2.1 Operation Principle

Figure 2 shows the principle diagram of the BOMPD based on a 3×3 coupler. An optical pulse signal and a microwave signal are synchronized using a phase-locked loop (PLL) with a BOMPD based on the 3×3 coupler as its phase detector.

Fig. 2Full-screen View

A schematic of BOMPD based on 3×3 coupler

The optical pulse signal is generated by a mode-locked laser with a repetition frequency f_R, which is split into three beams by the coupler. Then the input optical pulse signal is sent into the Sagnac loop in which a phase modulator is positioned. The two output pulses (port 1 and port 2) from the 3×3 coupler propagate in the Sagnac loop in the opposite direction. The output pulses of the Sagnac loop are detected by a balanced detector that directly acquires a difference signal ΔV for the two pulses. According to the operation principle of the PLL, ΔV is associated with the phase error Δθ between the extracted microwave and the input optical signal. When sinΔθ ≈ Δθ, the difference signal is proportional to the phase error, that is ΔV = K_PD·Δθ, where K_PD is the phase sensitivity in units of Volts/rad. The output voltage from the balanced detector is then transferred to a loop filter. The output of the loop filter is used as the control voltage of a VCO, which could change the VCO center frequency so that the phase error between the input optical signal and the VCO output is adjusted. The VCO output is then fed back to the phase modulator to form a closed loop. When the VCO's frequency is equal to Nf_R (N is a natural number)_, it locks on to the fiber laser. The phase error is constant when the PLL is in a locked state.

A BOMPD based on a 3×3 coupler includes a 3×3 coupler, a Sagnac loop, a high-speed LiNbO₃ phase modulator and a balanced detector (see Fig. 2). To lock the extracted microwave signal to the optical pulse train, a BOMPD based on a 2×2 coupler requires a π/2 phase shift bias in the Sagnac loop. However, this is not necessary for our BOMPD because of the inherent non-reciprocal performance of a 3×3 coupler. The input and output paths of the 3×3 coupler are different in the Sagnac loop, i.e., the smaller the output noise, the less the jitter of BOMPD. There is a fixed relationship between the phase and the output voltage of the three output ports of the 3×3 coupler, as shown in Fig. 3 [22]. Ideally, the outputs of port 1 and 2 at zero phase have equal amplitude and opposite slope. The Sagnac phase is determined by the difference signal of the two output optical pulses, without additional modulation in the loop. A BOMPD based on a 3×3 coupler is simple in structure and has fewer RF components. Therefore, this method could effectively eliminate the noise-based bottleneck problem associated with a BOMPD based on a 2×2 coupler. As a consequence, the BOMPD based on 3×3 coupler could extract higher precision microwave signals from the optical pulse trains.

Fig. 3Full-screen View

(Color online) The outputs from ports 1, 2, 3 of 3×3 coupler as a function of Sagnac phase

2.2 Experimental setup

Figure 4 shows a schematic of the 2.856 G Hz microwave signal extraction system based on BOMPD. The optical reference signal is emitted by a mode-locked Er-fiber laser (Origami-15, Onefive GmbH), which operates at a 1550-nm center wavelength with an average output power of approximately 114 mW and a 150fs pulse width. The fiber laser that has a repetition rate of 238 MHz, is locked to a low noise RF source to achieve long-term stability. The optical pulse signal generated from the fiber laser is sent to the BOMPD via a standard single mode fiber (SMF, D₂≈20 ps/km/nm) and a specific length of dispersion compensating fiber (DCF, D₂≈-143 ps/km/nm). The DCF is inserted after the SMF to compensate for temporal stretching of the optical pulse caused by dispersion in the SMF and other optical devices. Then the compressed optical pulse is sent to the fiber Sagnac interferometer after passing through an isolator and a circulator in succession. The isolator is employed to prevent the input optical pulse train from reflecting into the fiber laser, while the circulator is established to provide an auxiliary monitor port. The fiber Sagnac interferometer is composed of a 3×3 coupler, a Sagnac-loop and a 10 GHz LiNbO₃ phase modulator (PM-150-080, JDSU). There are three input ports and three output ports in the 3×3 coupler. Output port 1 is connected to the optical input of the phase modulator and output port 2 is connected to the optical output of phase modulator, so that a sagnac-loop is formed. As such, output port 3 is reserved as a monitor port while input port 3 is connected to the output port of the circulator. The two counter-propagating optical signals in the sagnac-loop are uni-directionally phase modulated by an external RF signal applied at the RF port of the LiNbO₃ phase modulator. Then the two optical signals are transmitted through the 3×3 coupler’s input port 1 and input port 2. Subsequently, the outputs from the 3×3 coupler’s input port 1 and input port 2 are transferred into a balanced detector (PDB450C, Thorlabs) for detecting the phase error between the two optical signals.

