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Instantaneous frequency measurement (IFM) of microwave signals is a fundamental functionality for applications ranging from electronic warfare to biomedical technology. Photonic techniques, and nonlinear optical interactions in particular, have the potential to broaden the frequency measurement range beyond the limits of electronic IFM systems. The key lies in efficiently harnessing optical mixing in an integrated nonlinear platform, with low losses. In this work, we exploit the low loss of a 35 cm long, thick silicon waveguide to efficiently harness Kerr nonlinearity and demonstrate, to the best of our knowledge, the first on-chip four-wave mixing-based IFM system. We achieve a large, 40 GHz measurement bandwidth and a record-low measurement error. Finally, we discuss the future prospect of integrating the whole IFM system on a silicon chip to enable the first reconfigurable, broadband IFM receiver with low latency.
© 2015 Optical Society of America
1. INTRODUCTION
The ability to measure the frequency of an unknown radio frequency (RF) or microwave signal, without relying on expensive spectrum analyzers and mixers, is a basic requirement for the development and testing of wireless systems. In particular, the ability to do so in real-time () and with high accuracy ( error) is crucial for radar receivers used in electronic warfare [1] and biomedical technology [2]. This is known as instantaneous frequency measurement (IFM), and it involves mapping the signal frequency to a more easily measurable quantity such as power.
The use of photonics for microwave IFM is attractive due to the possibility of pushing the frequency measurement range far beyond the capacity of electronic-based IFM systems [3,4]. Since its conception in 2006 [5], research into photonic-based IFM systems has progressed by various means [6–10] and has recently culminated with the demonstration of a number of on-chip IFM systems [11–14]. This trend toward integration is especially important for IFM receivers, where the IFM delay is directly related to the length of the path traveled by the light. The inherently reduced size of integrated systems can thus lead to sub-nanosecond latency as well as improved robustness and a lower footprint [15].
Nevertheless, most on-chip IFM demonstrations to date achieved measurement bandwidths below 10 GHz [11–13], lower than what is currently possible using electronic IFM systems. This limit was due to the trade-off between the quality factors and free spectral ranges of the ring resonators employed by these prior demonstrations. A different technique made use of a highly compact on-chip Bragg grating filter with promising results but a relatively high, 2% measurement error [14]. There are not many techniques that can simultaneously achieve wideband operation and low, sub-1% measurement error. One such technique relies on mapping the RF signal frequency to the power of an optical idler generated through efficient nonlinear optical mixing in a low-loss platform [7]. The stringent requirements on the nonlinear medium have meant that so far all implementations [7,16] were bound to use hundreds of meters of fiber, thereby introducing high measurement delays. For high-bandwidth IFM, where low latency is key, it is crucial to harness the nonlinearity efficiently in a low-loss, short platform.
In this work, we report, to the best of our knowledge, the first low-latency IFM system using on-chip four-wave mixing (FWM) and demonstrate a 40 GHz measurement bandwidth, limited only by the measurement equipment, with a record-low, 0.8% error. These groundbreaking results were enabled by ultralow-loss and efficient FWM in a unique platform: a 35 cm long, thick silicon waveguide with a highly compact footprint. This allowed us to generate an idler with an enhanced signal-to-noise ratio, thereby significantly reducing the measurement error below the level demonstrated in fiber-based systems [7]. This is a breakthrough for high-performance on-chip IFM systems and reveals a new and unique material platform for the nonlinear optical processing of microwave signals [17]. Finally, we discuss the feasibility of integrating the whole IFM system onto a silicon chip, highlighting the potential for implementing the first ultralow-latency, fully reconfigurable IFM system.
2. PRINCIPLE OF OPERATION
The basic structure of our FWM-based IFM system is shown in Fig. 1(a). An RF signal of unknown frequency is received and sent to an electro-optic modulator (EOM) where it modulates two continuous-wave (CW) optical carriers at different frequencies and . This results in two copies of an optical signal, in two different channels. These two optical signals are then de-multiplexed using a coarse wavelength-division multiplexer (CWDM). In this way, one signal is delayed by relative to the other before both are recombined. The two signals are then sent through a nonlinear medium where they mix through FWM, generating idlers in adjacent channels.
Fig. 1. (a) Schematic of the on-chip FWM-based IFM system. EOM, electro-optic modulator; CWDM, coarse wavelength-division multiplexer; , tunable delay element; BPF, optical bandpass filter. (b) Degenerate (DFWM) and nondegenerate (NDFWM) mixing processes between the two channels.
