Optical feedback induces polarization mode-hopping in vertical-cavity surface-emitting lasers

We study the influence of delayed optical feedback from a short external cavity (EC) on the emission dynamics of vertical-cavity surface-emitting semiconductor lasers (VCSELs). We find the emergence of pulse packages (PP) exhibiting characteristics which originate from the interplay of time-delay induced dynamics and polarization mode (PM) competition. We provide detailed analysis of the polarization dynamics applying complementary cross-correlation and spectral analysis techniques. The analysis reveals an interplay of the dynamics linked to the hierarchy of time scales present in the laser system: the fast time scale of the EC delay, the slower time scale of the PP, and the slow time scale of the polarization mode competition. For an analysis of the dynamics we provide a toolbox of methods adapted to the different relevant time scales and temporal variations of the dynamics. This complementary view unveils distinct changes in the relative oscillation phase of the two PM for increasing the injection current on both the fast and the slow time scales. Our results emphasize the significance of the polarization mode competition for PP dynamics in VCSELs, contrasting the observed behavior to what was reported for edge emitters.

The effects of optical feedback on the magnitude of the anticorrelation of polarization dynamics in vertical-cavity surface-emitting lasers (VCSELs) have been studied experimentally. The correlations are considered in the time domain and in the spectral domain. The correlation in the time domain shows that in the case of the polarization-preserved or orthogonal polarization beam optical feedback into the VCSEL a strong anticorrelation between orthogonal polarizations can arise; however, no strong anticorrelation is observed for parallel polarization optical feedback. Viewed in the frequency domain, the anticorrelation is found to be strong at low frequencies but poor at higher frequencies.

Two-mode coexistence in 1550-nm vertical-cavity surface-emitting lasers with optical feedback is experimentally investigated in detail. With the increase of the feedback strength, the two-mode coexistence region is enlarged for continually varied current. The feedback delay time has little influence on the two-mode coexistence region distribution under our experimental conditions. Moreover, a mapping of polarization-mode suppression ratio between two linear polarization (LP) modes is presented in the parameter space of the bias current and the feedback strength. In addition, the simultaneous chaos outputs of two LP modes are obtained for a certain two-mode coexistence region.

Vertical-cavity surface-emitting laser (VCSEL) has received much attention due to its high modulation response bandwidth, two linear polarization modes, and easy integration. The fundamental characteristics of lasers can be observed by simple optical feedback. Here, we experimentally investigate the dynamical characteristics in a 1550-nm VCSEL subjected to mirror optical feedback. The distribution of dynamics for different bias currents and feedback strength is in detail unveiled. Four different dynamic routes to laser chaos are observed at different bias currents. As the bias current increases, the route to chaos becomes complex. Apart from the well-known stable state, quasi-periodic state, chaotic state, and two previously reported dynamics switching phenomena, the dynamics switching between intermittently quasi-periodic state and quasi-periodic state is observed at a high bias current. Additionally, the laser chaos at different bias currents is also comparatively studied. The chaos bandwidth can reach 18 GHz. The systematic investigation provides the basis for utilizing the broadband laser chaos and understanding the nonlinear dynamics in VCSELs.

We study experimentally the dynamics of vertical-cavity surface-emitting lasers (VCSELs) with polarization-rotated (PR) optical feedback, such that the natural lasing polarization of a VCSEL is rotated by 90 deg and then is reinjected into the laser. We observe noisy, square-wave-like polarization switchings with periodicity slightly longer than twice the delay time, which degrade to (or alternate with) bursts of irregular oscillations. We present results of simulations that are in good agreement with the observations. The simulations demonstrate that close to threshold the regular switching is very sensitive to noise, while well above threshold is less affected by the noise strength. The frequency splitting between the two polarizations plays a key role in the switching regularity, and we identify wide parameter regions where deterministic and robust switching can be observed.

