## Abstract

A novel photonic-assisted technique for instantaneous microwave frequency measurement is proposed using two cascaded Mach-Zehnder modulators (MZMs) biased at the transmission null point. Then, the microwave frequency can be estimated by monitoring direct current (DC) optical power. Moreover, the measurement range and the measurement resolution can be optimized by setting the time delay between optical and electrical link and optical dispersion, respectively. The approach is theoretically investigated and experimentally verified with a measurement range of 8 GHz and a measurement error of less than ± 0.15 GHz.

©2011 Optical Society of America

## 1. Introduction

It is in strong demand that an electronic warfare (EW) system is capable of instantaneous frequency measurement (IFM) for fast threat warning and communications interception. A typical IFM system can identify the dominant frequency of an unknown microwave signal in nearly real time, which leads to high possibility of interception (POI). The measured frequency information is generally necessary for instructing the following countermeasure systems or matching a concentrated receiver that performs the information reception and analysis. However, the conventional electrical IFM approaches suffer from bulky implementation, high attenuation, and limited bandwidth [1]. Therefore, photonic technique is expected to be introduced in high-performance IFM systems thanks to its unique advantages such as wide band, potential parallel processing capability, and immunity to electromagnetic interference (EMI) [2]. According to their operation principles, those photonic-assisted IFM systems can generally be divided into three categories, i.e., frequency-to-time mapping, frequency-to-space mapping, and frequency-to-power mapping [3]. Recently, photonic-assisted IFM systems based on frequency-to-power mapping have been verified as a promising solution with a large frequency measurement range (>10 GHz) and a high resolution (<200 MHz), although the measurement is accurate for single carrier frequency signal only [4–10]. In those techniques, microwave frequency is estimated according to a unique relationship, named as the amplitude comparison function (ACF), between the frequency of the microwave signal and the ratio of two dispersion-induced RF power-fading functions. Thus, high-speed photodetectors (PDs) are commonly used to cover the whole measurement range. A novel method has been proposed to relax the setup complexity by monitoring the direct-current (DC) power [11]. However, the calibration is time-consumed and the measurement range is limited to 3 GHz only. Further simple schemes have been reported by monitoring the optical power directly [12,13]. A measurement range of 2-24 GHz is experimentally obtained with a measurement error of less than ±0.2 GHz, in case the stability of complementary optical filter pair using polarization-maintaining fiber (PMF) is well solved. In this paper, a novel photonic-assisted IFM approach is proposed based on frequency-to-optical power mapping. A proof-of concept experiment is performed to measure frequencies from 0.5 to 8 GHz with a measurement error less than ±0.15 GHz. Since the microwave frequency can be estimated by simply monitoring the DC optical power, the proposed approach is easier to implement by using low-frequency components at lower cost. Our proposed approach also features independent adjustment of the measurement range and the measurement resolution.

## 2. Operation Principle

The schematic setup of our proposed IFM approach is shown in Fig. 1 . The key observation is that a tunable optical delay line (TODL) is inserted between the two cascaded MZMs both of which are biased at the minimum transmission point (i.e. both MZMs are operated under carrier-suppressed mode). A laser diode (LD) provides the required optical carrier. The input unknown microwave signal is split by a 3-dB microwave power divider into two portions, one of which is delayed by a fixed microwave delay line (FMDL). The two portions of microwave signal are then applied onto the cascaded MZMs, respectively. Finally, the output optical signal from MZM2 is monitored by an optical power meter. The electric field of the optical carrier emitted from the LD with power ${P}_{0}$ and angular frequency ${\omega}_{0}$ can be expressed as $E\left(t\right)=\sqrt{{P}_{0}}{e}^{j{\omega}_{0}t}$. Likewise, the input microwave signal with amplitude $V$ and angular frequency $\Omega $ can be denoted as $v\left(t\right)=V\mathrm{cos}\left(\Omega t\right)$. Thus the microwave signals which are applied onto the two cascaded MZMs are respectively given by

It can be clearly seen from Eq. (5) that the output of MZM2 approximately contains three dominant frequency components which are located at ${\omega}_{0}\pm 2\Omega $ and ${\omega}_{0}$, respectively. Finally, we can obtain the monitored optical power by an optical power meter as follows.

## 3. Experimental Setup

Although Eq. (6) indicates a relation between the input microwave frequency and the output optical power, it cannot be directly utilized for frequency measurement because the optical power is also dependent on the several other uncertain parameters, such as the emission power from LD, link loss, and modulation index of MZMs etc. In a practical perspective, it is highly desired to exclude the dependence on these parameters for higher measurement accuracy and well repeatability of implementation.

