Linearly Chirped Microwave Waveform Research Articles

Mode locking mechanism in Fourier-domain mode-locked optoelectronic oscillators

Fourier-domain mode-locked (FDML) optoelectronic oscillators (OEOs) are regarded as a promising candidate to generate linearly chirped microwave waveforms (LCMWs) with large time-bandwidth products. Nevertheless, up to date, the mode locking mechanism in FDML-OEOs is still not clear enough. Here, a comprehensive theoretical analysis is made to reveal the mode locking mechanism in FDML-OEOs. In particular, the phase relationship among numerous oscillation modes under stable oscillation is obtained. In addition, the FDML oscillation process originated from either noise or single-mode oscillation and is numerically simulated based on the model. Therefore, the initial oscillation process is comprehensively analyzed in the time domain, the Fourier domain, and the fractional Fourier domain, which provides a deep insight into the FDML oscillation process. Finally, the initial oscillation process of a FDML-OEO is captured in the experiment. The corresponding analysis is carried out to reveal the real mode locking mechanism, where the experimental results fit in with the theoretical and numerical results. This work provides a new approach for in-depth analysis of FDML-OEOs.

On-Chip Photonic Generation of Tunable Wideband Phase-Coded Linearly-Chirped Microwave Waveforms

On-chip photonic generation of tunable wideband phase-coded linearly-chirped microwave waveforms (PC-LCMWs) is proposed and experimentally demonstrated. The on-chip generation system consists of two main parts. One part is a hybrid Fourier-domain mode-locked opto-electronic oscillator (FDML-OEO) for a wideband linearly-chirped microwave waveform (LCMW) generation; the other part is a high-speed microwave photonic phase shifter (MPPS) to perform the phase-coding. By synchronizing the two parts, a PC-LCMW is finally generated. In the proposed chip, a thermally-tunable ultrahigh-Q micro-ring resonator (MRR) is a key component which is incorporated in the FDML-OEO loop to select the oscillation frequency, and an electrically-tunable micro-disk resonator (MDR), as another key component, is used to code the phase of the generated microwave signal while maintaining the amplitude by controlling the free carrier concentration in the lateral PN junction of the disk. With the use of the two key component chips, an experiment is performed and different PC-LCMWs are generated with a tunable center frequency from 12 to 16 GHz, a bandwidth from 2 to 6 GHz, and phase code of 7-bit and 13-bit Barker code. In particular, a PC-LCMW with a maximum bandwidth as wide as 6 GHz and an ultra-large time-bandwidth product (TBWP) as large as 1.96×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sup> is experimentally demonstrated. The proposed integrated PC-LCMW generation system holds great advantages including ultracompact configuration and fast tunability, which holds a high potential for applications in modern high-resolution multi-functional radar system.

Broadband pulse generator based on a self-injection-locked Fourier domain mode-locked optoelectronic oscillator

A novel broadband pulse generator based on a Fourier domain mode-locked optoelectronic oscillator (FDML-OEO) is proposed and experimentally demonstrated. The system consists of a dual-loop self-injection-locked OEO with an on-off keying (OOK) bias-controlled Mach–Zehnder modulator (MZM) as an optical switch. By applying a square-wave voltage onto the bias port of the MZM the broadband pulses are directly generated by slicing the outputs of the FDML-OEO. The duty cycle can be easily changed by just tuning that of the square wave. Different microwave pulses with the duty cycles of 1:1, 1:10 and 1:100 are demonstrated. In particular, the tunability of the central frequency and the bandwidth of the generated signal is also displayed. Furthermore, the amplitude coherence superposition of 8 pulses is increased by ∼16 times and the frequency modulated pulse with different central frequencies are also demonstrated. The proposed broadband microwave signal pulse generator based on the injection-locked FDML-OEO can generate signals with large time bandwidth product (TBWP), and the linearly chirped microwave waveforms (LCMWs) are widely used in modern radar systems to achieve high-resolution detection and imaging.

