Down-conversion of a high-frequency beat note to an intermediate frequency is realized by a Mach-Zehnder intensity modulator. Optically-carried microwave signals in the 10–60 GHz range are synthesized by using a two-frequency solid-state microchip laser as a voltage-controlled oscillator inside a digital phase-locked loop. We report an in-loop relative frequency stability better than 2.5 × 10−11. The principle is applicable to beat notes in the millimeter-wave range.
© 2011 OSA
Optical delivery of high-spectral purity microwave signals is required for a growing number of applications such as radio-over-fiber or phased-array radars . Among the different microwave-optical sources existing today , optical heterodyning, the technique by which two optical frequencies beat on a photodetector, offers the important capability of generating frequencies from the low-frequency (MHz) up to the terahertz (THz) band. In this context, dual-frequency diode-pumped solid-state lasers oscillating in two orthogonally polarized eigenstates have been shown to provide high-spectral purity beat notes in the gigahertz (GHz) range [3, 4]. Higher frequency beat notes, i.e. at tens of GHz, can be reached by compact microlasers containing a birefringent element [5–7], but with an increased difficulty in implementing a phase-locked loop (PLL) to stabilize the beat note. Down-conversion of the beat note becomes mandatory at these frequencies, especially when the goal is to use digital PLLs for direct frequency synthesis . A recent demonstration was made at 40 GHz , in line with previous schemes using two separate lasers and analog PLLs [10–12]. In all these cases, down-conversion was performed in the electrical domain, after the photodiode, by mixing the beat note with a microwave oscillator. However, electrical components such as oscillators, amplifiers, and mixers used for down conversion at millimeter-wave frequencies are not of common use. An optical solution for generating an intermediate frequency would be highly desirable for stabilizing beat notes at millimeter- and sub-millimeter wave frequencies. Since electro-optic modulators are ultra-wideband devices , one may question their use as frequency down-converters in optoelectronic phase-locked loops.
The aim of this report is to show that cascading an optical intensity modulator after a dual-frequency laser permits to completely lift the constraints due to millimeter-wave electrical devices. In particular, we study a dual-polarization microlaser emitting at 1064 nm with a widely tunable beat note. We intend to show that an opto-electronic PLL (OEPLL) including an integrated intensity modulator yields a fully tunable phase-locked beat signal over the whole 10–60 GHz range with a high spectral purity. The principle of the two-frequency down-conversion is exposed in Section 2. The experimental OEPLL is described in Section 3, and the results on the stabilization of the beat note are presented in Section 4. Conclusions and perspectives are given in Section 5.
2. Optical down conversion
The key components of our stabilization principle are depicted in Fig. 1(a). It involves a dual-polarization microlaser, a polarizer P, and an electro-optic Mach-Zehnder modulator (MZM). The laser is a composite microchip containing an active medium (Nd:YAG) and a birefringent crystal (LiTaO3) described in Ref. . It emits two orthogonally polarized eigenstates along x and y directions with eigenfrequencies νx and νy with a typical output power of 5 mW. The frequency difference Δν = νy – νx is tunable either thermo-optically up to almost 60 GHz or electro-optically over a few hundred MHz. In a previous experimental setup , an electrical down-conversion of the beat note was implemented in order to find an intermediate frequency (IF) in the sub-GHz range. Namely, the beat note Δν was mixed with a phase-locked dielectric resonant oscillator at 39.5 GHz. This solution permitted to obtain a frequency synthesis tunable from 39.5 to 40.5 GHz.
Here, in order to benefit from the whole beat note tunability, we propose to use an intensity modulator before the photodiode, as explained in Fig. 1. The linearly polarized dual-frequency beam is injected into the MZM that can be exploited in two different configurations. On the one hand, if the MZM is biased in quadrature to yield a maximum first-harmonic modulation at fRF [see Fig. 1(b) where Vbias = Vπ/2], then the output beam contains the frequency spectrum depicted in Fig. 1(c). In this case, one can see that the IF, obtained between the two central, closely spaced, sidebands, is a low-frequency image of the beat note. On the other hand, if the MZM is biased in phase in order to maximize the second-harmonic response at 2fRF [see Fig. 1(d) where Vbias = 0], then the same IF is obtained with a twice as high beat note [see Figs. 1(e)]. In this case again, the IF provides a low-frequency image of the beat note. Under both biasing conditions, the MZM acts on the two optical frequencies and creates a down-converted IF at frequency fi = Δν – pfRF, with p = 2 (quadrature) or p = 4 (phase). It is important to note that here, contrary to microwave-photonic schemes using a MZM as a frequency generator , the sidebands produce a low-frequency error signal, not the microwave signal. A low-pass photodiode can then be used to exploit this down-converted IF signal in a PLL.
In order to investigate the IF optical power impinging on a photodiode through this method, we start from the well-known analysis of the MZM . We write Iin the optical intensity of one mode at the entrance of the modulator, ωRF the electrical angular frequency driving the modulator, and a and b the bias and RF voltages, respectively, normalized to Vπ. The intensity Iout at the output of the modulator can then be expressed by a sum of Bessel-functions. By biasing in quadrature, i.e., a = 0.5, the even-order functions vanish and the output intensity becomes
3. Optoelectronic phase-locked loop
The complete loop is schematized in Fig. 2. The free-space laser output beam is sent through a polarizing optical isolator OI and injected into a polarization-maintaining (PM) fiber coupler C. The input polarizer of OI is adjusted at 45° with respect to x and y. About 1 mW of optical power is injected in the loop. In order to be able to adjust the IF beat power level, the dual-frequency beam is amplified by a PM ytterbium-doped fiber amplifier YDFA. Amplifier pumping is adjusted to get an incident optical power impinging on the modulator equal to 10 dBm. Note that, if one could use an optimized microlaser delivering 100 mW of optical power, 20% of the power could be extracted for stabilization purpose without requesting optical amplification. Our MZM is a 10 GHz-bandwidth integrated LiNbO3 from Photline Technologies. The modulator output is detected by a pigtailed 45 GHz bandwidth photodiode D. Before describing the remainder of the loop, let us describe the experimental spectrum illustrating the down-conversion method. Figure 3 shows the electrical spectrum of the resulting photocurrent when the laser beat is chosen at 21 GHz (method described in Section 4) and the MZM is operated in quadrature at fRF = 8.5 GHz. It appears clearly that, in addition to the beat note at Δν, one finds the IF of interest at fi = Δν – 2fRF, here 4 GHz, as expected. The extra peaks at fRF and 2fRF correspond to extra beats between sidebands and carriers. These, as well as the main beat at Δν, are easily filtered out, leaving the IF for generating a clean error signal.
