Offset Frequency Research Articles

On-chip tunable parity‐time symmetric optoelectronic oscillator

Parity‐time (PT) symmetry breaking offers mode selection capability for facilitating single‐mode oscillation in the optoelectronic oscillator (OEO) loop. However, most OEO implementations depend on discrete devices, which impedes proliferation due to size, weight, power consumption, and cost. In this work, we propose and experimentally demonstrate an on-chip tunable PT‐symmetric OEO. A tunable microwave photonic filter, a PT‐symmetric mode‐selective architecture, and two photodetectors are integrated on a silicon‐on‐insulator chip. By exploiting an on‐chip Mach–Zehnder interferometer to match the gain and loss of two mutually coupled optoelectronic loops, single‐mode oscillation can be obtained. In the experiment, the oscillation frequency of the on-chip tunable PT‐symmetric OEO can be tuned from 0 to 20 GHz. To emulate the integrated case, the OEO loop length is minimized, and no extra-long fiber is used in the experiment. When the oscillation frequency is 13.67 GHz, the single‐sideband phase noise at 10-kHz offset frequency is −80.96 dBc / Hz and the side mode suppression ratio is 46 dB. The proposed on-chip tunable PT‐symmetric OEO significantly reduces the footprint of the system and enhances mode selection.

Modulation transfer spectroscopy offset laser frequency stabilization laser

One of the key parts of laser system of atomic gravimeter based on cold atoms is investigated. In order to construct optical system of atomic gravimeter the laser offset frequency stabilization is needed. Method for frequencydoubled fiber laser’s offset frequency stabilization is suggested and developed. This method is based on modulation transfer spectroscopy and the usage of fiber electro-optical modulator. The experimental scheme of this method is described. The error signals for offset frequency stabilization of frequency-doubled fiber laser are obtained. In order to maximize error signal’s amplitude, experimental parameters such as cell’s temperature, pump and probe beam intensities and electrooptical modulators signal amplitudes are optimized. The influence of polarization on error signal’s amplitude is investigated. It is shown that circular polarization allows to achieve error signal with higher amplitude. The achieved results can be applied to the construction of quantum gravimeter, quantum frequency standards and to the laser cooling experiments.

Resolving Doppler Ambiguity for Fast-moving Targets with FDA-MIMO Radar

Although the problem of range ambiguity is solved with the frequency diverse array (FDA)-multiple-input multiple-output (MIMO) radar by utilizing the degree-of-freedom (DOFs) in the range domain, the phenomenon of Doppler ambiguity occurs for fast-moving target. In this article, an offset frequency alignment (OFA) method is proposed to solve the problem of Doppler ambiguity in FDA-MIMO radar. At the design stage, the Doppler frequency offsets, corresponding to different transmit pulses, are aligned by eliminating the residual phases. In this regard, the point targets can be focused in the transmit spatial frequency domain. Furthermore, the Doppler ambiguity index is estimated after principal velocity compensation resorting to maximum likelihood (ML) criterion, where both the cases of known and unknown range ambiguity indexes are investigated respectively. Moreover, in order to ensure the estimation performance, the frequency offset across the transmit array elements is designed by enlarging the term related to the Doppler frequency offset. At the analysis stage, the performance of Doppler ambiguity index estimation in terms of root mean square error (RMSE) is assessed in comparison with the Cramer-Rao bound (CRB). Numerical results are provided to verify the effectiveness of the proposed method to resolve the Doppler ambiguity.

Application of a global–local full‐waveform inversion of Rayleigh wave to estimate the near‐surface shear wave velocity model

AbstractWe present a global–local full‐waveform inversion (FWI) of surface waves to estimate a high‐resolution shear wave velocity model of the near‐surface at the site of Grenoble (France). The seismic data we use have been acquired in the framework of the InterPACIFIC project. A first attempt is made by employing the multichannel analysis of surface waves (MASW) to invert the fundamental modes of Rayleigh waves. This inversion is solved through a global optimization driven by the neighbourhood algorithm. However, the limiting 1D assumption, together with the severely ill‐posedness of the MASW inversion motivate us to exploit all the information content of the recorded Rayleigh waves (i.e., travel‐times and amplitudes) by implementing a global–local FWI approach. We first perform a global FWI in which a genetic algorithm (GA) is used to minimize the L2 norm difference between observed and simulated seismic waveforms up to 30 Hz. This inversion employs a two‐grid scheme in which the subsurface is described by a fine grid input to the forward modelling, whereas the unknowns are defined on a coarse grid. A bilinear interpolation brings the coarse‐grid model into the fine grid. To accelerate the convergence, two strategies are considered; offset marching and frequency marching. Then, the long‐wavelength velocity profile provided by the GA inversion is used as the starting point for a local FWI for further refinement of the predicted model. In this case, we employ a frequency‐marching strategy up to a maximum frequency of 60 Hz. Both the global and local approaches use a finite difference code for the forward computation. Despite the limited a priori information infused into the inversion framework, the presented global–local FWI scheme provides reliable results as demonstrated by the good match between recorded and predicted seismograms and by the agreement of the estimated velocity with both nearby borehole data and stratigraphic information on the study site. Our global–local strategy also achieves better data fitting and improved matching with the available borehole data with respect to the velocity profile estimated when the local FWI is started from the MASW predictions.

