1. Introduction

The vertical-cavity surface-emitting laser (VCSEL) has many advantages such as single longitudinal mode operation, circular beam profile, low threshold, and high bandwidth of modulation [1]. These advantages make VCSEL a promising device in telecommunications and other optoelectronic applications. However, a linearly polarized VCSEL can switch to the orthogonal polarization due to changes in bias current or operating temperature [2–7]. Spontaneous polarization switching is unwanted in polarization-sensitive applications. Therefore, the physical mechanism and control of polarization switching (PS) in VCSELs has attracted considerable research interests [2–9].

It is well known that optical injection can improve performance of semiconductor lasers and induce rich dynamics [10]. Effects of optical injection have been extensively studied in VCSELs [11–21]. Depending on the polarization of the injected beam, optical injection can be classified into parallel, orthogonal or arbitrary polarized injection. The so-called parallel injection is that the polarization of the injected beam is parallel to that of the VCSEL [11]. For the orthogonal injection, the polarization of the injected beam is perpendicular to that of the VCSEL [12]. Optical injection of arbitrary polarization has included the case of elliptically polarized injection [20,21]. These schemes can induce polarization switching. Rich dynamics is observed inside and around PS regime, including stable frequency locking, periodic pulsations (P1) and period doubling (P2), bistability and chaos [13–17, 19].

For frequency locked states, the frequency of the linearly polarized slave laser has been observed to lock to that of master laser, and the polarization of the slave laser is the same as the injected beam [16]. Recently, Sciamanna and Panajotov predicted a new stationary state—elliptically polarized injection-locked (EPIL) state—induced by orthogonal optical injection in a single transverse mode, linearly polarized solitary VCSEL [13]. In the EPIL state, the two polarizations of the slave laser are frequency locked to the master laser. Homayounfar and Adams showed numerically that the stability of the EPIL state can be increased by reducing the spin relaxation or increasing the birefringence and pumping [15]. However, to our best knowledge, the EPIL state was not observed experimentally.

In this paper we report the first observation of the EPIL state in a VCSEL. We describe our setup and method in Section 2, and present the evidence of the EPIL state in Sec. 3. Then we discuss some issues encountered in our experiment and give our conclusion in Sec. 4 and Sec. 5, respectively.

2. Experimental setup and method

We search for the EPIL state using an all-fiber setup. A stabilized tunable laser (the master laser, TL) provides optical injection to a single-transverse-mode VCSEL (slave laser). The device is a commercially available quantum-well 1550 nm VCSEL (Raycan). The threshold current of the VCSEL is 1.6 mA. From threshold to 6 mA, the free-running VCSEL emits a linearly polarized beam that is named parallel polarization. The polarization perpendicular to this state is termed orthogonal polarization, which is more than 30 dB weaker than the parallel polarization. In our experiment, the maximum bias current is set at 4 mA, well below the 6 mA at which the intrinsic PS of the VCSELoccurs. The output power and the relaxation oscillation frequency of the VCSEL at 4 mA are 0.32 mW and 2.8 GHz, respectively. Figure 1(a) shows the experimental setup. The output power from the master laser can be adjusted with a variable attenuator (VA). We use a polarization controller, PC1, to make the polarization of the injected beam orthogonal to the parallel polarization of the VCSEL. The beam from the master laser goes through an optical circulator, OC, and is split by a 90:10 fibre directional coupler. Approximate 90% of the incident beam is sent to the VCSEL, and ~10% of the incident beam is monitored by a power meter, PM. After taking the loss at fiber adaptors into account, we measured that the power of injection, P_inj, in front of the VCSEL is five times the reading of the power meter. That is, P_inj = 5P_PM. The output of the VCSEL goes through a polarization controller, PC2, and is connected to a polarization beam splitter, PBS, with a nominal separation ratio of 26 dB. We use PC2 to maximize the contrast of two polarizations perpendicular to each other. The power of the strong polarization is around 30 dB stronger than that of the weak polarization. This agrees with the spectrum observed on the optical spectral analyzer (BOSA). Therefore, the strong beam from the PBS is the parallel polarization, and the weak beam is the orthogonal polarization. Wavelengths of the parallel and orthogonal polarizations are λ_// = 1538.01 nm and λ_⊥ = 1538.24 nm, respectively.

