Introduction. The invention of mode-locked lasers and optical frequency combs had a profound impact on optical metrology due to their ability to bridge the gap between optical and microwave frequencies [1,2]. More recently, the demand for ultra-low-noise microwaves at high carrier frequencies (>1 GHz) has driven the development of photonic microwave oscillators that rely on the high-quality factor of optical cavities [3] and the exceptionally low timing jitter of mode-locked lasers [4,5]. These oscillators leverage the pristine comb structure of the optical spectrum to generate microwaves through the optical frequency division (OFD) [6,7,8] or optoelectronic conversion [3,9]. Among the reported techniques, the OFD based on a frequency comb referenced to an ultra-stable optical frequency reference has demonstrated the lowest phase noise in the generated microwave signal [6,7,8]. However, this approach has challenging requirements such as nonlinear spectral broadening, detection and stabilization of carrier-envelope-offset frequency, optical interleavers, narrow-linewidth continuous-wave lasers, high-vacuum components, and complicated locking electronics. Consequently, conventional OFD systems are notably costly and difficult to operate and occupy a significant amount of space (e.g., half to full size 19″ rack). As a result, their use is confined to the most performance-critical applications.

Alternative approaches have been explored including the use of fiber-optic delay references to stabilize the repetition rate of femtosecond lasers and generate low-noise microwaves [10,11]. Such delay-locked oscillators rely on the interference of two narrow spectral regions filtered from the optical spectrum to detect the timing jitter of the optical pulse train. Hence, it requires a wide optical bandwidth to achieve high phase sensitivity. Furthermore, additional optoelectronics such as voltage-controlled oscillators and acousto-optical modulators are needed to separate and retrieve the laser’s timing jitter from other noise sources.

Here, we introduce a much simpler photonic microwave oscillator, named PRESTO, using only three key components: a femtosecond laser, a fiber delay reference, and a compact, highly sensitive pulse timing detector. PRESTO aims to provide precise noise control in a more practical and robust manner, potentially opening new possibilities for advanced optical and microwave technologies.

Timing jitter measurement. The fundamental requirement of any noise optimization process is the precise measurement of the noise level. First, we validate our delay-based approach by comparing it with two widely used methods for measuring the timing jitter of mode-locked lasers: i) electronic phase noise detection using a phase noise analyzer [12] and ii) the “timing-detector method” using an additional laser oscillator with similar or lower noise [13,14]. Figure 1 shows sample experimental setups. In the electronic phase detection [see Fig. 1(a)], the output optical pulse train of the laser under test (LUT) is converted to a microwave pulse train using a photodetector. A harmonic of the electronic spectrum is then filtered out, and its phase noise is measured with respect to the calibrated local oscillator of the analyzer. Similarly, the timing jitter of the LUT can be measured with respect to a reference laser using a pulse timing detector [e.g., a balanced optical cross-correlator (BOC)] [15] [see Fig. 1(b)].

 

Fig. 1. Schematics for measuring the timing jitter of a laser oscillator using: (a) a phase noise analyzer, (b) the timing-detector method, and (c) the timing-delay method. LUT, laser under test; QWP, quarter wave plate; BOC, balanced optical cross-correlator.

Download Full Size | PDF

Alternatively, the noise of the LUT can be measured using a delay mechanism [see Fig. 1(c)], which eliminates the need for a reference source. This “timing-delay method” draws inspiration from delay-based techniques previously used in the characterization of microwaves [16,17] and recently adapted by the optical community [18,19]. Unlike those based on interferometry [10,11], our method relies on a highly sensitive waveguide BOC [20]. When the laser pulses overlap with their delayed versions, the BOC generates a voltage spectral density which is directly proportional to the jitter spectral density. Then, the free-running jitter spectral density of the LUT, ${S_{\mathrm{\Delta t}}}(f )$, can be extracted using the relationship ${S_{\mathrm{\Delta t}}}(f )= {S_{BOC}}(f )/\; 2({1 - \cos ({2\pi f\tau } )} ),$ where ${S_{BOC}}(f )$ is the jitter spectral density measured by the BOC and τ is the delay time [13,18].

