1. Introduction

Polarization dynamics in Vertical-Cavity Surface-Emitting Lasers (VCSELs), which stems from the lack of strong polarization selectivity mechanism has attracted a lot of interest [1–4]. It can lead to deterministic polarization chaos in a solitary laser [5] or laser subject to optical feedback [6] or injection [7], vector cavity solitons [8] and spatially localized chaos [9] in broad area VCSELs, ultrahigh frequency oscillations [10]. Although a multitude of research has been devoted to polarization dynamics of VCSELs, such studies for Vertical External-Cavity Surface-Emitting Lasers (VECSELs) are quite limited. VECSELs, first developed in 1997 [11] are of interest in the scientific community due to the possibility of output power scalability, wavelength flexibility, and ultrashort pulse generation. Passive mode-locking VECSELs have been demonstrated using Semiconductor Saturable Absorption Mirror (SESAM), resulting in the generation of an optical pulse train [12]. Since then, great progress has been reported in terms of achieving higher intensity pulses with shorter duration [13]. Mode-locked VECSELs generating ultrashort pulses with high peak power can find useful applications in different areas, such as supercontinuum generation [14], spectroscopy [15], material ablation [16], and frequency comb generation [17]. Tremendous efforts have also been put into thoroughly investigating how the manufacture and materials used in VECSELs gain chips can improve the performance of the laser for the desired technological applications [18].

In contrast to VCSELs, there are not many studies on VECSEL polarization dynamics. Birefringent crystal in the external cavity has been utilized to split the laser emission in two spots on the chip combining the gain and saturable absorption media and to create in such a way two orthogonally polarized Optical Frequency Combs (OFC) with different pulse repetition rates [19]. In [20], circularly polarized lasing in the quantum dot VECSEL under Continuous Wave (CW) optical pumping has been realized as well as VECSEL output polarization ellipticity control via the pump polarization. In [21] the spin-flip dynamics of VECSEL with SESAM have been theoretically shown to lead to two orthogonally polarized combs, including chaotic dynamics. In this work, we undertake an experimental investigation of polarization dynamics of a VECSEL system with SESAM. We characterize the dynamics by acquiring experimental temporal traces of polarization-resolved intensities and, consequently of the Stokes parameters and the degree of polarization. We demonstrate that the polarization of the generated light changes during the pulse and is generally elliptical with significant $s_3$ Stokes parameter.

2. Experimental setup and VECSEL-SESAM characterization

The laser cavity is schematically shown in Fig. 1. It consists of a semiconductor gain chip, a SESAM, and an Output Coupler dielectric mirror (OC) of 100 mm radius of curvature with highly reflective coating layers (R=99.5%). The laser cavity is assembled in a V-shape with the gain chip as a folding mirror and its total length is almost 100 mm. The VECSEL heterostructure was grown on GaAs substrate by Molecular Beam Epitaxy in standard configuration. On the GaAs substrate first the 0.5$\mu$m buffer layer was deposited then AlAs/GaAs distributed Bragg reflector consisting of 24 pairs of quarter wavelength AlAs/GaAs, low and high index layers respectively. The GaAs microcavity of total optical thickness 9$\lambda$/2 followed. Eight single QW In$_x$Ga$_{1-x}$As, x=0.18 evenly distributed were separated by $\lambda$/2 barriers, thus positioned in antinode positions. On top of microcavity the $\lambda$/2 thick Al$_x$Ga$_{1-x}$As, x=0.34 window layer was grown to protect the carrier diffusion towards the wafer surface and the nonradiative recombination due to the surface states. The 15 nm thick GaAs cap layer protects the wafer from oxidation. The SESAM used in the cavity is the SAM-980-3-1ps from Batop Optoelectronics,with a high reflection band from 940 to 1000 nm. For these wavelengths, the SESAM is characterized by a saturation fluence of 70 $\mu$J/cm$^2$, 3% of saturable absorptance, 1.8% of modulation depth, 1.2% of non-saturable loss, and relaxation time of 1 ps. The 3$\times$3 mm$^2$ gain chip was cleaved off the wafer along the ${\{}$011${\}}$ plains then it was bonded to a copper submount using indium solder, and set into the resonator with <110> crystallographic directions parallel to the horizontal and vertical axes of the laboratory reference system. The temperature of the submount is stabilized at 9.5$^{\circ }$C by using a Peltier element, while the excess heat from the Peltier is removed by a water-cooled aluminum block. The gain chip is optically pumped with an 808 nm fiber-coupled diode laser with 105 $\mu$m core diameter and incidence angle of 55$^{\circ }$. The output power of the pump laser is fixed at 1.8 W. The pumped spot on the gain chip is approximately 97 $\mu$m of radius and the beam radius is 23 $\mu$m on the SESAM.

