1. Introduction

In the past decade, a continuous interest and a research effort have been dedicated to the study of spin-injection into semiconductor lasers with vertical geometry [1–12]. In such devices, the spin information carried by the injected electrons is encoded into circular polarization information carried by the emitted photons. This information transfer happens through the optical quantum selection rules for dipole radiation associated with the conservation of angular momentum z-projections m_z occurring in confined strained active medium or Quantum Wells (QWs) [13]. Spin-Lasers could provide interesting properties for next-generation optical communication systems such as enhanced bandwidth [14], fast modulation dynamics [15,16], polarization control [17, 18] as well as higher performances with laser threshold reduction [18–20], improved laser intensity and polarization stability. The ideas emerging from spin-lasers and polarization switching may also motivate original device concepts such as spin interconnects [21] or spin information amplifiers [22, 23]. Tremendous accomplishments have been achieved using optically spin-injected monolithic Vertical-Cavity Surface-Emitting Lasers (VCSEL) [4–6]. However, despite impressive technological effort [8, 24], highly efficient electrical spin-injection in VCSEL at room temperature and magnetic remanence remains to be demonstrated.

During the last years, we investigated the possibility of spin-injection in Vertical External Cavity Surface Emitting Lasers (VECSEL) based on 1/2-VCSELs. The external cavity of VECSEL enables to deposit an ultra-thin electrical spin-injector perpendicularly magnetized at magnetic remanence [25, 26] close to the active medium (QWs) (≈ 100–200 nm) as illustrated in Fig. 1 [27]. As opposed to previously proposed designs [8, 24], this architecture reduces the distance between the spin-injector and the active medium. Hence, this geometry minimizes the impact of the spin-relaxation mechanisms occurring during electron transport in the semiconductor structure [28–30]. As a direct consequence, an increase of the effective spin polarization degree of the carriers before radiative recombination can be observed in the active medium. The proof-of-concept of such a geometry has already been demonstrated in earlier work using optical pumping [27]. Additionally, VECSEL are pointed out as a technology of choice for beyond state-of-the-art laser light sources, demonstrating wavelength flexibility, high power, high spatial, temporal and polarization coherence, in CW or ultra short pulsed operation, as well as compactness and functionalities. They exhibit a class-A dynamics without relaxations oscillations leading to low intensity and frequency noise [31,32]. With such characteristics they stand out as attractive candidates for microwave-photonics applications [33]. Finally, as there is no preferential guiding for TE or TM modes like in conventional laser diodes, V(E)CSELs provide a relatively good isotropic emission.

 

Fig. 1 Conceptual illustration of an electrically spin-injected VECSEL operating at room temperature and magnetic remanence. The external laser cavity (L) is fixed between the bottom Distributed Bragg Reflector (DBR) and the output mirror. We deposit on top of the semiconductor 1/2-VCSEL, close to the active medium, a Magnetic-Tunnel-Junction (MTJ) spin-injector with perpendicular magnetization at magnetic remanence. The role of this spin-injector (here MgO(2.5nm)/CoFeB(1.2nm)/Ta(5nm)) is to spin-polarize the electrons which are electrically injected in the system through a top annular Ti/Au electrode. The spin-polarized electrons then drift from the spin-injector toward the active medium based on multiple quantum wells (QWs). In the QWs, the electrons-holes recombinations are driven by the conservation of angular momentum according to the optical selection rules [13]. Spin-up and spin-down electrons generate left (σ⁻) and right (σ⁺) circularly-polarized photons respectively. Accordingly, by switching the spin-polarization of the injected electrons, one can control the polarization emitted by the VECSEL.