 

Fig. 1 (a) Schematic diagram of the experimental setup. (b) Optical spectrum of the free-running VCSEL biased with a current of 4 mA.

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We study the effect of the orthogonal optical injection around λ_//. The power of each polarization of the VCSEL is measured with a power meter when the wavelength of the injection, λ_inj, is tuned with fine steps. Another method is to find the power of each polarization by using the power integral function of BOSA, an optical spectrum analyzer with resolution of 0.1 pm. Optical spectra of the VCSEL are measured with BOSA. An example of the optical spectrum of the free-running VCSEL is shown in Fig. 1(b). Figure 2 shows the dependence of the polarization resolved powers on λ_inj and frequency detuning, ∆ν, separately. The frequency detuning is defined as ∆ν≡ν_inj-ν_//,free, where ν_//,free is the frequency of the parallel polarization of the solitary VCSEL. For λ_inj<1538.00 nm, the VCSEL is in parallel polarization. As shown in Fig. 2(a), a polarization switching (PS) occurs when λ_inj is slightly above 1538.00 nm, in which the orthogonal polarization reaches high power abruptly and the parallel polarization is suppressed. Then the VCSEL gradually switches back, which is termed the second PS. The powers of parallel and orthogonal polarizations in Fig. 2(a) are read from the power meters. Powers are much smaller than the free-running VCSEL power due to the significant losses caused mainly by the PBS and by two cables with appropriate connectors to decrease optical feedback effects in the VCSEL. The power of the orthogonal polarization is ~2 μW before PS and after the second PS, which is caused by the reflection of the orthogonal injection at the front surface of the VCSEL. The polarization property of the VCSEL is confirmed in Fig. 2(b), where the independent variable is the frequency detuning and the power of the parallel and orthogonal polarizations, P_// and P_ort respectively, are measured from the BOSA. P_ort includes the contribution of the reflected power of the orthogonally polarized optical injection at the VCSEL mirror. Given the unavoidable, slight frequency shift in both the master and slave lasers, Fig. 2(b) is a more precise description of the polarization property of the VCSEL subject to orthogonal optical injection. However, the power of the orthogonal polarization is weaker than that in Fig. 2(a). This difference may be attributed to the very different frequency range considered in both instruments: the wideband spontaneous emission contributes to the power in power meters while only filtered optical power is measured at BOSA since we chose a narrow 5 GHz span in our measurements.

 

Fig. 2 Polarization resolved powers versus (a) λ_inj, and (b) ∆ν. Black: parallel polarization; red: perpendicular polarization. The power of injection is P_inj = 355 μW, and the bias current is 4 mA.

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3. Evidence of EPIL state

By definition, the EPIL state is such that both parallel and orthogonal polarizations of the VCSEL are frequency locked to the injected beam. The promising regime for finding the EPIL states is in the neighborhood of the second polarization switching [13] in which a smooth transition appears. Figure 3 displays optical spectra of each polarization for different values of frequency detuning.

 

Fig. 3 Polarization resolved optical spectra for I = 4.0 mA and P_inj = 270 μW. Upper row: the parallel polarization. Lower row: the orthogonal polarization.

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When ∆ν = 1.55 GHz, both parallel and orthogonal polarizations demonstrate periodic oscillations around λ_// and λ_⊥, respectively. The frequency of these oscillations is 2.6 GHz, close to the relaxation oscillation frequency and it does not change with ∆ν. The weak peak at λ_inj in the optical spectrum of the orthogonal polarization comes from the reflection of the injection. For −0.48 GHz and −1.34 GHz, the two polarizations operate with the same wavelength which equals λ_inj. This is the strong evidence of the EPIL state. As ∆ν is decreased to −2.45 GHz, the wavelength of the parallel polarization is not locked to λ_inj any more. Instead, it shows periodic oscillations again. Now the VCSEL is out of the EPIL regime.

The EPIL regime is measured in the parameter plane (P_inj, ∆ν) for two bias currents, as shown in Fig. 4. The EPIL states exist in the regime between the two boundaries. Comparing the EPIL maps for I = 2.4 mA (Fig. 4(a)) and 4.0 mA (Fig. 4(b)), one can see that the Δν range for the EPIL states is narrower for lower bias current. This is in agreement with [15]. Above the upper boundary, both polarizations manifest periodic intensity oscillations, with the optical spectra similar to the case of Δν = 1.55 GHz in Fig. 3. The stationary EPIL state is represented by the single peak spectrum of each polarization, as the case of Δν = −0.48 GHz and −1.34 GHz in Fig. 3. Their wavelengths are locked to the master laser.

