A novel all-optical system which independently measures both the amplitude and frequency of an RF signal is proposed and demonstrated. A photonic Hilbert transformer provides two orthogonal measurements of an RF signal. These are compared using four wave mixing in a highly nonlinear fiber, producing two independent outputs enabling determination of both signal frequency and amplitude. This all optical approach requires only simple, low cost DC electronics at the receiver. The system is demonstrated up to 20 GHz but can be scaled to 40 GHz and beyond.
© 2013 Optical Society of America
Instantaneous frequency measurement (IFM) systems are important components of modern electronic warfare receivers. These systems continuously monitor the dominant frequency components of incoming signals, which are matched against known signatures and thus provide an early warning indication of potential threats to be analyzed with more rigorous scanning systems. Electronic IFMs up to 20 GHz are common but are limited by the bandwidth of RF couplers, delay lines and mixers .
In recent years, microwave photonics has been investigated to realize IFM systems [2–4]. These implementations are often based on RF signal fading in dispersive photonic links ; discrimination of signal time of arrival ; or optical filtering . Each of these techniques relies on high-speed electro-optic components, careful alignment of optical filtering or precise maintenance of optical path lengths. Further, practical IFM systems require multiple implementations of these systems to enable broadband coverage and high sensitivity . The expense and vulnerability of these electro-optic components and complexity of stable optical path lengths and filtering would render parallel implementations of photonic IFM systems of this sort both challenging and prohibitively expensive.
Previously, we have demonstrated approaches to perform IFM measurements using optical mixing, producing DC optical outputs that can be received using low speed optoelectronics. We have demonstrated proof of this concept using cascaded Mach Zehnder modulators  and extended this system to perform amplitude independent frequency measurements  through incorporation of an optical Hilbert transformer . The key advantage of these systems was the DC outputs, which greatly reduced the complexity required of the receiver and thus had the potential to reduce cost and rate of failure. These techniques however were still limited by the need for RF delay lines which are both lossy and must be matched to parallel optical fibers causing vibration and thermal intolerance [5,6].
Recently, we have reported an improved photonic IFM system using four wave mixing in highly nonlinear fiber  that overcame the bandwidth limitation of the RF delay lines of the previous systems [5,6]. We have also demonstrated parallel operation of this system with only moderate increment of component count and complexity . These all-optical systems were extremely stable and could, in principle, be extended to operate with many channels for sophisticated functionality; however, up to this point, such a sophisticated implementation based on parallel all optical IFMs has not been reported.
In this paper, we demonstrate a sophisticated IFM system that exploits multiple IFM channels in an all-optical configuration. We show that it is possible to utilize the multiple channels of  and incorporate a photonic Hilbert transformer of  to achieve parallel orthogonal measurements of , but with the ultra-stable operation of . These orthogonal outputs can then be used together to independently measure both frequency and amplitude of input RF signal. The specific novelty of this paper is that through elegant use and re-use of a limited number of transversal channels, all of the required functions are achieved with a relatively compact and low component count system. Further, to our knowledge, the resulting system represents the first demonstration of an all-optical, amplitude independent IFM. It should however be noted that a preliminary proof of this concept was reported in , while this paper presented an improved system implementation with detailed analyses.
The organization of this paper is as follows. Section 2 reviews the fundamental concepts of the previously demonstrated all-optical IFM based on four wave mixing; orthogonal IFM measurements; and the photonic Hilbert transformer to provide the foundations for the remaining sections. The concept of our new, nonlinear orthogonal IFM is described in Section 3 together with a theoretical model that can be used to predict the expected output for a given RF input frequency and amplitude. Section 4 describes the system configuration used to experimentally demonstrate this concept and also presents the characterization of this system. The system is the then demonstrated in Section 5 showing that measurement of both frequency and amplitude of an input RF signal is possible. Finally, Section 6 discusses the obtained results, summarizes the finding and presents suggestions for future work.
