Phase Noise Level Research Articles

Optoelectronic oscillator system with low phase noise based on a microwave multiplexor: evaluation of construction possibilities

The paper is dedicated to the current issue of microwave photonics: the development of optoelectronic oscillators for ultra-high frequency signals. The interest in creating such oscillators is largely driven by the possibility of obtaining signals with low levels of phase noise. The use of multiplexers as fi lters in optoelectronic oscillators opens up new possibilities in building optoelectronic systems for generating ultra-high frequency signals at different frequencies. This implementation of the optoelectronic generator allows for discrete regulation of the frequency of the generated signal, or generating the signal simultaneously at multiple specifi ed frequencies. In the investigated system, phase noises were measured: less than 100 dBc/Hz at 1 kHz offset from the carrier frequency and less than 130 dBc/Hz at 10 kHz offset from the carrier frequency. The obtained results confirm the potential use of multiplexers as bandpass filters, which is important for the development and optimization of optoelectronic oscillators

Deep Learning Training Data for Phase Unwrapping of SAR Interferograms

Phase unwrapping is an essential process in synthetic aperture radar interferometry that restores phase signals constrained within the range of (-π, π) to their true phase values. Traditional algorithm-based methods can introduce significant errors due to rapid and steep phase gradient or noise, which negatively impact terrain elevation and surface displacement analyses. To overcome these limitations, deep learningbased phase unwrapping techniques have been proposed; however, there has been insufficient previous studies due to the lack of accurate training and test data. This paper aims to share the training data generated using the phase unwrapping simulation method with locally-different phase noise. The data were generated by the simulation of topographic phases and phase noise, atmospheric and orbital distortions. Additionally, data augmentation for phase variation and noise levels was applied to address data imbalance issues. The shared data consists of two types: one with a constant phase noise level for each patch, and another that simulates locally different phase noise based on augmented coherence data. This data is primarily effective for unwrapping topographic phase components and holds significance as the first phase unwrapping training data of synthetic aperture radar interferograms shared in Korea. We expect this resource to serve as foundational data for future phase unwrapping technology research, including applications for upcoming satellites like KOMPSAT-6 and water resource satellites.

Short-term stability of a microcell optical reference based on the Rb atom two-photon transition at 778 nm

We report on the development and short-term stability characterization of an optical frequency reference based on the spectroscopy of the rubidium two-photon transition at 778 nm in a microfabricated vapor cell. When compared against a 778 nm reference signal extracted from a frequency-doubled cavity-stabilized telecom laser, the short-term stability of the microcell frequency standard is 3.5×10−13τ−1/2 until 200 s, in good agreement with a phase noise level of +43dBrad2/Hz at 1 Hz offset frequency. The two main contributions to the short-term stability of the microcell reference are currently the photon shot noise and the intermodulation effect induced by the laser frequency noise. Retaining a relevant margin of progress, these results show the interest of this spectroscopic approach for the demonstration of high-stability miniaturized optical vapor cell clocks. Such clocks are poised to be highly beneficial for applications in navigation, communications, and metrology.

Demonstration of a photonic integrated circuit for quantitative phase imaging

Quantitative phase imaging (QPI) is an optical microscopy method that has been developed over nearly a century to rapidly visualize and analyze transparent or weakly scattering objects in view of biological, medical, or material science applications. The bulky nature of the most performant QPI techniques in terms of phase noise limits their large-scale deployment. In this context, the beam shaping properties of photonic chips, combined with their intrinsic compact size and low cost, could be beneficial. Here, we demonstrate the implementation of QPI with a photonic integrated circuit (PIC) used as an add-on to a standard wide-field microscope. Combining a 50 mm×50 mm footprint PIC as a secondary coherent illuminating light source with an imaging microscope objective of numerical aperture 0.45 and implementing a phase retrieval approach based on the Kramers–Kronig relations, we achieve a phase noise of 5.5 mrad and a diffraction limited spatial resolution of 400 nm. As a result, we retrieve quantitative phase images of Escherichia coli bacteria cells and monolayers of graphene patches from which we determine a graphene monolayer thickness of 0.45±0.15 nm. The current phase noise level is more than five times lower than that obtained with other state-of-the-art QPI techniques using coherent light sources and comparable to their counterparts based on incoherent light sources. The PIC-based QPI technique opens new avenues for low-phase noise, miniature, robust, and cost-effective quantitative phase microscopy.