Photonic generation of a microwave waveform with an ultra-long temporal duration using a frequency-shifting dispersive loop.

A photonic approach to generate a linearly chirped microwave waveform (LCMW) with an ultra-long temporal duration is proposed and experimentally demonstrated. The microwave waveform generation is achieved based on spectral-shaping and wavelength-to-time (SS-WTT) mapping by using a Mach-Zehnder interferometer (MZI) and a frequency-shifting dispersive loop (FSDL), respectively. To make the generated microwave waveform have an ultra-long temporal duration, the FSDL is operating to allow a spectrally shaped optical pulse to recirculate in a dispersive loop multiple times with a low propagating loss, to generate a microwave waveform with a temporal duration that is more than one order of magnitude longer than that of a microwave waveform generated using a dispersive element without recirculation. To generate a LCMW, the spectral shaper is configured to have a free spectral range (FSR) that is linearly increasing or decreasing with optical wavelength. The proposed approach is experimentally demonstrated. Two LCMWs, by allowing an optical pulse recirculating in the FSDL for three and seven round trips, tripled and septupled temporal durations of 64 and 182 ns are generated. The generation of two LCMWs with ultra-long temporal durations of 370 ns and 450 ns are also demonstrated.

Generation of Reconfigurable Linearly Chirped Microwave Waveforms Based On Fourier domain Mode-Locked Optoelectronic Oscillator

We propose and experimentally demonstrate an approach to generating reconfigurable linearly chirped microwave waveforms (LCMWs) based on a Fourier domain mode-locked (FDML) optoelectronic oscillator (OEO), in which a tunable and reconfigurable microwave photonic filter (MPF) based on a high-Q microring resonator (MRR) is used for mode selection. The MPF can be electrically tuned to achieve Fourier domain mode-locking by using a micro-heater deposited on the MRR. Adjusting the state of polarization of the optical carrier, the MPF is reconfigured and multi-band and multi-format LCWMs can be generated based on the FDML OEO. In the experiment, a dual-chirp LCMW with a bandwidth of 12 GHz consisting of an up-chirped waveform from 7 to 13 GHz and a down-chirped waveform from 19 to 13 GHz is realized, with a time-bandwidth product (TBWP) as high as 1.004&#x00D7;10⁶. By reconfiguring the MPF, we can also obtain LCMWs with a single chirp at C-band (from 4 to 8 GHz), X-band (from 8 to 12 GHz) and Ku-band (from 13 to 19 GHz), respectively. Further, the bandwidth and center frequency of the LCMWs and the dual-chirp LCMWs can be changed by adjusting the magnitude of the driving signal and the laser wavelength, respectively. This kind of reconfigurable LCMWs can be applied to advanced multi-band radar and wireless communication systems.

Photonic generation of flexible ultra-wide linearly-chirped microwave waveforms

Thanks to the large time bandwidth product (TBWP), linearly chirped microwave waveforms (LCMWs) are widely used in modern radar systems to achieve high-resolution detection and imaging. To overcome the challenge of small unmanned aerial vehicle detection and tracking, radar systems are required to have a higher resolution and multi-function operation, in which an ultra-wideband LCMW is highly preferred with a flexible tuning in the center frequency, instantaneous bandwidth, and multi-band operation. In this paper, we propose and experimentally demonstrate an approach to generating flexible ultra-wide LCMWs based on a Fourier-domain mode-locked optoelectronic oscillator (FDML-OEO) incorporating a dual-polarization quadrature phase-shift keying (DP-QPSK) modulator. In the DP-QPSK modulator, two dual-parallel Mach-Zehnder modulators (DP-MZMs) are integrated. With the use of the upper DP-MZM, an FDML-OEO is produced to generate a wideband LCMW with a tuning in the center frequency and instantaneous bandwidth. With the injection of the generated LCMW into the lower DP-MZM, an ultra-wideband LCMW is generated via microwave frequency multiplication, and multi-band waveform generation is enabled by controlling the bias condition of the lower DP-MZM. An experiment is performed and an LCMW with a maximum bandwidth as broad as 10.8 GHz is generated. By adjusting the driving signal applied to the FDML-OEO, the generated LCMW can be tuned in the center frequency from 16.2 to 23.2 GHz and the bandwidth from 3.6 to 10.8 GHz. By controlling the bias point of the lower DP-MZM, a dual-band LCMW is also experimentally demonstrated. Thanks to the ultra-wide bandwidth and strong flexibility of the generated LCMWs in terms of tunable center frequency, instantaneous bandwidth and multiband operation, the proposed approach offers a promising LCMW generator in the next-generation high-resolution radar systems.