2.1 All optical IFM based on nonlinear mixing
The previously demonstrated IFM system using optical mixing in Highly Nonlinear Fibre (HNLF)  is illustrated in Fig. 1. Two optical carriers (λi, λj) are modulated with an RF signal (Ω). We wish to measure the frequency Ω of this RF signal. The two modulated optical carriers are differentially delayed by time Δt and then mixed together. The mixing process produces idlers or new optical wavelengths at (2λi−λj) and (2λj−λi) via Four Wave Mixing (FWM) . The carriers at the idler wavelengths are the products of the two original carriers. It has been shown in  that the signal carried by these carriers is a coherent summation of the differentially delayed signals present on the two input carriers and the total DC optical power oscillates with RF frequency enabling frequency measurement.
This system has the advantage of ultra-broad bandwidth due to the use of all optical mixing and freedom from the need for high-speed electronic components since at the output only the DC optical power must be measured with no need to analyze the frequency of this optical output. Further, despite the output being a coherent superposition of two independently delayed optical carriers, it is also surprisingly stable  due to the fact that the idler carrier is the product of the original optical carriers and hence is immune to relative phase variations.
2.2 Orthogonal IFM
To use the system of Fig. 1 for IFM, the RF signal amplitude must be known . In order to determine the frequency of RF signals of unknown strength, it is necessary to obtain two orthogonal measurements . Figure 2 presents a block diagram of such an orthogonal IFM system. An RF tone, Acos(Ωt), of amplitude A and frequency Ω, is divided into two equal portions feeding modules M1 and M2. Within each module, the RF tone is further divided, differentially delayed by a known time, Δt, and these delayed components are multiplied and the product is filtered to extract the DC component. The output of M1 is proportional to Acos(Ω×Δt) while M2 has a 90° phase shift introduced to one arm to produce an output proportional to Asin(Ω×Δt). The ratio of these two outputs is cot(Ω×Δt) which depends on frequency, Ω, but is independent of amplitude, A, enabling simultaneous and independent measurement of both frequency and amplitude [1,6].
2.3. Photonic Hilbert transformer using transversal filtering
The IFM of Fig. 2, requires access to uniformly phase shifted version of the RF signal at both 0° and 90°. Mathematically, such functionality can be provided via a Hilbert transform. In electronic systems, this function is achieved through use of an 90° RF hybrid coupler which can exhibit relatively broad bandwidth with moderate phase ripple , however performance can degrade above 20 GHz. Microwave photonics can be more effective at such frequencies.
Figure 3 presents the principle of operation of a previously demonstrated transversal photonic Hilbert transformer . Figure 3(a) presents the temporal response. The solid red line presents the idealized response: a hyperbola, which is truncated at ± Δt. Figures 3(b) and 3(c) present the amplitude and phase of the expected frequency response, which is the Fourier transform of Fig. 3(a). The solid red line of Fig. 3(b) shows the amplitude, which should be constant at all frequencies, while the solid red line in Fig. 3(c) shows the phase, which alternates between −90° and 90° repeating at frequency intervals of 1/Δt.
This system can be implemented using a transversal approach by sampling the temporal response as indicated by the dashed green lines in Fig. 3(a). Samples are separated by Δt. The amplitude of the frequency response is presented in Fig. 3(b) and is now a sinusoid with period 1/Δt, typical of a two tap transversal system. Figure 3(c) presents the phase response which remains similar to the ideal, unsampled case, alternating between −90° and 90° at an interval of 1/Δt. This approach can thus achieve an approximate Hilbert transform, however the performance degrades due to the signal cancellation near the nulls of the amplitude response, which could be improved with additional sampling taps .
The predicted 90° phase will only be meaningful relative to a reference phase. In the case of Fig. 3, phase is relative to a signal with ‘zero’ time delay. A third tap with time delay half way between the two transversal filter taps as indicated in Fig. 3(a) can fulfill this role.
An implementation of this photonic transversal Hilbert transformer has been demonstrated previously  and has been used for achieving orthogonal IFM measurements . If the time delay were set such that Δt = 80 ps, as shown on the top x-axis of Fig. 3(a), then the frequency response would be as shown by the top x-axis in Figs. 3(b) and 3(c). This indicates that the system could be effectively operated in bands between 0 and 12.5 GHz and 12.5-25 GHz. This two tap Hilbert transform is deemed suitable for the current demonstration.
