We propose an optoelectronic phase-locked loop concept which enables to stabilize optical beat notes at high frequencies in the mm-wave domain. It relies on the use of a nonlinear-response Mach-Zehnder modulator. This concept is demonstrated at 100 GHz using a two-axis dual-frequency laser turned into a voltage controlled oscillator by means of an intracavity electrooptic crystal. A relative frequency stability better than 10−11 is reported. This approach of optoelectronic down conversion opens the way to the realization of continuously tunable ultra-narrow linewidth THz radiation.
©2011 Optical Society of America
Since the recent development of commercial THz spectrometers and imaging systems, THz has become as wide field of investigation opening new opportunities in numerous domains of physics, chemistry, and biology . Among the current pursued developments, continuous and tunable high spectral purity THz sources arouse a great deal of interest for high resolution spectroscopy, astronomy and metrology for instance . Even though THz ray linewidths of few kHz could be satisfactory for these applications, pushing the spectral purity to its fundamental limits is a first step towards the realization of new functions such as THz lock-in amplification for high sensitivity THz sensing at room temperature.
Photonics technologies are well suited to address this issue . Indeed, quantum cascade lasers (QCL) are becoming more and more powerful meanwhile their linewidth is getting narrower . Consequently, this approach is now mature to address the spectral domain ranging from several THz up to the far infrared domain. However, QCL are still inefficient for frequencies below few THz and need to be cooled down to cryogenic temperatures . Hence, in the spectral range lying between 100 GHz and 2 THz, photomixing or parametric conversion of two detuned high spectral purity optical frequencies is still unavoidable . The heterodyning approach offers a THz beat note whose spectral shape is the convolution product of the two optical rays unless they are phase locked. A linewidth as narrow as 1 Hz has been reported using two continuous external cavity lasers phase locked to a frequency comb provided by a third stabilized mode-locked laser [6,7]. Dual mode lasers have been developed using different active media and cavity architectures for generating microwave or millimeter-wave [8–13]
From a conceptual point of view, increasing the spectral purity of the beat note does not require each optical frequency to be independently phase locked but only their difference. With this goal in mind, we have been developing in the past years Dual Frequency Lasers (DFL) that sustain the oscillation of two detuned and tunable orthogonal polarizations [14,15]. This simple, compact and cost effective approach inherently offers a very narrow beat note, i.e., in the kHz range, owing to the fact that the two optical modes share a common optical resonator. Moreover, this linewidth can be further reduced using a Phase Locked-Loop (PLL) that drives an intracavity electro-optic birefringent crystal, leading to a spectral purity as good as that of the RF local oscillator driving the PLL [16–18]. Unfortunately, this approach, which relies on the use of electrical components, cannot be extended far above 40 GHz . To circumvent this problem, we have recently proposed a new scheme in which the beat note is optically down converted to an intermediate frequency signal. Such an opto-electronic phase-locked loop (OEPLL) has been successfully implemented on a microchip laser and has led to a proof of concept at 40 GHz using a PLL operating at 500 MHz . Again, considering both the laser and the down conversion scheme, this approach cannot be extrapolated to the millimeter-wave and THz domain. The first limit is related to the frequency difference provided by the single axis DFL laser which remains below the free spectral range of the laser. The second limit comes from the optical down-conversion apparatus which includes a Mach-Zehnder modulator limiting the reachable frequency to the millimeter-wave and thus below the THz spectral range.
In this paper, we show how a two-axis DFL laser improved to offer continuous tunability and used in conjunction with a dedicated non-linear electro-optic modulator opens the way to ultra-high spectral purity compact and cost effective beat note generation in the mm-wave and THz range.
2. Dual frequency laser continuously tunable form DC to THz
The proposed laser, depicted in Fig. 1(a) , is a two-propagation-axis cavity [14,15]. We have chosen this architecture because it enables large tunability well beyond the free spectral range of the laser. The active medium is a 1.5-mm-long phosphate glass doped with 0.8 × 1020 Er3+/cm3 and 20 × 1020 Yb3+/cm3. The input mirror M1 is directly coated on the active medium. It is coated so that its transmission at 975 nm is 95% and its reflection at 1550 nm is higher than 99.9%. The laser cavity is closed by a 5-cm radius of curvature mirror M2 transmitting 0.5% at 1550 nm. This laser sustains the oscillation of two linear polarizations. In order to adjust independently the wavelength of each eigenpolarization, an anti-reflection coated 10-mm-long YVO4 crystal cut at 45° of its optical axis is inserted into the cavity.
