Period-one Nonlinear Dynamics Research Articles

Entropy analysis on chaos excited through destabilization of semiconductor lasers at period-one nonlinear dynamics for physical random number generation

This study analyzes entropy of broadband chaos excited in a semiconductor laser subject to intensity-modulated optical injection for random number generation with guaranteed unpredictability. It is identified that the flattening of spectral profile around the laser relaxation resonance blurs the periodicity it brings, and thus leads to a high entropy value and a high random number generation rate. The effect of measurement device noise on entropy suggests that both the power of chaos needs to be kept at a level to achieve an adequate signal-to-noise ratio, 24 dB or more, and the entropy contribution of the measurement device noise is excluded in order to assert entropy that can be extracted solely from the intrinsic property of chaos. The effect of data sampling rate on entropy shows that entropy reaches its maximum at the Nyquist rate, which is two times the standard bandwidth of chaos, and the rate of change in entropy is much slower than that in sampling rate as the sampling rate varies, which leads to the dominance of the sampling rate, not entropy, in determining the random number generation rate. It is highly likely that modest oversampling (i.e., a sampling rate modestly higher than the Nyquist rate) gives rise to a higher random number generation rate while entropy slightly decreases.

All-optical, tunable, V- and W-band microwave generation using semiconductor lasers at period-one nonlinear dynamics with asymmetric mutual injection stabilization.

This study investigates an optically injected semiconductor laser operating at period-one nonlinear dynamics for all-optical microwave generation. A novel, to the best of our knowledge, all-optical stabilization scheme is proposed to greatly enhance the spectral purity of such generated microwaves, which sends a small fraction of the injected laser output back to the injecting laser, not the injected laser itself. Mutual injection with highly different injection power between the two lasers, i.e., highly asymmetric mutual injection, is thus formed. As a result, the microwave linewidth is reduced by up to at least 85 times, the phase noise variance is improved by up to at least 750 times, and a side-peak suppression ratio of more than 44 dB is achieved. Microwave generation that is tunable up to at least 110 GHz with a 3-dB linewidth down to below 2 kHz is realized.

Period-One Laser Dynamics for Photonic Microwave Signal Generation and Applications

Due to the advantages of rich dynamics, small size, and easy integration, semiconductor lasers have many applications in microwave photonics. With a proper perturbation to invoke period-one (P1) nonlinear laser dynamics, a widely tunable microwave signal can be generated. In this paper, we concentrate on the realization and application of photonic microwave signal generation based on the P1 oscillation state of semiconductor lasers. Recent developments in P1 dynamics-based tunable microwave signal generation techniques are reviewed with an emphasis on the optical injection system, which has a large frequency tuning range that is far beyond the intrinsic relaxation oscillation frequency. In order to improve the spectral purity and stability of the generated microwave signal, two typical approaches are introduced, i.e., microwave modulation stabilization, and delayed feedback stabilization. Various applications of the P1 dynamics-based microwave signal generator in diverse signal generation and photonic microwave signal processing are described. Development trends of the P1 dynamics-based photonic microwave signal generator are also discussed.

Effects of the linewidth enhancement factor on the microwave linewidth of the period-one oscillations of optically injected semiconductor lasers.

We investigate the microwave linewidth of the period-one (P1) nonlinear dynamics of an optically injected semiconductor laser as a function of the linewidth enhancement factor. Under proper conditions of optical injection, the destabilizing effect of a large value of the linewidth enhancement factor of the injected semiconductor laser is found to be unexpectedly suppressed in the P1 oscillation of the laser, thus resulting in a narrow P1 linewidth equal to that generated by a laser of a small linewidth enhancement factor. By properly choosing the operating point, P1 oscillations with microwave linewidths that are an order of magnitude narrower than the free-running optical linewidths of the master and slave lasers are observed.

Optical chaos generated in semiconductor lasers with intensity-modulated optical injection:a numerical study

We numerically report on an optical chaos signal generation scheme based on a semiconductor laser subject to intensity-modulated (IM) optical injection. In this scheme, the characteristics of the chaos signal obtained by destabilizing period-one nonlinear dynamics are numerically investigated. With the aid of bifurcation diagrams and the 0-1 tests for chaos, the chaotic dynamics excited by continuous-wave and IM optical injection are located, and the effects of injection and modulation parameters on chaotic regions are illustrated. Moreover, effective bandwidths and auto-correlation characteristics of chaos signals from the IM optical injection system are systematically investigated. The results show that although chaotic signals under the IM optical injection scenario have a limitation in unambiguous range detection in most parameter regions, wideband chaotic dynamics in large injection and modulation parameter regions can be easily achieved. This study paves the way for potential applications requiring no time-delay signature and broad bandwidth chaos, such as high-speed chaos communications and random bit generation.