There are three idler components generated in the vicinity of the frequency . The middle component is an idler “carrier,” resulting from degenerate FWM (DFWM) between the two original carriers. The two remaining components, or idler sidebands, occur at frequencies . There are in fact two FWM processes that occur simultaneously, as shown in Fig. 1(b), giving rise to two separate pairs of idler sidebands. The first is a DFWM process, which gives rise to a delayed pair of idler sidebands. Neglecting dispersion, the complex field for the upper DFWM idler sideband is
The second process is a nondegenerate FWM (NDFWM) process where the generated idler pair is a copy of the nondelayed optical signal. Neglecting dispersion, the complex field of the upper NDFWM idler sideband is The total sideband idler field is, therefore, a coherent sum of two separate idler fields with a differential delay of , resulting in an interference effect. The total upper idler sideband is given by a similar expression can be derived for the lower idler sideband.Using an optical bandpass filter (BPF), the total idler field (idler “carrier” and sidebands) can finally be isolated, and its power is measured with an optical power meter [i.e., a low-speed photodetector (PD)] to be
for some constants and , with . This expression clearly shows that once the system has been characterized, i.e., , , and are known, an optical power meter can be used to estimate the unknown RF frequency , without the need for expensive high-speed RF equipment.An inspection of Eq. (4) reveals the inherent trade-off between the measurement bandwidth () and the measurement resolution, defined as (). To bypass this trade-off and maximize the measurement resolution without compromising bandwidth, it is necessary to maximize the idler power, to both operate further above the noise floor and increase the slope of Eq. (4). It is then crucial to harness FWM in a low-loss, nonlinear platform.
3. EXPERIMENT
A. Device Description
In this work, the nonlinear platform used to harness FWM was a 35 cm long silicon strip waveguide [18]. Silicon is a highly attractive platform for nonlinear optics due in part to its large Kerr coefficient (100 times larger than that of silica) and to its compatibility with CMOS processes [19,20].
The distinguishing feature of this waveguide was its large mode area of combined with a small footprint. Ordinarily, waveguides with such large mode areas require millimeter-scale or even centimeter-scale bending radii, due to high mode coupling losses, and are thus constrained to lengths of a few centimeters [21]. This particular sample, however, used Euler bends where the bending radius varies continuously along the whole bend, ensuring minimum coupling to higher-order modes [18]. This resulted in micrometer-scale bending radii comparable to that of nanowires. Consequently, the whole 35 cm long spiral, shown in Fig. 2(a), occupied a less than surface area on a silicon-on-insulator (SOI) chip.
Fig. 2. (a) Top view of the 35 cm long, thick silicon spiral. (b) Simulation of the fundamental mode for the silicon strip waveguide. (c) Rib-to-strip converter for coupling to the fundamental mode.
The dimensions of the strip cross section were . There are several advantages that follow from this large size: a low, 0.15 dB/cm linear propagation loss (compared with 1–3 dB/cm for silicon nanowires), a higher nonlinear loss threshold, and efficient coupling to lensed fibers (1.5 dB/facet coupling losses). Coupling was done into a single-mode rib waveguide, which then tapered into the strip waveguide, as shown in Fig. 2(c), ensuring excitation of the fundamental mode. The waveguide dispersion at 1550 nm was normal, which led to an FWM 3 dB bandwidth of 6 nm. This is sufficient for most RF photonic applications, where the signal content is in the range of 1–100 GHz, or less than 2 nm.
The nonlinear optical properties of the waveguide were measured through a series of self-phase modulation (SPM) and FWM experiments. By launching picosecond pulses into the waveguide, we observed SPM broadening and were able to estimate the Kerr coefficient as . This value is slightly lower than that for a typical silicon waveguide, possibly due to the change in crystal orientation that occurs in the spiral bends [22]. The nonlinear parameter was then estimated as . We note that the maximum FWM conversion efficiency for this waveguide was comparable to that obtainable using a much shorter, 5 mm standard silicon nanowire. However, our thick silicon spiral was not optimized for FWM. More importantly, the low coupling losses meant that the total waveguide insertion loss was lower than that for a nanowire. This property is central to IFM applications, where the output idler power has a direct effect on the system performance.
B. Methods
The experimental setup was based on the structure shown in Fig. 3. Two distributed-feedback laser diodes were used to generate the optical carriers, with wavelengths of 1550.0 and 1551.7 nm. Each laser was biased for CW operation, with output power of 20 dBm. The EOM used was an EOSPACE Mach–Zehnder modulator (MZM), with a 20 GHz bandwidth, 8 dB insertion loss, and . This was biased at quadrature and was driven by a 12 dBm RF signal. Throughout the experiment, all nonlinear distortions were at least 40 dB weaker than the first-order sidebands. Following modulation, the two optical signals were amplified by an erbium-doped fiber amplifier (EDFA). A CWDM with a 200 GHz channel spacing (and 3 dB insertion loss) was then used to split the two modulated carriers along two paths of different lengths, allowing them to be delayed differentially. The delay was adjusted by using an optical tunable delay line (TDL). The two signals were then recombined and launched into the 35 cm long silicon spiral. An isolator was placed before the chip input to suppress backreflections. Upon exiting the spiral, the signal was sent through an optical BPF where the total idler field, comprising idler “carrier” and sidebands, was selected. The BPF had a 200 GHz bandwidth, centered at 1553.3 nm, with more than 40 dB stopband suppression; the filter insertion loss was 3 dB and its roll-off exceeded 200 dB/nm. Finally, the total idler field was sent to a low-speed PD, where its optical power was measured. A polarization controller (PC) was placed before the input of the silicon spiral to minimize its insertion loss, measured as 9 dB. A PC was also placed into one of the arms of the differential delay structure, in order to control the relative polarization between the two optical signals and maximize the strength of the FWM interaction.
