Frequency-induced polarization bistability in vertical-cavity surface-emitting lasers with orthogonal optical injection

We report theoretically on a pure frequency-induced polarization bistability in a vertical-cavity surface-emitting laser (VCSEL) subject to orthogonal optical injection, i.e., the master laser light polarization is orthogonal to that of the slave VCSEL. As the frequency detuning is scanned from negative to positive values and for a fixed injected power, the VCSEL exhibits two successive and possibly bistable polarization switchings. The first switching (from the slave laser polarization to the injected light polarization) exhibits a bistable region whose width is maximum for a given value of the injected power. Such a dependency of hysteresis width on the injected power is similar to that recently found experimentally by Hong et al.[Electron. Lett. 36, 2019 (2000)]. The bistability accompanying the second switching (from the injected light polarization back to the slave laser free-running polarization) exhibits, however, significantly different features related to the occurrence of optical chaos. Interestingly, the width of the bistable region can be tuned over a large range not only by modifying the injection parameters but also by modifying the device parameters, in particular the VCSEL linewidth enhancement factor.

Figure 1

Pure frequency polarization bistability induced by optical injection. Solid (dashed) line represents the evolution of the averaged optical intensity when the frequency detuning is increased from negative to positive values (decreased from positive to negative values) and for a fixed injection strength $P_{inj}∕I_0=0.09\%$: (a) $x$-polarized mode; (b) $y$-polarization direction.

Figure 2

Influence of the injection strength on pure frequency polarization bistability. Same as Fig. 1 but for $P_{inj}∕I_0=\left(\mathrm{a}1\right),\left(\mathrm{a}2\right),0.05\%$, (b1),(b2) 0.15 %, (c1),(c2) 1.5 %.

Figure 3

Bifurcation diagram of the LP mode intensities when the frequency detuning is increased from $-80$ to $80\mathrm{rad}∕\mathrm{ns}$ and for a fixed injection level $P_{inj}∕I_0=0.04\%$.

Figure 4

Polarization-resolved intensity time traces showing a period-doubling route to chaos in between the two PSs when the frequency detuning is increased from $-80$ to $80\mathrm{rad}∕\mathrm{ns}$ and for a fixed injection level $P_{inj}∕I_0=0.04\%$. The left- (right-) hand panels represent the evolution of the $x$-polarized ($y$-polarized) mode for selected detuning values $\mathrm{\Delta }\omega =\left(\mathrm{a}\right)-37.07$, (b) 5.00, (c) 15.00, (d) 19.31, (e) 21.98, and (f) $28.96\mathrm{rad}∕\mathrm{ns}$.

Figure 5

Dependency of the hysteresis width associated with the HF PS on the injected power.

Figure 6

Dependency of the hysteresis width associated with the LF PS on the injected power.

Figure 7

Influence of the linewidth enhancement factor $\alpha$ on the width of the hysteresis associated with the LF PS point, for either a weak (black) $(P_{inj}∕I_0=0.09\%)$ or large (gray) $(P_{inj}∕I_0=1.50\%)$ injection strength.

Figure 8

Effect of the linewidth enhancement factor $\alpha$ on the polarization bistability induced by frequency detuning. The averaged $x$ LP mode intensity is plotted as a function of the detuning, for a fixed injection strength $(P_{inj}∕I_0=0.09\%)$ and for increasing values of $\alpha =\left(\mathrm{a}\right)3.4$, (b) 3.9, (c) 4.3, and (d) 5.0.

Figure 9

Effect of the spin-flip relaxation rate ${\gamma }_s$ on the polarization bistability induced by frequency detuning. The averaged $x$ LP mode (left) and $y$ LP mode (right) intensities are plotted as a function of the detuning, for a fixed injection strength $(P_{inj}∕I_0=0.09\%)$ and for increasing values of ${\gamma }_s=\left(\mathrm{a}1\right),\left(\mathrm{a}2\right)1$ (b1),(b2) 20, (c1),(c2) 50, (d1),(d2) 75, and (e1),(e2) $100{\mathrm{ns}}^{-1}$.