Investigation of jitter in an optoelectronic oscillator with suppressed parasitic harmonics

The increasing demands on the level of phase noise and frequency stability of microwave signals in radar and communication systems have led to the search for new solutions beyond standard microwave devices. One of the perspective fields to respond to modern challenges is microwave photonics, which combines the principles and approaches of microwave technology with the application of a photonic component base. Optoelectronic oscillators (OEO) have a low level of phase noise, and as a result, low jitter, which corresponds to the high stability of the generated microwave signals. The principle of operation of the OEO is based on the circulation of a microwave signal through a microwave photonic ring resonator consisting of microwave and optical paths. The resonator with a high Q-factor, a wide frequency range between the resonant harmonics and feedback, that ensures a balance of amplitudes, is necessary to use in order to implement the OEO. Over the two decades, many methods have been proposed to reduce phase noise and jitter of OEO, among that not only an increase in the quality factor of the resonator, but also the suppression of parasitic harmonics, have been discussed. However, nowadays the multi-ring configurations of the OEO for suppression of parasitic harmonics have clearly not been sufficiently studied. The purpose of this work is to investigate the suppression of parasitic harmonics and jitter reduction in two-ring OEO. A dual-ring OEO with a parallel configuration of fiber-optic delay lines with different lengths was chosen as the object of research. The proposed configuration is based on an interference circuit on fiber-optic lines with passive optical amplification. The parameters of the interference circuit were selected in order to suppress the second harmonic to -25 dB, while a low noise level is hold on. It is shown that a dual-ring OEO with fiber-optic delay lines of 600 m and 531 m long has a jitter of 434 fs in the frequency range from 100 Hz to 7 GHz. The proposed design can be used to reduce the jitter of an optoelectronic oscillator.

Wideband microwave frequency response measurement based on optical phase-locked loop.

Frequency response measurement, or the forward transmission coefficient (S21) measurement for a two-port network, is the key function of a vector network analyzer (VNA). In this paper, a broadband and high dynamic range (DR) microwave S21 parameter measurement scheme based on an optical phase-locked loop (OPLL) is proposed. By heterodyning two phase-locked hybrid integrated ultra-narrow linewidth lasers, a microwave signal with low phase noise and spurious level is generated as the incident signal and reference signal, and the signal frequency can be easily manipulated over a wide range by tuning the master laser wavelength. In the receiver, the radio frequency (RF) signals are down-converted to intermediate frequency (IF) signals with the phase-locked lasers. By sampling and processing the IF signals the S21 parameter of the DUT can be acquired. A proof-of-concept experiment is performed, and with available photodetectors, phase modulators and phase-locked loops, a measurable range of 2 to 18 GHz is achieved. The demonstrated minimum frequency resolution of the OPLL-based RF signal synthesizer is 10 Hz. The system DR exceeds 68 dB at an equivalent resolution bandwidth of 1 kHz. The S21 parameters of a power divider and a bandpass filter are measured, and the results are well consistent with those of a commercial VNA. The DR and measurable range limit factors and possible extension methods are discussed. The proposed approach offers a high potential way to develop a wideband, high DR, and fully integrated VNA.

Density-profile imaging using a second harmonic dispersion interferometer configured with reflective-beam expanders.