3. Orthogonal nonlinear IFM concept
This section introduces a photonic approach that combines our previously demonstrated all-optical parallel IFM system  with the optical transversal Hilbert transformer  to implement an all optical version of the orthogonal IFM system .
Figure 4 shows the system configuration of the proposed all-optical, orthogonal IFM. The RF tone generated by the signal generator modulates four optical wavelengths. These are used to form a two-tap transversal filter (λ1 and λ3), a reference tap (λ2) and a reference pump (λ4). Carriers λ2, λ3 and λ4 are combined using a polarization maintaining arrayed waveguide grating (AWG). The carrier, λ1, is input to Port 1 of a 2 × 2 Mach Zehnder modulator (MZM) to achieve a negative modulation. The remaining carriers are input to Port 2 of the MZM and receive positive modulation. All four carriers are collected from the same MZM output and input to a cascaded fiber Bragg grating (CFBG) which reflects various wavelengths from different locations within the fiber. In this case, λ1, λ2 and λ3 experience incrementally increasing time delays and λ4 experiences a significantly greater delay. The differentially delayed carriers are amplified and input to a length of HNLF. The four carriers produce many idler products. Among these, the product of mixing between the reference tap (λ2) and the pump (λ4) occurs at (2λ4−λ2) and the products of the two-tap transversal filter (λ1 and λ3) with the pump (λ4) appear at (2λ4−λ1) and (2λ4−λ3). A programmable optical filter is used to isolate these particular products and direct them to two distinct optical outputs. The first output contains only the product at (2λ4−λ2) while the second output sums the products at (2λ4−λ1) and (2λ4−λ3). The DC optical powers of these two outputs are detected using low speed detectors. The measured voltages from each detector serve as orthogonal IFM outputs.9]; Δtij is the differential time delay introduced by the CFBG between λi and λj; Ω is the RF angular frequency and Pij is the optical power of the created idler at wavelength (2λi−λj) which can be measured when RF modulation is off (m = 0) and is independent of both the modulation index and the RF frequency. This invariant term can thus be subtracted as a constant DC offset during measurement leaving the frequency and power depended power on each idler as:
Since all carriers are modulated with the same modulator, the modulation index (mi) will be of the same magnitude for each channel such that m2 = m3 = m4 = m and m1 = −m. As shown in Fig. 4, PD1 detects P′42 and PD2 detects P′41 + P′43. It is also noted that the outputs of PD1 and PD2 corresponds to the two orthogonal measurements and exhibit identical properties to the outputs of . It is thus possible to use the technique developed in  to solve for the RF signal amplitude and frequency. Particularly, taking the ratio of the offset measurement from PD2 and dividing by the offset measurement of PD1 yieldsEquation (3) provides a relationship between the RF frequency on the right hand side and a continuously measured value on the left hand side. This equation is independent of m and hence independent of the RF signal power. Equation (3) was solved by calculating a look up table of the expected response for frequencies from 1 to 20 GHz in steps of 0.1 GHz and then linear interpolation between these values to estimate the frequency Ω corresponding to the measured responses. The value of m can then be determined by substituting Ω into Eq. (2) using the output of PD1 and P′42. From m, we can compute the RF signal amplitude. The system of Fig. 4 thus enables continuous and simultaneous determination of both RF frequency and amplitude.
4. Orthogonal nonlinear IFM setup
The system was configured as depicted in Fig. 4. DFB lasers provided carriers at wavelengths of λ1 = 1542.17, λ2 = 1543.72, λ3 = 1545.35 and λ4 = 1553.72 nm. These were associated with ports 1, 2, 3 and 8 of the arrayed waveguide grating (AWG, ANDevices, DWDM-F-100G) and they are thus named Ch1, Ch2, Ch3 and Ch8 for the remainder of this paper. The carrier powers were set to provide a total of 0 dBm at the input to the 2x2 MZM (EOspace). The signal generator (Sig. Gen., Anritsu MG3694A) provided 10 dBm of RF power to the 2 × 2 MZM which was biased at quadrature. The MZM output was amplified with an Erbium doped fiber amplifier (EDFA, Pritel PMFA-20-IO) to ~80 mW then reflected from a cascaded fiber Bragg grating (CFBG, Redfern Optical Components) and input to a highly nonlinear fiber (HNLF, OFS, 1 km, zero disp.: 1540 nm, disp. slope: 0.019 ps/(nm2km)).