 

Fig. 1. Scheme of the VECSEL-SESAM setup. The laser cavity is assembled in a V shape, with the gain chip as the folding mirror. The Saturable Absorber Mirror (SESAM) and Output Coupler (OC) act as ending mirrors. A Lens with focus 100 mm (L) is focusing the light into a high-speed photodetector (D). A prism polarizer (P) and a quarter-wave plate (QWP) are placed before the detector to study the polarization dynamics. The laboratory reference system is schematically depicted. The path of the laser light is displayed in red.

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The VECSEL is emitting in the fundamental transverse mode. The average output power is 9.8 mW when the gain chip is pumped with 1.8 W. The Radio Frequency (RF) spectrum shows that the fundamental repetition rate at 1.45 GHz and its higher harmonics have similar amplitudes (see Fig. 2(a)). The optical spectrum shows a peak at 973.4 nm with full-width of 0.8 nm measured at a level of -10 dBm relative to the signal maximum (see Fig. 2(b)). For the intensity autocorrelation trace, we assumed a Gaussian pulse fit and it results in a pulse duration of 2.27 ps (Fig. 2(c)). The temporal trace shows a clear pulse train, with a separation of 0.7 ns between the peak of the pulses (see Fig. 2(d)). From this trace, we can observe that the pulse train reaches a minimum value other than zero, which indicates a behavior of light pulsations on top of a constant component of light intensity.

 

Fig. 2. Laser characterization for 1.8 W of pumping power. (a) Radio-frequency spectrum. Fundamental repetition rate 1.45 GHz. (b) Optical spectrum. Peak at 973.4 nm with full-width, measured at a level of -10 dBm relative to the signal maximum, of 0.8 nm. (c) Intensity autocorrelation trace. The FWHM from the autocorrelation trace is 1.41 times the pulse duration when a Gaussian fit is considered. Therefore, the pulse duration is 2.27 ps. (d) Temporal trace. Pulse train with separation of 0.7 ns between peaks.

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3. VECSEL-SESAM polarization dynamics

In order to characterize experimentally polarization dynamics of the VECSEL-SESAM system, we measure dynamically the Stokes parameters of the output light. The polarization of the light is characterized based on the method of adjustable retarder and analyzer, as described in [22]. In the experimental setup, we use a polarizing prism as an analyzer and a quarter-wave plate as a retarder. The high-speed detector used is the Newport New Focus 1554-B, characterized by 12 GHz bandwidth. Then, the signal is acquired by the WavePro 804HD oscilloscope, with 8 GHz of bandwidth and up to 20 GS/s of sample rate. To obtain information about the polarization dynamics, the Stokes parameters are calculated by using the temporal traces of the detected output power. Different temporal traces are detected for the different configurations of the axes orientation of the analyzer and the retarder with respect to the laboratory horizontal axis (see reference system in Fig. 1). The four Stokes parameters are calculated as a function of time by using the amplitude in voltage of the temporal traces detected with the oscilloscope, following the equations

$S_0$ corresponds to the amplitude measured without using the polarizer or the quarter-wave plate, therefore, it is related to the total intensity of the laser. $S_1$ corresponds to the predominance of horizontal linear polarization over vertical linear polarization. $S_2$ describes the prevalence of 45$^\circ$ linearly polarized light over 135$^\circ$ linearly polarized light. $S_3$ is related to the excess of right-handed circular polarization over left-handed circular polarization. $S_0$ is used to normalize the quantities $S_1$, $S_2$, and $S_3$. Hence, the normalized Stokes parameters are determined by $s_1 = S_1 / S_0$, $s_2 = S_2 / S_0$, and $s_3 = S_3 / S_0$. The degree of polarization P is defined by $P= \sqrt {(S_1^2+S_2^2+S_3^2)}/S_0$ and, in this work, it is calculated as a function of time.

First, we analyze the polarization dynamics for the case shown in Fig. 2(d), where the time trace shows a pulse train whose intensity does not decay to zero. Figure 3 shows the temporal traces detected when the pump power was set to 1.8 W. The colors represent the rotation of the transmission and fast axes of the polarizing prism and quarter-wave plate, respectively, with respect to the horizontal axis.

 

Fig. 3. Temporal traces detected with a fast photodiode and an oscilloscope. The different colors correspond to the different orientations of the polarizing prism and quarter-wave axes. The gain chip was pumped with 1.8 W of power.

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At this pump power, the three normalized Stokes parameters vary as a function of time and are always negative (see Fig. 4(a)), indicating the light possesses vertical, 135$^\circ$ diagonal and left-handed circular components of polarization. Therefore, the light is elliptically polarized. The normalized Stokes parameters changes in a periodic manner, reaching maximum or minimum values around the pulse peaks. Likewise, the degree of polarization exhibits temporal dynamics, reaching maximum values around the pulse peaks as can be observed in Fig. 4(b).