A Second-Harmonic Dispersion Interferometer (SHDI) is assembled to measure the two-dimensional, line-integrated density profile of a pulsed-plasma jet using probe-beam diameters well beyond the 1mm diameters typically used in such instruments. An initial prototype demonstrated the technique using 7mm beam diameters, which are now increased to 35mm diameter using two types of beam expanders: an achromatic-beam expander (ABE) or a reflective-beam expander (RBE). ABEs were found to add a periodic background to the measured-phase image with a magnitude of the order of Δϕ ∼ 2π radians, compared to the background phase noise level in the system configured without beam expanders at Δϕbg ∼ 0.025 radians. Subtraction of the background phase in a sample image reduced the effect of the ABE phase offset to a level of Δϕ ∼ 0.1 radians, enhancing the quality of the density measurements. Reflective-beam expanders (RBEs) did not modify the background phase appreciably and were a significant improvement, allowing the instrument to be used for 2D (r, z) density-profile measurements of a 3cm diameter × 5cm long, pulsed-plasma jet. Variations in the timing parameters for the plasma gun, specifically the gas valve opening time and the gas-injection delay, for a constant discharge current were used to map the plasma gun's performance, indicating a nominal line-integrated electron density of Nedl ≳ 3 × 1015 cm-2 and a volumetric density of Ne ≃ 9 × 1015cm-3. The results obtained for the RBE configuration demonstrate that the 2D-SHDI platform may be scaled to even larger sample areas and a rep-rated system, with the ability to potentially provide for a reproducible, time-resolved (∼1 ns), high resolution (∼100μm) measurement of 2D plasma-density profiles.

Dual‐channel, high‐frequency optoelectronic oscillators utilizing optically‐injected lasers

AbstractWe propose a novel approach to dual‐channel optoelectronic oscillators (OEOs) with enhanced frequency band by leveraging directly modulated (DM) semiconductor lasers under optical injection. In this configuration, the frequency‐tuned optical signal from a master laser is introduced into a single‐mode slave laser, facilitating multioptical‐mode operation. The resulting multiple optical frequencies emitted by the slave laser facilitates a DM‐OEO signal at a frequency exceeding the laser's intrinsic modulation bandwidth. Through the deployment of a dual‐channel OEO based on the DM multimode laser signal, stable oscillation signals have been successfully achieved simultaneously at 15 and 18 GHz with phase noise levels of 96.43 and 95.62 dBc/Hz, respectively, at a 10‐kHz offset frequency.

The influence of phase noise and nonlinear distortions of high-speed digital-to-analog converters on the parameters of digital communication systems

Problem statement. The trend in modern microwave electronics to transfer analog functions to the digital domain has led to the emergence and active use of high-speed digital-to-analog converters (DACs) in special operating modes in promising communication systems. However, optimization of power consumption and economic costs of signal generators (for example, through the use of simplified clock generators or by saving FPGA memory) leads to an increase in phase noise and nonlinear distortions in the output signal, which has a significant impact on the parameters of the communication system. Goal. Evaluation of phase noise and nonlinear distortions of signal generators based on high-speed digital-to-analog converters, as well as the study of their effect on the parameters of a digital communication system. Results. Expressions for estimating the spectral power density of phase noise of a signal generator based on a high-speed DAC are proposed. It is determined that the level of phase noise of the shaper is mainly determined by the noise of the clock generator. The jitter of the communication system was evaluated when using a surfactant generator and a PLL-based synthesizer as a clock generator. A mathematical model of the output signal of the shaper is proposed, taking into account nonlinear distortions caused by sampling, phase code truncation and amplitude quantization. A model of a communication system with multi-position quadrature amplitude modulation has been developed to evaluate parameters taking into account phase noise and nonlinear distortion of the shaper based on high-speed DACs. It is determined that the intrinsic phase noise of the signal generator leads to an increase in the probability of bit error (by about an order of magnitude compared to ideal formers). The use of surfactant generators as clock generators makes it possible to reduce the probability of bit errors of the communication system by 3-5 times compared with PLL-based synthesizers. Practical significance. It is shown that the displacement of points in the signal constellation is mainly influenced by nonlinear distortions of the output signal of high-speed DACs caused by truncation of the phase code, as well as incomplete suppression of spectral components located in the neighboring Nyquist zone. The proposed mathematical apparatus makes it possible to determine the optimal frequency ratios in the structure of the shaper, at which the lowest values of the displacement of the constellation points are achieved.

