Chaos synchronization in vertical-cavity surface-emitting laser based on rotated polarization-preserved optical feedback.

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.

We numerically investigate the performance of Chinese herbal medicine (CHM) recognition using a time delay reservoir computing (TDRC) system consist of a vertical-cavity surface-emitting laser (VCSEL) subjected to optical feedback. A database of 960 images from 12 CHM categories is used to evaluate the recognition performance, most of which contain many CHM samples and have different backgrounds. The CHM image feature vector is masked and optically injected into the VCSEL, and the VCSEL output in two polarization modes are sampled as the virtual node states for readout. After testing the CHM recognition performance of TDRC under injecting the same information into two polarization modes of the VCSEL, we further test the performance of parallel processing by injecting half of the image information into each of the two polarization modes. By concatenating the virtual node states collected from two modes for readout, the recognition speed is doubled. Meanwhile, the influence of key parameters on recognition performance are investigated and the relationship between system idle state and recognition performance is also examined. The results show that, under parallel processing and orthogonal optical feedback, the TDRC achieves the minimum recognition error of 1.7% at a reservoir processing rate of 2×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">9</sup> images per second.

Semiconductor laser diodes are popular and widely-used sources due to their high power, low cost, tunability, and easy integration with miniaturized electronics. They can also serve as flexible signal sources of high-frequency oscillations and pulsations. To generate waveforms while taking advantage of their high frequency capabilities, all-optical feedback methods are often simpler to use than high-speed electronics, which can be costly, inefficient, or operationally limited. In this context, a square-wave signal is a particularly useful waveform, since its rising and falling edges require high-frequency components in their creation. One method that can generate square waves from diode lasers is polarization self-modulation, meaning that the laser output switches regularly between its two natural polarization modes rather than simply switching on and off in total intensity. This self-modulation can be achieved entirely optically by injecting light from one laser polarization mode into the orthogonal mode. This requires that the optical feedback be rotated from its original orientation by some means, typically a waveplate. Square-wave operation has been observed in vertical-cavity surface-emitting lasers (VCSELs), but can be difficult to achieve: the specific VCSEL characteristics or operating parameters that are required for such outputs are not well-understood. Another limitation is that, if the feedback path is short, the VCSEL will exhibit chaotic fluctuations rather than regular square waves. In edge-emitting lasers however, short feedback delays still allow square-wave operation. In these devices, one polarization mode is typically suppressed, and accordingly requires relatively strong feedback to be activated. Our recent work has explored the dynamical mechanisms of this Figure 1. Top: Schematic of our experimental apparatus showing the laser diode feedback elements (blue) and the detection system components (green). Bottom: sample square-wave data.

Vertical Cavity Surface Emitting Lasers (VCSELs) with isotropic optical feedback are studied especially in the so-called low frequency fluctuations regime. Correlation properties between linear polarizations are analyzed both analytically and numerically. The RF spectrum shows a double peak structure close to the external cavity frequency which can be predicted by our adapted Spin-Flip Model (SFM). We provide here numerical evidence of the interplay between modes and anti- modes which are solutions of the stability analysis of the VCSEL with feedback and demonstrate that this interplay is responsible for the double peak structure.

In this paper, the influence of variable-angle polarization-rotated optical feedback on the polarization switching properties of vertical-cavity surface-emitting lasers (VCSELs) is investigated theoretically and experimentally. The optical feedback (OF) level and the rotated polarization angle $\theta _{p}$ of OF are considered. Two configurations of OF are used to re-injected parallel and orthogonal polarization modes back into the VCSEL. For the parallel OF, it is shown that polarization switching (PS) of VCSELs’ modes can occur at a fixed feedback level and bias current with variable $\theta _{p}$ . However, in case of orthogonal optical feedback, PS occurs only at certain values of $\theta _{p}$ , particularly when the intensities of two polarization modes become comparable with each other. In the theoretical model for both OF conditions, there is good agreement between the experimental measurements and recent theoretical results reported in the literature.

Based on the spin-flip model (SFM), we theoretically investigate the dynamics of a vertical-cavity surface-emitting laser (VCSEL) subject to optical injection and positive optoelectronic feedback. The results show that under the joint action of positive optoelectronic feedback and optical injection from a master VCSEL (M-VCSEL), two polarization modes of a slave VCSEL (S-VCSEL) will show many dynamic states such as period one, period two, multi-period and chaos, and the evolution routes of these states are different for two polarization modes. Mapping of dynamic region as a function of feedback strength f and injection strength is varied with frequency detuning between M-VCSEL and S-VCSEL (=m-s, where m ands are the free-running frequencies of M-VCSEL and S-VCSEL, respectively). Compared with the case for zero or negative frequency detuning, the region of chaotic state is expanded significantly under positive . For a fixed , the influences of f and on the chaotic bandwidth of S-VCSEL are discussed. Through selecting proper f and , chaotic bandwidth of S-VCSEL can be improved obviously.