Figure 2 compares the measured phase noise spectra of the LUT at 10-GHz carrier using these three methods. Curve (i) shows the absolute phase noise measured by a commercial phase noise analyzer (R&SFSWP26). Notably, the curve reaches the noise floor of the analyzer at ∼50 kHz. Curve (ii) depicts the phase noise measurement using the timing-detector method. With a locking bandwidth of ∼700 Hz, the noise below is suppressed and does not reflect the laser’s actual phase noise. Above the locking bandwidth, the measured phase noise aligns seamlessly with the result from the phase noise analyzer. Due to the lower noise floor of the BOC, the laser’s noise is resolved even beyond 50 kHz, reaching −180 dBc/Hz at ∼900-kHz offset frequency. Finally, curve (iii) shows the results using the timing-delay method which combines the benefits of the two previous methods. It resolves close-to-carrier phase noise with a performance comparable to that of the phase noise analyzer and maintains a low wideband noise floor like the timing-detector method. The only drawback is the presence of “null points” observed at the harmonics of 1/τ (i.e., ∼90 kHz due to the ∼2250-m fiber length) where the noise detection sensitivity is nullified [17].

 

Fig. 2. Measured phase noise spectra of a mode-locked laser at 10-GHz carrier using (i) a commercial phase noise analyzer, (ii) the timing-detector method, and (iii) the timing-delay method.

Download Full Size | PDF

Feedback model. Once the laser’s timing jitter is correctly measured, it can be employed to generate a feedback signal for the intracavity actuator to enable noise suppression. Here, we study our delay-based feedback loop using a model similar to that in [21] (see Fig. 3).

 

Fig. 3. Feedback model for delay-based laser jitter suppression. J_I, inherent laser jitter when there is no feedback; J_O, laser jitter when the feedback is activated; H_BOC, H_PI, and H_PZT, transfer functions of BOC, PI controller, and laser PZT, respectively.

Download Full Size | PDF

The inherent timing jitter of the laser, J_I, is divided into two paths: one experiences a long fiber delay, τ, and the other is quite short (i.e., <<τ). The timing jitter between the two paths is measured by a BOC and converted to a voltage signal by the BOC transfer function, H_BOC. The voltage signal is fed to the PI controller, H_PI, in a negative feedback configuration. The output of the PI controller is amplified and converted to a round trip-cavity delay by the piezoelectric transducer (PZT), H_PZT, which suppresses the laser’s timing jitter by making precise mechanical cavity adjustments. Based on this model, the relation between the inherent laser jitter, J_I, and the laser output jitter when the feedback is active, J_O, is given by

 

Fig. 4. Simulated jitter transfer coefficient, $|{C_\tau }{ |^2},$for different fiber lengths (i.e., varied τ) when (a) there is only a proportional feedback (i.e., no integral feedback, f_PI= 0 Hz) and (b) there is both a proportional and an integral feedback (i.e., with f_PI = 30 kHz). Experimental parameters used in the calculations: k_BOC = 2 × 10¹²V/s at 45 MHz bandwidth, k_PI = 0 dB, k_PZT = 146.7 Hz/V, and f_R = 1 GHz.

Download Full Size | PDF

Experimental results. Figure 5 illustrates the experimental setup for the photonic microwave oscillator, PRESTO, based on a delay reference and a pulse timing detector. The primary oscillator is a commercially available mode-locked laser (MENHIR-1550) operating at 1-GHz repetition rate and 1564-nm center wavelength. The fiber-optic delay reference consists of a ∼1000-m standard fiber wound up into a fiber coil and a ∼125-m dispersion compensating fiber, terminated with a Faraday rotating mirror (i.e., 1125 m total). The optical pulse timing detector is a waveguide BOC (WBOC) based on an integrated PPKTP module [15], which boasts 100-times higher sensitivity when compared to a bulk-optic BOC [20]. WBOC has a packaged footprint of only 10 × 45 mm² (see its photo in Fig. 5) and can be potentially integrated into a photonic integrated circuit. The laser pulses pass through the delay reference twice and recombine with new pulses in the WBOC. As a result, the WBOC generates a baseband signal that is proportional to the timing jitter of the pulse train compared to its delayed counterpart. A primary feedback loop based on the WBOC output is applied to the laser, which adjusts the intracavity PZT to lock the laser’s repetition rate to the fiber delay reference. Subsequently, a secondary feedback loop is established to act on an external electro-optical phase modulator [22] positioned immediately after the laser output. This secondary loop provides an additional, fast control to remove the high-frequency noise beyond the PZT resonance. However, it can only be activated once the laser is locked to the reference with the first loop filter so that the residual timing jitter is within the dynamic range of the phase modulator. In this way, the secondary feedback loop further improves the laser’s output timing jitter.