Ultralow noise microwave synthesis via difference frequency division of a Brillouin resonator

Low phase noise microwave oscillators are at the center of a multitude of applications that span the gamut of photonics and electronics. Within this space, optically derived approaches to microwave frequency synthesis are particularly compelling owing to their unique combination of ultrawideband frequency access and the potential for resiliency to temperature and environmental perturbation via common-mode noise rejection. We demonstrate here an optical frequency divider that uses the 30 terahertz frequency gap between two stimulated Brillouin scattering (SBS) lasers as the basis for frequency division. The resulting microwave signal, centered at 10 GHz frequency, exhibits exceptionally low phase noise levels of −95dBc/Hz and −110dBc/Hz at 10 Hz and 100 Hz frequency offset, respectively. Moreover, the two SBS lasers, generated from a common fiber resonator, exhibit a high degree of correlated noise cancellation in their frequency difference. We measure 16.1 dB of noise rejection against intentionally applied vibrations, thus showcasing a promising pathway towards portable and robust ultralow noise photonic-microwave synthesis.

Microwave magnonic micro-oscillator based on a nm-thick YIG film

A numerical model describing a magnonic active ring oscillator (MARO) based on a microscopic spin-wave delay line is proposed. The model considers excitation, propagation, and reception of the magnetostatic surface waves in a yttrium iron garnet (YIG) magnetic film with a thickness in the nanometer range. The waves are excited and received with a microscopic coplanar antenna. We employed the model to analyze the influence of the YIG-film thickness and the distance between the antennas on the MARO performance characteristics. We showed that an increase in the delay time inserted by the delay line reduces the phase noise of the MARO and increases the auto-oscillation threshold. In addition, we found a relation between the auto-oscillation threshold, the thickness of the YIG film, and the distance between the antennas. The relation helps design miniature MAROs and suggests a way to reduce the phase noise of the device. The model predicts a phase noise level of −115 dBc/Hz at a 10 kHz offset from an oscillation frequency in the vicinity of 5 GHz for the MARO based on a 100 nm-thick YIG film and 56 μm of distance between the coplanar nano-antennas of the YIG-film based delay line. We believe that this is a clear way forward to microminiaturize the time-delay feedback microwave auto-oscillators. A further reduction in the phase noise down to −125 dBc/Hz at a 10 kHz offset is found in a model of cascaded connection of several microscopic spin-wave delay lines.

Low phase noise microwave oscillator based on gain driven polariton

Low phase noise oscillators are key building blocks of many high-end microwave systems. This work introduces a phase noise reduction mechanism through a gain driven polariton platform, where coherent coupling is used to suppress frequency distribution around the carrier, effectively reducing the phase noise. The design process for achieving low phase noise performance is outlined, and three prototypes are constructed, all of which feature key components, such as gain-embedded planar microwave cavity, yttrium iron garnet, and magnets. In particular, the first prototype is used to showcase the phase noise reduction mechanism, while the second prototype, a fixed-frequency oscillator working at 3.544 GHz, exhibits phase noise levels of −117 and −132 dBc/Hz at 10 and 100 kHz offset frequencies, respectively. The third prototype offers a tuning range from 2.1 to 2.7 GHz, while maintaining phase noise levels comparable to the second prototype.

Coherent multi-band MIMO radar: robustness analysis to SSMF-based RF signal delivery.

A numerical evaluation is conducted to assess the impact of distributing radio frequency (RF) signals through optical fiber links on the performance of a coherent multi-band multiple-input multiple-output (MIMO) radar system. The analysis focuses on scenarios where the antennas are widely separated in comparison to the employed signal wavelengths. The development of a model to quantify the phase noise (PN) induced on each RF band due to the signal transmission through optical fiber links between the centralized base station and each radar peripheral is described. Monte Carlo simulation results are collected to estimate the key performance indicators (KPIs) for varying standard single-mode fiber (SSMF) length and different PN contributions. The main contributors to the PN are revealed to be chromatic dispersion (CD), double Rayleigh scattering (DRS), and mechanical vibrations. In a shipborne scenario, a significant performance degradation occurs only when the length of the fiber links reaches approximately 20 km. Further, the PN impact has also been studied in a shipborne scenario to analyze the robustness of the system for worse phase noise level assumptions. The results reveal excellent robustness of the proposed centralized acquisition and processing approach in the presence of both very long fiber links and economically employed RF oscillators.