Bandwidth superposition of linearly chirped microwave waveforms based on a Fourier domain mode-locked optoelectronic oscillator

Optoelectronic oscillators (OEOs) are promising for radar, communication and electronic countermeasure systems. Among them, frequency-scanning OEOs with wide instantaneous bandwidth are needed for many advanced applications. In this work, we demonstrate a novel system to generate bandwidth-doubled linearly chirped microwave waveforms (LCMWs) based on bandwidth superposition using a Fourier domain mode-locked OEO (FDML OEO). In the proposed system, bandwidth-doubling is achieved by re-modulating the generated LCMW of the FDML OEO onto a frequency-scanning optical carrier signal with the help of an external Mach-Zehnder modulator. LCMWs with wide frequency scanning instantaneous bandwidth of 10 GHz are experimentally obtained. Meanwhile, these LCMWs are tunable in an ultra-wide frequency range from 1 to 39 GHz. Moreover, they are with high frequency sweep linearity of 0.5%. Our work presents a simple method to generate tunable wide-band LCMWs for potential microwave sources.

Photonic Generation of Linearly Chirped Microwave Waveforms With Tunable Parameters

We propose a linearly chirped microwave waveform (LCMW) generation scheme applying a stimulated Brillouin scattering (SBS)-based Fourier domain mode locked (FDML) optoelectronic oscillator (OEO). In this system, SBS-induced phase-modulation-to-intensity-modulation-conversion is adopted to build a microwave photonic filter, of which the pass-band can be rapidly tuned by adopting a high-order frequency sweeping modulation sideband as the optical carrier. Thanks to the frequency multiplication capability and the fast mode selection with a very narrow pass band, the proposed system can generate broadband LCMWs with a good frequency modulation linearity. Besides, the bandwidth, central frequency, duty cycle and repetition rate of the LCMWs can be easily adjusted to satisfy different radar applications. A proof-of-concept experiment is carried out. The results can soundly verify the feasibility as well as the flexibility of the proposed LCMW generation system.

Hybrid Fourier-domain mode-locked laser for ultra-wideband linearly chirped microwave waveform generation

We show the generation of a tunable linearly chirped microwave waveform (LCMW) with an ultra-large time-bandwidth product (TBWP) based on a hybrid Fourier-domain mode-locked (FDML) laser. The key device in the hybrid FDML laser is a silicon photonic integrated micro-disk resonator (MDR) which functions as an optical bandpass filter, to have strong wavelength selectivity and fast frequency tunability. By incorporating the integrated MDR in the fiber-based ring cavity to perform frequency-domain mode locking, an FDML laser is realized and a broadband frequency-chirped optical pulse is generated. By beating the frequency-chirped optical pulse with an optical carrier from a laser diode (LD) at a photodetector (PD), an LCMW is generated. The bandwidth of the LCMW is over 50 GHz and the temporal duration is over 30 µs, with an ultra-large TBWP of 1.5 × 106. Thanks to the strong tunability of the MDR in the FDML laser, the generated LCMW is fully tunable in terms of bandwidth, temporal duration, chirp rate, and center frequency.