This crystal leads to two orthogonally polarized eigenmodes (labeled respectively o and e) spatially separated by 1 mm in the active medium while superimposed at the output coupler. Moreover, to ensure single frequency oscillation of each eigenpolarization we use two 40µm-thick étalons coated on both sides to reflect 30% of the intensity at 1550 nm. By tilting the etalon the eigenfrequency changes by steps of 3 GHz corresponding to the free spectral range (FSR) of the cavity. Consequently, the beat note between the two eigenmodes can be adjusted by steps from DC to 2 THz. The active medium is pumped at 980 nm using a laser diode. In order to efficiently pump the two eigenmodes the pump beam is split into two parallel 400-mW 100 µm-diameter beams separated by 1 mm. To this aim, a second YVO4 crystal is inserted between the pump focusing lens and the laser input mirror (see Fig. 1(a)).
When the étalon is perpendicular to the propagation axis, the laser oscillates at 1540 nm. We keep the ordinary etalon perpendicular to the ordinary propagation axis while the extraordinary etalon is tilted to sweep the frequency difference Δν = ν e−ν ο. In this case, the frequency difference can be adjusted only by steps of 3 GHz. In order to obtain continuous tunability, an electrooptic crystal LiTaO3 is inserted along the ordinary path only. This crystal has been optimized to enable continuous tunability of the ordinary frequency over 3 GHz filling the frequency gap in between two successive longitudinal modes. As a result, the frequency difference Δν becomes continuously tunable over the whole spectral width of Er3+ gain, that is, from DC to 2 THz. Moreover, Δν can be now controlled either thermally or electrically by adjusting the crystal temperature or the applied voltage respectively. This is illustrated at low frequency in Fig. 1(b) where the beat note is electrically adjusted at four different values lower than the laser FSR. We insert the crystal on the ordinary axis. The voltage controlled oscillator (VCO) gain is measured to be 1 MHz/V.
3. Principle of the opto-electronic phase-locked loop
The operating principle of the OEPLL is sketched in Fig. 2 . The laser output beam TEM00 is sent through a polarizer, adjusted at 45° with respect to o and e. The beam is then focused into a polarization-maintaining (PM) fiber. 10% of the 2 mW available optical power is extracted for stabilization purpose. This beam is amplified by a PM erbium-doped fiber amplifier (EDFA) before detection. We adjusted the EDFA gain to maintain a power level of 1 mW on the 16 GHz bandwidth photodiode PD. The optoelectronic down-conversion apparatus, that will be detailed in the next section, permits to generate an intermediate frequency, IF, signal at the frequency f i.
Following Ref . and , the IF signal is fed into a common digital phase-locked frequency synthesizer (model LMX2430 from National Semiconductor). It mainly consists of a frequency/phase detector, with an input bandwidth 0.25-2.5 GHz, followed by a charge pump and a loop filter. The digital synthesizer and the frequency down-conversion driver are synchronized to the same reference source, here a quartz oscillator XO at f r = 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 microcontroller in order to program the values N and R of the input and reference dividers, respectively. It sets the command frequency to .
4. Nonlinear frequency down conversion principle
As emphasized, our goal is to generate an IF signal which carries the same phase noise as the beat note Δν keeping in mind that the frequency of the beat note is too high to be directly detected and processed efficiently. To this aim, we use a custom Mach-Zehnder intensity modulator (MZM) from Photline Technologies. Unlike, usual linearized modulators , this modulator is designed to provide a strong nonlinear transmission characteristic as shown in Fig. 3(a) . When the modulator is driven at ν RF, its rugged characteristic leads to the generation of a large number of harmonics. This is illustrated in the spectrum of Fig. 3(b) obtained with a 13.2 GHz-bandwidth spectrum analyzer. In this illustration, only one wavelength was sent to the MZM. Moreover, the modulation frequency, ν RF, was set to 1 GHz so that several harmonics can be displayed. It is worthwhile to notice that the power lying in a given harmonic can be more or less maximized by adjusting the bias voltage, V bias, as well as the RF power driving the MZM.
Let us now send the dual frequency beam through this MZM. The output optical spectrum will then exhibit, in addition to the two main frequencies ν o and ν e, two combs of sidebands separated by f RF around ν o and ν e, as sketched in Fig. 2. This behavior can be observed in the optical domain by increasing the MZM modulation frequency f RF. Figure 4 shows the optical spectra at the output of the laser (Fig. 4(a)) and at the output of the nonlinear-response MZM (Fig. 4(b)) where Δν ≈100 GHz and f RF = 10 GHz. As described in section 2, the frequency difference Δν ≈100 GHz is obtained by tilting the étalon inserted in the extraordinary axis of the laser. Furthermore, Fig. 4(b) clearly shows that a large part of the optical power contained in the mode at frequencies ν o and ν e is redistributed in the sidebands by properly adjusting V bias and P RF. The intermediate frequency, f i, which will be used to drive the phase locked loop, corresponds to the beat note between two closest adjacent sidebands as shown in Fig. 2(b). Assuming that the phase noise of the synthesizer driving the MZM is well below that of the laser beat note Δν, the IF signal is a perfect replica of the signal at Δν.
