Discussion and conclusion

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In conclusion, using FTSSI technique, we have studied the spectral and spatio-temporal characteristics of the pulse shapes: a single transform-limited pulse with a variable delay, a train of pulses, chirped pulses and pulses with a π phase-step at the center of their spectrum. These pulse shapes are the most applied pulse shapes in ultrafast quantum control experiments. Our work represents the first comprehensive spatio-spectral or spatio-temporal study of the shaped pulses by an AOPDF pulse shaper. In each case, we have observed spatio-spectral (spatio-temporal) coupling in the reconstructed intensity. We have shown that the all effects are consistent with a

single effect that is group delay dependent position of the pulses [100] with coupling speed of 0.25 mm/ps. The birefringent and geometric walkoff effects are therefore confirmed as the single physical cause for the spatio-temporal coupling effect reported in the AOPDF pulse shaper. This coupling has important consequences for the appli-cation of AOPDF-shaped pulses to control experiments, since the displacement of the control pulses with a variation of pulse parameters may result in a worsened alignment with the target. The studies of Borzsonyi and his colleagues [99] showed an angular dispersion for the AOPDF in IR region. Because of employing a narrow spectral band-width, we have not observed such coupling. Moreover, it was because we have studied the coupling effects of a low repetition laser source. In more detail, working with high repetition source requires a high repetition acoustic wave. This causes thermal effects inside the crystal that can result in generation of angular dispersion.

As a conclusion, apart from group dependent spatial displacement of pulse no further spatio-temporal coupling effects were identified, and the AOPDF was otherwise found to reproduce the programmed pulse shapes faithfully. The results above highlight the need for experimentalists to pay close attention to these coupling issues during the design of control experiments based on an AOPDF pulse shaper. Such concerns have been studied extensively for the more widespread 4f-line shapers (in IR and visible re-gions), with coupling speed ranging from 0.083 mm/ps [59] through 0.145 mm/ps [24]

to 0.595 mm/ps [11] already reported in the literature. The coupling speed reported here of 0.25 mm/ps is therefore non-negligible by comparison, albeit by taking into account the fact that KDF crystal has strong walk off effects in UV spectral region.

Characterization and control of ultrashort pulses transmitted through scattering media

Ultrashort pulses have numerous applications in coherent control of molecular dynam-ics [2,15,148–151], time resolved spectroscopy [152], nonlinear microscopy [153], etc.

Performing such experiments in the complex media such as biological tissues requires that the light maintains its initial spatio-temporal focused form. However, complex media strongly distort the initial spatio-temporal profile of the light.

Propagation of a quasi monochromatic laser light through a complex medium results in ballistic [154,155] and multiply scattered components [156]. Ballistic photons are those that travel undeviated through the medium and deplete exponentially according to Beer’s law [157]. Multiply scattered photons produce spatial speckle, which is due to the random constructive and destructive interference of light following different tra-jectories. Because of their random nature, the multiply scattered photons scramble the optical phase and energy of the transmitted light. Therefore, it is not straightforward to recover the optical information that is necessary for typical optical experiments, e.g. imaging, focusing, and transmitting ultrashort pulses. Numerous solutions to this problem have been proposed by discriminating against the scattered light and detection of the ballistic photons [158–164]. However, for a scattering medium with dimensions much larger than its transport mean free path lt (the average distance traveled by light before it becomes diffuse), these techniques cannot be applied be-cause the ballistic component is strongly attenuated.

Recently, Vellekoop and colleagues have demonstrated the possibility of spatial fo-79

cusing [29,165,166] and hence imaging [167] through multiply scattering medium by controlling the spatial modes of the incident light using a spatial light modulator.

This work, correction of the spatial distortion, has been later carried on by other groups using alternative techniques [168–172]. However, all these techniques have only addressed the use of the quasi monochromatic laser and no temporal correction has been reported.

Propagation of broadband ultrashort pulses through such thick samples results in additional large temporal spreading and irregular spiky intensity that gives rise to the spectral (temporal) speckle [173,174]. As mentioned above, both temporal and spatial corrections are crucial for the applications. There exist related techniques for the spatio-temporal concentration in acoustic and GHz-electromagnetic regimes called time reversal methods [31,175,176]. However, owing in particular to the inabil-ity to measure electric fields directly in the temporal domain at higher frequencies, an optical domain time-reversal experiment remains elusive. We have solved this lim-itation: in a parallel work (different techniques but similar results), we [35] and two other groups [177,178] have succeeded to spatio-temporally focus the ultrashort pulse at the rear surface of the scattering medium. For this goal, in our group in LCAR, we have applied FTSSI technique to measure the spatio-spectral phase of the output speckle and hence control them. Moreover, this measurement and characterization has resulted in other interesting results. Since studying the temporal behavior of the speckle field is one of a wide variety of methods for determination of the diffusion properties of the sample [179–189], we have demonstrated a simple technique of ex-traction of diffusion properties by using our well established FTSSI technique [34].

The goal of this chapter is to study the spatio-temporal characteristics of the fem-tosecond pulses transmitted through multiply scattering medium, extraction of the diffusion properties of such medium and finally exploiting such measurements to con-trol the scattered light behind the medium. Therefore, it is organized as follows: Sec-tion 3.1 is a review of the present state of art in controlling of the transmitted light from scattering media. Section 3.2 is about the analytical description of the spatio-temporal focusing of the femtosecond pulses behind the multiply scattering medium via spectral shaping the input pulses. Moreover, it describes the numerical simula-tion that I have performed in order to show the possibility of such spatio-temporal focusing. Section 3.3 details the experimental setup that we have used to study and control spatio-temporal speckles. Section 3.4 shows the experimental results of char-acterization and control of the spatio-temporal speckles. Section 3.5 describes two

other ways of spatio-temporal controlling of the pulses and compares their results with ours. Finally, Section 3.6 concludes and shows the potential applications and future directions of our studies.

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