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Nevertheless residual stress [34], lattice strains [35, 36], temperature [37, 38], cavity geometry [39–41] or even lithography processing of VCSELs can break the in-plane symmetry of the device and give rise to linear birefringence in the structure. The influence of dichroism and birefringence on polarization selection in VCSELs has been clearly highlighted by the Spin-Flip Model [42] and its application to basic polarization mode selection for a single mode emission [43]. We recently highlighted experimentally the strong influence of birefringence on the polarization selection of an optically spin-injected 12 (100)-In_22%Ga_78%As/GaAs_95%P_5% QWs VECSEL [27]. In spin-injected V(E)CSEL, the polarization of the oscillating mode is governed by the competition between the residual birefringence γ intrinsic to the semiconductor structure and the circular dichroism gain ΔG emerging from the spin imbalance in the active medium. Despite spin-injection using 100% right (σ⁺) or left (σ⁻) circularly-polarized pumping [13], we witnessed a locking of the laser on linearly-polarized modes due to the inherent residual birefringence. For our (100) InGaAs/GaAsP QWs VECSEL, the birefringence sets the linear polarization axis along [110] (TM) and [11̄0] (TE) with a preferential selection for the [11̄0] direction at threshold. In order to push forward our understanding of the competition between the birefringence γ and the circular dichroism gain ΔG generated in optically spin-injected VECSEL, it is necessary to accurately quantify the birefringence in the structure. In this paper, we report the birefringence measurements of the 12 (100)-In_22%Ga_78%As/GaAs_95%P_5% QWs 1/2-VCSEL used in our previous spin-injection experiment [27]. Even though the experiment is conducted in the framework of our research on spin-injection in VECSELs, here we do not focus on the optimization of the spin-injection through pure circularly-polarized pumping. The goal is to precisely quantify the effective birefringence of the semiconductor chip driving the polarization selection in the laser. The measurements are performed with a pump polarization given by the default polarization of the edge-emitting laser diode i.e. slightly elliptical. Accordingly, the spin polarization of the optically-injected carriers can be neglected.

In a semiconductor structure, the birefringence emerges from the difference of refractive indexes Δn = n_e − n_o between the ordinary (n_o) and extraordinary (n_e) axis. In this paper, we define the birefringence γ as the dephasing for a round-trip in the laser cavity associated with this difference of refractive indexes Δn:

2. Theoretical analysis

In this section, we aim at demonstrating the relationship between the frequency shift separating the TE and TM modes and the birefringence γ of the 1/2-VCSEL. We consider the general case of a VECSEL emitting on the TE mode linearly-polarized along the extraordinary-axis while the spontaneous emission of TM mode linearly-polarized along the ordinary-axis is amplified by the cavity but still below threshold [Fig. 2(a)]. In the model, we assume that the birefringence of the active medium (12 strained QWs distributed over 13λ/2) dominates in the structure and we neglect the influence of the DBR’s birefringence. The average optical length of the laser cavity is L_opt = L + n̄l, L being the cavity length without the active medium and l the thickness of the active medium (L = 0 for a monolithic VCSEL). $\overline{n}=\frac{n_e+n_o}{2}$ is the average optical index of the birefringent active medium. n_e and n_o are the refractive indexes seen along the extraordinary and ordinary axis respectively. λ defines the laser wavelength and c the celerity of light. We choose to identify the frequencies in the optical domain as ν and the frequencies in the electrical domain as f. Accordingly, the optical frequencies associated with the polarization TE and TM modes at the order p and q respectively are given by:

 

Fig. 2 Optical and electrical mode spectra: (a) Optical spectrum emitted by the laser. For a given mode, the frequency shift between two adjacent orders is equal to the Free Spectral Range (FSR) of the cavity. (b) Corresponding optical spectrum after projection on the same polarization axis using a polarizer. (c) Associated electrical spetrum after quadratic detection by a photodiode of the projected optical spectrum at 45°.

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However, as the birefringence is expected to be relatively small, the order p and q are equals. Hence, the system of Eqs. (3) becomes:

Using Eq. (5), we further calculate the frequency shifts f₁ − f₂ and f₃ − f₁ between the central peak (f₁) and the left (f₂) and right (f₃) satellite peaks respectively [Fig. 2(c)]:

The difference of refractive indexes Δn = n_e − n_o can then be extracted from Eq. (6):

Finally, we can express the birefringence γ as a function of Δf using the expressions given by Eq. (7) and Eq. (8):

This relation is established for a round-trip in the cavity. In the particular case of VECSELs with long external cavities: l << L and L_opt ≈ L.

