Ultrashort pulse propagation and linear interaction with matter

An ultrashort laser pulse generally refers to the optical pulse containing just a few cycles of optical waves. At this time scale, the behavior of the light wave deviates appreciably from the usual continuous wave in many aspects. In this paper, ultrashort pulse diffraction is studied in detail. Starting from monochromatic Fresnel-Kirchhoff diffraction formula, the ultrashort pulse diffraction is calculated for intensity distribution, spectral modification and temporal evolution. Experimental observations confirm the results that ultrashort pulse diffraction patterns are smoother than those of a continuous wave, the case for near field being more prominent. The calculations also demonstrate, in the form of two dimension images, the spectral changes for typical points on the image plane. For the temporal evolution of the pulse, precursor pulses have been observed which matches the statement of Young\u27s original ideal of boundary waves. With the goal of providing insight for underwater optical communication, pulse propagation through water has been studied. Optical Bloch wave equations provide the fundamental interaction mechanism between a pulse and a two level system, which may be extended to more complex systems. Macroscopically, the energy of the pulse will exhibit less than exponential decay with the existence of Sommerfeld and Brillouin precursors. These two pulses precede the main pulse and result in deviation of energy transmission described by Beer\u27s Law. However, the precursors occupy very low energy, and within a range of 3.6 meters of propagation distance through water in the carried experiment, the pulse attenuation does not behave with noticeable difference from the frequency domain analysis. In order to better understand ultrashort pulse phenomenon not limited to sinusoidal carrier waves, effort has been devoted to solving the nonseparable Glein-Gordan equations, the solutions of which are non-sinusoidal and are calculation efficient in comparison with the Fourier transform method. Orthogonal wavelet functions such as Hermitian and Laguerre waveforms have been introduced