Following Ref. , this IF signal is fed into a common digital phase-locked frequency synthesizer (model LMX2430 from National Semiconductor). It mainly consists in a frequency/phase detector, with an input bandwidth equal to 0.25–2.5 GHz, followed by a charge pump and a loop filter. Both the digital synthesizer and the MZM driver are synchronized to the same reference source, here a quartz oscillator at fr = 10 MHz. The error signal is applied to the LiTaO3 electro-optic crystal inside the laser through a high-voltage amplifier (HVA). Finally, we use a PIC microcontroller in order to program the values N and R of the input and reference dividers, respectively. It sets the command frequency to . The aim is hence to obtain a programmable beat note at frequency , with an integer p = 2 (quadrature) or p = 4 (phase).
4. Stabilization results
When the loop is left open, the free running laser beat note has a typical 100 kHz linewidth on a millisecond measurement time scale but fluctuates at a rate of typically a few hundred MHz over a few minutes . These fluctuations, originating from pump noise and environmental disturbances, are illustrated in Fig. 4(a). We emphasize the fact that such a short microchip laser offers a strong thermal sensitivity due to the thermo-optic effect in the LiTaO3 [5, 9]. It makes the laser easily tunable over the whole beat note tuning range, namely 10–60 GHz. Figure 4(b) depicts the experimental measures of the beat frequency versus temperature. A high gain of 3 GHz/K is measured. Once the beat frequency is thermally chosen, the loop permits to stabilize it electrically, as is now finally shown.
The dual-frequency laser acts as the voltage-controlled oscillator (VCO) in the PLL. Due to the electro-optic effect of the LiTaO3, the measured VCO gain is about 1 MHz/V. Taking into account the 300 V maximum output voltage of the HVA, the loop has a lock-in range of typically 300 MHz. Besides, the bandwidth of the loop filter is 100 kHz and the channel spacing of the digital synthesizer is 1 MHz (R = 10). In order to show the efficiency of the method in both quadrature and phase biasing configurations, we first set a free-running beat at 20 GHz, a MZM frequency fRF = 9.75 GHz, and a biasing voltage of a = 0.5 (quadrature). When the loop is closed, the beat is then stabilized at any frequency chosen by the operator through the PIC. For example, when N = 500 (Δν = 20GHz), Fig. 4(c) shows the IF signal on a 160 Hz span. The measured instrument-limited 1 Hz linewidth illustrates the quality of this stabilization method. Furthermore, by simply changing the laser temperature by a few degrees, we can obtain a free-running beat at 40 GHz. Then, to phase-lock at 40 GHz, a simple change of the MZM biasing voltage at a = 0 (phase) gives us again an IF in the synthesizer bandwidth, while all other parameters are left unchanged. Again, the beat note is stabilized with the same efficiency, as proved by Fig. 4(d). Any other beat frequency between 10 and 40 GHz can be locked using this method, by steps of 1 MHz (the channel spacing). The actual limit in our set-up is the 10 GHz bandwidth of the MZM, which prevents us from carrying on the demonstration up to 60 GHz. Besides, the sweeping rate of the synthesis is measured to be 1.25 MHz/μs (corresponding to a 50 MHz frequency step in a lock-in time of 40 μs).
In conclusion, we have demonstrated a new principle of stabilization loop of any beat note between two optical frequencies in the range of tens of GHz. It includes a MZM which efficiently down-converts in the optical domain the beat note to an IF in the sub-GHz range. A digital PLL allows then to stabilize the IF whose fluctuations are a replica of the beat note fluctuations. Such an opto-electronic phase locked loop (OEPLL) is implemented on a dual frequency microchip laser providing a beat note tunable from 10 GHz up to 60 GHz. The resulting relative stability is measured to be better than 1 Hz over 40 GHz, i.e., 2.5 × 10−11. Furthermore, we show that biasing the MZM in phase advantageously enables to double the operation range of the OEPLL. This is illustrated at 20 GHz and 40 GHz using a 10 GHz cut-off frequency MZM. Besides, the OEPLL operation principle inherently offers a large frequency tunability with a single servo-loop by adjusting the MZM modulation frequency.
The 1 Hz linewidth we have measured being limited by the resolution of our electrical spectrum analyzer, the next step will be to conduct absolute phase noise measurements. Relative phase noise measurements will be also carried out in order to estimate the residual degradation of phase noise due to the OEPLL itself. Finally, the OEPLL principle presented in this paper still apply to optically carried millimeter waves. To this aim, the current MZM has to be replaced by a 40 GHz MZM to address beat notes ranging up to 160 GHz.
The authors thank G. Danion for preliminary work on the microlaser. This work was funded in part by Région Bretagne (contract PONANT and an ARED grant) and by the Délégation Générale pour l’Armement (contract ARAMOS).
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