Solution of a second-order integro-differential equation which occurs in laser modelocking

A second-order integro-differential equation is discussed in terms of the theory of saturable absorber laser modelocking, which occurs by way of temporal modulation of the electric field within the laser cavity to produce short pulses of light. A steady state operating condition is reached when the nonlinearity of the absorber balances the dispersion due to limited bandwidth in the gain medium. Attention is given to a specific eigenfunction, which is linked to arbitrary pulse parameters in laser modelocking. It is noted that in the case where nu equals zero, discrete eigenfunctions may be assigned immediately.