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(Color online) Left: the optical spectrum of the two color laser. Right: locking and unlocking boundaries in K 1-K 2 plane with Δν 1 = Δν 2 = −14 GHz. The points show the experimentally determined locking (×) and unlocking (•) boundaries, and the lines show the numerically calculated saddle-node (SN) and subcritical torus (TR) bifurcations.
(Color online) The SN bifurcation for Δν 2 = −18 GHz and various values of Δν 1 in the K 1-K 2 plane. For Δν 1 > −12 GHz, a bistable region appears as shown by the shaded region with two cusp bifurcations in the corners. The inset shows the bifurcation diagram for Δν 2 = −18 GHz and Δν 1 = −4 GHz, including two Bogdanov-Takens points (BT) and the associated Hopf (HB) and homoclinic (P) bifurcation lines. The black shaded region, which is bounded by the Hopf bifurcation line and the horizontal saddle node bifurcation line, indicates the presence of a stable limit cycle. In the black and gray striped region within the triangle bounded by saddle node bifurcation lines, a stable limit cycle and a stable fixed point coexist.
(Color online) Partition of the K 1-K 2 plane for Δν 1 = −8 GHz and Δν 2 = −18 GHz into three regions: I contains no locked states; II comprises of one locked state and one unlocked state; and region III consists of only locked states. The inset shows hysteresis of the linear power in mode 1 at K 1 = 0.01 for up (P ↑) and down (P ↓) sweep in K 2 as indicated by the arrows in the main panel. The color of region III represents the contrast ratio P ↑ to P ↓ (in dB) between these up and down sweeps, where the dark shading indicates a large contrast of optical power in mode one.
The intensity times traces of the modulated injection K 2 (top), and the modes ν 1 (middle) and ν 2 (bottom) for detunings as in Fig. 3. The modulation range is indicated by the arrows in Fig. 3. The inset shows the falling edge of mode ν 1 switching from on to off states, where the 90:10 switching time is < 500 ps.
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