Composite pulse combinations for chirp excitation

Composite pulses are the efficient method for broadband excitation to get control of the limitations of high field NMR, such as resonance offset effects with constraints on rf power that leads to signal intensity distortion. Phase-modulated chirp pulses are used as ordered composite pulse sequences in this paper as CHORUS sequence in a high-field NMR spectrometer (BRUKER 750 MHz) for broadband excitation. The composite pulse sequence applies chirp pulses with the forward and the reverse sweep mechanisms. A single excitation pulse combines adiabatic and non-adiabatic rotation, explained as a three-phase rotation, which leaves the magnetizing vectors to a non-uniform phase dispersion as a function of the offset frequency. One adiabatic refocusing pulse of the double sweep rate after the excitation pulse cannot satisfactorily compensate for the phase dispersion. Hence, composite self-refocussing CHORUS excitation pulse, with forward, reverse, and their combinations are used to remove the non-uniform phase dispersion generated due to offset resonance frequency. Four such combinations of composite pulses are produced with analytical explanation in this paper. MATLAB simulation results and experimental verification on the BRUKER 750 MHz NMR spectrometer of the composite pulses are also presented in this paper.

Complete characterization of picosecond optical pulses by the offset frequency intensity modulation.

We present a method for characterizing the intensity waveform, spectrum, frequency chirp, and spectral phase of picosecond pulses at a moderate repetition rate of ∼100 MHz. The proposed method exploits the intensity modulation at ∼10 GHz, which is slightly offset from the integer multiple of the repetition rate of the pulses. The modulated pulses are split into two, and one is measured by an optical spectrum analyzer, whose output is detected by a lock-in amplifier, while the other is directly detected by a photodiode and its output is used as a reference signal of the lock-in amplifier. In the experiment, we demonstrate the measurement of picosecond Ti:sapphire laser pulses to investigate frequency chirp induced by self-phase modulation. We anticipate that the proposed method will be useful for the characterization of various types of picosecond pulses.

Time Domain IRCI-Free Pulse Compression for OQAM-OFDM Radar System

In this article, a novel majorization-minimization (MM)-based time domain pulse compression method (MM-based TDPCM) is proposed for offset quadrature amplitude modulation-based orthogonal frequency division multiplexing (OQAM-OFDM) radar system. We first propose a TDPCM by constructing a general linear model from the time domain with the estimated weights of the OQAM-OFDM signal and solving the model with a whitening operation to complete the pulse compression. The proposed TDPCM greatly reduces the required number of subcarriers for the given range cells and achieves inter range cell interference (IRCI)-free pulse compression. Furthermore, the MM-based TDPCM is proposed to maximize the signal-to-noise ratio (SNR) of the TDPCM. By theoretically analyzing the SNR performance of the TDPCM, we develop an optimization model to design the transmitted weights of the OQAM-OFDM signal. Then, the MM algorithm is proposed to solve the optimization model, realizing the maximum SNR output. Finally, numerical simulation results verify the superior performance of the proposed MM-based TDPCM.

Time and Frequency Synchronization for OTFS

In this letter, we propose timing offset (TO) and carrier frequency offset (CFO) estimators for orthogonal time frequency space modulation (OTFS). The proposed estimators do not require any additional training overheads as they deploy the same pilot signal that is used for channel estimation. Hence, no additional training overhead is required for synchronization, thanks to the periodic properties of the pilot signal in the delay-time domain. Our proposed TO estimator finds the start of each OTFS block by searching for a periodic sequence in delay and time dimensions. The CFO is then estimated by finding the mean of the angles of a two-dimensional correlation function at the best timing instant. As a novel aspect of these estimators, the multipath diversity of the channel is exploited to achieve a high estimation accuracy. Finally, we show the efficacy of our proposed synchronization techniques through extensive simulations.