The optical injection dynamics of weakly index-guided vertical-cavity surface-emitting lasers (VCSELs) under single and multiple transverse modes are studied numerically. We consider the spatial dependences of the model and eliminate the spatial variables by integrating the spatially dependent rate equations over the cross section of the VCSELs' active region. Based on the simplified equations, a visual Simulink model is established. In the single-mode case, rich dynamics are observed. In the multimode case, when all modes are injected equally they exhibit similar injection-locking behaviors; however, if only one type of these modes is injected, all modes with parallel polarization are enhanced, while the other orthogonally polarized modes are suppressed greatly. It is shown further that the frequencies of those suppressed modes cannot be locked as in the case of the enhanced modes, although there are certain frequency shifts.

We propose a novel mode multiplexer based on phase plates followed by a Mach-Zehnder interferometer (MZI) with image inversion. After the higher-order modes are selectively converted from fundamental linear-polarized (LP) modes by the phase plates, the converted modes are coupled without fundamental loss using MZI with image inversion, in which the original spatial pattern and inverted pattern of the optical signal are interfered. Our scheme is also applicable to the coupling of degenerated LP modes such as LP(11a) and LP(11b). First, we numerically and experimentally evaluate the performance of the mode converter based on phase plates. The mode converter is suitable as long as the five LP modes such as LP(01), LP(11ab) and LP(21ab) are sustained in a few-mode fiber (FMF), although the crosstalk due to excitation of undesirable modes is unavoidable when the higher-order modes over LP(02) are sustained in FMF. Next, we develop and characterize the proposed mode multiplexers based on phase plates and MZIs with image inversion. The insertion loss is suppressed to around 3 dB for mode multiplexing of LP(11a) and LP(11b). Using a fabricated mode multiplexer for LP(31a) and LP(31b), we measure the bit-error rate performance of single-polarization mode-multiplexed quadrature-phase shift keying optical signals.

Using two orthogonal polarization mode outputs from a vertical-cavity surface emitting lasers (VCSEL) with double optical feedback as two chaotic carriers, a dual-channel chaos secure communication system is established, and the synchronization and communication performances of such a system are numerically investigated. The results show that under suitable operated condition, the time-delay signatures of two chaotic carriers originating from two linear polarization modes in the T-VCSLE with double optical feedback can be suppressed efficiently. Under the strong injection locking case, high-quality chaos synchronization between two corresponding modes of T-VCSEL and R-VCSEL can be realized by polarization-preserved optical injection from T-VCSEL to R-VCSEL. Moreover, the tolerance of the synchronization quality on the frequency detuning between T-VCSEL and R-VCSEL is enhanced with the increase of the injection strength. Adopting additive chaos modulation encryption scheme, two pieces of 500 Mbit/s encoded message can be hidden efficiently in the two chaotic carriers in the propagation process and can be successfully extracted at the receiver. Although Q factor decreases with the increase of message transmission rate, the values of Q factor for two channels are still larger than 6 for 6 Gbit/s message.

Random source is important for the security of key distribution. In this paper, a novel secure key distribution scheme based on unidirectional injection of vertical cavity surface emitting laser (VCSEL) system is proposed. In the proposed scheme, a chaotic signal without time delay signature is generated by a VCSEL subject to unidirectional optical injection, which is regarded as a master laser. The chaotic signal generated by the master VCSEL is further injected into two slave VCSELs to obtain synchronized bandwidth-enhanced chaotic signals. After that, by sampling, quantizing and XOR operation on the two synchronized chaotic signals, two key streams can be obtained. Based on the well-known spin-flip model, the time delay signature of chaotic signals generated by master VCSEL and the synchronization performance between the master VCSELs and two slave VCSELs are numerically investigated in detail. It is shown that by the unidirectional injection, the chaotic outputs can be achieved in the master VCSEL in a wide range of frequency detuning and coupling strength. More importantly, no time delay signature can be observed in the auto correlation function of the chaotic intensity time series generated by the master VCSEL. Besides, we find that high quality synchronization is achieved between the bandwidth-enhanced chaotic signals generated by two slave VCSELs under the common driving of master VCSEL. The synchronization coefficient between two slave VCSELs increases up to 0.99, and the synchronization coefficient between master VCSEL and salve VCSEL is only 0.74. Note that such a high quality synchronization between two slave VCSELs while relatively low quality synchronization between the master and slave VCSEL is conducible to ensuring the security of key distribution. In addition, the effects of tunable parameters on key bit error rate are considered, and two quantization methods are employed for comparison. Numerical simulation results show that the key bit error rate between two legitimate users is as low as 1%, and the key bit error rate between legitimate user and eavesdropper is higher than 10% in the single-threshold case; the bit error rate can even be as low as 10-6 in the double-threshold case. The influence of parameter mismatch on key bit error rate is also discussed, and it is suggested that two salve VCSELs should be finely matched to ensure low bit error rate. Finally, NIST randomness test is performed for the generated key streams. Hence, the proposed scheme enhances the security of key distribution, which is valuable for further developing the chaos communication systems.