The CFBG introduced different time delays on Ch1, Ch2, Ch3 and Ch8. The differential delays between Ch8 and each of the channels (Ch1, Ch2 & Ch3) were measured to be 285, 245 and 205 ps respectively. This configuration therefore corresponds to spacing between the transversal Hilbert transform taps (Ch1 and Ch3) of ΔtHT ~80 ps, resulting in a Hilbert transform response with an expected free spectral range (FSR) of ~12.5 GHz as shown in Fig. 3(b). In addition, the delay difference between the reference tap (Ch2) and the pump (Ch8) is ΔtIFM ~245 ps resulting in a predicted IFM period of 4.08 GHz.
Four wave mixing of Ch1, Ch2, Ch3 and Ch8 in the HNLF created many new wavelengths. Among them, the terms resulting from Ch8 mixed with Ch1, Ch2 and Ch3 appearing at 1564.37, 1562.82 and 1561.19 nm, corresponding to Ch15, Ch14 and Ch13 respectively, were of particular interest. A programmable optical filter (Finisar WaveShaper WS4000) was configured to provide flat-top, pass-band filtering with 100 GHz bandwidth centered at Ch13, Ch14 and Ch15 and simultaneously directed Ch14 to output Port 1 while outputting the sum of Ch13 and Ch15 at Port 2. The DC output optical powers at each port were measured using low speed photodectors (New Focus 2011) and digital voltmeters (HP 3478A).
The Hilbert transformer of Fig. 3 requires the transversal taps at Ch13 and Ch15 to have exactly the same amplitude but opposite sign while imposing no constraint on the actual amplitude of the reference tap at Ch14. For simplicity, we chose to set all three taps to the same amplitude. We would also expect that if the Ch1, Ch2 and Ch3 were set to the same power level, the amplitudes of the created idlers at Ch15, Ch14 and Ch13 would also be equal, assuming the mixing efficiency of the HNLF is uniform over the entire spectrum. Since the HNLF exhibits a small variation of mixing efficiency over c-band, small adjustments of the optical powers for Ch1, Ch2 and Ch3 were required to achieve powers at Ch13, Ch14 and Ch15 within0.2 dB of each other. This completes the setup for the system of Fig. 4.
5. Orthogonal nonlinear IFM characterizations
Before demonstrating the operation of the amplitude independent all optical IFM, the various components of the system were characterized. This characterization included the frequency response of the modulation index, the spectral response of the mixing products and the frequency response of the individual idlers.
5.1 Frequency response of the modulation index
It was established in previous publications [8,9] that the output power versus frequency of the IFM system depends on both the amplitude of the RF signal and the combined responses of the modulator and RF cabling at the system input. We have also shown in  that the combined frequency response could be modeled by a simple RF conduction loss relationship:, where α is the frequency roll off factor of the photonic transmitter and f is the RF signal frequency (Ω = 2πf). Since for the all optical system α will not include the frequency response of a broadband photodetector or an output RF cable as the output measured at DC, we could not obtain empirical values for α, or and also the modulation index, m, through direct measurement of the photonic link using a vector network analyzer. Instead, the photonic link DC output voltage was measured at null biasing with 10 dBm RF input power, and the technique of  was used to extract m = 0.19 and α ≈ 0.091 (GHz-1/2).