A fully digital open‐loop clock and data synchronizer for ultra‐low power super‐regenerative receivers

SummaryIn this paper, a clock and data synchronizer (CDS) is presented to improve channel selectivity of digitally assisted super‐regenerative receivers (SRRs). The proposed CDS performs phase and frequency adjustment of the quench signal using a fully digital open‐loop architecture removing the need for conventional phase‐locked loop (PLL) architectures. The required signal shaping of the recovered data is also performed by the proposed CDS to restore the nonreturn‐to‐zero data format without using any pulse width expander or sample and hold circuit. A multichannel SRR is implemented employing the proposed CDS where a Q‐enhancement procedure is also adopted to further improve the channel selectivity. The proposed SRR operates at 2.4‐GHz ISM band and supports a data rate of 1 Mb/s, while the sensitivity is about −88 dBm, and the selectivity is better than −18 dB at a 10‐MHz offset frequency. Implemented using a 0.18‐μm standard CMOS process and with a 1.1‐V supply voltage, the proposed SRR consumes about 0.4 mW.

Dual-comb spectroscopy using free-running mechanical sharing dual-comb fiber lasers

We demonstrate balanced-detection dual-comb spectroscopy using two free-running mechanical sharing dual-comb fiber lasers assisted by an all-computational digital phase correction algorithm. The mutual coherence between the combs allows us perform mode-resolved spectroscopy of gaseous hydrogen cyanide by digitally compensating residual timing and offset frequency fluctuations of the dual-comb signal. Setting the repetition rate difference between the combs to 500 Hz (1.5 kHz) yields more than 2000 resolved radio frequency comb lines after phase correction in a 3-dB bandwidth centered at 1560 nm of wavelength. Through coadding the corrected interferograms, we obtain a single time-domain trace with a signal-to-noise ratio (SNR) of 6378 (13 960) and 12.64 (13.77) bits of dynamic range in 1 s of averaging. The spectral SNR of the coadded trace reaches 529 (585), corresponding to a figure of merit of SNR of 1.3 × 106 (1.4 × 106). The measured absorption spectrum of hydrogen cyanide agrees well with the HITRAN database.

Miniaturizing Ultrastable Electromagnetic Oscillators: Sub- 10−14 Frequency Instability from a Centimeter-Scale Fabry-Perot Cavity

The best performance from compact, portable, and repeatably manufactured electromagnetic (EM) oscillators has for decades been built upon crystalline quartz resonators operating at radio frequencies. Such a source of frequency-stable EM waves has enabled a wide range of applications of significant technical and societal benefit, such as navigation and communication systems, distributed sensing, geodesy, and fundamental physics. However, meeting demands for increased measurement sensitivity requires pushing beyond a fractional frequency stability of ${10}^{\ensuremath{-}13}$, typical of the best ovenized quartz. To date, such performance has been available in the microwave domain only with the use of complex cryogenic systems, or in the optical domain at the expense of larger volume and weight. In either case, the size, weight, and power of state-of-the-art EM oscillators has relegated their use to laboratory experiments. Here we demonstrate the validity of a manufacturable, compact Fabry-Perot reference that improves upon all other centimeter-scale oscillators by more than a factor of 10, including those based on solid-state optical resonators as well as quartz. In a specific implementation, we show an 8 ml bonded assembly containing three vacuum-gap Fabry-Perot optical cavities with mirrors lithographically fabricated on a single substrate, each with quality factor exceeding 10 billion. A laser stabilized to one of the cavities exhibits thermal-noise-limited phase noise for offset frequencies ranging from 1 Hz to nearly 1 kHz, and fractional frequency stability of $7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$ at 1 s. Our advance with lithographically defined and microfabricated mirrors is validated by rigorous models, which highlight a path to oscillators with size comparable to ovenized quartz, but with significantly improved performance. For example, we predict sub-${10}^{\ensuremath{-}14}$ performance is readily attainable with a Fabry-Perot cavity volume less than 2 ml.