This paper provides an experimental investigation of the polarization stabilization at the output power of an 850 nm vertical-cavity surface-emitting laser (VCSEL) with optical feedback (OF) and a range of polarization angles, OF strength, and the bias current. The VCSEL's polarization stabilization is evaluated using the extinction ratio measurements of the optical output power of the polarization modes of the VCSEL. The results clearly show that rotation of the polarization angle and the OF level can radically change the polarization stabilization of the VCSEL. Both the polarization angle and OF introduce polarization switching (PS) and instability in the optical output power of the VCSEL. Consequently, these lead to performance degradation of the VCSEL in terms of the operating point and the modulation bandwidth. At a fixed OF level of −7 dB, polarization destabilization is first observed at 45° with the increasing level of polarization angle, whereas for the fixed polarization angles of 40° and 90°, polarization destabilization is observed at −14.5 dB and −14 dB, respectively, with the increasing level of orthogonal OF. We show that, with parallel OF, no PS is observed over the entire OF level. The results also indicate that the VCSEL with no polarization angle requires higher levels of OF in order to ensure PS compared with the case with the polarization angle.

Based on the framework of the spin-flip model (SFM) for GHz level modulation frequency, the polarization performances of current-modulated vertical-cavity surface-emitting lasers (VCSELs) subject to weak optical feedback have been theoretically investigated. The results show that, for type 1 polarization switching (PS), the influences of optical feedback intensity and the current modulation amplitude on the high-frequency modulation response is not obvious. For low-frequency modulation, optical feedback will result in the output of a VCSEL having rich dynamics. A new style PS can be obtained under large-signal modulation through adjusting the modulation frequency. For type 2 PS the situation is more complex, and optical feedback increases the probability of polarization conversion and competition, while also affecting the PS point. The modulation amplitude also affects the output dynamics of the VCSEL.

The generation mechanism of self-sustained pulsation in vertical cavity surface emitting lasers is analyzed theoretically. The influence of self-focusing, diffraction loss as well as optical feedback is taken into consideration. It is shown that the condition of self-sustained pulsation can be modified significantly by optical feedback. In addition, it is possible to obtain self-sustained pulsation in vertical cavity surface emitting lasers by using external mirror.

We numerically investigate how polarization properties of vertical cavity surface emitting lasers (VCSELs) are affected by optical feedback from an extremely short external cavity. In order to do it we use a two modes rate equation model that accounts for infinite round trips in the external cavity. With it we perform maps of bistability finding out a modulation of the polarization switching currents when increasing the external cavity length with a period equal to half the wavelength of operation of the device. When the external mirror reflectivity is high enough there is a region within each period of modulation where the VCSEL polarization is stable at any injected current within the operation range. Moreover, using polarized feedback the map of bistability is channelled and the bistable region is almost suppressed. A preliminar study of the effects of temperature variations on the map of bistability is also carried out and presents polarized feedback as a more robust technic to obtain polarization stabilization. An experimentally obtained map of bistability supports the model showing very good agreement with it.

We introduced the vertical cavity surface emitting laser (VCSEL) as the laser diode in tour external cavity system. Because VCSELs are now commercially available, and the External cavity diode laser (ECDL) systems using them are expected to improve their frequency stability, we have replaced a Fabry-Perot type laser diode with a VCSEL, and examined its oscillation-frequency stability. Therefore we were able to expect that the VCSELs with our double optical feedback system have good oscillation frequency stability. The obtained VCSEL's oscillation-frequency stability, i.e., the square root of Allan variance &sigma; was 4&times;10^-10, at an averaging time of &tau;=1 sec.

The effect of isotropic optical feedback from an extremely short external cavity on the emission properties of vertical-cavity surface-emitting lasers (VCSELs) is experimentally investigated. When changing the external cavity length a modulation of the total power and the wavelength emitted by the VCSEL is observed with a period of half the wavelength of operation of the device. When biasing the VCSEL around its solitary (without optical feedback) polarization switching (PS) current, PS between the two linearly polarized modes is observed by changing the external cavity length. This PS is found to occur through a hysteresis region. Our experimental results show a modulation of the PS currents and the hysteresis width when changing the external cavity length with a period of half the wavelength of operation. The experimental results are well explained by a two mode rate equation model.

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.

The polarization of vertical-cavity surface-emitting laser (VCSEL) can be controlled by electro-optic birefringence. We calculated the birefringence resulted from external electric field which was imposed on the top DBR of VCSEL by assuming that the two polarization modes were in the same place of the gain spectra in the absence of electric field beginning. By modifying SFM, the affection of the electric field strength on the polarization switching currents between the two polarization modes had been shown.

Based on the chaos synchronization between two pairs of corresponding linear polarization modes in two 1550 nm vertical-cavity surface-emitting lasers (1550 nm-VCSELs) subject to optical injection of common chaotic signals, a novel bidirectional and dual-channel long-distance chaos secure communication system is proposed. The chaotic synchronization characteristics, bidirectional dual-channel communication performance, and the influences of the fiber channel on the message transmission are numerically investigated. Results show that, driven by a common chaotic signal generated from a driver VCSEL (D-VCSEL), two pairs of responding linear polarization modes in two response 1550nm-VCSELs (R-VCSELs) can be synchronized completely and isochronally. Meanwhile, the synchronization coefficients between the two pairs of responding linear polarization modes in D-VCSEL and R-VCSELs are low. Based on the high quality chaos synchronization between two pairs of responding linear modes in two R-VCSELs, bidirectional and dual-channel chaos secure communication can be achieved. After adopting a single mode polarization-maintaining fiber (or dispersion-shifted polarization-maintaining fiber), for 2.5 Gbit/s messages, the Q factor of the decryption signals after transmitting 60 km (or 200 km) can be more than 6.