Fig. 3. Experimental setup for the FWM-based IFM system, including DFB, distributed feedback lasers; PC, polarization controllers; MZM, Mach–Zehnder modulator; EDFA, erbium-doped fiber amplifier; CWDM, coarse wavelength division multiplexer; TDL, tunable delay line; BPF, bandpass filter; and PD, photodetector.
The EDFA gain was adjusted such that both optical carriers entered the silicon spiral with 18.7 dBm power. At this power level, the FWM conversion efficiency, here defined as , was measured to be . Figure 4 shows the optical spectrum at the output of the silicon spiral when both carriers are modulated by an input microwave signal with frequency . By adjusting the TDL, we were able to vary the product between 0 and . According to Eq. (4), these two points corresponded to the maximum and minimum idler sideband power. This is clearly visible in Fig. 4 where there is a 10 dB power contrast for the idler sidebands as the delay is tuned.
Fig. 4. Optical spectra at the output of the silicon waveguide for two different values. The 10 dB power difference between the idler sidebands is a manifestation of the interference effect between the idlers generated through DFWM and NDFWM.
C. IFM Results
In the IFM experiment, the time delay between the optical signals was initially set to 8.3 ps. The IFM system was then characterized by sweeping the frequency of the output from an RF signal generator from 0 to 40 GHz and measuring the generated idler power. This measurement is shown in Fig. 5(a), together with a theoretical fit. Fitting involved selecting appropriate values for and [from Eq. (4)] to find the combinations that matched the data best. This process also required accounting for the frequency roll-off of the modulator, which was found to be relatively smooth up to a frequency of 40 GHz even though its nominal bandwidth was 20 GHz. The fit was then used to estimate unknown frequencies in the measurement range, and the results are shown in Fig. 5(b). The estimation process involved single-shot measurements with no averaging. The increased measurement error at high frequencies, observable in Fig. 5(b), was due to the lower slope (i.e., ) of the system response, which, as explained in Section 2, reduces the resolution of the frequency measurement. This reduction in slope is caused partly by the sinusoidal functionality of the response [i.e., Eq. (4)] and partly by the frequency roll-off of the modulator. We note that the frequency estimation procedure only works for signals with the same RF power used to obtain the fit. To cope with a varying signal power, one could use an electrical limiting amplifier (as done by electronic IFM systems [1]) at the input of the MZM. An all-optical approach is also possible, by generating multiple idler copies and measuring the ratio of their powers [16].
Fig. 5. (a) IFM RF system response with . (b) Frequency estimation measurement over a single 40 GHz frequency band (inset, histogram of the frequency measurement error; rms ).
The root mean square (rms) of the frequency estimation error was 318.9 MHz, which corresponded to 0.8% of the 40 GHz measurement bandwidth. This combination of a wide measurement bandwidth (limited only by the range of the RF signal generator) and sub-1% error is a record for an integrated microwave photonic (IMWP) IFM system, as indicated in Table 1. This table provides a comparison of current on-chip photonics-assisted IFM systems. A figure of merit for these systems is the measurement error as a percentage of the measurement bandwidth.
Table 1. Performance Comparison of IMWP IFM Systems
As explained in Section 2, increasing the delay can lead to an enhanced measurement resolution (i.e., lower error), at the cost of a reduced measurement bandwidth. This trade-off is displayed in Fig. 6 where, as is increased, a given idler power measurement no longer maps to a single RF frequency band, but to multiple, narrower bands. Nevertheless, by rapidly reconfiguring , it is possible to exploit the high accuracy of a high- measurement, combined with the wide bandwidth of a low- measurement. This is a process consisting of two steps. Initially, a small is chosen to obtain a rough estimate of the frequency band in which the RF signal resides (e.g., Band 4 in Fig. 6). Following this, is increased, producing a highly accurate, unambiguous, estimate of the signal frequency.
Fig. 6. Reconfiguration of the IFM system response between (a) a high-bandwidth/error state (low ) and (b) a low-bandwidth/error state (high ).
