Characterization of Long-Term Stable Photonic Microwaves based on a Difference Frequency Comb

TL;DR

This work addresses the challenge of generating ultra-stable, low-phase-noise microwaves in the GHz range without the crosstalk complications of dual stabilization loops for $f_{ ext{ceo}}$ and $f_{ ext{rep}}$. It introduces a difference-frequency-generation comb that passively removes $f_{ ext{ceo}}$ while locking $f_{ ext{rep}}$ to an optical reference; an interleaver raises the effective repetition rate to $f_{ ext{rep}}^{ ext{eff}} = 3.2\ ext{GHz}$, enabling optoelectronic conversion in a high-linearity MUTC photodiode to yield a 9.6 GHz OFDµW signal. The paper reports a measured phase noise of approximately $-147\ \text{dBc/Hz}$ at 1 kHz offset and identifies shot-noise, AM-to-PN conversion (about 23 dB), and flicker noise as key factors, with long-term absolute stability achieved by GPS-disciplining the 800 MHz reference to reach OADev levels around $4\times 10^{-17}$ at $10^4\ \text{s}$. The results demonstrate a robust, offset-free optical microwave source with strong potential for precision timing, radar, and optical quantum technologies, owing to its simplified stabilization and GPS-based absolute timing capability.

Abstract

We report on a novel method for optical microwave generation using a frequency comb based on difference-frequency generation, which passively eliminates the carrier-envelope offset frequency ($f_{\mathrm{ceo}}$), with the repetition rate ($f_{\mathrm{rep}}$) locked to an optical reference. We demonstrate the generation of ultra-low phase noise microwave signals by transferring the stability of the optical reference to 9.6 GHz, reaching noise levels of -147 dBc/Hz at 1 kHz offset. The optimization of pulse timing after interleaving and a scheme for additional long-term stabilization of the microwave signal to GPS standards are discussed. This work presents a new variant of highly stable RF signal generation for precision applications, such as radar, atomic clock local oscillators and optical quantum technologies.

Figures (5)

• Figure 1: The optical microwave setup consists of a reference laser, the comb based on difference frequency generation (DFC CORE 200 +), a pulse interleaver and a modified uni-travelling carrier photodiode (PD) with 9.6 GHz RF bandpass filter (BPF). MD: Monochromatic detector (bandpass + photodiode) BC: Beam combiner, FALC: Fast analog laser controller, PFD: Phase frequency detector
• Figure 2: To characterize the OFDµW signals with increased sensitivity, two identical systems are measured against each other. This is done for the microwave signals, as well as the optical beat between both combs. For long-term stability analysis, a frequency counter (K+K FXE) simultaneously records the microwave signals mixed to 100 MHz with a common local oscillator (SMA100B) as well as the optical comb beat and beat between the two fiber lasers. A periodically-poled $\mathrm{LiNbO_3}$ crystal (PPLN) is used to analyze the pulse timing via cross-correlation of the pulse train before and after the pulse interleaver. DFC: Difference frequency comb, AOM: acusto-optical modulator, OFDµW: Optical frequency division microwave consisting of interleaver and optical-to-RF conversion. A) The two combs are optically locked to two independent fiber lasers, which in turn are referenced to a common GPS disciplined RF signal. B) Both combs are locked to a common cavity-locked diode laser.
• Figure 3: A): Cross-correlation time trace of the 16 pulses generated from the 4-stage interleaver, including the first pulse of the next cycle. Amplitude variation is due to the polarization sensitivity of the nonlinear crystal and does not represent pulse energy B) Pulse time offset from their respective ideal timing position n / (16$\times f_{\mathrm{rep}}$).
• Figure 4: Phase noise measurement of a single optical microwave signal at 9.6 GHz (blue), locked to the CLS, limited by the cross-correlation measurement time at low offset frequencies, as indicated by the shaded area. The comparison of both microwaves against each other (orange) as well as the scaled phase noise on the optical beat between the frequency combs (green).
• Figure 5: The fractional frequency stability of the two systems. The OADev of the individual microwaves mixed with the 9.5 GHz LO (orange and green), respectively. The OADev evaluated for the difference between the two-time traces, suppressing the contribution of the common 9.5 GHz LO. The Beats between combs (blue) and reference lasers (violet), respectively. The single points show the phase noise computed from the phase noise data of the respective signals.