Square-wave switching by crossed-polarization gain modulation in vertical-cavity semiconductor lasers

We study experimentally and theoretically the effects of crossed-polarization reinjection (XPR) on the output characteristics of a vertical-cavity semiconductor laser. We find a set of parameters values for which each polarization component develops a square-wave modulation at a period close to twice the reinjection delay. We analyze the regularity of this modulation in terms of the laser pumping current and of the reinjection level. These observations are numerically reproduced within the spin-flip model modified to account for XPR. In particular, the degradation of the square-wave switching is linked to the finite value of the spin-flip rate, and it occurs when the current approaches the boundaries of polarization bistability.

Figure 1

Experimental setup. $V$: Vertical cavity surface emitting laser. $C$: Collimator. $\lambda ∕2$: $\lambda ∕2$ waveplates. PR: $+45°$ polarization rotator. $45°P$ polarizer placed at $+45°$ with respect to VCSEL $x$ polarization axis. $P$: Polarizer. $D1$: fast detector. $D2$: Detector. OI: Optical isolator. FP: Fabry-Pérot resonator. DS: Digital scope. SA: Spectrum analyzer. BS: Beam splitter.

Figure 2

$x$-polarization (black curve) and $y$-polarization (gray curve) output of the reinjected VCSEL: Time series (left panels) and power spectrum (right panels). In the time series the gray curve has been displaced vertically by 100 units, while in the power spectra it has been displaced vertically by $10\mathrm{dBm}$. Three different levels of reinjection: (a) $0.2\%$, (b) 1%, and (c) 10%. The signals are amplified and AC coupled to the scope.

Figure 3

$x$-polarization output of the reinjected VCSEL: Time series (left panels) and power spectrum (right panels). Three different levels of pumping current for reinjection fixed at 1%: (a) $J=1.125J_{\mathrm{th}}$, (b) $J=1.25J_{\mathrm{th}}$, and (c) $J=1.55J_{\mathrm{th}}$.

Figure 4

Comparison between the solitary laser emission and the XPR injected laser. (a) Power spectra of the $x$-polarization component and of the $y$-polarization component (black and gray lines, respectively). The gray line is also vertically shifted of $10\mathrm{dBm}$ for clarity. $J=1.25J_{\mathrm{th}}$. (b) As in (a) but for XPR reinjected VCSEL; parameters are the same of Fig. 2 central panel $J=1.25J_{\mathrm{th}}$ and XPR reinjection level fixed at 1%. (c) Optical spectra of the $x$ and $y$ polarization components (black and gray lines, respectively). $J=1.25J_{\mathrm{th}}$. (d) Same as in (c) but for XPR reinjected VCSEL; parameters are the same of Fig. 2 central panel $J=1.25J_{\mathrm{th}}$ and XPR reinjection level fixed at 1%.

Figure 5

(Left panels) Intensity of the $\mathrm{LP}\text{−}x$ (black) and $\mathrm{LP}\text{−}y$ (gray) components of the VCSEL under different levels of XPR: (a) $\beta =0.04$, (b) $\beta =0.1$, and (c) $\beta =0.25$. The traces of the $\mathrm{LP}\text{−}y$ component have been vertically shifted for the sake of clarity. (Right panels) The corresponding power spectra of the time traces. ${\eta }_{\mathrm{sp}}={10}^{-3}$ and $\mu =1.25$.

Figure 6

(Left panels) Intensity of the $\mathrm{LP}\text{−}x$ (black) and $\mathrm{LP}\text{−}y$ (gray) components of the VCSEL for different currents: (a) $\mu =1.05$, (b) $\mu =1.20$, and (c) $\mu =1.5$. The $\mathrm{LP}\text{−}y$ component trace has been vertically shifted for the sake of clarity. (Right panels) The corresponding power spectra of the time traces. Parameters: Same as Fig. 5 except for $\beta =0.1$.

Figure 7

(a), (b) Power and optical spectra for the solitary VCSEL and (c), (d) for a XPR level $\beta =0.1$. The current is set to $\mu =1.25$.

Figure 8

(a) Steady states solution of Eqs. (9, 10, 11, 12, 13) in the $(\omega ,N,n)$ projection for $\beta =0.25$. (b) Bifurcation diagram as function of the reinjection rate $\beta$. In both cases, the bias current is $\mu =1.25$.

Figure 9

(Color online) Bifurcation diagram of the $\mathrm{LP}\text{−}y$ solution as a function of $\mu$ for different reinjection rate $\beta$. The $\mathrm{LP}\text{−}y$ mode is stable after the bifurcation point. The supercritical quasiperiodic solutions [(c), (d), and (e)] are stable in some current range below ${\mu }_h$. The circles denote the folding point ${\mu }_f$ for the supercritical branches.