Kerr-resonanced bifurcation switching in a photonic Ising machine with a long lossless optical fiber loop

We describe in detail the optical Kerr nonlinearity in our photonic Ising machine (PIM), which employs ultrahigh-speed optical pulse propagation in a lossless fiber loop. Although the peak power of the pulses in the fiber loop is set as low as ∼1 mW, the present PIM requires ultralong-distance pulse propagation of the order of 100,000 km (e.g., ∼2,000 circulations in a 50 km loop) to calculate large-scale optimization problems. As a result, a nonlinear phase rotation of greater than π/2 is accumulated due to the Kerr effect. This nonlinear phase rotation makes it possible to couple between the real (I) and imaginary (Q) parts of the recirculating optical pulse. Thus, as the amplitude of the I-channel changes due to the nonlinear phase rotation, the Q-channel also varies accordingly, and vice versa. We show that this mutual coupling gives rise to a new phenomenon, which we name Kerr-resonanced bifurcation switching, where the accumulated nonlinear phase rotation results in a periodic dip in the cut value of a max-cut problem. This dip phenomenon can be understood as a consequence of optical power peaking in a nonlinear optical fiber loop resonator with Kerr phase rotation. Finally, we propose a method for preventing dip generation by combining a large core fiber and a chirped fiber Bragg grating (CFBG) over a short length, which can reduce the Kerr-induced nonlinear phase rotation.