Light bullets in waveguides with the cubic nonlinear Kerr effect

Summary form only given. Optical wave packet which is localized both in space in the form of the narrow beam and in time in the form of the short pulse is called "light bullet". Power ultra short laser pulse with Gaussian spatial-temporal profile induces in the waveguide with Kerr nonlinearity light field with the same profile. Other nonlinearities have finite time of the response and cannot determine properties of squeezed, in space and time, light bullets. It is known that in Kerr nonlinear medium only 1-dimensional spatial solitons are stable. Nevertheless, soliton squeezing process takes finite period of time and some distance in space. Nowadays laser pulses of femtosecond and even picosecond range are available. For the case of ordinary spatial solitons the estimation for the focal length of the collapse is well-known and is of the order of 10^-3 cm. Spatial extension of the femtosecond light bullet is by 3-4 orders of magnitude less than the focal length of the collapse. Thus light bullet just doesn\´t have enough time to collapse at such a short distance and the focus of the collapse moves all the time at some distance ahead of the light bullet along with the bullet propagating in the waveguide. Our studies show that in the cases of spherically symmetrical and elliptical waveguides both transverse dimensions and temporal duration of the light bullet slightly oscillates along with the pulse propagating in the waveguide. This confirms stability of the light bullets in the waveguides with Kerr nonlinearity.