3. Experimental setup

The experimental setup is described in Fig. 3. We used an anti-resonant 1/2-VCSEL grown by Metal Organic Chemical Vapor Deposition (MOCVD) consisting in a 27.5-period GaAs/AlAs Bragg reflector (99.9% reflectivity). In operation, the output wavelength of the laser is λ = 1 μm. The gain, at λ = 1 μm, is ensured by twelve strained balanced In_22%Ga_78%As/GaAs_95%P_5% QWs in a 13λ/2 cavity. The sample consists in a 10×5 mm² cleaved and non-processed piece of raw wafer. The structure is maintained at 282 K with a Peltier thermo-electric cooler throughout the experiment. Instead of clamps, the VECSEL is mounted on the Peltier with thermal grease to avoid any parasitic stress on the structure that could bias the birefringence measurements. The pumping system consists of a Lumics 808 nm pigtail multimode laser diode delivering up to 2 W and focused on the gain medium to a 100 μm spot with a 30° incidence angle. We make this angle as small as possible in order to limit the thermally induced birefringence. We pump the VECSEL in a continuous regime throughout the experiment. The pump polarization is given by the default polarization of the Lumics laser diode i.e. slightly elliptical (long axis along the x-axis) and the spin polarization of the optically-injected carriers can be neglected. The linear cavity is closed by a 25 mm radius of curvature concave mirror M with 1% transmission at 1μm. The total physical length of the laser cavity is set to 2.3 cm. Such a long cavity implies that the laser is multimode longitudinally. We then introduce and carefully adjust a 100 μm thick Yttrium Aluminum Garnet (YAG) acting as a filter inside the laser cavity to set the laser monomode. The VECSEL is then oscillating on one linearly-polarized mode (TE). However, the ASE of the non-oscillating modes is still detectable near the laser’s harmonics (spaced by the FSR) even though the laser is perfectly single mode. Spontaneous photons being emitted with random polarizations, they experience the laser gain along both TE and TM polarizations. Thus the ASE of the orthogonal polarization mode (TM) is still detectable above the shot-noise. At the laser output, the beam is collimated (l₃) and fiber-coupled with a monomode optical fiber to send the emitted light on a high speed photodiode with 20 GHz bandwidth. Due to the quadratic nature of such detection, the photodiode measure the beatings between all the spectral components of the optical field and in particular those involving the lasing mode. The electrical signal is then amplified using a low noise, high bandwidth amplifier and sent to a Electrical Spectrum Analyzer (ESA). We insert a polarizer between the laser output and the fiber-coupling to project the orthogonal linear polarizations of the lasing mode and the ASE on the same optical axis [Fig. 3 (Inset 2)]. In the electrical domain, we then focus on the beatnotes between these two linearly-crosspolarized modes near the first adjacent mode. In good agreement with theory, we observe on the ESA [Fig. 3 (Inset 3)]: (i) the central peak f₁ (light blue) corresponding to the beatnote frequency between the lasing TE mode at the order p and the ASE of the TE mode at the order p+1 and (ii) the satellite peaks at f₂ and f₃ (purple) corresponding to the beatnote frequencies between the lasing TE mode at the order p and the ASE of the TM mode at the order p−1 and p+1 respectively. As detailed in the previous section, the birefringence γ can then be extracted from the measurements of the frequency shift Δf between two beatnote frequencies (f₁, f₂ and f₃) using Eq. (9).

 

Fig. 3 Experimental and characterization setup: L = 23mm, l₁ = 10mm, l₂ = 25mm, l₃ = 175mm, M : (R = 25mm, T = 1%). The Insets 1, 2 and 3 illustrate the evolution of the emitted raw optical spectrum (Inset 1) after projection through a 45°-polarizer (Inset 2) and conversion into a RF spectrum by a photodiode (Inset 3). In the optical spectrum, the TE and TM polarization modes are represented in blue and red respectively. In the electrical spectrum, the beatnotes between modes are identified by the frequencies $f_0={\nu }_{\mathit{TE}}^p-{\nu }_{\mathit{TM}}^p$, $f_1={\nu }_{\mathit{TE}}^p-{\nu }_{\mathit{TE}}^{p-1}$ (also $f_1={\nu }_{\mathit{TE}}^{p+1}-{\nu }_{\mathit{TE}}^p$), $f_2={\nu }_{\mathit{TE}}^p-{\nu }_{\mathit{TM}}^{-1}$ and $f_3={\nu }_{\mathit{TM}}^{p+1}-{\nu }_{\mathit{TE}}^p$. The beatnotes between lasing and non lasing modes of same polarization are represented in light blue while the beatnotes between the lasing mode and the cross polarized nonlasing modes are represented in purple (regardless to the mode orders).

