Conical emission is a kind of interesting phenomenon, which occurs as ultrashort laser pulses interact with media. In this dissertation, theoretical and experimental studies on the properties of different kinds of conical emissions as femtosecond laser pulses propagate in a quadratic nonlinear medium-BBO crystal, the main contents are classified as follows.Blue-green conical emissions caused by spatiotemporal modulational instability by means of femtosecond laser pulses second harmonic generation have been investigated. With the larger pumped intensity, the shorter pulse width and the thicker crystal, the central wavelength of the blue-green conical emission spectrum had a blue shift, which was a characteristic of spatiotemporal modulational instability. A theoretical model based on the emergence of blue-green conical emission was numerically calculated conical angles on different wavelengths, which was accord with the experimental results. The observed conical emission was originated from spatiotemporal coupling the fundamental and second harmonic pulses.Green and red conical emissions caused by spatiotemporal modulational instability have been investigated pumped by second harmonic femtosecond laser pulses. A theoretical model based on the emergence of green and red conical emissions was numerically calculated conical angles on different wavelengths, which explained the observed phenomenon of green and red conical emission overlapping and inversing. Green and red conical emission was originated from parametric down conversion process, in which second harmonic photons decay into photon pairs.Several interpretations on supercontinuum conical emissions have been introduced: four-wave mixing, Cerenkov radiation, nonlinear X-wave and self-phase modulation. The conical angles on different wavelengths were numerically calculated by the former three theoretical models on the quadratic nonlinear medium and isotropic amorphous medium.Supercontinuum conical emissions have been experimentally investigated in quadratic nonlinear medium and isotropic amorphous medium by femtosecond laser pulses with different polarization. As the polarization of pumped laser pulses changed, blue-green conical emissions associated with second harmonic pulses and supercontinuum conical emissions occurred alternately in a quadratic nonlinear medium, while only supercontinuum conical emissions occurred alternately in an isotropic amorphous medium. The spectrum and according conical angles of supercontinuum conical emissions was accurately measured experimentally, which can be explained well by nonlinear X-wave model other than FWM model.
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