Class‐F power oscillator based on complementary split ring resonator for sub‐6 GHz fifth generation and multistandard applications

SummaryA coupled complementary split‐ring resonator (CSRR) has been proposed. The proposed resonator consists of two coupled 50‐Ω transmission lines and complementary split rings in the ground plane (bottom layer) as defected ground structure (DGS). The proposed bandpass filter (BPF) has a measured stopband attenuation loss of less than −20 dB in the frequency band between 2.3 and 2.9 GHz and a low insertion loss of 1.15 dB. The measurement is carried by a VNA (vector network analyzer) meter of model ZVA67. Then, the proposed resonator (BPF) is utilized with an active device (SiGe BFP 640) as an output matching network of a class‐F oscillator. Fundamentally, this research aims to design and model an optimum achievement of BPF for optimum oscillator performance. The design simulation of the CSRR oscillator has been obtained by ADS and CST programs. The proposed band pass filter is designed and fabricated on a Rogers (RO4003C) micro‐strip material printed with a dielectric constant epsilon of 3.38 and a thickness of 0.813 mm. Depending on this study, the oscillator displays a minimum phase noise of −109.3 dBc/Hz at 1 MHz offset frequency and maximum dBm output power equals 13.4 dBm at 2.45 GHz oscillation frequency. The power dispassion of the proposed oscillator equals 8.3 mW from a 2 V supply voltage. The obtained maximum dBm output power and minimum phase noise is a benefit for power charger wireless applications, sub‐6 GHz fifth generation applications, and multistandard applications.

Microwave signal generation from a parity-time-symmetric optoelectronic oscillator with optical injection locking.

A parity-time (PT) symmetric optoelectronic oscillator (OEO) with optical injection locking is proposed and experimentally demonstrated to generate single-mode microwave signals. A distributed feedback laser is injection locked, which functions as a frequency multiplier for the coarse mode selection of the PT-symmetric OEO. The PT symmetry in the OEO is implemented by using a polarization-dependent Sagnac loop to form two identical loops for coupling. By tuning the two polarization controllers in the Sagnac loop, the gain/loss and coupling coefficient of the two loops can be controlled, and single-mode oscillation in the OEO could be achieved at the broken PT-symmetry condition. Microwave signal generation at the frequency of 6.427GHz is obtained from the proposed OEO. The phase noise is about -105dBc/Hz at an offset frequency of 10kHz.

600-GHz High-Power Signal Sources Based on 250-nm InP HBT Technology

Two 600-GHz radiation signal sources, a single- and four-element oscillators, have been developed based on a 250-nm InP heterojunction bipolar transistor technology. The single-element unit oscillator adopts the common-emitter cross-coupled structure with reactive emitter degeneration, which enables second harmonic oscillation around 600 GHz with enhanced output power. Based on the unit oscillator, the four-element coupled oscillator with cascaded two-way shunt power combiners was developed to further increase the output power. Both oscillators are integrated with on-chip patch antennas with simulated antenna gain of 3.5 dBi and directivity of 8.0 dBi at 600 GHz. The measured oscillation frequencies of the two signal sources are 580–586 GHz and 583–591 GHz, respectively, varied with the base bias. They exhibited the measured peak effective isotropic radiation power (EIRP) of 1.1 and 2.7 dBm, respectively, which correspond to the radiated output power of −7.5 and −5.9 dBm. The total dc power consumptions are 34.5 and 129.6 mW, which lead to the estimated dc-to-RF efficiencies of 0.52 and 0.2% for the two sources. The measured phase noises are −88.6 and −90.1 dBc/Hz at 10-MHz offset frequency for the single- and four-element oscillators, respectively.

Low frequency-to-intensity noise conversion in a pulsed laser cavity locking by exploiting carrier envelope offset

We report on the dependence of the frequency-to-intensity noise conversion in the locking of an ultrafast laser against a high-finesse optical enhancement resonator from the carrier envelope offset frequency. By a proper combination of the cavity finesse and laser carrier envelope offset frequency, it is possible to optimize the signal-to-noise ratio of the laser intensity trapped into the optical resonator. In this paper, we describe the effect of the laser-enhancement cavity coupling on the intracavity power relative noise, and we demonstrate both theoretically and experimentally its reduction.