 

Fig. 4 EPIL regime in the parameter plane (P_inj, Δν) for (a) I = 2.4 mA, and (b) I = 4.0 mA.

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Below the lower boundary, the VCSEL operates in parallel polarization which demonstrates periodic pulsations. The dynamical feature of the VCSEL beyond the EPIL regime agrees with the theoretical prediction [13]. Generally speaking, the Δν range of the EPIL regime is wider with increasing injection power, P_inj. However, the variation of the Δν range is not monotonic. For example, the width of the Δν range is narrower for ~100 μW than for ~50 μW in Fig. 4(a). When the injection power is increased to the order of 1 mW, the width of the Δν range is still around a couple of GHz. Thus this width does not increase proportionally with P_inj.

In addition to its wavelength feature, we have explored the power of each polarization in the EPIL state. Since the EPIL state exists when the VCSEL is undergoing the second polarization switching, it is necessary to confirm that the measured state is elliptically polarized instead of linearly polarized. Figure 5(a) illustrates the data measured with the BOSA for I = 4.0 mA and P_inj = 1.32 mW in the EPIL regime. For the power of the orthogonal polarization, P_⊥, P_ort is corrected by substracting the reflected power of the orthogonal optical injection at the front surface of the VCSEL, P_r, in contrast to Fig. 2(b) that included this reflection. In this way P_⊥ = P_ort-P_r. This background power, P_r, is the power measured at BOSA when the VCSEL is off. P_⊥ is much weaker than P_//. Figure 5(b) gives the ratio P_⊥/ P_// as a function of Δν in the EPIL regime. This ratio varies from 0.9% to 4.8%, of the same order as the theoretical result (Fig. 6 in [13]) in which P_⊥/ P_// is about 5%. This ratio and the similarities between theoretical and experimental dynamics around the EPIL states indicate that the single-frequency state is elliptically polarized, however further measurements would be desirable to make this evidence complete, discarding that the VCSEL is not still linearly polarized at a slightly shifted angle with respect to the parallel direction.

 

Fig. 5 (a) Power of each polarization (black: P_//; red: P_⊥). (b) Ratio of P_⊥ to P_//. The other parameters are I = 4.0 mA and P_inj = 1.32 mW.

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4. Discussion

In the measurement of P_// and P_⊥ for large values of P_inj, sometimes P_r is higher than P_ort. This indicates that there is some destructive interference between the reflection and the output of the VCSEL [22]. Assume that the amplitudes of the orthogonal polarization and reflected injection are E_⊥ and E_r, respectively. According to the theory on two-beam interference, the resultant amplitude is less than E_r if E_⊥ < 2E_r for complete destructive interference. That is, when the power of the orthogonal polarization is close to the reflection power, the total power can be less than the background reflection. For low values of P_inj, we have observed that P_r is always smaller than P_ort. This situation is consistent with the previous equation because E_r is proportional to the square root of P_inj. However, this is difficult to detect directly in our all-fiber setup. Our current theoretical study is studying the coherence effect in the measurements.

Periodic dynamics in which both polarizations oscillate with a frequency (2.6 GHz) very close to the relaxation oscillation frequency (2.8 GHz) is found above the upper boundary of the EPIL region. We have checked that the oscillation frequency depends on neither Δν nor P_inj. This situation is similar to the Hopf bifurcation on the EPIL steady state found in [13]. The region below the lower boundary of the EPIL zone is characterized by periodic dynamics in the parallel polarization. The frequency of this oscillation is given by |Δν|. The mechanism responsible for these oscillations is wave mixing since the beating occurs at a frequency that results from the interaction between the slave and master fields [13]. Bifurcation located in this boundary corresponds to a saddle-node bifurcation [13].

5. Conclusion

We have identified a parameter regime in which the two polarizations of the VCSEL are wavelength locked to the master laser. The power ratio of the two polarizations in this regime shows that the VCSEL is elliptically polarized. Therefore the stationary state in this regime is the so-called EPIL state. The EPIL state is found for a wide range of injection power. Within the parameter region we have explored, the EPIL states exist in a wider range of frequency detuning for higher bias currents.