To demonstrate this process, we reconfigured the system by increasing the time delay to 69.4 ps. The system characterization and theoretical fit are shown in Fig. 7(a). The decaying sinusoid response is due to the frequency roll-off of the modulator. Each linear region of the system response was then assigned to a particular frequency band. This resulted in six 7.2 GHz bands, which were then used to estimate the frequency of various RF tones. The result of this measurement, shown in Fig. 7(b), exhibits a low estimation error, with an rms value of 40.2 MHz, or 0.56% of the 7.2 GHz measurement bandwidth.
Fig. 7. (a) IFM system response with . (b) Frequency estimation measurement for six separate 7.2 GHz frequency bands (inset, histogram of the frequency measurement error; rms ).
These measurements show a unique and important feature of FWM-based IFM: the ability to easily tune the system response to optimize for bandwidth or resolution. Therefore, it is crucial to be able to quickly tune the delay, so as to perform fast consecutive measurements with a wide bandwidth and with high accuracy [24]. Our technique for implementing the delay constitutes a significant improvement over that used in previous FWM-based IFMs [7,16] where a dispersive element introduced a delay between the two channels. This is because a TDL offers a much faster mechanism for tuning , compared with tuning a laser wavelength. Furthermore, a recent breakthrough in continuously tunable true-time delay achieved a sub-nanosecond settling time [25]. This opens the way to achieve the first IFM system that overcomes the bandwidth/error trade-off through sub-nanosecond reconfiguration.
4. FUTURE VISION
The ability to harness nonlinear optical processes efficiently, in a low-loss integrated platform, is fundamental for a wide variety of microwave photonic applications [15]. This is particularly true of FWM-based IFM where, as we have seen, the generated idler power has a direct effect on the measurement error. In this work, we have shown that long, thick silicon waveguides exhibit all of these properties, while being able to maintain low footprints and a high nonlinear loss threshold.
Nevertheless, to be able to monolithically integrate all critical components of the IFM system, one will need to combine the thick silicon platform with a more standard SOI technology. One such technology is 220 nm SOI (i.e., thin SOI), which enables access to a full library of active and passive components.
Our vision of the layout of a future fully integrated SOI FWM-based IFM system is presented in Fig. 8, featuring a single transition from thin to thick silicon. This transition could be implemented using a section of tapered rib waveguide that minimizes the excitation of higher order modes [26], or even through photonic wire bonding [27].
Fig. 8. Future vision of the SOI integrated FWM-based IFM system. The chip is divided into thin and thick silicon sections. The RF input signal is applied to the intensity modulator. The tunable time delay unit consists of an optical delay interferometer and a phase modulator [25]. Tuning of is achieved by varying the voltage input to the phase modulator. The PD outputs a DC voltage proportional to the idler power, which is then mapped to an estimate for the RF input signal frequency.
The thick silicon part of the chip houses the FWM waveguide, BPF, and PD. One of the main advantages of the current FWM-based IFM scheme is that it requires only a simple low-speed PD. Such a device has already been demonstrated using vertical p-i-n germanium, integrated on a thick SOI waveguide [28]. BPFs composed of cascaded Mach–Zehnder interferometers have also been demonstrated in thick silicon [29]. For these components, Euler bends will need to be implemented so as to maintain a low footprint.
The thin silicon section of the chip hosts the EOMs and an arrayed waveguide grating. The intensity modulator used by the input RF signal would be implemented using the doped thin SOI technology. Such MZMs have been shown to be capable of high performance, with a low, 1.6 dB insertion loss and a wide, 27.8 GHz bandwidth [30]. De-multiplexing of the two channels would occur in an arrayed waveguide grating, which has also been demonstrated in a thin SOI with a 200 GHz channel spacing [31]. Finally, tunable time delay could be realized using a novel approach [25], employing an optical delay interferometer and a phase modulator. High-speed phase modulators have been implemented using the silicon–organic hybrid technology [32] and would allow fast tuning of the delay. Such a chip, boasting a fast tunable delay and a compact size, will result in the first ultralow-latency and highly accurate IFM system with bandwidth and capabilities beyond what is achievable using state-of-the-art RF technologies.
5. CONCLUSION
We have presented, to the best of our knowledge, the first IFM system using on-chip FWM, capable of extremely high-frequency measurements and low error through easy reconfiguration of the system response. The enabling technology is a low-loss, long silicon waveguide, which was used to generate strong FWM idlers. This allowed us to achieve a record-low measurement error over a wide frequency range, greatly surpassing that of previous IMWP IFM systems. The novel setup we have presented consists of components that are all capable of SOI integration, opening the way for the first reconfigurable, monolithically integrated IFM receiver.
Funding
Australian Research Council (ARC) (CE110001018, DE150101535, FL120100029).
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