Controllable non-uniformly distributed spiking cluster generation in broadband optoelectronic oscillator.

An approach to achieve controllable non-uniformly distributed spiking cluster generation is proposed and demonstrated based on an externally-triggered broadband optoelectronic oscillator (OEO). The theory of controlling the distribution of the spiking pulses in a spiking cluster is established. Based on the theory, the dynamic and the distribution characteristics are analyzed and revealed in the stable spiking oscillation state under different externally-injected trigger signal voltages. The peak-voltage envelop of the cluster and the interval of the spiking pulses are demonstrated to have an approximate negative linearity relationship with the externally-injected trigger signal voltage in both the numerical simulation and the experiment, where a square waveform, a trapezoidal waveform, a parabola waveform, and a half-sinusoidal waveform are used as the externally-injected trigger signals. The results indicate that the spiking pulse distribution in the generated spiking cluster can be well controlled through tuning the externally-injected trigger signal voltage. The proposed scheme can be utilized in spiking encoding and reservoir computing.

Phase-locked dual-frequency microwave signal generation in an optoelectronic oscillator based on frequency mixing mutual injection.

An approach to generating stable phase-locked dual-frequency microwave signals is proposed and demonstrated based on a dual-passband optoelectronic oscillator (OEO). Mode gain competition is broken by employing frequency mixing mutual injection effect to realize phase locking between the two oscillation signals, which is achieved by applying a single-tone signal to a microwave mixer in the OEO cavity. In addition, a dual-loop configuration with balanced detection is utilized to ensure a high side mode suppression ratio (SMSR) and ultra-low phase noise, which also enhances the stability of the generated signal. In the experiment, a phase-locked dual-frequency microwave signal at 9.9982 GHz and 10.1155 GHz is generated by using the proposed OEO scheme. The SMSR and the phase noise are 75 dB and -141 dBc/Hz@10 kHz, respectively. Additionally, the Allan deviation of the generated signal is in the order of 10-11@1 s. These parameters are superior to those based on the same OEO but with a single-loop configuration, which are also compared in detail.

High-resolution real-time Fourier transform based on optical frequency comb injected frequency shifting loop.

A high-resolution real-time Fourier transform scheme is proposed and demonstrated based on injecting an optical frequency comb (OFC) into a frequency shifting loop (FSL). Through setting the frequency interval between neighboring teeth in the coherent OFC to be equal to an integer multiple of the frequency shift and also the free spectral range of the FSL, the number of the effective signal replicas from the FSL is increased by M times, where M is the tooth number of the OFC. Hence, it breaks the limitation on the number of round trips due to the gain saturation effect and the cumulative amplified spontaneous emission noise in the FSL under a single optical carrier injection, which greatly enhances the frequency resolution. In the experiment, a coherent three-tone optical carrier is injected into an FSL to realize real-time spectrum analysis, where the frequency resolution is enhanced by three times compared with that by using a single-tone optical carrier injection, i.e., from 60 kHz to 20 kHz.

Time-delay signature suppression of the chaotic signal in a semiconductor laser based on optoelectronic hybrid feedback.

An approach to generating chaotic signals with low time-delay signatures (TDSs) from a semiconductor laser (SCL) is proposed and demonstrated based on optoelectronic hybrid feedback. Through using a chirped fiber Bragg grating (CFBG) to provide distributed feedback, a chaotic signal with a low TDS is generated from the SCL. With the assistance of the nonlinear optoelectronic feedback provided by a microwave photonic link, the relaxation oscillation effect in the SCL is effectively suppressed, and the periodicity of the oscillation is greatly weakened. Hence, the TDS of the generated chaotic signal from the SCL is further suppressed, and the effective bandwidth is enlarged. Both simulation and experiment are carried out to verify the feasibility of the proposed scheme to suppress the TDS. In the experiment, a chaotic signal with a large effective bandwidth of 12.93 GHz, an extremely high permutation entropy (PE) of 0.9983, and a low TDS of 0.04, is generated by using a CFBG with a dispersion coefficient of 22.33 ps/nm. This TDS value is at the same level as that obtained by using the SCL-based scheme relying solely on distributed feedback in a CFBG with a dispersion coefficient of 2000 ps/nm.

Neuromorphic regenerative memory optoelectronic oscillator.

