Generation of ultrastable microwaves via optical frequency division

There has been increased interest in the use and manipulation of optical fields to address the challenging problems that have traditionally been approached with microwave electronics. Some examples that benefit from the low transmission loss, agile modulation and large bandwidths accessible with coherent optical systems include signal distribution, arbitrary waveform generation and novel imaging1. We extend these advantages to demonstrate a microwave generator based on a high-quality-factor (Q) optical resonator and a frequency comb functioning as an optical-to-microwave divider. This provides a 10 GHz electrical signal with fractional frequency instability of ≤83 10 at 1 s, a value comparable to that produced by the best microwave oscillators, but without the need for cryogenic temperatures. Such a low-noise source can benefit radar systems2 and improve the bandwidth and resolution of communications and digital sampling systems3, and can also be valuable for large baseline interferometry4, precision spectroscopy and the realization of atomic time5–7. Several photonic systems, including optical delay-line oscillators8, whispering-gallery-mode parametric oscillators9 and dual-mode lasers10 have been investigated for the generation of low-noise microwave signals. An alternative approach, based on a high-Q optical resonator and all-optical frequency division, shows promise for the generation of microwaves with excellent frequency stability6,7,11–13. This is because low absorption and scattering in the optical domain can yield quality factors approaching 1× 10 in a room-temperature Fabry–Pérot (FP) resonant cavity. For a well-isolated cavity, average fluctuations in the cavity length amount to 100 am on a 1 s timescale. A continuous wave (c.w.) laser stabilized to such a cavity can achieve a fractional frequency instability as low as 2× 10 for averaging times of 1–10 s (refs 14–18). Transfer of this stability to a microwave signal is the topic of this paper, and we demonstrate a 10 GHz electronic signal with exceptional frequency stability and spectral purity. Figure 1 outlines the principle of the photonic oscillator we have developed. Phase-coherent division of the stable optical signal to the microwave domain preserves the fractional frequency instability, while reducing the phase fluctuations by a factor of 5× 101⁄4 (500 THz/10 GHz). Such frequency division is accomplished by phase-locking a self-referenced femtosecond laser frequency comb to the optical reference11. This transfers the frequency stability of the stable c.w. laser oscillator to the timing between pulses in the laser pulse train, and hence to a microwave frequency that is detected as the pulse repetition rate ( fr≈ 0.1–10 GHz). In the case of a high-fidelity optical divider, the sub-hertz optical linewidth of the reference laser is translated into a microhertz linewidth on fr. A fast photodiode that detects the stabilized pulse train generates photocurrent at frequencies equal to fr and its harmonics, continuing up to the cutoff frequency of the photodiode. Using this photonic oscillator approach, we demonstrate a 10 GHz signal with an absolute instability of ≤8× 10 at 1 s of averaging. This corresponds to a single-sideband phase noise L( f )1⁄42104 dBc Hz at 1 Hz offset from the carrier, decreasing to near the photon shot-noise-limited floor of 2157 dBc Hz at an offset of 1 MHz. The integrated timing jitter over this bandwidth is 760 as. This measurement represents a significant improvement over previous work, with a reduction of phase noise power by a factor of 10 to 1,000 across the measured spectrum (1 Hz–1 MHz)7 and a factor of 4 reduction in the 1 s instability7,11. This absolute timing characterizes one of the lowest phase-noisemicrowave signals generated by any source. As the microwaves generated from our photonic approach have a phase noise that is lower than that available from commercially available microwave references, characterization of the generated phase noise requires that we build and compare two similar, but fully independent systems. The optical dividers in our photonic systems are based on octave-spanning 1 GHz Ti:sapphire femtosecond lasers and cavity-stabilized lasers at 578 nm and 1,070 nm (nopt1 and nopt2 in Figs 1 and 2). Compared with results from 250 MHz Er:fibre combs13, the 1 GHz Ti:sapphire combs provide a 25 dB reduction in the shot-noise floor. Although the exact wavelength of the c.w. lasers is not critical for microwave generation, what is significant is that the two systems are independent. In fact, the FP cavities are situated in laboratories on different wings and floors of our research building. The pulsed output of the frequency-stabilized Ti:sapphire laser illuminates a high-speed, fibre-coupled InGaAs P-I-N photodiode that produces a microwave signal at 1 GHz and harmonics up to 15 GHz. A band-pass filter selects the 10 GHz tone, which is subsequently amplified in a low phase-noise amplifier. The amplified signal is combined on a mixer with a similar signal from the second system, and the output of the mixer is analysed to determine the relative frequency and phase fluctuations. In addition to the 10 GHz microwave signal, we also measure the optical stability of the frequency comb and the c.w. lasers, thereby obtaining a lower limit of the timing stability of the microwave signals. This is accomplished by measuring and analysing the optical beat signal fb between the second stabilized c.w. laser nopt2 and a tooth of the frequency comb that is independently stabilized by nopt1 (Fig. 1). Phase noise data are presented in Fig. 3. The absolute single-sideband phase noise L( f ) on an individual 10 GHz signal is given by curve (a) in Fig. 3. This curve is 3 dB below the measured noise, under the assumption that the contribution from both oscillators is equal and uncorrelated (see Supplementary Information). The phase noise from the optical heterodyne between the two c.w. lasers using one of the combs is given by curve (b), which has been normalized to the 10 GHz carrier. This represents the present noise floor given by a single c.w. laser and the frequency