Robust square-wave polarization switching in vertical-cavity surface-emitting lasers

We study theoretically and experimentally the combined effects of polarization-selective optical feedback and of crossed-polarization reinjection in a vertical-cavity surface-emitting laser. We show that the application of polarization-selective optical feedback, which induces an effective dichroism in the system, allows one to generate a robust and regular square-wave output signal in each polarization component. The period of the square-wave signal is determined by twice the reinjection delay. We analyze the regularity of the induced modulation as a function of laser bias current, dichroism, and of the levels and delays of reinjection and feedback, thus revealing the robustness of the square-wave emission in the parameter space. We also show that the feedback is more effective when acting on the long-wavelength polarization mode, which can be traced to the asymmetry of the bistable region of the vertical-cavity surface-emitting lasers for low dichroism.

Figure 1

Stability diagram of the solitary VCSEL for ${\gamma }_p>0$, i.e., the LP-y mode being the bluest. Modal stability is indicated as $(X,Y)=(a,b)$, where a negative value denotes stable and vice versa. The vertical line depicts a current scan in the bistability diagram. In the case shown (LP-y mode selected at threshold), the red (blue) circle at low (high) value of $\mu$ represents the critical value of the current ${\mu }_h$ (${\mu }_{\in }$), where the LP-x (LP-y) mode gains (loses) stability via a subcritical Hopf (supercritical pitchfork) bifurcation; see [23] for details.

Figure 2

Power spectra (left) and temporal traces (right) of the intensity of the LP-y components of the VCSEL for increasing values of the PSF rate $\eta$ with $\mu =2$ and $\beta =0.3$. For too small values of $\eta$, the system operates on the stable LP-x polarization, and there is an optimal feedback value $\eta \sim 0.01$ above which the regularity of the square waves deteriorates. The vertical red line in the spectra marks the frequency spacing of the external cavity modes.

Figure 3

Power spectra (left panel) and traces (right panel) of the intensity of the LP-y component of the VCSEL for increasing values of the PSF delay ${\tau }_f$, with $\eta =0.03$, $\mu =2$, and $\beta =0.3$. The vertical red line in the spectra marks the spacing of the external cavity modes.

Figure 4

Peak power in the first (solid blue), second (dashed red), and third (dash-dotted green) harmonic of the square-wave signal as a function of the delay in the PSF arm normalized to the XPR delay.

Figure 5

Power spectra (left) and temporal traces (right) of the intensity of the LP-y components of the VCSEL for increasing values of the bias current $\mu$, with $\eta =0.03$, $\Omega =0$, $\mu =2$, and $\beta =0.3$ in the optimal case where ${\tau }_f=2{\tau }_r$. The quality of the square-wave oscillation is strictly increasing with the bias current since no bistability is encountered along the way.

Figure 6

Power spectra and time trace (inset) of the LP-x polarization when the LP-x is fed back and re-injected turned into LP-y. The parameters are ${\gamma }_a=-2.6\times {10}^{-3}$, $\mu =2$, and $\beta =0.15$. The feedback rate is $\eta =0.005$.

Figure 7

Power spectra and time trace (inset) of the LP-y polarization when the LP-y is fed back and re-injected turned into LP-x. The parameters are ${\gamma }_a=-2.6\times {10}^{-3}$, $\mu =2$, and $\beta =0.15$. The feedback rate is $\eta =0.02$.

Figure 8

Experimental setup. COL: collimator. $\lambda /2$: half-wavelength wave plates. $\lambda /4$: quarter-wavelength wave plates. BS: Polarization-preserving beam splitter. PBS: Polarizing beam splitter. FR: Faraday rotator. POL: Polarizer. FM: Feedback mirror. M: Mirror. ISO: Optical isolator.

Figure 9

Upper panels: power spectrum and corresponding time signal (inset) of the LP-x output of the first device when $J=0.85$ mA, $T=30{}^{\circ }$C, and the VCSEL is submitted to XPR only (rate $17\%$) of the LP-y component (left column) and both to XPR (rate $17\%$) and PSF (rate $0.15\%$) on LP-y (right column). Lower panels: power spectrum and corresponding time signal (inset) of the LP-y output when $J=0.55$ mA and the VCSEL is submitted to XPR only (rate $17\%$) of the LP-x component (left column) and both to XPR (rate $17\%$) and PSF (rate $0.15\%$) on LP-x (right column). In all cases, $L_{\text{XPR}}=33$ cm and $L_{\text{PSF}}=58.8$ cm.

Figure 10

Power spectrum and time trace (inset) of the LP-y signal when the VCSEL is submitted to both XPR and PSF of the LP-x component for $J=3$ mA, $T=30{}^{\circ }$C, $L_{\text{PSF}}=98$ cm, and $L_{\text{XPR}}=49$ cm. The XPR rate is $17\%$ and the PSF rates are, from top to bottom, $0.03\%$, $0.05\%$, $0.44\%$, and $2.5\%$, respectively.

Figure 11

Left column: power of the LP-y (blue dotted trace) and LP-x (red trace) components when the VCSEL is submitted to both XPR and PSF of the LP-x component for $L_{\text{PSF}}=98$ cm, $L_{\text{XPR}}=49$ cm, $T=30{}^{\circ }$ C, $\text{PSF}=0.4\%$, and $\text{XPR}=17\%$ for $J=0.5$ mA (a), $J=1.0$ mA (c), $J=1.5$ mA (e), and $J=3.0$ mA (g). Right column: corresponding power spectrum of the LP-y component.

Figure 12

Power spectra (left panel) and temporal signal (right panel) of the LP-y polarization when the VCSEL is submitted to both XPR (rate $17\%$) and PSF (rate $0.1\%$) of the LP-x component, for different values of ${\tau }_f$ as indicated. ${\tau }_r=2.6$ ns and $J=2.5$ mA; $T=30{}^{\circ }$C. For clarity, the spectra have been vertically offset by 55 dB and the time traces have been shifted by 3 units.

Figure 13

LP-x output emission together with LP-x power spectrum when the VCSEL is submitted to both XPR and polarization-selective optical feedback. Both XPR and optical feedback circuits are set to select LP-y and all parameters are optimized to obtain the most regular square signal. $L_{\text{feed}}=58.8$ cm, $L_{\text{XPR}}=69.8$ cm, $\text{PSOF}=0.15\%$, $\text{XPR}=17\%$, $J=2.8$ mA, and $T=30{}^{\circ }$C.