Frequency-Sweep-Range-Reconfigurable Complementary Linearly Chirped Microwave Waveform Pair Generation by Using a Fourier Domain Mode Locking Optoelectronic Oscillator Based on Stimulated Brillouin Scattering

A Fourier domain mode locking (FDML) optoelectronic oscillator (OEO) based on stimulated Brillouin scattering (SBS) is proposed to generate complementary linearly chirped microwave waveform (LCMW) pairs with flexibly-reconfigurable frequency sweep range and excellent frequency sweep linearity. The FDML OEO involves an SBS-based dual-passband microwave photonic filter with its two passbands linearly and fast scanning in the opposite direction at an identical frequency sweep rate, which is realized by using a single laser source to obtain a fast frequency sweep probe light and a two-tone pump light through electro-optic modulation. A proof-of-concept experiment is carried out to demonstrate the proposed scheme. In the experiment, frequency-sweep-range-reconfigurable complementary LCMW pairs with period of 20.5 μs are generated in the range of 5 GHz to 18 GHz, where the maximum time-bandwidth product and chirp rate are 82000 and ±0.195 GHz/µs, respectively. Most importantly, the frequency sweep linearity is measured to be 1.76%, which is much better than the results obtained in the existing FDML OEOs.

Frequency-definable linearly chirped microwave waveform generation by a Fourier domain mode locking optoelectronic oscillator based on stimulated Brillouin scattering.

A Fourier domain mode locking (FDML) optoelectronic oscillator (OEO) scheme based on stimulated Brillouin scattering (SBS) is proposed to generate linearly chirped microwave waveforms (LCMWs) with excellent frequency sweep linearity and a precisely controllable frequency sweep range. The kernel of the proposed scheme is a center-frequency-definable SBS-based fast-tunable microwave photonic bandpass filter based on frequency-selective phase-to-intensity conversion, which is realized by using a single laser source to generate a fast frequency-swept probe light and a tunable pump light via electro-optic frequency shifting. A proof-of-concept experiment is carried out to demonstrate the proposed scheme, where LCMWs with flexibly-tunable center frequency and bandwidth are generated. In the experiment, the maximum time-bandwidth product and chirp rate are 82000 and 0.195 GHz/µs, respectively. Most importantly, the frequency deviation is less than 1 MHz and the frequency sweep linearity is smaller than 1.7%, which indicate that the proposed SBS-based FDML OEO can generate frequency-definable LCMWs with excellent frequency sweep linearity.

Polarization Manipulated Fourier Domain Mode-Locked Optoelectronic Oscillator

We report a polarization manipulated Fourier domain mode-locked optoelectronic oscillator (FDML-OEO) using a polarization modulator (PolM). Frequency and bandwidth doubling linearly chirped microwave waveforms (LCMWs) are generated from a PolM-based FDML-OEO. The multiplying operation is capable of increasing the frequency and bandwidth of LCMWs, which doubles the time-bandwidth product of the LCMWs and makes it possible to increase the center frequency of the LCMWs beyond the bandwidth of the optical modulator. Moreover, by simply adding the other laser diode, it is also possible to generate a dual-chirp LCMW. The polarization manipulated of two optical signals avoids the undesired beating signals from optical carriers. Thus, an electrical bandpass filter which is essential in previous work is no longer required. To the best of our knowledge, this is the first time that polarization manipulation is used in FDML-OEO, which can further satisfy the demands of modern radars in terms of improved range-Doppler resolution, higher carrier frequency, and larger bandwidth.

