point methods, from which it is difficult to retrieve our asymptotic forms.

The propagation of short pulses in a dispersive medium can be described in simple physical terms by employing the concept of the group velocity provided the medium is lossless. When the medium is absorbing, the group velocity description breaks down. In a previous paper,1 we presented a similar description employing the velocity of energy of monochromatic waves in place of the group velocity which is valid for a particular dispersive medium with absorption known as the Lorentz medium. That model describes the entire dynamics of the pulse as it propagates with the exception of the early stages of the evolution of the second precursor (otherwise known as the Brillouin precursor). Since that region contains the peak values of the pulse, it is important to include it in the model. The present paper describes the arrival of the Brillouin precursor in terms of the group velocity of a propagating field of the form exp [ωttω z] where ω and kω are real and positive.