Coherent combination of outputs from fiber amplifiers may be accomplished by correcting linear phase errors via electronic or nonlinear optical feedback when the input signal is a common continuous wave laser signal with a bandwidth up to several hundred megahertz (MHz).  Coherent combination of laser pulse trains from fiber amplifiers is also straightforward when the separate laser pulses have a low peak intensity.  However, for shaped laser pulses at high peak power, accumulation of nonlinear phase errors becomes difficult to correct.  Nonlinear phase errors become important at intensities greater than Ipkn2L˜λ/2, where Ipk is the peak intensity, n2 is the Kerr coefficient (˜3×10−20 m2/W), λ is the wavelength, and L is the fiber amplifier length.  Such a condition will exist, for example, for an average optical power of only 3.5 W in a 10 m long fiber amplifier with a train of ins duration, 1 μm wavelength optical pulses at a repetition rate of 100 MHz.  For coherent combining of outputs, linear phase differences between amplifiers may be corrected using electronic or nonlinear optical feedback loops.  However, electronic or nonlinear optical feedback loops may be ineffective in compensating for the nonlinear phrase errors in high-power, short-duration shaped laser pulses.  Failing to compensate for nonlinear phase errors may result in poor signal coherence, poor beam quality, and unstable signal power levels in a coherently combined output.