We study the dynamics of vertical-cavity surface-emitting lasers (VCSELs) with direct current modulation in the framework of a model for index-guided VCSELs that takes into account two orthogonal linear polarizations. We analyze the effect of current modulation near the polarization switching (PS) of type I, from the high to the low frequency polarization, and near the PS of type II, from the low to the high frequency polarization. We find that the oscillations of the total power are as those of a single-mode laser, unaffected by the underlaying polarization coexistence or polarization competition. We also study the small-signal modulation response in the Fourier domain, for modulation dc values near the PS point. Close to type I PS the response of the total power as well as the response of the orthogonal polarizations has the same functional dependency on the modulation frequency, and can be fitted by the response function of a single-mode laser. Close to type II PS, polarization competition is a significant process at low modulation frequencies. The polarization-resolved modulation response displays features at low frequencies that are not present in the response of the total power, which is as that of a single-mode laser. The dynamics becomes increasingly complex as the modulation amplitude grows, and there is multistability of solutions.

As a key part of vertical cavity surface emitting laser (VCSEL), active region will seriously affect the threshold and efficiency of the device. To obtain the appropriate laser wavelength and material gain, the design of In<sub>0.18</sub>Ga<sub>0.82</sub>As strain compensated quantum well is optimized. The relationship between the lasing wavelength of multiple quantum wells (MQWs) and the thickness is calculated. Considering the influence between the active region temperature and the lasing wavelength, the thickness of the quantum well is chosen as 6 nm, and the quantum barrier thickness is chosen as 8 nm, corresponding to the lasing wavelength of 929 nm. The material gain characteristics of the MQWs at different temperatures are simulated by Rsoft. The material gain exceeds 3300/cm at 300 K, and the temperature drift coefficient of the peak wavelength is 0.3 nm/K. In this work, Al<sub>0.09</sub>Ga<sub>0.91</sub>As and A<sub>l0.89</sub>Ga<sub>0.11</sub>As are chosen as the high- and the low-refractive index material of distributed Bragg reflector (DBR), and 20 nm graded layer is inserted between two types of materials. The influence of the graded layer thickness of DBR on the valence band barrier and reflection spectrum are calculated and analyzed. The increase of graded layer thickness can lead the band barrier peak and the reflection spectrum bandwidth to decrease. The reflection spectrum and phase spectrum of P-DBR and N-DBR are calculated by the transmission matrix mode (TMM): the reflectance of DBR is over 99% and the phase shift is zero at 940 nm. The optical field distribution of the whole VCSEL structure is simulated, in which the standing wave peak overlaps with the active region, and the maximum gain can be obtained. Using the finite element method (FEM), the effect of oxidation confined layer on the injection current is simulated. The current in the active region is effectively limited to the position corresponding to the oxidation confined hole, and its current density is stronger and more uniform. The optical field distributions in different modes of photonic crystal-vertical cavity surface emitting laser (PC-VCSEL) are simulated, and different modes have different resonant wavelengths. The values of quality factor Q in different modes of VCSEL and PC-VCSEL are calculated, Q of the fundamental mode is higher than that of higher transverse mode. It is demonstrated that the photonic crystal air hole structure can realize the output of basic transverse mode by increasing the loss of high order transverse mode. The VCSEL and PC-VCSEL with oxidation hole size of 22 μm are successfully fabricated, in which the photonic crystal period is 5 μm, the air pore diameter is 2.5 μm, and the etching depth is 2 μm. Under continuous current test, the maximum slope efficiency of VCSEL is 0.66 mW/mA, the output power is 9.3 mW at 22 mA, and the lasing wavelength is 948.64 nm at 20 mA injection current. Multiple wavelengths and large spectrum width are observed in the spectrum of VSCEL, which is an obvious multi-transverse mode. The maximum fundamental transverse mode output of PC-VCSEL reaches 2.55 mW, the side mode suppression ratio (SMSR) is more than 25 dB, and the spectrum width is less than 0.2 nm, indicating that the photonic crystal air hole has a strong control effect on the transverse mode, and the laser wavelength is 946.4 nm at 17 mA.

