Why the 1986 model couldn’t see it
The 1986 equations, and the many papers built on them, track the intensity of each mode—but they discard the optical phase. It was the right simplification for two or three modes, where the phases turn out not to matter, and it kept the problem small enough for the computers of the time.
Cancellation depends entirely on the phases. Two hundred modes with random phases beat noisily against one another and produce an intensity that fluctuates on a nanosecond timescale within every round trip. But the same 200 modes with the right phase arrangement can produce an intensity constant in time. Which arrangement the laser adopts can’t be asked of a model that has thrown the phases away.
What the crystal does to the phases
My new model follows the amplitude and phase of every mode, several hundred of them, through the cavity one round trip at a time—through the gain medium with its spatial hole burning, through the nonlinear crystal twice, and back. The workstation that runs it is about 100,000x faster than the computers of 1986, and it made the 200-mode, phase-resolved model solvable numerically.
What the model shows can be stated without equations. The crystal isn’t a one-way converter. Green generated from one pair of IR modes is converted back into other IR modes, and the returned light carries the phase of the pair that produced it. This is the lever, and through it the crystal adjusts the phase of every mode on every pass—the adjustment isn’t random. A single quantity, the mean of the intensity squared divided by the square of the mean, which is one for a constant intensity and larger for anything bunched, can’t increase on a forward pass through the crystal; it’s a theorem, which my paper proves. The phase changes move the modes toward the arrangement that makes the total intensity constant, because this arrangement loses the least IR to the green. And the crystal reaches it within a fraction of a microsecond—far faster than the gain medium can respond.
The gain medium doesn’t care about the phases. Changing them costs the laser nothing in extracted power. So the phases are free to move and the nonlinear crystal moves them to create a nearly constant total intensity, while the division of that power among the modes is only weakly constrained and can drift. The modes trade power back and forth on the gain-recovery timescale, each one switching on and off. Two things keep the sum steady while this happens: The crystal’s coupling ties the modes’ gains and losses together so power leaving one mode is taken up across the rest of the set, not by any single partner, and the exchanges are collectively nearly zero-sum. And, on a much faster timescale, the phases are rearranged so the new set of mode powers still adds to a smooth waveform. A detector that sees the whole beam sees only the steady sum. The result? Loud, noisy modes, quiet total.
The same coupling that makes two modes fight makes 200 cooperate. With two modes the phases have no arrangement available that removes the beat, and the crystal’s coupling drives the competition. With hundreds, the arrangement exists, the crystal finds it, and the competition becomes invisible in the output.