Optimal pulse penetration in Lorentz-Model dielectrics using the Sommerfeld and Brillouin precursors.

Kurt Edmund Oughstun

doi:10.1364/oe.23.026604

Abstract

Under proper initial conditions, the interrelated effects of phase and attenuation dispersion in ultrawideband pulse propagation modify the input pulse into precursor fields. Because of their minimal decay in a given dispersive medium, precursor-type pulses possess optimal penetration into that material at the frequency-chirped Lambert-Beer's law limit, making them ideally suited for remote sensing and medical imaging.

Highlights

The dynamical evolution of an ultrashort optical pulse propagating through a causally dispersive dielectric is a classic problem [1,2,3,4,5,6] in electromagnetic wave theory with application in imaging and remote sensing
These combined effects result in a complicated dynamical pulse evolution that is accurately described by the modern asymptotic theory [8,9,10,11] as the propagation distance exceeds a value set by the absorption depth at some characteristic frequency of the input pulse
The numerical results presented in this paper were performed with MATLAB 7.10.0 using a 224 point FFT-algorithm to compute the temporal structure of each propagated optical pulse based on a numerical synthesis of Eq (1)

Summary

Introduction

The dynamical evolution of an ultrashort optical pulse propagating through a causally dispersive dielectric is a classic problem [1,2,3,4,5,6] in electromagnetic wave theory with application in imaging and remote sensing. The phasal relationship between the spectral components of the pulse changes with propagation, and because of attenuation dispersion, the relative spectral amplitudes change with propagation These combined effects result in a complicated dynamical pulse evolution that is accurately described by the modern asymptotic theory [8,9,10,11] as the propagation distance exceeds a value set by the absorption depth at some characteristic frequency of the input pulse. This is because the peak amplitude of the Brillouin precursor in either a Lorentz- or Debye-type dielectric decays only as the square root of the inverse of the propagation distance while the peak amplitude of the Sommerfeld precursor in a Lorentz-type dielectric possesses an exponential decay rate that is typically much smaller than that at the input pulse frequency This unique property may be used to advantage through the design of precursor-type pulses that possess optimal penetration into a given dispersive material. Applications include deep tissue imaging [18], tumor detection [19], and cellular therapy [20]

Asymptotic Description

The Brillouin Pulse

The Sommerfeld Pulse

Conclusion