Quiet point engineering for low-noise microwave generation with soliton microcombs

Low-noise microwave signals can be efficiently generated with microresonator-based dissipative Kerr solitons (microcombs). However, the phase noise level in integrated microcombs is presently several orders of magnitude above the limit imposed by fundamental thermorefractive noise, resulting from residual pump laser frequency noise transduction to the soliton repetition rate. This effect can be substantially reduced by accessing a quiet point (QP) in the parameter space, where the transduction is compensated by the dispersive wave (DW) recoil, which conventionally relies on accidental mode crossings. Here we present a method to deterministically engineer the QP, both in terms of spectral width and position, and we discover a continuum of possible QPs within the soliton existence region. Using two controlled mode crossings, we obtain regions where the QPs interact with each other, extending the noise suppression range. Our work demonstrates a promising way to reach the fundamental limit of low-noise microwave generation in integrated microcombs.

A low power varactor based digitally controlled oscillator design in 180 nm CMOS technology

This paper reports two distinct architectures for digitally-controlled oscillators (DCOs) utilizing MOS varactor, designed in TSMC 180 nm CMOS technology. The first DCO design employs a CMOS inverter, while the second design features a Three-Transistors (3T) NAND gate as a delay stage inverter. Using these delay stages, three-bit, five-bit, and seven-bit controlled DCO circuits have been designed. For the inverter-based DCO circuit, the frequency spans from 4.844 to 2.708 GHz, 2.523 to 0.853 GHz, and 1.364 to 0.253 GHz, with a power consumption of 0.958 mW, 1.597 mW, and 2.236 mW for three-bit, five-bit, and seven-bit DCO variants, respectively. Further, the 3T-NAND gate-based DCO circuit exhibits oscillation frequencies ranging from 2.024 to 0.517 GHz, 0.867 to 0.131 GHz, and 0.341 to 0.033 GHz, with the resulting power consumption of 0.335 mW, 0.559 mW, and 0.782 mW. Equally significant, the proposed inverter-based DCO attains phase noise of − 102.61 dBc/Hz@1MHz, − 99.65 dBc/Hz@1MHz, and − 117.54 dBc/Hz@1MHz, accompanied by corresponding figures of merit (FoM) 174.94 dBc/Hz, 161.27 dBc/Hz, and 165.10 dBc/Hz for three-bit, five-bit, and seven-bit control words, respectively. For the 3T-NAND gate-based DCO, phase noise levels register at − 93.51 dBc/Hz@1MHz, − 113.07 dBc/Hz@1MHz, and − 106.96 dBc/Hz@1MHz, with FoM values of 160.23 dBc/Hz, 166.70 dBc/Hz, and 150.30 dBc/Hz for three-bit, five-bit, and seven-bit DCO variants, respectively. The comprehensive analysis of the proposed DCOs demonstrates the power supply variations, phase noise deviations, and frequency variations. The reported DCOs perform better with regard to output frequency range, power consumption, and overall FoM.

The photodetection of ultrashort optical pulse trains for low noise microwave signal generation.

Electrical signals derived from optical sources have achieved record-low levels of phase noise, and have demonstrated the highest frequency stability yet achieved in the microwave domain. Attaining such ultrastable phase and frequency performance requires high-fidelity optical-to-electrical conversion, typically performed via a high-speed photodiode. This paper reviews characteristics of the direct photodetection of optical pulses for the intent of generating high power, low phase noise microwave signals from optical sources. The two most popular types of photodiode detectors used for low noise microwave generation are discussed in terms of electrical pulse characteristics, achievable microwave power, and photodetector nonlinearities. Noise sources inherent to photodetection, such as shot noise, flicker noise, and photocarrier scattering are reviewed, and their impact on microwave phase fidelity is discussed. General guidelines for attaining the lowest noise possible from photodetection that balances power saturation, optical amplification, and amplitude-to-phase conversion, are also presented.