5.2 Optical spectrum characterisation
Optical specra measured at the input and output of the HNLF using an optical spectrum analyzer (OSA, Anritsu, MS9710C, attenuation ~8.5 dB) are presented in Figs. 5(b) and 5(c) respectively. Figure 5(b) shows four wavelength channels at the input of HNLF. Figure 5(c) shows that the output of HNLF consists of many idlers. Among these, the idlers of interest are at Ch13, Ch14 and Ch15. It can be seen from Fig. 5(c) that these three idlers are of the same power confirming the calibration conducted during the system configuration.
5.3 Individual tap frequency response characterization
We now characterize the frequency responses of Ch13, Ch14 and Ch15 individually to confirm that they behaved as predicted by Eq. (1).
Figures 6(a)–6(c) present the optical spectra obtained at the output of the HNLF with the WaveShaper configured to output the isolated idlers centered at Ch13, Ch14 and Ch15 respectively. These figures show that the required channels can be isolated from the other spectral components of Fig. 5(c) with extinction better than 35 dB. Figure 6(d) presents the spectrum with the WaveShaper configured to output both Ch13 and Ch15 simultaneously, which appears as the superposition of the spectra of Figs. 6(a) and 6(c), demonstrating that the system outputs were as predicted in Figs. 4(b) and 4(c).
The frequency responses of the various outputs of the HNLF were measured by recording the photodetector DC voltage with the RF frequency swept from 1 to 20 GHz in 0.25 GHz steps. Figures 6(e)–6(g) present the recorded optical power as a function of RF frequency for Ch13, Ch14 and Ch15 in isolation respectively. These oscillate with frequency as expected from Eq. (1). The oscillation period in Fig. 6(f) is approximately 4 GHz, which is in excellent agreement with the inverse of the differential time delay difference of Δτ = 245 ps between Ch2 and Ch8. The oscillation period decreases from Ch13 to Ch15 due to the increment of differential time delays relative to Ch8 from Ch3 to Ch1, namely 205, 245, 285 ps respectively. The measured responses of Ch13 and Ch14 are in phase with each other and are out of phase with the response of Ch15 as predicted by Eq. (1). In addition, the measured voltages of Figs. 6(e)–6(g) are almost the same, confirming that these channels are of the same amplitude. Figure 6(h) presents the DC optical power measured as a function of RF frequency with the WaveShaper configure to simultaneously output Ch13 and Ch15. This appears as the sum of the responses of Figs. 6(e) and 6(g) as expected.
Figure 6(f) represents an IFM measurement with no phase shift, similar to that previously demonstrated . Figure 6(f) also presents the prediction of Eq. (1). The excellent match to the measured data confirms that Eq. (1) can be used to extract the frequency of the input RF signal, given that the RF modulation depth m is known. Figure 6(h) should represent the orthogonal IFM measurement, including a 90° phase shift on one arm. The response predicted by Eq. (2) for P′41 + P′43 is also presented with excellent agreement evident.
The amplitude of Fig. 6(h) is about twice that of Fig. 6(f) as expected since it is the sum of two idlers. The oscillation period of Figs. 6(h) and 6(f) are similar, indicating the transversal summation of the higher and lower period responses of Figs. 6(e) and 6(g) respectively does indeed produce the desired intermediate period. Figure 6(h) exhibits amplitude fading at 12.5 GHz as predicted in Fig. 3(b) due to the use of only two transversal taps. The oscillations of Fig. 6(h) are shifted by a quarter period relative to Fig. 6(f) and hence these two outputs can be considered orthogonal.
6. Demonstration of orthogonal nonlinear IFM
Having established that two orthogonal IFM outputs are available, we now demonstrated that the system of Fig. 4 can be used to measure both RF frequency and power independently. The system was set up as explained in Section 5. To demonstrate the ability of this system to measured both RF signal frequency and power, experiments were conducted at RF power levels of 10 mW (10 dBm), 5 mW (7 dBm) and 2.5 mW (4 dBm), and the signal frequency and power level were determined from the measured outputs. Figure 7 presents the measured outputs of the system associated with PD1 and PD2, on Fig. 4, for three different RF power levels when the RF frequency was swept from 1 to 20 GHz in 0.25 GHz steps. The predictions of Eq. (1) are also presented on Fig. 7 as solid lines.
