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arXiv:1107.5011 · Physical Review A

Prospects of coherent control in turbid media: Bounds on focusing broadband laser pulses

Evgeny A. Shapiro, Thomas M. Drane, Valery Milner

Published Nov 4, 2011• 4 citations
arXivHTMLPDF

Abstract

We study the prospects of controlling transmission of broadband and bichromatic laser pulses through turbid samples. The ability to focus transmitted broadband light is limited via both the scattering properties of the medium and the technical characteristics of the experimental setup. There are two time scales given by pulse stretching in the near- and far-field regions which define the maximum bandwidth of a pulse amenable to focusing. In the geometric-optics regime of wave propagation in the medium, a single setup can be optimal for focusing light at frequencies $\ensuremath{\omega}$ and $n\ensuremath{\omega}$ simultaneously, providing the basis for the $1+n$ coherent quantum control. Beyond the regime of geometric optics, we discuss a simple solution for the shaping, which provides the figure of merit for one's ability to simultaneously focus several transmission modes.

DOI
10.1103/physreva.84.053807

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We study the prospects of controlling transmission of broadband and bichromatic laser pulses through turbid samples. The ability to focus transmitted broadband light is limited via both the scattering properties of the medium and the technical characteristics of the experimental setup. There are two time scales given by pulse stretching in the near- and far-field regions which define the maximum bandwidth of a pulse amenable to focusing. In the geometric-optics regime of wave propagation in the medium, a single setup can be optimal for focusing light at frequencies \ensuremathω\ensuremath{\omega}\ensuremathω and n\ensuremathωn\ensuremath{\omega}n\ensuremathω simultaneously, providing the basis for the 1+n1+n1+n coherent quantum control. Beyond the regime of geometric optics, we discuss a simple solution for the shaping, which provides the figure of merit for one's ability to simultaneously focus several transmission modes.
The experimental work in this thesis is divided into two distinct parts. In both parts, broadband femtosecond laser pulses are "shaped" by adjusting the relative phase and amplitude of spectral components. In the first set of experiments, time-dependent perturbation theory is used to show that the probability of a quantum transition in atomic rubidium can be substantially enhanced or suppressed using pulse shaping, compared to the probability of transition observed when a transform-limited or "flat phase" optical pulse is used. These enhancement or suppression effects are also demonstrated experimentally. As quantum interference (the material phase having been transferred from the optical phase) is used to enhance or diminish a particular final quantum state, this can be classified as a quantum coherent control experiment. In the second set of experiments, an optical pulse is scattered into a train of pulses by a layered structure. The layered structure is used to simulate the effect of optical pulses travelling through certain types of complex media. One consequence of the disruption of a single pulse into a train of pulses is lower per-pulse peak intensity, and thus a greatly diminished nonlinear signal. It is shown that spectral pulse shaping (in phase only) is sufficient to pre-compensate for the scattering structure, allowing a single transform-limited pulse to be obtained at the output.
Coherent preparation by laser light of quantum states of atoms and molecules can lead to quantum interference in the amplitudes of optical transitions. In this way the optical properties of a medium can be dramatically modified, leading to electromagnetically induced transparency and related effects, which have placed gas-phase systems at the center of recent advances in the development of media with radically new optical properties. This article reviews these advances and the new possibilities they offer for nonlinear optics and quantum information science. As a basis for the theory of electromagnetically induced transparency the authors consider the atomic dynamics and the optical response of the medium to a continuous-wave laser. They then discuss pulse propagation and the adiabatic evolution of field-coupled states and show how coherently prepared media can be used to improve frequency conversion in nonlinear optical mixing experiments. The extension of these concepts to very weak optical fields in the few-photon limit is then examined. The review concludes with a discussion of future prospects and potential new applications.
Slow light study is discussed in various methods of generation, materials and approaches. In this study, the control of group velocity, Vg and group velocity dispersion (GVD) of a pulse propagating in optical fiber is simulated and demonstrated. The slow light generation, which is closely related to Vg of a light pulse for this study is based on stimulated Brillouin scattering (SBS), the most efficient approach as reported by previous researchers. By using Matlab R2011b software, the slow light generation is simulated for the slow light structure in the form of hollow conical shape resonator, focusing on the geometrical parameters. The simulation work is extended to the control of Vg and GVD, to investigate the influences of refractive index of the materials and wave number of the light pulses. While most of slow light researches neglect the effect of dispersion, this study explicitly includes the second term of the wave number’s expansion to represent GVD. Therefore, the experimental work investigates the creation of a strongly dispersive material with large chirp and small group delay via SBS in a highlynonlinear optical fiber as opposed to previous SBS experiments which mainly focus on the creation of a slow light material with minimum dispersion and chirp. To demonstrate the control of Vg and GVD, a two-frequency pump field which consists of two distributed feedback lasers with the relative frequency separation nearly twice the Brillouin frequency and a slow light medium in the form of a 2-km high nonlinear single mode optical fiber are employed. For input field with slowly varying amplitude, the experiment obtained output pulses with large GVD and decreased intensity. All-optical control of the GVD is demonstrated by measuring the linear frequency chirp impressed on a 28-nanosecond-duration optical pulse and it is tunable over the range of ± 7.8 ns2 m-1. In addition, the maximum observed value of GVD is 109 times larger than that obtained in a typical single-mode silica optical fiber. The simulation results for Gaussian pulses as input signal are in good agreement with the experimental ones, and therefore the control of Vg and GVD for different shapes of input pulses using the developed system can be predicted.
On the basis of coherently induced photonic gap structures,a new all-optical routing control scheme is proposed to simultaneously control the propagation dynamics of two weak light signals.With the transfer-matrix method to describe the coherent scattering of light waves in periodic media and the density-matrix equations to describe the resonant interaction between monochromatic laser fields and multi-level atoms,the steady reflection and transmission spectra are calculated for a coherently driven ultra-cold atomic ensemble as the control medium.The results show that,by changing the spatial patterns,intensity,and frequencies of two strong laser fields,a pair of special frequency bands(with ~95% reflectivity or ~95% transmissivity) can be first established near the probe resonance and then be manipulated at any time to induce two weak light signals of different frequencies into the desired network channels.This scheme well satisfies the basic requirements of low-deformation and low-loss for all-optical routing control of weak light signals in the field of quantum information processing.