5. Stabilization: experimental results
The beat note phase noise of the free running laser is mainly due to pump noise and environmental disturbances. By reducing the frequency difference of the laser to a few GHz, we have measured a beat note linewidth of 30 kHz for a measurement time of 1 ms. This beat note drifts over few tens of MHz for a measurement time of a few minutes in agreement with . We have checked that these spectral characteristics remain the same when the beat note frequency Δν is changed.
Let us now turn again the beat note Δν to approximately 100 GHz and the MZM modulation frequency, f RF, to 10 GHz. As mentioned, the intermediate frequency of interest comes from the beating between the closest sidebands, that is, in the present case from the harmonics n + k and n–k of each comb, where k is an integer. Theoretically, k can take any value. In our case n = 5 stands for beatings between harmonics couples (5,5);(6,4);(4,6);(7,3);(3,7);… In practice, and in particular when Δν is high (> 100 GHz), only the lowest values of k (k = 0,1,2 typically) are efficiently involved in the generation of the IF signal. For the sake of clarity and to avoid heavy notations, will use in the following the term n to quote the considered harmonic for which k = 0. The intermediate frequency then reads f i = Δν – 2nf RF. In our case, n = 5 leads to an intermediate frequency f i of 3.59 GHz as shown in the electrical spectrum of Fig. 5(a) . As expected the IF signal exhibits a linewidth of 30 kHz which confirms our assumption that the phase noise brought by the synthesizer driving the MZM is negligible compared to that of the laser beat note Δν. This also proves that the phase noise of the beat note at Δν is independent of the value of Δν, even for extremely high frequencies.
Since the laser acts as a VCO, it is now possible to phase lock the intermediate frequency on a stable local oscillator by sending the error signal on the intracavity LiTaO3 crystal. The intermediate frequency being a replica of the laser beat note, phase locking the intermediate frequency will automatically phase lock the beat note Δν. Both the digital synthesizer and the MZM driver are synchronized to the same reference source, here a quartz oscillator at fr = 10 MHz. We use a PIC microcontroller similar to that of Ref .Taking into account the 300 V maximum output voltage of the HVA and the 1 MHz/V VCO gain, 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). When the loop is closed, the beat note is stabilized at any frequency chosen by the operator, either by adjusting the MZM modulation frequency or through the microcontroller itself. Indeed, when the loop is closed, the stabilized laser beat note reads
In the example of Fig. 5(b), the intermediate frequency has been set to f i = 700 MHz so that the stabilized laser beat note is actuallyΔν = 100.7 GHz. In these conditions, the beat note linewidth is measured to be 1 Hz limited by the resolution of our electrical spectrum analyzer. This leads to a relative stability better than 10−11, i.e., 1 Hz over 100 GHz. However, as previously demonstrated on two frequencies solid-state laser at lower frequencies [16,17], we expect the actual linewidth to lie in the mHz range.
A novel stabilization scheme aiming at generating tunable and ultra-narrow linewidth optically carried beat notes from few GHz up to the mm-wave is proposed and demonstrated. It is relies on the use of a continuously tunable two-axis dual-frequency laser in conjunction with a nonlinear optoelectronic phase locked loop (OEPLL). To handle such high frequencies, we have implemented in the OEPLL a nonlinear-response MZM that generates a frequency comb in the vicinity of each wavelength. The beating between these two combs efficiently down-converts the laser phase noise to an intermediate frequency. This permits us to measure a 30 kHz linewidth of the beat note at 100 GHz. A digital PLL is then used to stabilize the intermediate frequency whose fluctuations are a replica of the laser beat note fluctuations. A linewidth narrower than 1 Hz is thus demonstrated up to 100 GHz which corresponds to a relative stability better than 10−11. The 1 Hz linewidth we measure here being limited by the resolution of our electrical spectrum analyzer.
The approach proposed here is not restricted to dual frequency lasers but also applies to any beat note between two independent lasers. Moreover, by adjusting the non-linear MZM modulation frequency, this approach offers continuous and full bandwidth tunability meanwhile the stabilization loop itself operates at a fixed intermediate frequency. We are currently pushing the experiments to obtain ultrahigh spectral purity signals up to 2 THz corresponding to the tunability range of our dual-frequency laser. To this aim, the stabilization will be carried on the 25th harmonics of a 40 GHz cutoff frequency MZM. Such high harmonics could be easily generated using a MZM with a highly nonlinear response or a high power dual drive MZM [23,24].
The authors acknowledge C. Hamel and A. Carré for their technical support and Jérôme Hauden from Photline for providing the nonlinear-response Mach-Zehnder. Part of this work is funded by Région Bretagne (contract PONANT and an ARED grant).
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