A vertical-cavity surface-emitting laser (VCSEL) is easily made into a two-dimensional array to improve its output power. However, if the near-field complex amplitude output cannot be stabilized in the lowest supermode generated by the fundamental transverse mode, the spot cannot converge on the center normal of the far-field array geometry, and the energy will be diverged. The external cavity is prepared for the VCSEL array, and the output of the array can be stabilized in the lowest order supermode generated by the fundamental transverse mode by supermode control through diffraction coupling. In this study, the parallel-coupled model for the 2-dimensional VCSEL array based on Fresnel diffraction integration was established and used to numerically calculate and analyze the influence on the supermodes’ thresholds of different array distributions, array elements’ transverse modes and duty ratios versus the length of the external cavity. The simulation results show that the square array provides a wider range of external cavity control length (0.2d2/λ and approximately 0.9 to 1.0d2/λ). The lowest supermode of the fundamental transverse mode can be outputted. For the regular hexagonal array with the length of the external cavity of 0.15d2/λ and 0.6d2/λ. The results have important reference significance for the design of an external cavity VCSEL array, which can control the supermode and obtain VCSEL coherent array beams with high power and near diffraction limits.

We experimentally demonstrate multi-channel physical random bits (PRBs) generation by utilizing chaotic outputs from two linear polarization modes in a vertical-cavity surface-emitting laser (VCSEL) under a chaotic optical injection. The polarization-resolved chaotic signal is obtained with a master-VCSEL subject to optical feedback, and then injects into a slave-VCSEL for driving its two linear polarization modes into chaotic state. We analyze the influences of injection parameters on bandwidth, complexity, and the correlation of two-channel chaotic signals. By using the two chaotic signal outputs from the slave-VCSEL under optimized parameters as entropy sources, we have obtained the PRBs at the dual-channel rate of 160 Gbits/s by adopting the $m$ least significant bits extraction with logical exclusive-OR (XOR) post-processing. Further utilizing the $n$ -bit cross-merging method, the PRB at a rate of 320 Gbits/s could be obtained.

Recent works have shown the possibility to control through optical injection frequency combs generated by gain switching in Vertical-Cavity Surface-Emitting Lasers (VCSELs) [1] . The opposite situation, in which VCSEL is subject to injection of an optical frequency comb (OFC) deserves close attention and has not been addressed so far. In this work, we analyze the nonlinear polarization dynamics of a single-mode VCSEL with optical injection. Here, we select and reveal several bifurcations scenarios leading to generation of a two polarization OFC.

We report explicit analytical and numerical results for the polarization resolved intensity noise of vertical-cavity surface-emitting lasers operating in the fundamental transverse mode. We describe the fluctuations of the linear and circular polarization components of linearly polarized states on both sides of a nonthermal polarization switching. Our description is valid for small and large birefringence and arbitrary values of the spin flip rate, giving a complete description of the role of these parameters. Normalized cross-correlation functions for both linear and circular components are discussed in detail. They show different degrees of anticorrelated fluctuations in different frequency ranges.