V- and W-band microwave generation and modulation using semiconductor lasers at period-one nonlinear dynamics.

Microwave generation and modulation over the V- and W-bands are investigated using a semiconductor laser subject to both comb-like optical injection and direct modulation. The former not only excites period-one (P1) nonlinear dynamics for tunable microwave generation but also improves the stability and purity of such generated microwaves. The latter upconverts data onto the generated microwaves by superimposing the data effectively only onto the lower oscillation sideband of the P1 dynamics, which prevents the data from dispersion-induced degradation over fiber distribution. As a result, microwaves that are continuously tunable from 40 to 110 GHz with a 3-dB linewidth of less than 1 Hz and with phase noise better than -95dBc/Hz at 10-kHz offset are generated. A bit-error ratio better than the forward error correction limit, 3.8×10-3, is achieved for 12-Gb/s 16-quadrature amplitude modulation data after 25-km fiber distribution.

Broadband chaotic microwave generation through destabilization of period-one nonlinear dynamics in semiconductor lasers for radar applications.

This Letter studies a photonic approach for chaotic microwave generation through destabilization of period-one (P1) nonlinear dynamics in a semiconductor laser subject to intensity-modulated (IM) optical injection. Chaos can be excited when the modulation sideband perturbation carried by the IM optical injection is a few gigahertz higher than the lower oscillation sideband of the P1 dynamics. As a result, chaotic microwaves with a spectral distribution of more than 50 GHz and a bandwidth of about 33 GHz are generated without any time-delay signature or modulation-induced peak. Such features provide the generated chaotic microwaves with preferable characteristics for radar applications, including high detection resolution, superior detection unambiguity, strong anti-jamming capability, and simultaneous multi-band detection.

Linewidth characteristics of period-one dynamics induced by optically injected semiconductor lasers.

Period-one (P1) nonlinear dynamics of optically injected semiconductor lasers exhibit periodic intensity fluctuations with operating frequencies that are tunable in the micro/millimeter-wave range. Through numerical experiments, the characteristics of the microwave linewidth of the P1 oscillation and the linewidths of its optical frequency components due to intrinsic laser noise sources are investigated. The field noise and carrier noise of the master and slave lasers are systematically considered. The contribution of the field noise of the master laser is significant; it considerably broadens the microwave linewidth of the P1 oscillation. When the operating conditions in the regions of high microwave power are properly adjusted, the microwave linewidth of the P1 oscillation becomes narrower than the free-running optical linewidths of the master and slave lasers. Regions with low sensitivity to time-dependent fluctuations in an operating parameter show reduced microwave linewidth of the P1 oscillation.

Photonic microwave harmonic down-converter based on stabilized period-one nonlinear dynamics of semiconductor lasers.

Photonic microwave harmonic down-conversion is demonstrated using an optically injected semiconductor laser operating at period-one (P1) nonlinear dynamics. In this method, the P1 oscillation is stabilized through low-frequency local oscillator signal modulation, thus generating high-order harmonics in the optical domain. Meanwhile, a radio-frequency (RF) signal is received by an intensity modulator. After the subsequent optical heterodyning, photonic microwave harmonic down-conversion can be realized. In the proof-of-concept experiment, the 4th, 6th, 9th, and 12th harmonic down-conversions are demonstrated; i.e., an RF signal with a frequency of 39GHz is down-converted to frequency-tunable intermediate frequency (IF) signals within 2GHz. The resultant IF signal mainly holds the microwave linewidth and phase noise comparable to those of the original high-frequency one.

Frequency-modulated continuous-wave microwave generation using stabilized period-one nonlinear dynamics of semiconductor lasers.

Frequency-modulated continuous-wave (FMCW) microwave generation is studied using a semiconductor laser operating at stabilized period-one (P1) nonlinear dynamics when subject to comb-like (CL) optical injection. The phase locking established between the P1 dynamics and the CL optical injection not only improves the P1 oscillation stability considerably but also provides a mechanism to change the P1 oscillation frequency through varying the modulation frequency of the CL optical injection. As a result, a stable FMCW microwave at a central frequency of up to 40GHz is generated with its frequency varying linearly, triangularly, or step-wisely over a range of 4GHz during a repeated time period that can be reconfigured at least from 100ns to 10ms. This system is capable of operation up to at least 100GHz.

Doppler-free coherent detection using period-one nonlinear dynamics of semiconductor lasers for OFDM-RoF links.