A Chirp-Rate-Tunable Microwave Photonic Pulse Compression System for Multi-Octave Linearly Chirped Microwave Waveform

A chirp-rate-tunable microwave photonic pulse compression system for multi-octave linearly chirped microwave waveform (LCMW) is proposed in this paper. The key components are a dual-parallel Mach-Zehnder modulator (DPMZM) and a dispersive loop (DL) structure based on a linear chirped fiber Bragg grating. By controlling the output of the DL to change the accumulated group velocity dispersion, the chirp rate of the system can be tuned. By adjusting the wavelength of the optical carrier to select the single sideband modulated optical signal (positive or negative sideband), the chirp direction (down or up chirped) can also be tuned. The performance of the multi-octave LCMW pulse compression can be improved by eliminating the second-order harmonic distortion through configuring the bias voltages of the DPMZM. Detailed theoretical analysis is conducted. A verification simulation demonstrates the pulse compression of the multi-octave LCMWs with the chirp rates of 23.877, 11.939, 3.979, and -3.979 GHz/ns. In the proof-of-concept experiment, the matched chirp rates 23.229, 12.051, -22.568, and -11.355 GHz/ns are obtained. The multi-octave LCMW pulse compressions with the compression ratios of 14.3, 29.3, 15.0, and 28.6 are verified. The simulation and experiment results are in good agreement with the theoretical analysis.

High-Speed and High-Resolution Interrogation of a Silicon Photonic Microdisk Sensor Based on Microwave Photonic Filtering

High-speed and high-resolution interrogation of a silicon photonic microdisk sensor based on microwave photonic filtering and advanced signal processing is proposed and experimentally demonstrated. An integrated microdisk resonator (MDR) with a high Q factor is used as a sensor which is interrogated by incorporating the MDR into a microwave photonic filter (MPF) consisting of a laser source, a phase modulator (PM), the MDR, and a photodetector (PD), with the central frequency of the MPF being a function of the resonant wavelength of the MDR. A broadband linearly chirped microwave waveform (LCMW) is applied to the input of the MPF to generate a filtered microwave waveform. By measuring the temporal location of the filtered microwave waveform, the sensing information is revealed. To increase the signal-to-noise ratio (SNR) of the filtered microwave waveform, a phase-only filter (POF) realized based on the LCMW is correlated with the filtered microwave waveform, to generate a compressed pulse, which is filtered using a Hamming window to remove the noise and recorrelated with the POF to recover the filtered microwave waveform. Since the SNR is significantly increased, the interrogation accuracy is improved. The use of the proposed sensor for temperature and refractive index (RI) sensing is performed. The experimental results show that the sensor has a sensitivity of 76.8 pm/°C and a resolution of 0.234 °C as a temperature sensor, and a sensitivity of 33.28 nm/RIU and a resolution of 1.32 × 10−3 RIU as an RI sensor. The interrogation speed is as high as 100 kHz.

Breaking the limitation of mode building time in an optoelectronic oscillator

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.

Photonic generation of linearly chirped microwave waveforms using a monolithic integrated three-section laser.

Photonic generation of linearly chirped microwave waveforms (LCMWs) using a monolithic integrated three-section laser is experimentally demonstrated in this work. All three sections of the laser cavity, including the front DFB section, phase section and rear DFB section, have the same active layer, which can avoid the butt-joint re-growth process. The gratings in both DFB sections are fabricated by the Reconstruction Equivalent Chirp technique, which can significantly decrease the difficulties in realizing precise grating structure. By adjusting the integrated three-section semiconductor laser to work in the period-one (P1) state and applying a sweeping signal to the front DFB section, the beating signal, i.e., an LCMW with a large time bandwidth product (TBWP), can be generated. In the current proof-of-concept experiment, an LCMW with a large TBWP up to 5.159 × 105 is generated, of which the bandwidth and the duration time are 6.7 GHz and 77 us respectively. The compressed pulse width is 150 ps. In addition, by adjusting the bias currents of the rear DFB section and front DFB section as well as the amplitude of the sweeping signals, LCMWs with tunable center frequency and tunable bandwidth can be achieved.