 

Fig. 5. Schematic of the delay-stabilized photonic microwave oscillator using a waveguide BOC (i.e., PRESTO). MUTC, modified uni-traveling-carrier photodetector; BPF, electrical bandpass filter, PNA, phase noise analyzer, EDFA, erbium-doped fiber amplifier, DCF, dispersion compensating fiber, WDM, wavelength division multiplexer, PPKTP, periodically poled potassium titanyl waveguide, DC, dichroic coating, BPD, balanced photodetector.

Download Full Size | PDF

A microwave signal is generated by coupling a fraction of the laser output after the phase modulator into a modified uni-traveling carrier (MUTC) photodetector [23]. The photocurrent pulse train is filtered at the 10-GHz harmonic frequency, and the phase noise of the extracted microwave is measured using a phase noise analyzer (R&SFSWP26). The complete setup including the 1125-m-long fiber delay reference and the timing detector is constructed simply on an optical breadboard without additional measures for environmental stabilization or vibration damping.

Figure 6 shows the absolute phase noise measurements of the photo-detected microwave signal at 10 GHz and their integrated timing jitter. At first glance, the noise reduction for frequencies lower than 50 kHz is clearly seen from curve (ii). The limiting factor of the first feedback loop becomes apparent at the peak around 45 kHz where the feedback loop is in resonance with the laser’s PZT. Further increasing the loop gain only leads to instability with an increased noise peak. When the second feedback loop on the external optical phase modulator is activated, an additional noise suppression of ∼10 dB is achieved between 200 Hz and 50 kHz [see curve (iii) in Fig. 6]. Compared to that of the free-running laser [curve (i)], the phase noise of the stabilized laser is suppressed by more than 35 dB for offset frequencies below 1 kHz. The noise floor of ∼−165 dBc/Hz beyond 100 kHz is currently limited by the phase modulator and the available photocurrent at the 10-GHz harmonic. The integrated timing jitter (1 Hz–1 MHz) of the free-running laser is greatly improved from ∼10-ps RMS down to 30-fs RMS.

 

Fig. 6. Measured absolute phase noise at 10 GHz and integrated timing jitter of PRESTO with a commercial phase noise analyzer when (i) the laser is free running, (ii) only the first feedback loop is activated, and (iii) both feedback loops are activated.

Download Full Size | PDF

In Fig. 7, we compare the absolute phase noise of PRESTO with the previously reported performance of other state-of-the-art photonic microwave oscillators. At present, conventional OFD systems exhibit the lowest phase noise. The most compact setup, whose phase noise is shown with curve (i), has been realized with approximately half size 19″ rack [24]. A recent work shows an alternative, compact approach called electro-optic frequency division (eOFD) [25], which employs an electro-optic comb. While its performance is reduced compared to the OFD, it still outperforms other photonic microwave oscillators, as shown by curve (ii). The initial results of PRESTO (blue curve) indicate an excellent performance, which is already quite comparable to the eOFD. Other delay-stabilized photonic oscillators, such as those based on regular mode-locked lasers [11], micro-combs [26], and continuous-wave lasers [27], are represented by curves (iii), (iv), and (v), respectively. They show comparable or slightly inferior performance to PRESTO, particularly for the offset frequency range of 1 kHz–100 kHz.

 

Fig. 7. Phase noise comparison of PRESTO with other photonic microwave oscillators, all scaled at 10-GHz carrier frequency.

Download Full Size | PDF

Conclusion. We demonstrate a simple and novel photonic microwave oscillator whose oscillation frequency is referenced to an optically delayed version of itself using a compact, highly sensitive pulse timing detector. The first lab prototype exhibits an outstanding phase noise performance comparable to other state-of-the-art photonic microwave oscillators, including the OFD and delay-locked oscillators. We anticipate further improvements in phase noise by optimizing feedback loop parameters, improving the optical power budget, decreasing the free-running laser noise, and isolating system components. In this way, we aim to match PRESTO’s phase noise with that of the best performing OFD systems [7,24] in the future. Currently, the complete setup shown in Fig. 5 can fit into the 6U rack-mountable housing, constrained by the shoe-box size of the existing mode-locked laser. However, the scheme is compatible with various laser types including chip-scale lasers. Certain system components such as the delay reference and the timing detector already have compact dimensions and can be integrated in a much smaller volume. Therefore, PRESTO has the potential to revolutionize photonic oscillators by simplifying their structure, shrinking their size, and ultimately driving down their cost. These advancements would make them more affordable and accessible, opening new applications in various fields.