Study of dual-loop optoelectronic oscillators Etgar Levy and Moshe Horowitz Electrical Engineering, Technion - Israel Institute of Technology, Haifa, Israel Email: etgarlevy@gmail.com Olukayode Okusaga, Curtis Menyuk and Gary Carter Computer Sci. and Elec. Eng., Univ. of Maryland Baltimore County, Baltimore, MD USA Weimin Zhou U.S. Army Research Laboratory, Adelphi, MD USA Abstract— Dual-loop optoelectronic oscillators are used to ob- tain high-frequency harmonic signal with a very low phase noise while maintaining very low spurs. However, the fundamental limits of these devices are not known. Therefore, it is essential to develop theoretical models to improve the performance of dual-loop optoelectronic oscillators (OEOs) and in particular the performance of the dual-injection-locked optoelectronic oscillator (DIL-OEO). In this work we use a multi-time scale approach to model dual-loop OEOs. The model enables calculating the phase noise and the spurs level for an arbitrary coupling strength between the two locked OEOs. A good quantitative agreement between theory and experiments is obtained for the DIL-OEO. I. I NTRODUCTION Optoelectronic oscillators are used to generate high- frequency harmonic signals with a very low phase noise [1]. Modeling optoelectronic oscillators is a challenging task since the frequency of the output signal is of the order of 10 GHz while the frequency range of the phase noise of interest is between 100 Hz to 10 KHz. However, since the bandwidth of the intracavity ﬁlter is about three orders of magnitude narrower than the carrier frequency we could efﬁciently applied a multiscale approach to model single-loop optoelectronic oscillators (OEOs) [2]. In our model we have calculated for each roundtrip the evolution of the phasor that represents the electrical signal. White noise was added to the signal in each roundtrip. In this work we extend our model to simulate the dual injection-locked optoelectronic oscillator (DIL-OEO). The model is especially important to analyze strongly coupled OEOs where the injected signals between the two OEOs are not small in comparison with the oscillating signal. A good quantitative agreement between theory and experiments is obtained for the phase noise spectrum and the spur level for both the slave and the master OEOs. The forward and backward injection reduces the spur level in the master OEO while maintaining a very low phase noise in the locking frequency range (below about 2 kHz) in the slave OEO. II. MODEL DESCRIPTION In this section we shortly describe our model for studying dual-loop OEOs. The model is based on the single-loop OEO model which is described with details in [2]. We implement the dual-loop model to analyze the dual injection-locked OEO (DIL-OEO) with the conﬁguration shown in Ref. [3] that is described schematically in Fig. 1. A long cavity OEO, called the master OEO, generates an RF signal with low phase noise. However, a long cavity implies a mode spacing that is too small for a single mode to be selected by an RF ﬁlter. Therefore, in addition to the oscillating signal strong spurs are generated in the uncoupled master OEO. In order to reduce the spur level, the master OEO is injection-locked to another short-cavity OEO, which we refer to as the slave OEO. In our model we have calculated for each roundtrip the evolution of the phasor V (T ), that represents the electrical signal, where T is a time scale of the order of the OEO roundtrip. In each roundtrip we took into account the effect of all OEO components: an electro-optic modulator, a ﬁber delay, a photodiode, and a RF ﬁlter. Additive white Gaussian noise due to the ampliﬁer, the detector, and the laser is included in the model and is added to the signal phasor at the input of the RF ampliﬁer. To improve the agreement between theory and experiment, we added into the model described in [2], the gain saturation of the RF ampliﬁers and a ﬂicker 1/f noise. In Ref. [2] the nonlinear transfer curve of the modulator determined the oscillation power. In our experiments the small signal gain of the RF ampliﬁers was about 60 dB while the signal gain in stationary condition was about 45 dB. Therefore, the oscillation power was determined by the gain saturation of the RF ampliﬁers rather by the electrooptic modulator. Phase ﬂicker noise is obtained near dc frequency in most electronic devices and especially in RF ampliﬁers. Due to nonlinearity in electronic devices, the ﬂicker noise near dc frequencies is upconverted to the carrier frequency [4]. The phase ﬂicker noise in our system is added by electronic ampliﬁers, laser, and by transmission through the optical ﬁber. The phase ﬂicker is modeled in our system by multiplying the phasor of the oscillating signal by exp[iθ(T )] at the output of the RF ampliﬁer, where the spectral density of θ(T ) is proportional to 1/f . The ﬂicker noise θ(T ) is modeled using the method given in Ref. [5]. In another work, we have shown that in single-loop OEOs the power of the phase ﬂicker noise depends on the loop length. Therefore, this noise source was found to limit the performance of long-cavity single-loop OEOs (L> 4 km) at frequencies below about 1 kHz. We have analyzed a dual OEO with the conﬁguration described in Ref. [3]. A long-length master OEO with a loop delay τ 1 = 20 μs is coupled to a short-length slave OEO with a loop delay of τ 2 =2 μs. The two OEOs are locked to each other by using forward injection from the master to the slave OEO and a back injection from the slave to the master OEO. 978-1-4244-3510-4/09/$25.00 ©2009 IEEE 505 Authorized licensed use limited to: University of Maryland Baltimore Cty. Downloaded on September 22, 2009 at 10:52 from IEEE Xplore. Restrictions apply.