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.
Microwaves are ubiquitous among modern society, permeating many realms of technology including cellular wireless [1], radar [2], atomic clocks [3], and global positioning systems [4]. The core of such systems is a microwave synthesizer providing the steady rhythm to which everything is synchronized. In practice, microwave frequency synthesis is characterized by a trade-off between tunability and spectral purity: architectures that support wide frequency tuning rely on active electronic control and modulation stages that introduce phase noise [5], whereas architectures that achieve exceptional spectral purity do so by strongly constraining the oscillator frequency through passive resonators with high quality factor, such as sapphire microwave cavities [6]. This trade-off is evident even in the highest-performance voltage-controlled oscillators, such as yttrium iron garnet (YIG) oscillators. These offer exceptionally wide tuning ranges and low phase noise among tunable microwave sources [7,8], but still fall short of the spectral purity achievable with fixed-frequency oscillators.
The most spectrally pure microwaves yet demonstrated are derived from optical frequency division (OFD), where oscillators disciplined by the extremely high quality factors available in the optical domain are divided down to the microwave regime [9][10][11]. There are three distinct architectures for OFD that we will highlight. First, is full-OFD, in which a self-referenced optical frequency comb divides down the phase stability of a single optical carrier (e.g. stabilized laser) to the microwave regime [12]. While capable of zeptosecond timing noise [13], full-OFD produces a fixed microwave frequency and requires lab-grade metrology equipment, such as an ultra-stable optical reference cavity and a self-referenced optical frequency comb, limiting applications beyond precision metrology.
Second, is two-point OFD, in which an optical frequency comb is locked simultaneously to two optical carriers, dividing the differential phase stability down to the microwave domain [14,15]. While an optical frequency comb is still required, it no longer needs to be self-referenced, reducing system complexity. Furthermore, common mode noise rejection of the dual optical carriers removes the need for an ultra-stable optical reference cavity. This architecture opens the door for compact, even integratedphotonic-based demonstrations [16][17][18]. However, the tunability is tightly constrained by the comb repetition rate (typically less than 1%). Recent work with direct digital synthesis and single-sideband mixing has partially relaxed this constraint by adopting downstream electronic synthesis techniques [19][20][21]. Because the frequency agility is introduced after optical-to-microwave conversion, phase-noise performance away from the carrier is ultimately limited by the electronic synthesis stage, removing some of the spectral purity benefits of OFD.
The third architecture is electro-optic frequency-division (eOFD). Like two-point OFD, a pair of optical carriers is again used as the reference. Instead of comparing the two references through an external optical frequency comb, eOFD uses an electro-optic modulator to generate a comb from a microwave source that spans the optical frequency difference, carying the phase information of both electrical and optical oscillators. One of the principal advantages of this technique is arbitrary choice of microwave frequency used for the optical modulation. Dividing the optical difference stability is then typically accomplished via feedback on the microwave source, requiring intrinsically low-noise oscillators that support wideband phase actuation [22][23][24].
In practice, this generally restricts operation to dielectric resonator oscillators (DROs) or sapphire-resonator stabilized sources. While these oscillators offer favorable noise properties, they also provide limited tuning ranges, typically below 5% of the carrier frequency, and necessitate control loops with bandwidths approaching or exceeding 1 MHz. Fully agile microwave synthesizers cannot be used in feedback-based eOFD, as their intrinsic phase noise and limited actuation bandwidth prevent the feedback loop from reaching the noise floor set by the optical reference. As a result, spectral purity and wideband tunability remain incompatible in feedback-stabilized eOFD systems.
Feed-forward noise cancellation provides an alternative to feedback-based stabilization. Nakamura et al. demonstrated electrical feed-forward correction to suppress repetition-rate noise in free-running optical frequency combs, removing loop dynamics and avoiding servo-induced artifacts [25]. However, this approach relied on fixed repetition-rate combs (two-point OFD) and produced fixed microwave outputs, leaving the constraint on frequency tunability unaddressed.
Here we introduce a feed-forward electro-optic frequency-division (eOFD) synthesizer that divides the spectral pu
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