## 1.

## Introduction

The optoelectronic oscillator (OEO) has attracted many researchers because it is a very useful optical and electrical microwave signal source.^{1, 2, 3} Recently, a few significant works for extending the concept of OEO were reported, for instance, an OEO performs as an optical pulse source without an external microwave-driving source.^{2, 3, 4, 5} But the reported pulse width is around 15 to
$20\phantom{\rule{0.3em}{0ex}}\mathrm{ps}$
(at
$10\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$
),^{3, 4, 5} which limits their applications in high-speed optical time division multiplexing (OTDM) systems.

Compared with these schemes, an electro-optic phase modulator (PM)-based OEO is another effective way to perform the same function.^{6, 7} When continuous-wave (cw) light is injected in an electro-optic PM, it is deeply chirped. After an optical synthesizer or group-delay-dispersion (GDD) circuit, the chirped cw light is compressed and trains of short pulses are generated. Enhancement of linear chirp is the key to generating short pulses. Furthermore, performing amplitude modulation (AM) before PM is effective to eliminate the residual optical power in the midpoint between adjacent pulses after compression.^{6}

We present a scheme for a phase-modulator-based dual-loop OEO, which can simultaneously produce ultra-low-jitter short optical pulse streams with high repetition rate capabilities, and corresponding high spectral purity and low phase noise electrical microwave signals. A joint of a large-signal directly modulated laser (DML) and a phase modulator is for chirp enhancing and pulse shaping. An optical domain combined dual-loop configuration is employed for side-mode suppression without adding electrical active devices. The experimental setup is depicted in Fig. 1.

## 2.

## Principle of Operation

As shown in Fig. 1, the system includes a directly modulated distributed feedback (DFB) laser, a ${\mathrm{LiNbO}}_{3}$ phase modulator with ${V}_{\pi}$ of $3.5\phantom{\rule{0.3em}{0ex}}\mathrm{V}$ , an erbium-doped fiber amplifier (EDFA), a high-speed PIN photodetector, and an rf amplifier centered at $9.8\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$ with $150\text{-}\mathrm{MHz}$ bandwidth. The electrical filter is not used due to the signal frequency already limited by the rf amplifier. The directly modulated light is injected into the PM after adjustment of the optical delay line (ODL) to achieve the maximum chirping rate. Polarization controller 1 (PC1) is used to obtain the best modulation. The EDFA is used for compensating the insertion loss in the system. PC2 controls the power distribution in optical path1 and path2, which are 10 and $2\phantom{\rule{0.3em}{0ex}}\mathrm{km}$ , respectively. PC3 and PC4 tune the power distribution and correct the polarization variation caused by dispersion shift fiber (DSF). Once the oscillation threshold is reached, a stable output is achieved.

The output of large-signal DML can be approximately expressed as:

## 1

$$E\left(t\right)={E}_{0}\phantom{\rule{0.2em}{0ex}}\mathrm{exp}(-\frac{{t}^{2}}{{2{t}_{0}}^{2}})\mathrm{exp}\left[i({\omega}_{0}t-\phi \left(t\right))\right],$$^{7}

## 2

$${E}_{PM}\left(t\right)={E}_{0}\phantom{\rule{0.2em}{0ex}}\mathrm{exp}(-\frac{{t}^{2}}{{2{t}_{0}}^{2}})\mathrm{exp}\left\{i[{\omega}_{0}t-\phi \left(t\right)-\mathrm{\Delta}\theta \phantom{\rule{0.2em}{0ex}}\mathrm{sin}\phantom{\rule{0.2em}{0ex}}2\pi {f}_{m}(t+\mathrm{\Delta}t)]\right\},$$## 3

$$\nu \left(t\right)={\omega}_{0}\u22152\pi -\partial \phi \left(t\right)\u22152\pi \partial t-\mathrm{\Delta}\theta {f}_{m}\phantom{\rule{0.2em}{0ex}}\mathrm{cos}\left(2\pi {f}_{m}t\right).$$## 4

$${(\partial \nu \u2215\partial t)}_{\mathrm{max}}=-{\partial}^{2}\phi \left(t\right)\u22152\pi \partial {t}^{2}\pm 2\pi {{f}_{m}}^{2}\mathrm{\Delta}\theta .$$## 5

$${(\partial \nu \u2215\partial t)}_{-\mathrm{max}}=-\frac{1}{2\pi}\mid {\partial}^{2}\phi \left(t\right)\u2215\partial {t}^{2}\mid -2\pi {{f}_{m}}^{2}\mathrm{\Delta}\theta .$$To suppress side modes, a polarization beamsplitter (PBS) and polarization beam combiner (PBC) are employed to compose an optical domain combined dual-loop structure.^{8} Little close-to-carrier noise is introduced, and the synthetical noise performance is greatly improved.^{8}