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An excellent SNR is predicted for the measurements. The 2.3 cm cavity exhibits a net round-trip losses of 1% giving a photon lifetime of 7.4 ns, which is higher than the carrier lifetime in stimulated emission regime at about twice the threshold (around 1 ns). As a direct consequence, the laser operates in the class-A regime leading to a behavior exclusively governed by the filtering function of the cold cavity [32]. Thus, one expects the amplitude noise to be shot noise limited around the FSR frequency as opposed to previous measurements reported on class-B VCSEL around the lasing mode [45]. Moreover, owing to the high finesse and significant length of the laser cavity, the ASE lines around the lasing mode are intrinsically very narrow which favors accurate measurement of the frequency shift and consequently of the birefringence. In the following, we consider that the laser beam k-vector of the VECSEL propagates along the z-axis ([001]-axis of the 1/2-VCSEL) while the linear polarizations associated with the emission evolve in the (x,y)-plane. Accordingly, we define the 1/2-VCSEL Horizontally-oriented when the 1/2-VCSEL [110]-axis (long side of the GaAs chip) is parallel the the x-axis and Vertically-oriented when the 1/2-VCSEL [11̄0]-axis (short side of the GaAs chip) is parallel the the x-axis [Fig. 3 (Top-Left)].

4. Experimental results

4.1. Identification of two linearly-polarized orthogonal modes

In this preliminary experiment, we demonstrate that the lasing TE mode can be used as a local oscillator to generate beatnote frequencies in the electrical domain. The study is performed for different polarizer angles θ ranging from 0° to 90°. Figure 4 displays the RF power evolution of the beatnote frequencies. As already emphasized, the measurements are performed near the first adjacent mode where the noise floor is minimum [Fig. 3 (Inset 3)]. The amplitude for the central beatnote frequency (f₁) is maximum when the polarizer is aligned with the polarization direction of the lasing mode (reference: 0°) and then progressively decreases until complete extinction at 90°. However for the satellite peaks amplitude, the amount of intensity projected increases from 0° to 45°, where the beatnote amplitude between the TE and TM modes reaches a maximum. Then, by further rotating the polarizer, the measured amplitude of the satellite peaks starts decreasing as the projection of the central mode start to vanish, until complete extinction is reached at 90°. From 0° to 45°, we can clearly see the opposite amplitude evolution of the central peak f₁ and the satellite peaks f₂ and f₃ [Fig. 4(b)]. This behavior confirms that we are indeed detecting a beatnote between two orthogonal polarization modes. We also conclude from this preliminary experiment that the SNR for the central and satellite peaks is maximized by setting the polarizer at 45° from both the TE and TM modes. It is also worthwhile to notice that the high finesse external cavity configuration leads to narrow ASE peaks and thus a high discrimination capability of the experiment.

 

Fig. 4 (a) Amplitude variations of the projected orthogonal polarization modes as a function of the polarizer angle θ for the VECSEL oriented horizontally with a pumping power P_pump = 515 mW at T=282 K. (b) Variation of amplitude maxima of the central peak f₁ (blue) and the satellite peak f₂ (red) as a function of the polarizer angle. The data are fitted using the Malus’s Law applied to the electrical power at the frequency f₁ (P_f1, black dashed line) and at the frequency f₂ (P_f2, black solid line). We find that P_f1 is proportional to (1 + cos(2θ))² and that P_f2 is proportional to sin²(2θ). For polarizer angles where the electrical power approaches zero (θ = 90°), the fit gives values below the measurement noise floor. The SNR for the central peak (f₁) and the satellite peaks (f₂) is optimal when the polarizer is set at 45° from both the TE and TM modes.

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4.2. Birefringence measurements

We performed the frequency shift measurements for two orientations of the 1/2-VCSEL. We emphasize that the birefringence values γ reported below include the contributions of the 1/2-VCSEL’s intrinsic birefringence γ_int and of a thermal birefringence γ_therm induced by the optical pumping so that γ = γ_int + γ_therm. In the 1/2-VCSEL, γ_int is mainly link to the birefringence of the 12 strained balanced In_22%Ga_78%As/GaAs_95%P_5% QWs playing the role of active medium with a minor contribution of the bottom DBR. We already know that the structure exhibits a dominant polarization mode (TE) along the [11̄0]-direction with an average gain 10% higher than the orthogonal mode (TM) polarized along the [110]-direction. The pump is by default elliptically polarized with the long axis along the x-axis. We first place the 1/2-VCSEL’s [11̄0]-direction along the y-axis (1/2-VCSEL oriented Vertically) to strengthen the stabilization of the dominant mode. We start by investigating this stabler situation before rotating the 1/2-VCSEL in the horizontal orientation. For both measurements we maximize the SNR by setting the polarizer at 45° from the TE and TM mode directions. We define the pumping rate as being the ratio between the applied pumping power (P) and the threshold power (P_th): $r=\frac{P}{P_{\mathit{th}}}$.