This study investigates coherent detection that is free from the Doppler frequency shift effect for orthogonal frequency division multiplexing radio-over-fiber (OFDM-RoF) links using period-one (P1) nonlinear dynamics of semiconductor lasers. Even under a dynamically time-varying Doppler frequency shift of up to 100kHz, corresponding to a relative motion between a transmitter and a receiver with a velocity of more than 3850km/h at 28GHz, the microwave carrier of a received OFDM-RoF signal can be successfully regenerated instantaneously and uninterruptedly with its phase highly preserved through the P1 dynamics. No carrier frequency offset (CFO) due to the Doppler frequency shift effect happens if the regenerated microwave carrier is used as a microwave local oscillator for coherent detection of the received OFDM-RoF signal. As a result, a bit-error ratio of around 10-9 is achieved for coherent detection of a 28GHz OFDM-RoF signal carrying 4Gb/s 16-quadrature amplitude modulation data. Thus, no digital signal processing, either photonic or electronic, is required to compensate for such a CFO. This all-optical system is capable of operation up to at least 100GHz.

Optical double-locked semiconductor lasers

Abstract Self-sustained period-one (P1) nonlinear dynamics of a semiconductor laser are investigated when both optical injection and modulation are applied for stable microwave frequency generation. Locking the P1 oscillation through modulation on the bias current, injection strength, or detuning frequency stabilizes the P1 oscillation. Through the phase noise variance, the different modulation types are compared. It is demonstrated that locking the P1 oscillation through optical modulation on the output of the master laser outperforms bias-current modulation of the slave laser. Master laser modulation shows wider P1-oscillation locking range and lower phase noise variance. The locking characteristics of the P1 oscillation also depend on the operating conditions of the optical injection system

Numerical study of ultrashort-optical-feedback-enhanced photonic microwave generation using optically injected semiconductor lasers at period-one nonlinear dynamics.

This study numerically investigates the enhancement of photonic microwave generation using an optically injected semiconductor laser operating at period-one (P1) nonlinear dynamics through ultrashort optical feedback. For the purpose of practical applications where system miniaturization is generally preferred, a feedback delay time that is one to two orders of magnitude shorter than the relaxation resonance period of a typical laser is emphasized. Various dynamical states that are more complicated than the P1 dynamics can be excited under a number of ultrashort optical feedback conditions. Within the range of the P1 dynamics, on one hand, the frequency of the P1 microwave oscillation can be greatly enhanced by up to more than three folds. Generally speaking, the microwave frequency enhances with the optical feedback power and phase, while it varies saw-wise with the optical feedback delay time. On the other hand, the purity of the P1 microwave oscillation can be highly improved by up to more than three orders of magnitude. In general, the microwave purity improves with the optical feedback power and delay time, while it only varies within an order of magnitude with the optical feedback phase. These results suggest that the ultrashort optical feedback provides the optically injected laser system with an extra degree of freedom to manipulate/improve the characteristics of the P1 microwave oscillation without changing the optical injection condition.

Photonic microwave carrier recovery using period-one nonlinear dynamics of semiconductor lasers for OFDM-RoF coherent detection.

This study investigates an all-optical scheme based on period-one (P1) nonlinear dynamics of semiconductor lasers, which regenerates the microwave carrier of an orthogonal frequency division multiplexing radio-over-fiber (OFDM-RoF) signal and uses it as a microwave local oscillator for coherent detection. Through the injection locking established between the OFDM-RoF signal and the P1 dynamics, frequency synchronization with highly preserved phase quality is inherently achieved between the recovered microwave carrier and the microwave carrier of the OFDM-RoF signal. A bit-error ratio down to 1.9×10^-9 is achieved accordingly using the proposed scheme for coherent detection of a 32-GHz OFDM-RoF signal carrying 4 Gb/s 16-quadrature amplitude modulation data. No electronic microwave generators or electronic phase-locked loops are thus required. The proposed system can be operated up to at least 100GHz and can be self-adapted to certain changes in the operating microwave frequency.

Photonic microwave stabilization for period-one nonlinear dynamics of semiconductor lasers using optical modulation sideband injection locking.

Photonic microwave generation using period-one nonlinear dynamics of semiconductor lasers suffers from poor spectral purity. A stabilization approach based on optical modulation sideband injection locking is investigated. An optical signal carrying a highly correlated modulation sideband comb simultaneously injection-locks the regeneration of the optical carrier and the lower oscillation sideband in the dynamics, establishing a phase-locking between the two spectral components. A linewidth of below 1 Hz is therefore achieved for microwave generation up to at least 40 GHz. Because of the frequency multiplication in yielding the comb-like optical signal, only an electronic microwave reference at the tenth subharmonic or higher of the generated microwave frequency is required.

