Integration of the whole mode-locked laser onto a single piece of semiconductor offers a number of advantages, including total elimination of optical alignment processes, improved mechanical stability, and the generation of short optical pulses at much higher repetition frequencies. Semiconductor laser processing technologies were used to implement the colliding-pulse mode-locking (CPM) scheme, which is known to effectively shorten the pulses and increase stability, on a miniature monolithic semiconductor cavity. The principles of and recent progress in monolithic CPM quantum-well lasers are reviewed. >

Monolithic colliding-pulse mode-locked quantum well lasers

An optoelectronic oscillator (OEO) is a microwave photonic system with a positive feedback loop used to create microwave oscillation with ultra-low phase noise thanks to the employment of a high-quality-factor energy storage element, such as a fiber delay line. For many applications, a frequency-tunable microwave signal or waveform, such as a linearly chirped microwave waveform (LCMW), is also needed. Due to the long characteristic time constant required for building up stable oscillation at an oscillation mode, it is impossible to generate an LCMW with a large chirp rate using a conventional frequency-tunable OEO. In this study, we propose and demonstrate a new scheme to generate a large chirp-rate LCMW based on Fourier domain mode locking technique to break the limitation of mode building time in an OEO. An LCMW with a high chirp rate of 0.34 GHz/μs and a large time-bandwidth product of 166,650 is demonstrated.

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Breaking the limitation of mode building time in an optoelectronic oscillator.

Chaotic dynamics of a semiconductor laser subject to optical feedback from a frequency-detuned fiber Bragg grating (FBG) is investigated experimentally and numerically. Although the FBG is similar to a mirror in perturbing the laser into chaos, it is not the same as a mirror because it provides spatially distributed reflections. Such distributed reflections effectively suppress the undesirable time-delay signature (TDS) contained in the autocorrelation function of the chaotic intensity time-series. The investigation shows that the best suppression of TDS is attained when the FBG is positively detuned from the free-running laser frequency. The TDS suppression is due to dispersion at frequencies near an edge of the main lobe of the FBG reflectivity spectrum. The suppression prefers the FBG at a positive detuning frequency because the laser cavity is red-shifted by the antiguidance effect. Numerically, the dynamical behavior is mapped in the parameter space of detuning frequency and feedback strength, where wide regions of chaos are identified. Experimentally, the TDS suppression by FBG feedback is demonstrated for the first time. The positively detuned FBG suppresses the TDS by over ten times to below 0.04 in the experiments.

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Chaotic Time-Delay Signature Suppression in a Semiconductor Laser With Frequency-Detuned Grating Feedback

Based on an optically injected semiconductor laser (OISL) operating at period-one (P1) nonlinear dynamical state, high-purity millimeter-wave generation at 60 GHz band is experimentally demonstrated via 1/4 and 1/9 subharmonic microwave modulation (the order of subharmonic is with respect to the frequency fc of the acquired 60 GHz band millimeter-wave but not the fundamental frequency f0 of P1 oscillation). Optical injection is firstly used to drive a semiconductor laser into P1 state. For the OISL operates at P1 state with a fundamental frequency f0 = 49.43 GHz, by introducing 1/4 subharmonic modulation with a modulation frequency of fm = 15.32 GHz, a 60 GHz band millimeter-wave with central frequency fc = 61.28 GHz ( = 4fm) is experimentally generated, whose linewidth is below 1.6 kHz and SSB phase noise at offset frequency 10 kHz is about −96 dBc/Hz. For fm is varied between 13.58 GHz and 16.49 GHz, fc can be tuned from 54.32 GHz to 65.96 GHz under matched modulation power Pm. Moreover, for the OISL operates at P1 state with f0 = 45.02 GHz, a higher order subharmonic modulation (1/9) is introduced into the OISL for obtaining high-purity 60 GHz band microwave signal. With (fm, Pm) = (7.23 GHz, 13.00 dBm), a microwave signal at 65.07 GHz ( = 9fm) with a linewidth below 1.6 kHz and a SSB phase noise less than −98 dBc/Hz is experimentally generated. Also, the central frequency fc can be tuned in a certain range through adjusting fm and selecting matched Pm.

High-purity 60GHz band millimeter-wave generation based on optically injected semiconductor laser under subharmonic microwave modulation.

Chaotic external-cavity semiconductor laser (ECL) is a promising entropy source for generation of high-speed physical random bits or digital keys. The rate and randomness is unfortunately limited by laser relaxation oscillation and external-cavity resonance, and is usually improved by complicated post processing. Here, we propose using a physical broadband white chaos generated by optical heterodyning of two ECLs as entropy source to construct high-speed random bit generation (RBG) with minimal post processing. The optical heterodyne chaos not only has a white spectrum without signature of relaxation oscillation and external-cavity resonance but also has a symmetric amplitude distribution. Thus, after quantization with a multi-bit analog-digital-convertor (ADC), random bits can be obtained by extracting several least significant bits (LSBs) without any other processing. In experiments, a white chaos with a 3-dB bandwidth of 16.7 GHz is generated. Its entropy rate is estimated as 16 Gbps by single-bit quantization which means a spectrum efficiency of 96%. With quantization using an 8-bit ADC, 320-Gbps physical RBG is achieved by directly extracting 4 LSBs at 80-GHz sampling rate.

