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RESEARCH PRODUCT

Controlling the Carrier-Envelope Phase of Few-Cycle Laser Beams in Dispersive Media

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During the last decade it has been practicable to achieve a full control of the temporal evolution of the wave field of ultrashort mode-locked laser beams (1). Advances in femtosecond laser technology and nonlinear optics have made possible to tailor the phase and magnitude of the electric field leading to a wide range of new applications in science. Many physical phenomena are dependent directly on the electric field rather than the pulse envelope such as electron emission from ionized atoms (2) and metal surfaces (3), or carrier-wave Rabi-flopping (4). Moreover, attosecond physics is for all practical purposes accessible by using femtosecond pulses with controlled carrier-envelope (CE) phase conducting to coherent light generation in the XUV spectral regions (5). Additional applications in the frequency domain includes optical metrology where the laser spectrum is employed (6). In this chapter we apply fundamental concepts of three-dimensional wave packets to illustrate not only transverse but what is more fascinating on-axis effects on the propagation of few-cycle laser pulses (7). The frequency-dependent nature of diffraction behaves as a sort of dispersion that makes changes in the pulse front surface, its group velocity, the envelope form, and the carrier frequency. The procedure lays on pulsedGaussian beams, in which these changes are straightforwardly quantified. In particular, the carrier phase at any point of space near the beam axis is evaluated. Anomalous pulse front behavior including superluminality in pulsed Gaussian beams is also found. Finally the CE phase is computed in the focal volume and in the far field. Generally focused pulses manifest a strong phase dispersion in the neighborhood of the geometrical focus, so that enhanced spatial resolution is achieved in CE phase-dependent phenomena. In some circumstances, however, increased depth of focusmay be of convenience so that a stationary CE phase should be required in the near field. It is noteworthy that Gouy wave modes (8) show some control over on-axis phases demonstrating undistorted pulse focalization even in dispersive media. Practical realizations may be driven by angular dispersion engineering of ultrashort laser beams. In this concern we introduced the concept of dispersive imaging (9) as a tool for controlling the dispersive nature of broadbandwave fields. Achromatic (10) and apochromatic (11) corrections of the angular spectrum of diffracted wave fields may be achieved with the use of highly-dispersive lenses such as kinoform-type zone plates. This procedure has been employed previously to compensate the longitudinal 8