1/2-VCSEL oriented vertically:

When the 1/2-VCSEL is oriented vertically, the dominant TE polarization mode starts lasing at threshold (P_th = 295 mW) and prevents the orthogonal TM mode to oscillate in the cavity due to the gain saturation. Nevertheless, ASE is detectable for the TM mode. Accordingly, on the ESA we detect the intense central peak associated with the beating of the oscillating mode (TE) with the ASE in the first adjacent TE longitudinal mode. Whereas the two satellite peaks correspond to the beating with the TM modes. When increasing the pumping rate from r = 1.03 to r = 1.85, the amplitude of the three peaks increases (Fig. 5). We also notice a negligible increase of the frequency shift Δf between the central and the two satellite peaks due to an increase of the total birefringence in the structure originating from thermal pumping effect. For this range of pumping rate, we measured a frequency shift Δf included between 38.08 and 40.81 MHz giving an average birefringence estimated around $\frac{\gamma }{2\pi }=6.4\times {10}^{-3}\hspace{0.17em}\text{rad}$. However closer to threshold, the thermal birefringence γ_therm induced by the pump is minimized and γ ≈ γ_int so that $\frac{{\gamma }_{\mathit{int}}}{2\pi }=6.3\times {10}^{-3}\hspace{0.17em}\text{rad}$.

 

Fig. 5 Frequency spectra of the monomode emission near the first adjacent mode for the 1/2-VCSEL oriented vertically for both low (Cyan) and moderate (Blue) pumping power: The central peak f₁ correspond to the beatnote of the lasing TE mode with the ASE in the first adjacent longitudinal mode while the two side peaks f₂ and f₃ both originate from the cross-beating of the TE and the TM mode. For this VECSEL’s orientation Δf ∈ [38.08 – 40.81] MHz corresponding to a birefringence $\frac{\gamma }{2\pi }\in \left[6.3\times {10}^{-3}-6.4\times {10}^{-3}\right]\hspace{0.17em}\text{rad}$. All the measurements were performed at T= 282 K.

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At low pumping rate (r=1.03), the slight splitting of the central peak into two peaks is a signature of residual Coherent Population Oscillation (CPO) effect. This effect induces a non-perfect overlap of the lasing TE mode with ASE in the longitudinal modes of order p−1 and p+1. As can be noticed, this behavior which is actually due to aliasing effects is not present on the satellite peaks because unlike for TE-TE the TE-TM beatnote of p−1 and p+1 orders with the lasing mode leads to two different frequencies. Moreover, the CPO splitting effect is not expected to play a role for cross-polarized modes because they do not interfere in the active medium. Consequently, the accuracy of the birefringence measurement is maximized by considering the frequency difference between the two satellite peaks, that is, 2Δf.

1/2-VCSEL oriented horizontally:

When the 1/2-VCSEL is oriented horizontally, the TM mode polarized along the [110] direction starts lasing at threshold (P_th = 316 mW) and the ASE of the [11̄0] orthogonal TE mode is also observable. On the RF-spectrum we detect the intense central peak this time associated with the beatnote of the TM oscillating mode and the TM ASE and the two satellite peaks corresponding to the beating between the TM oscillating mode and TE ASE. The amplitude of the three peaks increases when the pumping rate is increased from r = 1.17 to r = 1.97 [Fig. 6(a)]. Here, as opposed to the Vertically-oriented case, we also witness a clear increase of the frequency shift Δf between the central and the two satellite peaks when the pumping power increases: Δf_r=1.17 < Δf_r=1.97. This observation is attributed to an increase of γ_therm generated by the thermal strains in the structure. For this range of pumping rate, we measured a frequency shift Δf included between 33.3 and 40.2 MHz giving an average birefringence estimated around $\frac{\gamma }{2\pi }=6.12\times {10}^{-3}\hspace{0.17em}\text{rad}$. Closer to threshold where γ_therm is minimized γ ≈ γ_int and $\frac{{\gamma }_{\mathit{int}}}{2\pi }=5.8\times {10}^{-3}\hspace{0.17em}\text{rad}$.