Figure 7 presents the output voltage as a function of input RF frequency showing that when the RF power is reduced by 3 dB, the oscillation amplitude reduces by a factor of 2. The response also has a DC offset that depends on the RF power. Both of these features are as predicted by Eq. (1). The oscillations of Figs. 7(a) and 7(b) are clearly orthogonal as established in Section 5. The responses exhibit very low noise and are highly stable.
To interpret the RF frequency from measurements obtained from Fig. 7, it is necessary to solve Eq. (3), which requires prior determination of several system parameters. In particular, the DC voltages measured at various channel wavelengths as explained in Section 5. For this calibration, the RF input was switched off, and the output voltages on Ch13, Ch14 and Ch15 were recorded as being identical and equal to ~0.1925 V. This invariant DC offset, together with the data of Fig. 7 was used to solve Eq. (3), to obtain the RF frequency. Figure 8(a) plots the interpreted frequency against the actual input RF frequency.
Figure 8(a) shows that the interpreted frequency is close to the actual input RF frequency, independent of the RF signal power. There is an increase in error toward 12.5 GHz. This is due to the null in the orthogonal IFM response at this frequency. Figure 8(b) presents the calculated frequency measurement errors using the data of Fig. 8(a). It is evident that the interpreted frequency is within ± 0.5 GHz of the actual signal frequency.
Having determined the RF frequency, the RF power was calculated using Eq. (1). The calculated RF power is presented in Fig. 8(c). It can be seen from Fig. 8(c) that the interpreted power (dots) cluster around the power levels of 9, 4.5 and 2.25 mW (lines) for RF input powers of 10, 5 and 2.5 mW respectively. The slightly lower than expected measured RF power levels are attributed to the loss of the RF cable used at the system input which is estimated to be ~0.5 dB in this case. The errors in interpreted power with respect to the predicted power levels of 9, 4.5 and 2.25 mW are presented in Fig. 8(d). It is evident that the error is approximately ± 20% of the actual RF power for all cases. It is also observed from Fig. 8(d) that the error in interpreted power enlarges at frequencies where the slopes of the curves of Fig. 7(a) are greatest. This is because the RF power is determined from the interpreted frequency as described in Section 3 and the error in frequency will therefore amplify the error in interpreted power, most significantly when the slope is greatest. Statistical analysis of this error should be performed, but such analysis deemed beyond the scope of this paper and will be conducted in the context of system optimisation. There is also increased error of the interpreted power, especially around the nulls of Fig. 7(a) and this is most pronounced around 12.5 GHz where Fig. 7(b) fades in amplitude. This could be addressed with additional transversal taps.
With the experimental results of Fig. 8, we have shown that the system of Fig. 4 is indeed capable of independently determining both the signal frequency and amplitude. The proof of concept is thus demonstrated.
7. Discussion and conclusions
We have introduced a new system that is capable of independently determining both frequency and amplitude through the use of parallel all optical mixing and a photonic Hilbert transformer. This is accurate, low noise and highly stable. The demonstration was conducted from 0 to 20 GHz limited by the available equipment, especially the RF signal generator and the fixed wavelength DFB lasers and the cascaded fiber Bragg grating. Since the system is all optical, with appropriately adjusted equipment it could easily be extended to 40 GHz or beyond. The demonstrated system used only four optical wavelengths, which enabled a simple implementation, but also presented a number of limitations. The result of Fig. 8(b) shows that there is an increase in the uncertainty of the RF amplitude toward the null of the transversal Hilbert transformer. The range of affected frequencies depends on the bandwidth of the transversal system and this bandwidth can be extended through the use of additional taps . The addition of more taps is certainly possible, as shown in , but would increase system complexity; however, as shown in  this would only require a modest increase in component count. Another factor to consider when increasing the number of wavelength channels is the difficulty in isolating the spectral components required for the two orthogonal outputs. It may be necessary to utilize wavelength labeling as demonstrated in  to clearly identify the products of multiple input channels. Demonstration of this more sophisticated multi-tap system is proposed for future work.
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