Neuromorphic spiking information processing based on neuron-like excitable effect has achieved rapid development in recent years due to its advantages such as ultra-high operation speed, programming-free implementation and low power consumption. However, the current physical platforms lack building blocks like compilers, logic gates, and more importantly, data memory. These factors become the shackles to construct a full-physical layer neural network. In this paper, a neuromorphic regenerative memory scheme is proposed based on a time-delayed broadband nonlinear optoelectronic oscillator (OEO), which enables reshaping and regenerating on-off keying encoding sequences. Through biasing the dual-drive Mach-Zehnder electro-optic modulator in the OEO cavity near its minimum transmission point, the OEO can work in excitable regime, where localized states are maintained for robust nonlinear spiking response. Both simulation and experiment are carried out to demonstrate the proposed scheme, where the simulation results and the experimental results fit in with each other. The proposed OEO-based neuromorphic regenerative memory scheme exhibits long-term response ability for short-term excitation, which shows an enormous application potential for high-speed neuromorphic information buffering, optoelectronic interconnection and computing.

Instantaneous bandwidth expansion of photonic sampling analog-to-digital conversion for linear frequency modulation waveforms based on up-sampling and fractional Fourier transform signal processing.

An approach to expanding the instantaneous bandwidth of a photonic sampling analog-to-digital converter (ADC) for receiving linear frequency modulation waveforms (LFMWs) is proposed and experimentally demonstrated based on up-sampling and filtering in the fractional Fourier domain. Through twice zero interpolation, the equivalent sampling rate is quadrupled, which also quadruples the nominal instantaneous bandwidth of the photonic sampling ADC. In addition, with the assistance of bandpass filtering in the fraction Fourier domain, the image signals and the harmonic distortions generated in the interpolation process are filtered out. As a result, the effective instantaneous bandwidth of the photonic sampling ADC is doubled. In the experiment, the instantaneous bandwidth of a photonic sampling ADC with a sampling rate of 5 GSa/s for receiving LFMWs is increased from 2.5 GHz to 5 GHz by using the proposed method. Input LFMWs within the frequency range of 24-27 GHz and 30-33 GHz, i.e., with an instantaneous bandwidth of 3 GHz, are digitized without frequency-domain aliasing. Besides, the ability of the proposed method to enhance the ranging accuracy in a broadband radar system is demonstrated. This method reduces the hardware complexity of the photonic sampling ADC for receiving broadband LFMWs in radar systems.

High-resolution radar ranging based on the ultra-wideband chaotic optoelectronic oscillator.

A high-resolution radar ranging scheme is proposed and demonstrated based on the ultra-wideband chaotic optoelectronic oscillator (OEO). Through biasing the electro-optic intensity modulator near its minimum transmission point, high-dimensional chaotic signals with flat spectra and low time-delayed signatures can be generated in the OEO, which are favorable for increasing the ranging resolution and the confidentiality. In the experiment, the optimized broadband OEO generates a high-dimensional chaotic signal with a flat spectrum in the frequency range of 2 GHz to 16 GHz and a high permutation entropy of 0.9754. This chaotic signal is used to achieve multiple target ranging, where a ranging resolution of 1.4 cm is realized.

Pulse generation with programmable positions based on a phase-modulated optical frequency-shifting loop.

An approach to generating pulses with programmable positions is proposed and demonstrated based on a phase-modulated optical frequency-shifting loop (OFSL). By setting the OFSL to operate in the integer Talbot state, pulses are generated in the phase-locked positions, since the additional phase introduced by the electro-optic phase modulator (PM) in the OFSL is equal to an integer multiple of 2π in each round trip. Therefore, the pulse positions can be controlled and encoded by designing the driving waveform of the PM in a round-trip time. In the experiment, linear, round-trip, quadratic, and sinusoidal variations of pulse intervals are achieved by applying the corresponding driving waveforms to the PM. Pulse trains with coded pulse positions are also realized. In addition, the OFSL driven by waveforms with repetition rates equal to double and triple the free spectral range of the loop is also demonstrated. The proposed scheme paves a way to generate optical pulse trains with user-defined pulse positions, which can be used for such applications as compressed sensing and lidar.

Characterization of high-speed electro-optic phase modulators based on heterodyne carrier mapping at a fixed low-frequency.

