Tunable microwave frequency synthesis with optically-derived spectral purity

Abstract

Microwave synthesizers are central to test and measurement systems across applications including wireless communications, radar, spectroscopy, and time and frequency metrology. State-of-the-art microwave sources, however, are fundamentally constrained by trade-offs between frequency tunability and spectral purity. Electro-optic frequency division (eOFD) is an emerging technique for dividing down the purity of optical sources to the microwave domain. Previously reported eOFD-based synthesizers generally have limited tunability due to feedback stabilization requirements. Here we demonstrate a feed-forward eOFD architecture in which the frequency tunability of a microwave source is preserved while optical spectral purity is divided through feed-forward cancellation, without any downstream electronic frequency synthesis. By canceling the phase noise of the microwave source without feedback, this eOFD approach removes loop bandwidth and source noise constraints observed in prior eOFD architectures. We achieve octave-spanning tunability, including the entire X-band, with phase noise below -140 dBc/Hz at kilohertz offsets and a high-frequency noise floor between -155 dBc/Hz and -145 dBc/Hz for carrier frequencies from 8 to 16 GHz. This performance corresponds to single-femtosecond integrated timing jitter, enabling, to our knowledge, the first demonstration of coherent, optically referenced microwave synthesis under wide tuning with this level of spectral purity.

Figures (9)

• Figure 1: eOFD with feed-forward concept. The phase and frequency of a microwave oscillator denoted by $\varphi_m$ and $f_m$, respectively. They are tracked above and below the arrows through the conceptual diagram. Meanwhile, the phase and frequency difference of a two-tone, optical reference are denoted by $\varphi_0$ and $f_0$, respectively. Electro-optical modulation allows the microwave signal to be multiplied by an integer $N$, up to the optical frequency difference and compared. The phase difference is carried by a beat-note $f_b$. Subsequent division of the beat-note and combination with a delayed copy of the original microwave source produces the output of the oscillator. The output phase is determined by the divided optical frequency reference phase, while the output frequency is mostly determined by the input microwave source frequency.
• Figure 1: Phase-noise power spectral density (PSD) of feed-forward eOFD outputs obtained using three different microwave sources under identical delay-compensation conditions. The dotted traces show the free-running phase noise of each microwave source, while the solid traces show the corresponding output phase noise after feed-forward eOFD. Results are shown for a modest-performance commercial synthesizer (black), a high-end commercial synthesizer (red), and a dielectric resonator oscillator (DRO, blue). Although the applied delay compensation is the same in all cases, the residual output phase noise at higher Fourier frequencies depends on the input microwave source phase noise $S^{m}_{\phi}(f)$, consistent with the delay-dependent term of the feed-forward phase-noise model. These data illustrate that, for a fixed delay mismatch, microwave sources with lower intrinsic phase noise enable deeper suppression and improved high-frequency performance. However, at lower Fourier frequencies, the optically divided reference performance is achieved independently of the microwave source phase noise.
• Figure 2: eOFD with feed-forward schematic and output phase noise.a Schematic used for experimental demonstration of eOFD with feed-forward. DWBL: dual-wavelength Brillouin laser, EDFA: erbium-doped fiber amplifier, EOM: electro-optic modulator, OBPF: optical band-pass filter, PD: photodiode, DRO: dielectric resonator oscillator, SSBM: single-sideband mixer. b Optical power spectra along the lower arm of the eOFD path. c Phase noise power spectral density (PSD) of the 10 GHz input and output after feed-forward. The scaled optical reference (DWBL) and divider residual floor are also shown, which provide the limits for the output phase noise.
• Figure 2: Integrated timing jitter of the presented oscillators as a function of Fourier frequency. The integrated timing jitter is computed by integrating the measured phase-noise PSD from high to low Fourier frequency for 10 GHz outputs. Results are shown for the free-running DRO (red), tunable microwave source (blue), the synthesizer output after feed-forward eOFD (green), and the DRO-based eOFD output (black). At intermediate and high Fourier frequencies, feed-forward eOFD yields a substantial reduction in integrated timing jitter relative to the free-running synthesizer, reaching the single femtosecond level. Below approximately 300 Hz, drift of the dual-wavelength Brillouin laser (DWBL) optical reference contributes excess low-frequency noise, causing the integrated jitter to approach that of the commercial synthesizer. This low-frequency contribution is mitigated by external referencing of the optical splitting, as demonstrated in the main text.
• Figure 3: Synthesizer phase noise at different output frequencies and corresponding integrated timing jitter. a Phase noise PSD before and after eOFD with feed-forward for several output frequencies. The dotted traces are the microwave source phase noise while the solid traces are the phase corrected outputs. Above 1 kHz Fourier frequency, the synthesizer output has a significantly lower phase noise than its corresponding microwave source input. b Integrated timing jitter from 1 kHz to 10 MHz as a function of output frequency. The eOFD and feed-forward technique improves the integrated timing noise by a full factor of 10 over an octave spanning output. The result is a synthesizer with single-digit femtosecond timing jitter.