Subharmonic Microwave Modulation Stabilization of Tunable Photonic Microwave Generated by Period-One Nonlinear Dynamics of an Optically Injected Semiconductor Laser

We have proposed and experimentally demonstrated a novel approach to stabilize the photonic microwave generated by the period-one (P1) nonlinear dynamics of an optically injected semiconductor laser by introducing external subharmonic microwave modulation technique. External optical injection first drives a semiconductor laser into single sideband (SSB) P1 nonlinear dynamics whose frequency can be tuned by varying the optical injection strength, and then an external subharmonic microwave modulation is applied to the laser for stabilizing the frequency of the P1 oscillation. The experimental results show that after adopting 1/3 and 1/4 subharmonic microwave modulation, significant reduction up to more than three orders of magnitude of generated microwave linewidth can be achieved. Furthermore, we have analyzed the linewidth narrowing effects under subharmonic modulation with different powers and frequencies, and mapped the subharmonic microwave locking region in the parameter space of the power and frequency of the external subharmonic microwave.

Optical feedback stabilization of photonic microwave generation using period-one nonlinear dynamics of semiconductor lasers.

Effects of optical feedback on period-one nonlinear dynamics of an optically injected semiconductor laser are numerically investigated. The optical feedback can suppress the period-one dynamics and excite other more complex dynamics if the feedback level is high except for extremely short feedback delay times. Within the range of the period-one dynamics, however, the optical feedback can stabilize the period-one dynamics in such a manner that significant reduction of microwave linewidth and phase noise is achieved, up to more than two orders of magnitude. A high feedback level and/or a long feedback delay time are generally preferred for such microwave stabilization. However, considerably enhanced microwave linewidth and phase noise happen periodically at certain feedback delay times, which is strongly related to the behavior of locking between the period-one microwave oscillation and the feedback loop modes. The extent of these enhancements reduces if the feedback level is high. While the microwave frequency only slightly changes with the feedback level, it red-shifts with the feedback delay time before an abrupt blue-shift occurs periodically. With the presence of the laser intrinsic noise, frequency jitters occur around the feedback delay times leading to the abrupt blue-shifts, ranging from the order of 0.1 GHz to the order of 1 GHz.

Photonic microwave amplification for radio-over-fiber links using period-one nonlinear dynamics of semiconductor lasers

For radio-over-fiber links, microwave-modulated optical carriers with high optical modulation depth are preferred because high optical modulation depth allows generation of high microwave power after photodetection, leading to high detection sensitivity, long transmission distance, and large link gain. This study investigates the period-one nonlinear dynamics of semiconductor lasers for optical modulation depth improvement to achieve photonic microwave amplification through modulation sideband enhancement. In our scheme, only typical semiconductor lasers are required as the amplification unit. The amplification is achieved for a broad microwave range, from less than 25 GHz to more than 60 GHz, and for a wide gain range, from less than 10 dB to more than 30 dB. The microwave phase quality is mainly preserved while the microwave power is largely amplified, improving the signal-to-noise ratio up to at least 25 dB. The bit-error ratio at 1.25 Gbits/s is better than 10(-9), and a sensitivity improvement of up to at least 15 dB is feasible.

Optical double-sideband modulation to single-sideband modulation conversion using period-one nonlinear dynamics of semiconductor lasers for radio-over-fiber links

To distribute microwaves over fibers, optical single-sideband (SSB) modulation signals are preferred to optical double-sideband (DSB) modulation signals. This study investigates an optically injected semiconductor laser at period-one nonlinear dynamics for optical DSB-to-SSB conversion. For the operating microwave frequencies up to 40 GHz investigated in this study, the proposed system regenerates or even enhances the microwave features of an optical DSB input while converting its optical feature into SSB with an intensity difference of at least 20 dB. The bit-error ratio at 622 Mb/s is down to 10(-9) with a sensitivity improvement of up to 3 dB. The proposed system can be self-adapted to certain changes in the operating microwave frequency and can operate stably under certain fluctuations in the input optical power and frequency.

Tunable photonic microwave generation using optically injected semiconductor laser dynamics with optical feedback stabilization

The period-one (P1) nonlinear dynamics of a semiconductor laser subject to both optical injection and optical feedback are investigated for photonic microwave generation. The optical injection first drives the laser into P1 dynamics so that its intensity oscillates at a microwave frequency. A dual-loop optical feedback then stabilizes the fluctuations of the oscillation frequency. Photonic generation at 45.424 GHz is demonstrated with a linewidth below 50 kHz using a laser with a relaxation resonance frequency of only 7 GHz. The dual-loop feedback effectively narrows the linewidth by over an order of magnitude, reduces the phase noise variance by more than 500 times, and suppresses side peaks in the power spectrum.