Time-delayed optoelectronic oscillators are at the center of a large body of scientific literature. The complex behavior of these nonlinear oscillators has been thoroughly explored both theoretically and experimentally, leading to a better understanding of their dynamical properties. Beyond fundamental research, these systems have also inspired a wide and diverse set of applications, such as optical chaos communications, pseudorandom number generation, optoelectronic machine learning based on reservoir computing, ultrapure microwave generation, optical pulse-train synthesis, and sensing. The aim of this review is to provide a comprehensive survey of this field, to outline the latest achievements, and discuss the main challenges ahead.

Optoelectronic oscillators with time-delayed feedback

In this article, we investigate exact soliton solutions of nonlinear Schrodinger equation (NLSE) with quadratic-cubic nonlinearity. The Jacobi elliptic functions are employed to study optical solitons. Dark and bright solitons are obtained. Also, the stability analysis of dark and bright solitons for the NLSE with quadratic-cubic nonlinearity is considered.

Soliton solutions of NLSE with quadratic-cubic nonlinearity and stability analysis

On-chip frequency generators for high frequency applications suffer from degradation of key passive components, variable capacitors in particular. In this framework, frequency multipliers can play a key role, allowing the design of voltage-controlled oscillators running at a frequency lower than required with advantage in terms of signal spectral purity and frequency tuning range. In this paper we present two injection locked frequency doublers for Ku-band and F-band applications respectively. Despite differences in implementation details, the same topology where a push-push pair injects a double frequency tone locking an autonomous differential oscillator is adopted. The circuits require limited input signal swing and provide a differential output over a broad frequency range. Dissipating 5.2 mW, the Ku-band multiplier, realized in a 0.13 μm CMOS node, displays an operation bandwidth from 11 GHz to 15 GHz with a peak voltage swing on each output of 470 mV. The F-band multiplier, realized in 65 nm CMOS technology, displays an operation bandwidth from 106 GHz to 128 GHz with a peak voltage swing on each output of 330 mV and a power dissipation of 6 mW. A prototype including the multiplier, driven by a half-frequency standard LC-tank VCO, demonstrates an outstanding 13.1 % tuning range around 115 GHz.

Injection-Locked CMOS Frequency Doublers for μ-Wave and mm-Wave Applications

An ultra-low power wake-up receiver for body channel communication (BCC) is implemented in 130 nm CMOS process. The proposed wake-up receiver uses the injection-locking ring oscillator (ILRO) to replace the RF amplifier with low power consumption. Through the ILRO, the frequency modulated input signal is amplified to the full swing rectangular signal directly demodulated by the following low power PLL-based FSK demodulator. In addition, the energy-efficient BCC link mitigates the sensitivity and selectivity requirements for the receiver, which significantly reduces the power consumption. Furthermore, the auto frequency calibrator (AFC) is adopted to compensate the free running frequency of the ring oscillator which is caused by temperature variation and leakage current. The AFC reuses the PLL-based demodulator to periodically set the free running frequency to the desired frequency without any area overhead. As a result, the proposed wake-up receiver achieves a sensitivity of -62.7 dBm at a data rate of 200 kbps while consuming only 37.5 μW from the 0.7 V supply.

A 37.5 /spl mu/W Body Channel Communication Wake-Up Receiver With Injection-Locking Ring Oscillator for Wireless Body Area Network

An all-optical microwave generation using a multi- wavelength photonic crystal fiber Brillouin laser is presented. A highly nonlinear photonic crystal fiber with the length of 25 m is used as Brillouin gain medium. A Fabry-Perot cavity with two fiber Bragg gratings as reflectors are designed in order to enhance the Brillouin conversion efficiency. The fiber Bragg gratings can be used to selectively excite the jth-order Stokes' wave and suppress other order Stokes' waves. The mechanism for microwave/millimeter- wave generation is theoretically analyzed. In the experiment, both 9.788 GHz and 19.579 GHz microwave signals are achieved through mixing the pump wave with the first-order and the second-order Stokes' waves.

/pdf/microwave-millimeter-wave-generation-using-multi-wavelength-3v76k7z0ex.pdf

Microwave/Millimeter-Wave Generation Using Multi-Wavelength Photonic Crystal Fiber Brillouin Laser

Injection locking characteristics of oscillators are studied both qualitatively and analytically and the closed-form expressions of frequency-pulling and spectrum of the unlocked driven oscillator is estimated with negligible amplitude perturbation. Modifications in spectrum, lock range, and pulling of the oscillator are shown under significant amplitude perturbation. Also an approximate expression of amplitude perturbation is presented. Numerical simulations and experimental results describing the oscillator's pulling process under significant amplitude perturbation are given.

Study of Injection Locking With Amplitude Perturbation and Its Effect on Pulling of Oscillator

Injection-locking characteristics of a single-loop optoelectronic oscillator (OEO) under an independent sinusoidal RF signal injection are investigated. The mathematical model of the unlocked-driven system is developed to represent phase perturbation of the generated output RF signal caused by the RF injection signal. The closed-form expressions of the output RF spectra distorted due to RF signal injection are derived to formulate the behavior of the injection-pulled OEO. Using the phase dynamics equation, a phase noise model is developed to quantify the influence of RF injection signal on the phase noise performance of the oscillator. It is shown that our analytical model is capable of predicting the injection locking and estimating the injection pulling behavior of the single-loop OEO under RF signal injection. The theoretical results are validated by the experimental results.

Analysis of Injection Locking and Pulling in Single-Loop Optoelectronic Oscillator

In this paper, we analyze the phase-locking phenomenon in a single-loop optoelectronic microwave oscillator, when subjected to the influence of small radio-frequency (RF) signal. We derive the differential equations for the amplitude and phase variations in the oscillator. Using quasi-linear approximation, analytical expressions for the lock range and phase-shift after phase-locking are presented. In addition, beat frequency of the unlocked-driven optoelectronic oscillator (OEO) is obtained and the phase-locking dynamics of the driven oscillator is discussed. Also, the spectrum components of the pulled OEO is derived as a function of the frequency detuning, lock range, beat-frequency, and frequency-shift induced by the phase perturbation of the injection signal. It is shown that all the analytical closed-form expressions clearly demonstrate the phase-locking mechanism starting from the fast-beat state through the quasi-locked state to the locked state of the pulled OEO. Finally, the simulation results are given to validate the analytical results.

Analysis of Phase-Locking in Optoelectronic Microwave Oscillators Due to Small RF Signal Injection

Phase-locking dynamics in optoelectronic oscillator

The theoretical approach to investigate the frequency pulling phenomenon, when the optoelectronic oscillator is injected by a weak radio frequency (RF) signal, is presented. The differential equation for the phase perturbation is derived. The analytical expressions of the phase-difference after locking and lock-range are derived here. Here, we also study the influence of the injection RF signal on the beat frequency, average frequency, and actual pull-in frequency. Also, the dependency of beat frequency and average frequency on injection frequency is studied here. All the analytical expressions clearly reveal the frequency pulling phenomenon from fast-beat state through quasi-locked state to locked state. Simulation results are also given in support of the theoretical study.

Abhijit Banerjee

Papers

Study of Injection Locking With Amplitude Perturbation and Its Effect on Pulling of Oscillator

Analysis of Injection Locking and Pulling in Single-Loop Optoelectronic Oscillator

Analysis of Phase-Locking in Optoelectronic Microwave Oscillators Due to Small RF Signal Injection

Phase-locking dynamics in optoelectronic oscillator

Analysis of frequency pulling phenomenon in an optoelectronic oscillator