 

Fig. 6 Frequency spectra of the monomode emission near the first adjacent mode for the 1/2-VCSEL oriented horizontally: (a) Frequency shift measurement for both low (Cyan) and moderate (Blue) pumping power. For this VECSEL orientation Δf ∈ [33.3–40.2] MHz corresponding to a birefringence $\frac{\gamma }{2\pi }\in \left[5.8\times {10}^{-3}-6.12\times {10}^{-3}\right]\hspace{0.17em}\text{rad}$. (b) For pumping rates r = 2.03, a polarization switch is triggered by a pump induced birefringence favoring the stability of the TE mode in the cavity. All the measurements were performed at T=282 K.

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For pumping rates higher than r = 2.03, a polarization switch is triggered by the thermal birefringence induced by the optical pumping which favors the stability of the TE mode in the cavity [Fig. 6(b)]. This observation is coherent with previous polarization stability experiment performed on monolithic VCSELs [34,38]. Indeed in our laser system, a polarization bistability regime between the TE and TM modes is unlikely to establish due to a non-linear coupling constant C close to unity (C ≈ 0.9) [27,52]. By further increasing the pumping power, the detected amplitudes increase until the signal becomes unstable due to the beginning of mode hopping and multimode lasing.

5. Discussion

Figure 7 summarizes the birefringence measurements for both the vertical and the horizontal orientations of the 1/2-VCSEL. We remind that the total birefringence measured for the two orthogonal VECSEL’s orientations [110] and [11̄0] is a combination of: (i) the intrinsic birefringence γ_int of the 1/2-VCSEL structure with a main contribution from the 12 strained balanced In_22%Ga_78%As/GaAs_95%P_5% QWs and a minor contribution from the DBR mirror and (ii) the birefringence induced by the optical pumping mainly through thermal effects γ_therm. The average values of birefringence extracted above threshold are $\frac{\gamma }{2\pi }=6.12\times {10}^{-3}\hspace{0.17em}\text{rad}$ and $\frac{\gamma }{2\pi }=6.4\times {10}^{-3}\hspace{0.17em}\text{rad}$ for the 1/2-VCSEL oriented horizontally and vertically respectively. The small difference witnessed between the two orientations can be attributed to the influence of γ_therm. The pump polarization is elliptical with the long axis oriented along the x-axis. When the 1/2-VCSEL is oriented vertically (dominant polarization TE along x-axis) the thermal birefringence induced by the pump slightly enhances the intrinsic birefringence of the semiconductor structure. Oppositely, when the VECSEL is oriented horizontally (dominant polarization TE along the y-axis) this thermal birefringence slightly compensates the intrinsic birefringence of the semiconductor structure. Accordingly, we estimate the average birefringence of the VECSEL operating in a laser regime to $\frac{\overline{\gamma }}{2\pi }\approx 6.26\times {10}^{-3}\hspace{0.17em}\text{rad}$.

 

Fig. 7 Birefringence variations as a function of the pumping rate $r=\frac{P}{P_{\mathit{th}}}$ for the VECSEL oriented horizontally (blue) and vertically (black) at T= 282K.

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A more accurate value of the intrinsic birefringence is given for low pumping rate where the contribution of γ_therm is minimized. Close to threshold, the average values of intrinsic birefringence extracted are $\frac{{\gamma }_{\mathit{int}}}{2\pi }=5.8\times {10}^{-3}\hspace{0.17em}\text{rad}$ and $\frac{{\gamma }_{\mathit{int}}}{2\pi }=6.3\times {10}^{-3}\hspace{0.17em}\text{rad}$ for the 1/2-VCSEL oriented horizontally and vertically respectively. Accordingly, we estimate the average intrinsic birefringence of the 1/2-VCSEL to $\frac{{\overline{\gamma }}_{\mathit{int}}}{2\pi }\approx 6.05\times {10}^{-3}\hspace{0.17em}\text{rad}$.