A self-referenced method based on heterodyne carrier mapping is proposed to characterize the modulation efficiency of high-speed electro-optic phase modulators (EOPMs). The heterodyne carrier mapping replicates the optical carrier after phase modulation to an electrical replica, which enables observing the power variation of the optical carrier at a fixed low-frequency in the electrical domain. The modulation depths and half-wave voltages within the frequency range of up to 40 GHz are determined by measuring the amplitude ratio of the mapped low-frequency component at 80 MHz in the cases of on and off single-tone modulation of the EOPM. The measured results are compared to those obtained with the traditional optical spectrum analysis method and the electrical spectrum sweep method to check the consistency and accuracy. Surpassing the heterodyne spectrum mapping (HSM) scheme, our method only requires a single-tone driving of the EOPM under test and completely avoids the roll-off responsivity of the photodetector through the fixed low-frequency detection.

High-frequency characterization of electro-optic modulation chips based on photonic down-conversion sampling and microwave fixture de-embedding.

A self-reference and on-chip method for extracting the intrinsic frequency responses including modulation index and half-wave voltage of electro-optic modulator (EOM) chips is proposed based on photonic down-conversion sampling and microwave fixture de-embedding. The photonic down-conversion sampling is firstly employed to extract the combined response of the source network SxN, the adapter network SAN and the EOM chip. Then the Open-Short-Load (OSL) calibration is exploited to realize the on-chip microwave de-embedding of SxN and SAN in terms of the transmission attenuation and the impedance mismatch. Finally, the power leveling technique is used to track the incident microwave power to obtain the intrinsic half-wave voltage of the EOM chip. Our method features self-reference and on-chip capability, which is applicable for the EOM chips even without a good impedance match, and is free of any extra optical/electrical (O/E) transducer standard, which will be helpful to chip evaluation and packaging optimization.

Time-domain convolution model for studying oscillation dynamics in an injection-locked optoelectronic oscillator.

A time-domain convolution model is proposed to study the oscillation dynamics in the injection-locked optoelectronic oscillator (OEO). The model has the ability to calculate multiple characteristics of the oscillation signal, such as the spectrum and the phase noise. Based on the model, the injection locking, the frequency pulling and the asymmetrical spectrum generation phenomena are numerically simulated in success. The simulation results fit in with the experimental results, indicating that the proposed model accurately describes the oscillation dynamics in the injection-locked OEO. In addition, the building-up process of the oscillation signal in the OEO is simulated. Alternating appearance of the sidebands on both sides of the primary oscillation mode is observed for the first time in the asymmetrical spectrum generation. This model is a powerful tool to study the oscillation dynamics in the injection-locked OEO.

Relative frequency response measurement of Mach-Zehnder modulators utilizing dual-carrier modulation and low-frequency detection.

A self-calibrated approach is proposed to measure the relative frequency response of Mach-Zehnder modulators (MZMs) based on dual-carrier modulation and low-frequency detection. In this scheme, a dual-carrier is generated by combining a continuous-wave light from a distributed feedback laser diode with its frequency-shifted replica. Through modulating the dual-carrier by a frequency-scanned single-tone microwave signal via the MZM under test biased at its minimum transmission point, a fixed low-frequency heterodyne signal carrying the electro-optic modulation response information is generated after photodetection, from which the relative frequency response of the MZM can be obtained. In the experiment, the relative frequency response of a commercial MZM is measured by using the proposed method, where the result fits in with those obtained by using the conventional optical spectrum analysis method and the microwave network analysis method. The proposed method features self-calibration, high frequency resolution, low-frequency detection, and usage of only a single frequency-scanned microwave source, which is favorable for characterizing the microwave performance of MZMs in backbone optical communication and microwave photonic systems.

Photonic sampling analog-to-digital conversion based on time and wavelength interleaved ultra-short optical pulse train generated by using monolithic integrated LNOI intensity and phase modulator.