Linearly Chirped Microwave Generation Using a Monolithic Integrated Amplified Feedback Laser

A linearly chirped microwave waveform (LCMW) generator based on a monolithically integrated dual-mode amplified feedback laser (AFL) is demonstrated. The proposed LCMW generator is very simple, only consisting of an AFL, an arbitrary waveform generator, and a photodetector. By applying a sweeping signal to the amplifier section of the AFL, the beating frequency of the AFL’s output can be changed in a chirped manner. LCMW is experimentally demonstrated using a heterodyne-beating technique. The measured microwave waveform has a pulse duration of $1~\mu \text{s}$ , a bandwidth of 3.3 GHz (ranging from 31.5 to 34.8 GHz), corresponding to a time-bandwidth product of $3.3 \times 10^{3}$ and a compression ratio of $2.6 \times 10^{3}$ .

A Microwave Photonic Signal Processor for Arbitrary Microwave Waveform Generation and Pulse Compression

A microwave photonic signal processor for arbitrary microwave waveform generation and pulse compression based on a microwave photonic filter (MPF) and a time reversal module (TRM) is proposed and experimentally demonstrated. In the proposed signal processor, an arbitrary microwave waveform is generated by allowing an ultrashort microwave pulse to pass through an MPF and a TRM, to get a microwave waveform to have a spectrum that is the complex conjugate of the spectral response of the MPF. When the generated microwave waveform is transmitted and received, by passing the received microwave waveform through the same MPF, matched filtering is performed and the microwave waveform is compressed. The proposed microwave photonic signal processor is verified by two experiments, in which a linearly chirped microwave waveform (LCMW) with a bandwidth of 7.7 GHz and a 7-bit phase-coded microwave waveform (PCMW) with a carrier frequency of 4.08 GHz are generated and compressed. The temporal durations of the generated LCMW and PCMW are 5.57 and 5.4 ns, respectively, and the widths of the compressed pulses are 0.27 and 0.58 ns, corresponding to pulse compression ratios of 20.6 and 9.3, respectively.

High speed and high resolution interrogation of a fiber Bragg grating sensor based on microwave photonic filtering and chirped microwave pulse compression.

High speed and high resolution interrogation of a fiber Bragg grating (FBG) sensor based on microwave photonic filtering and chirped microwave pulse compression is proposed and experimentally demonstrated. In the proposed sensor, a broadband linearly chirped microwave waveform (LCMW) is applied to a single-passband microwave photonic filter (MPF) which is implemented based on phase modulation and phase modulation to intensity modulation conversion using a phase modulator (PM) and a phase-shifted FBG (PS-FBG). Since the center frequency of the MPF is a function of the central wavelength of the PS-FBG, when the PS-FBG experiences a strain or temperature change, the wavelength is shifted, which leads to the change in the center frequency of the MPF. At the output of the MPF, a filtered chirped waveform with the center frequency corresponding to the applied strain or temperature is obtained. By compressing the filtered LCMW in a digital signal processor, the resolution is improved. The proposed interrogation technique is experimentally demonstrated. The experimental results show that interrogation sensitivity and resolution as high as 1.25 ns/με and 0.8 με are achieved.

Linearly chirped microwave waveform generation with large time-bandwidth product by optically injected semiconductor laser.

A scheme for photonic generation of linearly chirped microwave waveforms (LCMWs) with a large time-bandwidth product (TBWP) is proposed and demonstrated based on an optically injected semiconductor laser. In the proposed system, the optically injected semiconductor laser is operated in period-one (P1) oscillation state. After optical-to-electrical conversion, a microwave signal can be generated with its frequency determined by the injection strength. By properly controlling the injection strength, an LCMW with a large TBWP can be generated. The proposed system has a simple and compact structure. Besides, the center frequency, bandwidth, as well as the temporal duration of the generated LCMWs can be easily adjusted. An experiment is carried out. LCMWs with TBWPs as large as 1.2x105 (bandwidth 12 GHz; temporal duration 10 μs) are successfully generated. The flexibility for tuning the center frequency, bandwidth and temporal duration is also demonstrated.