Minimal-post-processing 320-Gbps true random bit generation using physical white chaos.

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.

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

Phase noise of the period-one (P1) nonlinear dynamical oscillation in an optically injected semiconductor laser is numerically investigated. The P1 dynamics causes the laser output intensity to oscillate at a widely tunable frequency for photonic microwave generation, although the intrinsic spontaneous emission in the laser inevitably degrades the microwave signal and manifests as the oscillation phase noise. To characterize the phase noise, the P1 microwave linewidth is first numerically examined through the rate equations with a Langevin term. The P1 microwave linewidth is found to vary with the injection parameters. It is nearly minimized when the microwave power maximizes. Owing to the laser nonlinearities, the P1 microwave linewidth can even be smaller than the free-running optical linewidth. By adding an optical feedback to the laser, the P1 microwave linewidth is found to reduce as the feedback strength and feedback delay increase, in which an inverse-square dependency is followed asymptotically. By modification to a dual-loop feedback, noisy side peaks around the central P1 frequency are effectively suppressed through the Vernier effect. The dual-loop feedback maintains a low phase noise variance over a wide tuning range of the P1 frequency, while allowing long delay times for significant P1 microwave linewidth narrowing.

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Phase noise characteristics of microwave signals generated by semiconductor laser dynamics

Generation of frequency-modulated continuous-wave (FMCW) microwave signals is investigated using the period-one (P1) dynamics of a semiconductor laser. A modulated optical injection drives the laser into P1 oscillation with a modulated microwave frequency, while adding feedback to the injection reduces the microwave phase noise. Using simply a single-mode laser, the tunability of P1 dynamics allows for wide tuning of the central frequency of the FMCW signal. A sweep range reaching 7.7 GHz is demonstrated with a sweep rate of 0.42 GHz/ns. When the external modulation frequency matches the reciprocal of the feedback delay time, feedback stabilization is manifested as an increase of the frequency comb contrast by 30 dB for the FMCW microwave signal.

Frequency-modulated microwave generation with feedback stabilization using an optically injected semiconductor laser.

A semiconductor laser with distributed feedback from a fiber Bragg grating (FBG) is investigated for random bit generation (RBG). The feedback perturbs the laser to emit chaotically with the intensity being sampled periodically. The samples are then converted into random bits by a simple postprocessing of self-differencing and selecting bits. Unlike a conventional mirror that provides localized feedback, the FBG provides distributed feedback which effectively suppresses the information of the round-trip feedback delay time. Randomness is ensured even when the sampling period is commensurate with the feedback delay between the laser and the grating. Consequently, in RBG, the FBG feedback enables continuous tuning of the output bit rate, reduces the minimum sampling period, and increases the number of bits selected per sample. RBG is experimentally investigated at a sampling period continuously tunable from over 16 ns down to 50 ps, while the feedback delay is fixed at 7.7 ns. By selecting 5 least-significant bits per sample, output bit rates from 0.3 to 100 Gbps are achieved with randomness examined by the National Institute of Standards and Technology test suite.

Random bit generation at tunable rates using a chaotic semiconductor laser under distributed feedback.

State-space reconstruction is investigated for evaluating the randomness generated by an optically injected semiconductor laser in chaos. The reconstruction of the attractor requires only the emission intensity time series, allowing both experimental and numerical evaluations with good qualitative agreement. The randomness generation is evaluated by the divergence of neighboring states, which is quantified by the time-dependent exponents (TDEs) as well as the associated entropies. Averaged over the entire attractor, the mean TDE is observed to be positive as it increases with the evolution time through chaotic mixing. At a constant laser noise strength, the mean TDE for chaos is observed to be greater than that for periodic dynamics, as attributed to the effect of noise amplification by chaos. After discretization, the Shannon entropies continually generated by the laser for the output bits are estimated in providing a fundamental basis for random bit generation, where a combined output bit rate reaching 200 Gb/s is illustrated using practical tests. Overall, based on the reconstructed states, the TDEs and entropies offer a direct experimental verification of the randomness generated in the chaotic laser.

Jun-Ping Zhuang

Papers

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

Phase noise characteristics of microwave signals generated by semiconductor laser dynamics

Frequency-modulated microwave generation with feedback stabilization using an optically injected semiconductor laser.

Random bit generation at tunable rates using a chaotic semiconductor laser under distributed feedback.

Randomness evaluation for an optically injected chaotic semiconductor laser by attractor reconstruction.