Fig. 4Full-screen View

Experiment setup for the 2.856 GHz microwave signal extraction system based on BOMPD and the out-of-loop measurement setup

The phase error is transferred to a loop electronics PCB designed for appropriate filtering and amplification (see Fig.4). A variable gain amplifier and a proportional-integral loop filter are employed to adjust the loop bandwidth to optimum the relative jitter. An additional two-order lead-lag filter is arranged before the VCO (CRO2856A-LF, Z-Communication) to further minimize the absolute jitter of the extracted microwave signal. The loop electronics PCB adopts low noise electronic components to ensure excellent noise performance. The VCO with a 70 MHz tunable frequency range and a 7 MHz/V tuning sensitivity are also integrated into the loop electronics PCB. This ensures that an appropriate DC voltage bias is provided to maintain the VCO frequency at approximately 2.856 GHz, which is the 12^th harmonic of the pulse train repetition rate. The VCO output is applied to the RF port of the aforementioned LiNbO₃ phase modulator for optical phase modulation. To achieve the high half-wave voltage Vπ of the LiNbO₃ phase modulator, a low noise amplifier (ZX05-33LN+, Mini-circuits) is deployed to amplify the VCO output signal to an appropriate average power at +13 dBm. Then the amplified VCO signal is fed back into the RF port of the phase modulator. The average input optical power is 20 mW, which further degrades the BOMPD’s noise floor.

When the PLL is closed, the phase error from the BOMPD is appropriately handled by the loop electronics and then sent to the VCO tune voltage port to change the VCO instantaneous oscillation frequency. The phase of the optical pulse during propagation in the Sagnac loop can be influenced by the driving frequency of the phase modulator microwave. The VCO frequency is continually adjusted by the processed phase error signal until the optical pulse coincides with the zero-crossing point of the microwave driving signal of the phase modulator. Then the average input optical power sent to the balanced phase detector will be balanced, and the PLL is locked. In order to measure the relative jitter between the extracted microwave signal and the input optical signal when the PLL is locked, an out of loop measurement setup is also implemented (see Fig.4). The monitor port output of the 3×3 coupler is detected by a photodetector (XPDV2120R-VF-FP, u²t), then transmitted through a bandpass filter (BPF), then amplified by a high gain and low phase noise amplifier (AFS27002900-06-13, Miteq) at 16 dBm average power. Finally the amplified signal is added to the LO port of a balanced frequency mixer (ZEM4300-MH+, Mini-circuits) of which the RF port is driven by the VCO signal. A phase shifter (D3448B, ARRA) is used to adjust the VCO signal’s phase so that the phases of the VCO signal and the monitor signal from the 3×3 coupler are orthogonal in the mixer. The mixer’s IF port is connected to a signal source analyzer (E5052B, Agilent) for base-band measurements to calculate the relative jitter between the extracted microwave signal and the input optical pulse. The extracted microwave signal’s absolute jitter can be measured and evaluated by the signal source analyzer directly.

2.3 Short-term timing jitter measurement

Short-term stability measurement results are shown in Fig. 5. Fig. 5(top) depicts the single sideband (SSB) phase noise curves at the 2.856 GHz carrier in the10 Hz-10 MHz frequency offset range. The free-running VCO phase noise (see green line) is obtained via a test board (MINIEVAL, Z-Communication). When the loop is closed, the phase error signal from the in-loop BOMPD (see Fig.4) changes from a sine signal into a DC signal. This phenomenon that was observed using an oscilloscope indicated that the PLL was locked.

Fig. 5Full-screen View

(Color online) (top) Single-side band phase noise and (bottom) Integrated noise (10 Hz –10 MHz)

When the PLL is locked, the timing jitters of the in-the-loop and out-of-loop measurements are represented by a blue line and red line, respectively. The locked VCO phase noise is obtained via in-loop measurement setup. The relative jitter phase noise is obtained via out-of-loop measurement setup. The noise floor of the out-of-loop setup is represented by the orange line. This noise floor measurement setup includes an RF reference source, a power divider, a phase shifter, a mixer and the E5052B. The 2.856GHz signal generated from an RF reference source can be divided into two signals by a 1:2 power divider. The noise floor is obtained by measuring the relative timing jitter of two 2.856GHz signals originated from one source by the out-of-loop measurements setup. It should be noted that a phase shifter is inserted to adjust one signal’s phase to assure the phases of the two signals are orthogonal in the mixer based phase detector of the out-of-loop measurements setup.

The repetition rate of the mode-locked Er-fiber laser is locked to a RF reference source that is used as an external RF clock. As a result, the phase noise of the mode-locked Er-fiber laser below 1 kHz, follows the phase noise of the RF reference source. The locked VCO phase noise follows the phase noise of the fiber laser within 50 kHz of the locking bandwidth, but follows the free-running VCO phase noise beyond the locking bandwidth. Low phase noise at the high offset frequency is the important characteristic of a VCO. We therefore exploited this trait to avoid transferring the phase noise of the mode-locked lasers to the high offset frequency by the photoelectric conversion. Some noise spurs from 50 Hz power frequency interference are present, including the 50 Hz power frequency and its harmonics in the 50-400 Hz range. It is important to note that the locking bandwidth is adjustable. The 50 kHz locking bandwidth is selected to minimize the relative jitter.

In a pass-band from 10 Hz to10 MHz at the locked status, the in-loop timing jitter is as low as 34 fs (see Fig. 5(bottom)). The relative timing jitter between the extracted 2.856 GHz microwave signal and the input optical pulse is 16 fs at the same frequency offset range. The noise floor of the out-of-loop measurement setup is 9.3 fs. In order to optimize the total jitter of this scheme, the higher performance VCO will be used to reduce the noise floor, Other methods are also planned for improving the SNR of BOMPD detection, such as compressing pulse broadening using DCF, maintaining the phase using a PM fiber, eliminating 50 Hz power interference etc.