| During the propagation of ultra-short laser pulse in normal dispersive quadratic nonlinear media, the input wave-packet can be spontaneously converted into X-shaped light bullets, where "light bullet" is a kind of propagation invariant wave-packet and localized both in space and time, and "X" refers to the hyperbolic structured spatiotemporal spectrum. X-shaped light bullet can be used, for example, light induced particle acceleration, optical information storage and transmission and ultra-violent attosecond pulse generation, etc. In addition, the tunability of X-shaped light bullet makes it becomes a possible pump source for quantum control.This article focused on the discussion of the conditions under which X-shaped light bullets forms, together with the modulations on the output wave-packet induced by input parameters, such as pump intensity, phase mismatch, group velocity mismatch, and anisotropic diffraction etc. The main contents are listed below:1. We establish 3-D model of ultra-short pulse propagating in normal dispersive quadratic nonlinear media whose prototype is type-I BBO crystal, and this 3-D model can be numerically resolved by our home-made software. The numerical simulation reveals that the input Gaussian wave-packet can be converted into X-shaped light bullets under the conditions of (1). Large enough input intensity, (2). Short enough input pulse width, and (3). Self-focusing type phase mismatch with proper value.2. Numerically investigate the stability of X-shaped light bullet with anisotropic diffraction, where we find the input elliptic Gaussian beam can be converted into stable elliptic X-shaped light bullet and no beam splitting occurs. This originates from the virtual waveguide which forms accompany with elliptic X-shaped light bullet and prevents the wave-packets from splitting during propagation.3. Numerically investigate the modulation effects of group velocity mismatch. Wefind that with unvanishing group velocity mismatch, wave-packets of fundamental wave and a part of second harmonic wave can still combine together in the form of walking X-shaped light bullets. And the output spectrum is strongly modulated, where the direction of spectrum shifting is governed by the sign of phase mismatch and group velocity mismatch. The numerical simulation indicate that the spontaneously generated phase front tilting can balance the attracting force between harmonics induced by group velosity mismatch and lead to zero-velocity (view in retarded frame) walking X-shaped light bullets.4. Experimental research of X-shaped light bullet. We observe the compression of output pulse both in time and space with proper selected parameters. And the hyperbolic structured spatiotemporal spectrum of output wave-packet is also observed via home-made spatiotemporal spectrometer. The experimental results agree well with numerical simulations on elliptic and walking X-shaped light bullets.5. Selective resonant excitations can be realized with ultrashort pulse in an optical dense collection of three-level individual atoms, where the near dipole-dipole interactions induce intrinsic frequency shifts of the atomic resonance. The intrinsic frequency shifting can be controlled by modulating the wave-packet profile and phase of excitation pulses or varying the density of optical media, which will lead to constructive or destructive quantum interference between different excitation pathways towards a desired selective resonant excitation.
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