Next, we compare the birefringence measured in our VECSEL to the birefringence of monolithic VCSELs. Table 1 summarizes the VCSELs’ birefringence $\frac{\gamma }{2\pi }$ calculated from frequency shifts Δf measured using different experimental techniques. For VCSELs with GaAs QWs, AlGaAs QWs and InGaAs QWs active mediums, the birefringence is ranging from the high 10⁻⁶ rad to the low 10⁻⁴ rad depending on the number of QWs, the temperature and the pumping rate. Accordingly, we conclude that the birefringence of our 1/2-VCSEL is approximately 100 times higher than the birefringence of monolithic VCSELs. Such high values of residual birefringence are suspected to origin from the lack of top distributed Bragg reflector inducing a symmetry breaking of the crystalline structure close to the active medium (≈ 100–200 nm). This symmetry breaking could increase the lattice strain on the active medium and therefore increase the phase anisotropy between the ordinary (n_o) and extraordinary (n_e) axis leading to an increase of the linear birefringence. Additionally, our active medium is build on twelve strained-balanced QWs (to compare with 3–6 for standard VCSEL [6]). The stacking these In-GaAs QWs, each doped with 22% Indium, requires to work with GaAsP barriers doped with 5% Phosphorous to generate a compression factor of 0.18 over 560 nm and balance the strains in the structure. These strain-balanced QWs are also suspected to increase the phase anisotropy in the active medium.

Table 1. State-of-the-art measurements of the frequency split (Δf) reported for electrically pumped monolithic VCSELs, with different active mediums, using different experimental setups: Fabry-Perot Interferometers (FPI), Polarization Beat Technique (PBT), Polarization Noise Fitting (PNF), Reflectance Difference Spectroscopy (RDS), Photo-Current Difference Spectroscopy (PCDS) and Polarized Electro-Luminescence (PEL). The birefringence $\frac{\gamma }{2\pi }\hspace{0.17em}(\text{rad})$ associated with Δf is calculated using Eq. (9). The optical lengths (L_opt) of the laser cavities can be found in the associated references. In most cases, VCSELs exhibit 1λ-cavities corresponding to L_opt = λ.

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The measurement of a large birefringence in VECSEL compared to monolithic VCSEL pulls the blind on the difficulties faced to observe efficient optical spin-injection in the system through emission of circularly-polarized light [27]. Contrary to the state-of-the-art results reported on optical spin-injection in VCSEL [4–6], we witnessed a locking of the VECSEL on linearly-polarized modes despite 100% right (σ⁺) or left (σ⁻) circularly-polarized pumping [13]. The birefringence of the structure completely overpowers the circular gain dichroism ΔG generated by the spin-injection in the active medium. A short term solution is to insert a non-reciprocal material in the external laser cavity to mask this birefringence [27]. However optimizing the ΔG/γ-ratio is much more challenging and requires to: (i) minimize the intrinsic birefringence γ by developing a new design to reduce the strain on the semiconductor lattice; (ii) increase the circular gain dichroism ΔG by increasing the spin lifetime (τ_s) and decreasing the carrier lifetime (τ_r) in the active medium.

6. Conclusion

The measurement approach described here is performed in the microwave domain and is perfectly adapted to assess accurately the effective linear birefringence of the gain structure in the oscillating condition. This approach is based on spectral analysis of the beatnotes between the ASE lying in the two cross-polarized non-lasing successive longitudinal modes and the lasing mode of the laser. In order to get rid of CPO effects that might lead to some offset of the measured beatnotes, the analysis is performed around the first harmonics of the laser FSR rather than in the vicinity of the lasing mode. This peculiar arrangement offers a measurement noise floor at the shot noise level owing to class-A operation of the laser and a narrow beatnotes owing to the high finesse of the laser cavity [53]. The frequency shift between two orthogonal polarizations, which is directly linked to the linear birefringence, can be measured with an accuracy as high as 1%. We quantified the average birefringence of the VECSEL operating in a laser regime to $\frac{\overline{\gamma }}{2\pi }\approx 6.26\times {10}^{-3}\hspace{0.17em}\text{rad}$ (for a round-trip in the cavity). Close to threshold, where the thermal birefringence induced by the pump is minimum, we estimated the average intrinsic birefringence of the 1/2-VCSEL to $\frac{{\overline{\gamma }}_{\mathit{int}}}{2\pi }\approx 6.05\times {10}^{-3}\hspace{0.17em}\text{rad}$. Thus, the birefringence of the 1/2-VCSEL is more than 100 times higher than previous values reported on monolithic VCSELs [44–50]. Within the framework of spin-injection in lasers, such a high value of residual birefringence can inhibit the influence of spin-polarized carriers on the polarization selection of the laser. This work supports previous polarization behavior highlighted in previous experiments on spin-injected VECSEL [27].