Continuous optical generation of microwave signals for fountain clocks.

For the optical generation of ultrastable microwave signals for fountain clocks, we developed a setup based on a cavity stabilized laser and a commercial frequency comb. The robust system, in operation since 2020, is locked to a 100MHz output frequency of a hydrogen maser and provides an ultrastable 9.6GHz signal for the interrogation of atoms in two cesium fountain clocks, acting as primary frequency standards. Measurements reveal that the system provides a phase noise level that enables quantum projection noise limited fountain frequency instabilities at the low 10-14(τ/s)-1/2 level. At the same time, it offers largely maintenance-free operation.

Wrapped phase aberration compensation using deep learning in digital holographic microscopy

In digital holographic microscopy (DHM), phase aberration compensation is a general problem for improving the accuracy of quantitative phase measurement. Current phase aberration compensation methods mainly focus on the continuous phase map after performing the phase filtering and unwrapping to the wrapped phase map. However, for the wrapped phase map, when larger phase aberrations make the fringes too dense or make the noise frequency features indistinct, either spatial-domain or frequency-domain based filtering methods might be less effective, resulting in phase unwrapping anomalies and inaccurate aberration compensation. In order to solve this problem, we propose and design a strategy to advance the phase aberration compensation to the wrapped phase map with deep learning. As the phase aberration in DHM can be characterized by the Zernike coefficients, CNN (Convolutional Neural Network) is trained by using massive simulated wrapped phase maps as network inputs and their corresponding Zernike coefficients as labels. Then the trained CNN is used to directly extract the Zernike coefficients and compensate the phase aberration of the wrapped phase before phase filtering and unwrapping. The simulation results of different phase aberrations and noise levels and measurement results of MEMS chip and biological tissue samples show that, compared with current algorithms that perform phase aberration compensation after phase unwrapping, the proposed method can extract the Zernike coefficients more accurately, improve the phase data quality of the consequent phase filtering greatly, and achieve more accurate and reliable sample profile reconstruction. This phase aberration compensation strategy for the wrapped phase will have great potential in the applications of DHM quantitative phase imaging.

High-speed digital-to-analogue converters phase noise modelling

The paper presents a mathematical model of the phase noise power spectral density of a high-speed digital-to-analogue converter. The shapes of the envelopes of the spectrum of the output signal in RFZ3, RFZ4 operating modes are given. The phase noise transfer coefficients for RFZ3, RFZ4 operating modes are obtained. The modelling of the power spectral density of phase noises in the studied operating modes was carried out. The analysis of the received dependences is carried out. It is concluded that RFZ3, RFZ4 modes of operation allow to obtain a lower level of PSD phase noise for images n = 1, 3, 4, 5, which indicates the possibility of generating high-frequency signals with a frequency that is 5-11 times higher than the generated frequency in NRZ mode without noise degradation.

Phase Locking of a THz QC-VECSEL to a Microwave Reference

High resolution frequency study and phase-locking have been performed on a terahertz quantum-cascade vertical-external-cavity surface-emitting-laser operating around 2.5 THz. A subharmonic diode mixer is used to down convert the THz signal to a 100 MHz intermediate frequency that is phase locked to a stable 100 MHz microwave reference. Between 90-95% of the QC-VECSEL signal is locked within 2 Hz of the multiplied RF reference, and amplitude fluctuations on the order of 1-10% are observed, depending on the bias point of the QC-VECSEL. The bandwidth of the locking loop is ∼1 MHz. Many noise peaks in the IF signal are observed, likely corresponding to mechanical resonances in the 10 Hz-10 kHz. These peaks are generally -30 to -60 dB below the main tone, and are below the phase noise level of the multiplied RF reference which ultimately limits the phase noise of the locked QC-VECSEL.