Notice that DSF is used in this experiment to prevent extra GDD. It is well known that the dispersion of DCF is equal in magnitude and opposite in sign to that of the single-mode fiber (SMF). As a result, the pulses compressed by DCF are rebroadened if SMF is used. In addition, the transmission of short pulses in DSF will excite self-phase modulation, which provides the potential for further compression.

## 3.

## Experimental Results and Conclusion

In this experiment, breaking either optical path between PBS and PBC, it is a completed single loop OEO that can freely run when enough optical power and amplifier gain is supplied. For an electrical signal, with path 1 broken, the measured side-mode suppression ratio is $55\phantom{\rule{0.3em}{0ex}}\mathrm{dB}$ and mode spacing is $93.3\phantom{\rule{0.3em}{0ex}}\mathrm{kHz}$ [see Fig. 2a]. With path 2 broken, the measured side-mode suppression ratio is $45\phantom{\rule{0.3em}{0ex}}\mathrm{dB}$ and mode spacing is $19.8\phantom{\rule{0.3em}{0ex}}\mathrm{kHz}$ [see Fig. 2b]. In the dual-loop case, the side modes are perfectly suppressed [see Fig. 2c] and the measured phase noise is $-112\phantom{\rule{0.3em}{0ex}}\mathrm{dBc}\u2215\mathrm{Hz}$ at $10\phantom{\rule{0.3em}{0ex}}\mathrm{kHz}$ [see Fig. 2d]. To evaluate the timing jitter $\left(\sigma \right)$ of the optical pulse stream, we integrate the spectral noise-power density from 100-Hz to 10-MHz offset using the following equation:

Figure 3a shows the optical spectrum of the pulse stream. The full-width at half-maximum (FWHM) is measured to be $0.830\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ , which is about $0.3\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ wider than that generated by large-signal DML alone. In this case, the modulation voltage is $3.54\phantom{\rule{0.3em}{0ex}}\mathrm{V}$ (corresponding to the modulation depth of $1\pi $ ) on PM and $22.3\phantom{\rule{0.3em}{0ex}}\mathrm{dBm}$ on DML with a bias of $50\phantom{\rule{0.3em}{0ex}}\mathrm{mA}$ . The sampling oscilloscope trace for the optical pulse stream is given in Fig. 3b, where the pulse width is $6.5\phantom{\rule{0.3em}{0ex}}\mathrm{ps}$ measured by an autocorrelator [see Fig. 3c]. It is also clearly shown in Fig. 3b that the optical energy at the tail far from the pulse peak is almost perfectly eliminated. The bandwidth product of $\mathrm{\Delta}\nu \mathrm{\Delta}t\sim 0.65$ is not transform limited for an assumed Gaussian pulse shape, because the dispersion magnitude $(-21.68\phantom{\rule{0.3em}{0ex}}\mathrm{ps}\u2215\mathrm{nm})$ of DCF is not optimum and the modulated light includes uncompressible nonlinear chirps. Nevertheless, this result is better than that generated by DML or PM alone.

In conclusion, we have demonstrated a self-starting phase-modulator-based OEO for generating low-timing jitter short optical pulses and low phase noise rf signals. Pulse shaping and side-mode suppression techniques are employed in the cavity of OEO. The output is 6.5-ps-wide pulses at 9.8-GHz repetition rate with 141-fs timing jitter. A low phase noise, high-quality, 9.8-GHz electrical signal is simultaneously generated that can serve as a synchronized reference in applications of this pulse source. The phase noise and timing jitter performance can be improved by controlling environment effects and using a high performance light source. In addition, the pulse rate can be directly scaled to $40\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$ or higher by changing some optoelectronic components in the system.

## Acknowledgments

The work was supported by the National Basic Research Program of China (973 Program) grant number 2003CB314900, and the National Nature Science Foundation of China under grant 60572013.