A Microwave Photonic Link With Quadrupled Capacity Based on Coherent Detection and Digital Phase Noise Cancellation

A microwave photonic link (MPL) with quadrupled capacity based on coherent detection and digital phase noise cancellation is proposed and experimentally demonstrated. At the transmitter, a continuous-wave (CW) light wave is intensity modulated by four independent microwave vector signals with two having an identical center microwave frequency at a dual-parallel Mach-Zehnder modulator (DPMZM) consisting of two dual-drive MZMs (DEMZMs) with the sub-DEMEMs biased at the quadrature transmission point. Four intensity-modulated optical signals are generated and transmitted over a single-mode fiber (SMF) to a coherent receiver. To perform coherent detection, a second CW laser source as a local oscillator (LO) is also applied to the coherent receiver. To recover the microwave vector signals, a novel digital phase noise cancellation algorithm is developed and applied to eliminate the joint phase noise from the transmitter laser source and the LO laser source as well as the unstable offset frequency between the two laser sources. A theoretical analysis is performed to show the recovery of the microwave vector signals which is verified by an experiment. For four independent 16 quadrature amplitude modulation (16-QAM) microwave vector signals with a symbol rate of 0.5 GSymbol/s, error-free transmission over a 9-km SMF is achieved when the received optical power at the coherent receiver is higher than −18 dBm with forward error correction (FEC).

Stability improvement of a dual-loop optoelectronic oscillator based on self-phase locking.

In this study, we experimentally demonstrate what we believe is a novel dual-loop optoelectronic oscillator (OEO) with a self-phase locking loop (SPLL). Using this feedback loop, the phase of the oscillating signal is locked to its past by adjusting the DC bias voltage of the used Mach-Zehnder modulator. In this way, the oscillating frequency stability can be improved. Proving experiments on a 10-GHz OEO are performed. The results show that more than 20 dB improvements in the phase noise at low offset frequencies are achieved, the frequency fluctuation is reduced to less than 4 kHz in an hour, and the corresponding Allan deviation is decreased by 1 order of magnitude owing to the SPLL. This frequency stabilization scheme without use of any external reference sources has a great prospect in an integrated OEO.

Frequency combs with multiple offsets in THz-rate microresonators.

Octave-wide frequency combs in microresonators are essential for self-referencing. However, it is difficult for the small-size and high-repetition-rate microresonators to achieve perfect soliton modelocking over the broad frequency range due to the detrimental impact of dispersion. Here we examine the stability of the soliton states consisting of one hundred modes in silicon-nitride microresonators with the one-THz free spectral range. We report the coexistence of fast and slow solitons in a narrow detuning range, which is surrounded on either side by the breather states. We decompose the breather combs into a sequence of sub-combs with different carrier-envelope offset frequencies. The large detuning breathers have a high frequency of oscillations associated with the perturbation extending across the whole microresonator. The small detuning breathers create oscillations localised on the soliton core and can undergo the period-doubling bifurcation, which triggers a sequence of intense sub-combs.

Collinear opto-optical loss modulation for carrier-envelope offset stabilization of a fiber frequency comb.

Opto-optical loss modulation (OOM) for stabilization of the carrier-envelope offset (CEO) frequency of a femtosecond all-fiber laser is performed using a collinear geometry. Amplitude-modulated 1064 nm light is fiber coupled into an end-pumped semiconductor saturable absorber mirror (SESAM)-mode-locked all-polarization-maintaining erbium fiber femtosecond laser, where it optically modulates the loss of the SESAM resulting in modulation of the CEO frequency. A noise rejection bandwidth of 150 kHz is achieved when OOM and optical gain modulation are combined in a hybrid analog/digital loop. Collinear OOM provides a simple, all-fiber, high-bandwidth method for improving the CEO frequency stability of SESAM mode-locked fiber lasers.

CMOS Fractional-N Frequency Synthesizer for UHF RFID Reader Applications With Transformer-Based ISF Manipulation VCO

This brief presents the CMOS fractional-N frequency synthesizer for UHF RFID reader applications. With stringent phase noise (PN) specifications for UHF RFID transceiver, our proposed synthesizer is designed to have a narrow loop bandwidth and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2^{nd}$ </tex-math></inline-formula> -order loop filter as the optimum solution paired with low noise VCO. Then, we propose the transformer-based impulse sensitivity function (ISF) manipulating VCO that supports the target PN of the frequency synthesizer, albeit with large pass-band characteristic. Compared to conventional ISF manipulating VCO, our proposed solution improves the PN by 11.3 and 14.7 dB at 10 kHz and 1 MHz offset frequencies, respectively. Figure of merit (FOM) is also superior to conventional one by 7.4 and 10.9 dB at aforementioned offset frequencies. The frequency synthesizer is implemented in a 55nm CMOS technology as a part of the UHF RFID transmitter and consumes 38.4 mW power with 0.413 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$mm^{2}$ </tex-math></inline-formula> active area. With comparison to the state-of-the-art frequency synthesizer at sub-6GHz operating frequency, only our solution satisfies the target PN for EPC global standard and various local regulations across the entire UHF RFID operating frequency range.