High-speed analog-to-digital conversion (ADC) is experimentally demonstrated by employing a time and wavelength interleaved ultra-short optical pulse train to achieve photonic sampling and using wavelength division demultiplexing to realize speed matching between the fast optical front-end and the slow electronic back-end. The sampling optical pulse train is generated from a cavity-less ultra-short optical pulse source involving a packaged device that monolithically integrates an intensity modulator and a phase modulator into a chip based on lithium niobate on insulator (LNOI). In the experiment, the fiber-to-fiber insertion loss of the packaged modulation device is measured to be 6.9 dB. In addition, the half-wave voltages of the Mach-Zehnder modulator and the phase modulator in the LNOI-based modulation device are measured to be 3.6 V and 3.4 V at 5 GHz, respectively. These parameters and the device size are superior to those based on cascaded commercial devices. Through using the packaged modulation device, two ultra-short optical pulse trains centered at 1541.40 nm and 1555.64 nm are generated with time jitters of 19.2 fs and 18.9 fs in the integral offset frequency range of 1 kHz to 10 MHz, respectively, and are perfectly time interleaved into a single pulse train with a repetition rate of 10 GHz and a time jitter of 19.8 fs. Based on the time and wavelength interleaved ultra-short optical pulse train, direct digitization of microwave signals within the frequency range of 1 GHz to 40 GHz is demonstrated by using a two-channel wavelength demultiplexing photonic ADC architecture, where the effective number of bits are 5.85 bits and 3.75 bits for the input signal at 1.1 GHz and 36.3 GHz, respectively.

Self-referenced electro-optic response measurement of dual-parallel Mach-Zehnder modulators employing single-tone level control and low-frequency bias swing.

A self-referenced method is proposed to characterize the electro-optic frequency response of dual-parallel Mach-Zehnder modulators (DPMZMs) based on single-tone level control and low-frequency bias swing. The single-tone driving signal and the low-frequency bias signal of the DPMZM mix with each other after photodetection, and a low-frequency beat note is generated in the electrical domain. The functional relationship between the desired low-frequency amplitude and the single-tone driving level is investigated and established, from which the modulation depth and half-wave voltage are extracted with the help of regression analysis. We experimentally demonstrate the feasibility of the proposed method and compare it with the conventional ones to check the consistency. The self-referenced method features single-tone modulation and low-frequency detection for measuring high-speed DPMZMs, which avoids the use of a broadband photodetector (PD) and the influence of the uneven response of the PD.

Self-reference frequency response characterization of photodiode chips based on photonic sampling and microwave de-embedding.

In this work, we propose and demonstrate a self-reference on-chip testing method to obtain the frequency response characteristics of photodiode chips based on photonic sampling and microwave de-embedding. The half-frequency photonic sampling enables self-reference extraction of the combined response of the photodiode chip, the adapter network and the receiver network. The microwave de-embedding under short-open-load-device (SOLD) termination is used to realize on-chip de-embedding of the adapter network and the receiver network in terms of the transmission loss and the impedance mismatch. The proposed on-chip testing method is free of any extra electro-optical transducer standard, which is favorable for performance monitoring in chip evaluation.

Simultaneous frequency response measurement of electro-absorption modulation transceivers based on a self-referenced pilot operation.

An electro-optic method based on a self-referenced pilot operation is proposed for simultaneously characterizing electro-absorption modulation optoelectronic transceivers with a shared setup. Through inserting and extracting the self-referenced pilot, the frequency responses of electro-absorption modulated lasers (EMLs) and photodetectors (PDs) are independently obtained in a single measurement, and any extra optical-to-electrical or electrical-to-optical calibration is avoided. Specifically, the relative frequency response of the EML at fm is determined through the extracted difference-frequency pilot at fp (close to DC), realizing the low-frequency analysis for an EML. The relative frequency response of PD at 2fm+fp is obtained from the amplitude ratio of the extracted sum- and difference-frequency pilots at 2fm+fp and fp under the microwave driving signal at fm, verifying the doubled measuring frequency range. In the proof-of-concept demonstration, the frequency response of an electro-absorption modulation transceiver is measured up to 40 GHz. Thereinto, the frequency response of the EML is obtained by detecting the fixed low-frequency pilot of 10 kHz, and the frequency response of the PD is extracted with frequency-swept modulation to 20 GHz. The experiment results are compared with those obtained with the electro-optic frequency sweeping method to check for accuracy.

Costas-coded linear frequency modulation waveform generation based on a VCO-controlled Fourier domain mode locking optoelectronic oscillator.

