摘要： The analytical breather-solutions of the Nonlinear Schr¨odinger Equation (NLS) have been intensively studied and veri?ed experimentally in the time-space system of optical pulse propagation in ?bers. In space-space systems, i.e. in optical beam propagation breathers in ultra-fast nonlinear media have not been observed due to the breather’s in?nite background and a resulting extremely large power. In a lithium niobate slab waveguide with two second-harmonic (SH) resonances the resulting quasi-cubic cascaded quadratic nonlinearity provided together with the intrinsic cubic susceptibility enough nonlinearity for breather excitation at experimentally reachable powers. We could characterize the ?rst ultra-fast spatial-spatial optical breathers in a 5-cm-long titanium in diffused lithium niobate slab waveguide at power levels down to tens of kW. The guided fundamental wave (FW) TM0 ?lm mode at l=1.32mm is phase-matched for type-I SH generation to TE0 and TE1 SH modes at temperatures near 295 and 344C. With temperature tuning the phase-mismatch and the two effective cascaded nonlinearities were adjusted. For breather observation, we aimed for a large phase-mismatch with low SH levels such that the cascaded nonlinearity is quasi-cubic and the propagation is well approximated by the NLS and its breather solutions. A frequency-doubled Nd:YAG-pumped OPA with CW-seeding delivered 5-ps long pulses with up to 200kW peak power in the waveguide. With a cylindrical telescope the beam was transformed into a very wide elliptical beam to approximate the breather background. The beam was end-?re coupled into the FW TM0 mode. A variable few% of the beam were separated and coupled with a tilt and good overlap to the main beam into the waveguide to produce a spatial modulation of the input with adjustable period and modulation depth. A beam width of 1.5mm was large enough in the compromise between available beam power and in?nite beam width. A beam with a transverse modulation with periods between 130 to 300mm approximates a constant background with modulation well enough to trigger modulation instability that develops eventually into the breather. The FW and the SH output of the waveguide were imaged into cameras. By changing the power the breather moves along the waveguide and the whole breather can be sampled at the waveguide end during a power scan. Each sample is normalized to its total power. An example is shown in Fig.1. Fig.1(left) Measured breather, scanned at the waveguide output dependent on power. (right) Simulation of the measurement. The in?uence of deviations from ideal theory and real world conditions like ?nite beam width, damping, non-uniform phase-mismatch, pulsed input, and cascading instead of an exact cubic nonlinearity was investigated in simulations describing the experiment very well (see example in Fig.1). The new platform is very versatile. A wide parameter space of different nonlinearity, varying transverse breather period and input modulation depth was investigated. Higher-order breathers were observed (see the grow-ing maxima between the main peaks in Fig.1). The drastic temperature-dependent reduction of the power level for breather formation due to cascading was observed. The expected speci?c details of quadratic breathers like a SH following the FW was documented. The spatial breather spectra showed the expected triangular shape.