Frequency combs with record low phase noise

Frequency combs enable the generation of microwaves with ultralow noise via direct division of frequencies between the optical and the radio frequency (RF) regions. A frequency comb comprises an optical frequency spectrum, represented by adding multiples of the comb mode spacing to an offset frequency. Both the comb mode spacing and the offset frequency are in the RF region, whereas the frequency spectrum is in the optical region. A coherent link between the optical and RF regions is therefore established. A frequency comb can be further related to an optical frequency standard via the observation of a beat signal. This signal corresponds to the beat frequency between the optical frequency standard and one of the frequency comb tones. Typically, the optical frequency standard is provided by using a continuous-wave laser locked to a cavity with a high quality (Q) factor, which corresponds to low damping of resonant modes.¹ To meet the requirements of applications in the field (e.g., navigational devices, optical clocks, space applications, and radar) devices for generating frequency combs need to be based on robust technology.

When the beat signal is phase-locked to a microwave reference signal with the use of a conventional phase-locked loop, a low-noise RF signal can be extracted via direct photodetection of the comb output using a photodiode with a high saturation current. The phase noise of this RF signal is reduced by a factor of n² compared with the phase noise of the optical frequency standard, where n is the ratio of their respective frequencies. At present, state-of-the-art optical frequency standards typically have frequency noise spectral densities of less than 0.1Hz/Hz^1sol2 at a frequency of 1Hz.¹ Accounting for a division factor, n², of 3.7×10⁸ (which corresponds to the frequency ratio of an optical signal at 1.56μm and a 10GHz RF signal), frequency combs can be used to produce a 10GHz RF microwave signal with a single-sided spectral phase noise density of less than −108dBc/Hz at a frequency offset of only 1Hz from the carrier frequency. This was recently demonstrated by using a frequency comb based on a mode-locked titanium–sapphire laser.²

We have developed a new device for generating frequency combs that is based on robust technology, in the form of a highly integrated mode-locked erbium fiber laser (see Figure 1).³ In such frequency combs, which are based on mode-locked lasers, the comb mode spacing corresponds to the pulse repetition rate and the offset frequency is related to the carrier phase. Operation with low phase noise therefore requires the construction of mode-locked erbium fiber lasers with low intrinsic timing jitter. In addition, precision control of the comb mode spacing and offset frequency, via high-bandwidth actuators, are necessary.

Figure 1. Device (left) for generating low-noise frequency combs based on an erbium fiber laser. A smart phone (right) is shown for scale.

We used high-bandwidth lithium niobate and graphene modulators to control the comb mode spacing and offset frequency, respectively, inside an erbium fiber laser cavity. This cavity was constructed with an all-polarization-maintaining fiber, while ensuring operation near the zero dispersion point. In this way, we fulfilled all three requirements to ensure operation with low phase noise. Moreover, our whole fiber comb system can be integrated into a small package and operated with low power consumption in challenging environments (e.g., at operating temperatures above 60°C).

The frequency comb we generated with our optimized mode-locked erbium fiber laser exhibited a record low timing jitter of less than 40as (integrated from 10kHz to 10MHz) in a free-running laser configuration. We measured this jitter with a balanced cross-correlator,⁴ as shown in Figure 2. When this frequency comb was phase-locked to an optical frequency reference at 1.56μm, we obtained a single-sided spectral phase noise density of the beat signal of less than −90dBc/Hz over a wide frequency range (see Figure 3). This result was close to the shot noise limit at high frequency offsets. Accounting for n², the frequency comb we generated is, in principle, capable of producing a 10GHz RF microwave signal with a phase noise of less than −170dBc/Hz at frequency offsets of as little as 10kHz from the carrier.

Figure 2. Measured value (red curve) and theoretical estimate (black curve) of the jitter power spectral density (PSD) of a low-noise frequency comb, generated by an erbium fiber laser in a free-running configuration (both on left axis). The integrated timing jitter (blue curve) of the comb is also shown (right axis).

Figure 3. Phase noise PSD of the beat signal obtained from an erbium fiber laser with low phase noise.

In conclusion, we have developed a new device for the generation of frequency combs that is based on an erbium fiber laser. We have achieved ultralow phase noise levels with this device by operating the laser with low timing jitter, as well as by precision control of the comb mode and offset frequency. The compact form of our device, and the low phase noise that it enables, presents a wide range of new applications for frequency combs in science, technology, and precision metrology. Such microwave signals with ultralow noise promise to significantly improve the performance of current precision radar, timing, and navigation systems. We are currently making further improvements to our frequency combs so as to be compliant with the most challenging environmental conditions, such as those encountered in space and rocket launches. We are also testing our ultralow phase noise comb designs in conjunction with precision optical clocks, with the aim of surpassing the frequency stability of current global positioning system devices.