A novel approach to generating tunable Costas-coded linear frequency modulation waveforms (LFMWs) from an optoelectronic oscillator (OEO) is proposed and experimentally demonstrated. The OEO works under Fourier domain mode locking, where the oscillation modes are selected by using a fast-scanning microwave bandpass filter based on phase-modulation-to-intensity-modulation conversion via stimulated Brillouin scattering. Costas coding is realized by using an open-loop voltage-controlled oscillator (VCO) with a fast tuning speed to generate an agile fast-scanning probe light via electro-optic frequency shift. The bandwidth of the generated Costas-coded LFMWs can be tuned by varying the voltage range of the low-frequency waveform applied to the VCO, and the center frequency can be finely tuned by varying the electro-optic frequency shift of the pump light. In the experiment, Costas-coded LFMWs with a 12-bit Costas code sequence of [9 5 7 12 6 4 1 8 11 10 2 3], a period of 20.39 µs and tunable frequency range are generated. The cross-correlation result with a time delay of 102.5 µs indicates that the generated Costas-coded LFMWs have excellent pulse-to-pulse coherence. In addition, the bad phase noise performance of the open-loop VCO has a negligible influence on the generated Costas-coded LFMWs. Benefited from employing an open-loop VCO with a fast tuning speed and a broad operation bandwidth, this approach has potential in generating agile broadband multi-format radar waveforms with low phase noise and excellent pulse-to-pulse coherence directly from an OEO.

Modeling an actively mode-locked optoelectronic oscillator based on electric amplitude modulation.

A theoretical model and its calculation method are proposed to simulate an actively mode-locked optoelectronic oscillator (OEO) based on electric amplitude modulation. The model includes electric amplitude modulation to achieve mode locking and convolution of electric signal and filter impulse response function to achieve mode selection. Numerical simulation is carried out through enhancing the calculating time window to an integral multiple of the roundtrip time and employing pulse tracking method with a precise delay. Through using this model, the waveform, the spectrum and the phase noise characteristic of the generated microwave pulse train from an actively mode-locked OEO are numerically simulated, where the simulation results fit in with the experimental results. This model can be used to design an actively mode-locked OEO based on electric amplitude modulation. More importantly, it is favorable for studying the dynamic process in an actively mode-locked OEO, which is difficult to grasp by carrying out an experiment.

Multi-format microwave signal generation based on an optoelectronic oscillator.

A novel approach to generating multi-format microwave signals directly from an optoelectronic oscillator (OEO) is proposed and experimentally demonstrated. Through applying different low-frequency electrical waveforms to the bias port of the electro-optic Mach-Zehnder modulator, the net gain in the OEO cavity is dynamically controlled to make the OEO work at different status. Hence, different microwave signals can be generated in the oscillation process. In the proof-of-concept experiment, a single-tone microwave signal at 4.005 GHz is generated by using a direct-current driving voltage. Microwave pulse trains centered at 4 GHz and with repetition rates of 390 kHz and 3.9 MHz are generated under fundamental and 10th-order harmonic mode locking, respectively, by using sinusoidal driving voltages. Besides, rectangular microwave waveforms centered at 4 GHz and with duty cycles of 25%, 50%, and 75% are generated under gain switching status by using rectangular driving voltages. The proposed method is also able to generate other types of microwave signals in a broad frequency range, which can find applications in a multi-functional microwave photonic system.

Real-time observation of pulsating period-doubled vector solitons in a passively mode-locked fiber laser.

Dissipative solitons (DSs) are self-organized localized structures in non-conservative systems, which require a continuous energy exchange with external sources. In addition to parameter-invariant stationary DSs, there exists a variety of dynamical ones manifesting breathing behaviors. Such intriguing phenomena, termed as soliton pulsations, have been widely studied in recent years under the impetus of advances in real-time spectroscopy. Here, we experimentally investigate various pulsating period-doubled solitons (PDSs) in a fiber laser mode-locked by single-wall carbon nanotubes. Both single- and double-periodic PDS pulsations are found in the cavity. Thanks to the emerging dispersive Fourier transform technique, the polarization-resolved transient spectra of these pulsating PDSs are measured. It is shown that their polarization ellipses rotate with a period of two cavity roundtrips. Moreover, the intensity-modulation behaviors of the two orthogonal polarization components in the odd (even) roundtrips are always asynchronous, which confirms additional slower polarization modulations. Especially, we demonstrate that three combined intensity-modulation periods are involved in the double-periodic PDS pulsation process for the first time, to the best of our knowledge. Our results would stimulate further research on the vector features of multiple-period pulsating solitons in mode-locked fiber lasers.