Consider a Gaussian beam with the beam waist w0 at the front face of a sample. The beam radius is w0 = 1 mm, and the sample has a positive nonlinear refractive index of n2 = 0.5 1019 m2/W. The average power of the 1260 nm pulsed laser is P=1 W, pulse width =60 fs, repetition rate f=100 MHz, and the sample has refractive index of n0 = 2

a. Calculate the angle of divergence due to the diffraction, and neglecting the sample's nonlinearity. b. Calculate the angle of divergence/convergence due to the sample's nonlinearity, and neglecting diffraction. c. What should be the power of the laser such that the two factors, namely nonlinearity and diffraction, balance each other.