 

Fig. 4. Polarization dynamics, when pump power is 1.8 W. (a) Normalized Stokes parameters. (b) Degree of polarization.

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By changing the pumped region to a different area on the gain chip and adjusting the pump power, we found a temporal behavior of the laser that resembles more to the mode-locked regime since the temporal traces obtained show a pulse train that reaches minimum values closer to zero. We studied this behavior by setting the pump power to 1.45 W and the temporal traces are shown in Fig. 5.

 

Fig. 5. Temporal traces detected with a fast photodiode and an oscilloscope. The different colors correspond to different orientation of the polarizing prism and quarter-wave axes. The gain chip was pumped with 1.45 W of power.

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When the pump power is set to 1.45 W, the normalized Stokes parameters indicate that the light is elliptically polarized with vertical ($s_1 < 0$), 135$^\circ$ diagonal ($s_2 < 0$) and right-handed circular ($s_3 > 0$) components of polarization (see Fig. 6(a)). The normalized Stokes parameters exhibit temporal dynamics with extreme values around the pulse peaks. The degree of polarization follows the same temporal behavior as can be observed in Fig. 6(b). It is important to note that in this case, the maxima in the normalized Stokes parameters and the degree of polarization are delayed with respect to the pulse peak by approximately 0.1 ns. This observation may be attributable to an issue when performing the temporal measurements and will be thoroughly investigated in future works where the laser is in the stable mode-locking regime.

The effects of the SESAM orientation on the polarization dynamics were also studied while pumping the gain chip with 1.825 W. The SESAM chip orientation was defined as the angle between one side of the chip and the horizontal axis, as Fig. 7(a) shows. Three cases were studied: when the SESAM chip was parallel to the x-axis (i.e. 0$^\circ$), and when the orientation of the chip was +45$^\circ$ and -45$^\circ$ with respect to the same axis. The results show that the orientation of the SESAM strongly influences the sign of $s_3$. Figure 7(b) presents this observation. When the SESAM is parallel to the x-axis, the value of $s_3$ is very close to zero. By changing the SESAM orientation to +45$^\circ$ and -45$^\circ$, $s_3$ varies to positive or negative values, respectively. It is worth noticing that the orientation of the SESAM chip is close to -45$^{\circ }$ (with respect to the reference system shown in Fig. 7(a)) for the case shown in Figs. 3 and 4. On the other hand, in the case shown in Figs. 5 and 6, the orientation of the SESAM chip is close to +45$^{\circ }$. These observations suggests that it is possible to control the rotation of electromagnetic wave from right-handed ($s3 > 0$) to left-handed ($s_3 < 0$) by merely changing the SESAM orientation from +45$^\circ$ to -45$^\circ$. This result also indicates the possibility to extinguish the circular polarization component ($s_3 \sim 0$) by setting the SESAM chip to be parallel to the horizontal axis (i.e. 0$^\circ$).

 

Fig. 6. Polarization dynamics, when pump power is 1.45 W. (a) Normalized Stokes parameters. (b) Degree of polarization.

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Fig. 7. (a) SESAM orientation. The orientation of the SESAM is determined by the angle between the side of the chip (dashed red line) and the x-axis. (b) $s_3$ as a function of time. The curves show the results of $s_3$ for different angles between the SESAM and the horizontal axis.

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4. Conclusions

We have studied experimentally the polarization dynamics of a VECSEL with a SESAM in the cavity as a third mirror. The experimental results show that output light has a vertical ($s_1 < 0$) and 135$^\circ$ diagonal ($s_2 < 0$) components of polarization. The circular component can be right-handed ($s_3 > 0$) or left-handed ($s_3 < 0$), depending strongly on the SESAM crystallographic axes orientation with respect to a reference system. Therefore, the light from the laser is elliptically polarized. It is worth noticing that there is always a small residual anisotropy due to unintentional strain introduced during processing and bonding both in the gain chip and SESAM, which is relevant when the orientation of the chips is changed. The results on the normalized Stokes parameters also show that the polarization components depend strongly on time, exhibiting extreme values around the pulse peaks. Furthermore, the degree of polarization also reaches extreme values around the pulse peaks proving that is a dynamic variable in all the studied cases. We believe that the observed polarization dynamics in our VECSEL with SESAM is due to nonlinear effects, more in particular to the spin-flip dynamics in the quantum well gain medium due to the surface emission combined with the small residual birefringence and similar to the well-understood polarization dynamics in VCSELs [1–10,20,21,23,24]. However, theoretical modeling and studies along these lines are left for future work.