Figure 2
shows a typical experimental setup for the proposed photonic-assisted IFM approach. Two distributed feedback (DFB) laser diodes (LDs) are used to obtain two mapping functions at 1550 nm and 1551nm, respectively. After combination by a wavelength-division multiplexer (WDM), the continuous wave (CW) lights are modulated by a LiNbO_{3} Mach-Zehnder modulator (MZM 1, Avanex SD-10) biased at the transmission null point with a portion of unknown microwave signals from a vector network analyzer (VNA, Anritsu 3769C). An electrical bias controller is used to lock the operation points of MZM and ensure a stable operation over time and environmental conditions. Then, the modulated carriers are sent to a wavelength selective switch (Finisar WaveShaper [14] 4000S), whose dispersion-bandwidth product is approximately 80 ps. This means that dispersions of up to ± 80 ps/nm can be comfortably generated over an optical bandwidth of 1 nm. As a result, the definition of ${\tau}_{2}$ in Eq. (6) can be modified by adding the delay of WaveShaper. Moreover, the WaveShaper will introduce a certain differential group delay between two optical wavelengths due to its dispersive characteristics. Then, the delayed carriers is re-modulated by MZM2 (Avanex SD-10) biased at the transmission null point with another portion of unknown microwave signals after properly delayed using a length of co-axial cable. The twice-modulated signals at different wavelengths are de-multiplexed by another WDM and monitored by optical power meters (Anritsu MA9331A optical sensor head plus MU931001A mainframe), respectively. The optical sensor head has a 3dB bandwidth of 100 KHz, permitting us monitor DC optical power easily. The measured results are recorded for subsequent data processing. Finally, the microwave frequency is estimated based on a look-up table established in the calibration stage.

As mentioned above, the WaveShaper introduces a wavelength-dependent group delay. It will accordingly lead to a delay difference between $\Delta {\tau}_{1}$ and $\Delta {\tau}_{2}$ in Eq. (6), where $\Delta {\tau}_{1}$ and $\Delta {\tau}_{2}$ corresponding to the two wavelengths, respectively. We assume that $\Delta {\tau}_{2}>\Delta {\tau}_{1}$, and define $\Delta \Gamma =\Delta {\tau}_{2}-\Delta {\tau}_{1}$ here. On the other hand, the difference between the modulation characteristics of an MZM at different operating wavelengths can be neglected due to the small wavelength spacing of 1 nm. The optical power from the two LDs is experimentally tuned to be identical 0 dBm. Therefore, the optical powers recorded by the optical power meter, at the two wavelengths, can be expressed as,

The ratio of those measured powers, referred to the commonly defined ACF, can be derived

Based on Eq. (9), a unique relationship between the output power and the frequency of unkonwn microwave signal is obtained and a calibrated look-up table can be established in its monotonic power variation region. Moreover, Δτ_{2} can be adjusted by optimizing the delay between the optical and electrical link, while ΔΓ can be chosen by setting the dispersion characteristics of WaveShaper. For previous frequency-to-power mapping based IFM systems, a higher resolution is achieved at the cost of a relatively smaller measurement range. However, in our proposed scheme, we can optimize measurement resolution without compromising the measurement range by setting Δτ_{2} and ΔΓ value, respectively. Fig. 3 (a)
shows the theoretically calculated ACF with respect to the variation of Δτ_{2}, when ΔΓ is fixed to 20 ps. Generally, the measurement range of our proposed approach is a monotone region of the generated ACF, e.g. from DC to the first notch of the ACF. Thus, with the decrease of Δτ_{2}, the measurement range of our proposed scheme can be substantially enlarged. However, since Δτ_{2} is the delay between optical and electrical link, its value cannot be set too small due to the constraints of real implementation. Meanwhile, Fig. 3 (b) shows the theoretically calculated ACF with respect to the variation of ΔΓ, when Δτ_{2} is fixed to 30 ps. It is clearly observed that the dynamic range of generated ACF is improved with the growing of ΔΓ. Usually, the measurement resolution is characterized by the first-order derivative of generated ACF. Thus, in order to have a higher measurement resolution, we need to set a relatively larger value of ΔΓ. However, the maximum value of ΔΓ is limited by Δτ_{2} due to the symmetry of cosine function, as shown in Eq. (9), and the achievable dispersion from the WaveShaper.

## 4. Experimental results

Based on the experimental setup shown in Fig. 2, microwave frequency measurement is carried out in order to verify the proposed approach. First, by properly choose the delay between the optical and electrical link, Δτ_{2} is set to be 30 ps. Meanwhile, we properly set WaveShaper to introduce a dispersion of 20 ps/nm. Considering that the wavelength spacing between two LDs is 1 nm, $\Delta \Gamma =20\text{ps}$is satisfied in our IFM system. According to Eq. (9), we store a look-up table with a frequency resolution of 1 MHz. Then, the microwave frequency can be estimated from such look-up table. Figure 4 (a)
summarizes the measured ACF, which agree well with the calculated ACF. The ACF monotonically decreases as long as the frequency does not exceed the notch point, which is located at around 8 GHz. Therefore, the measurement range of our proposed IFM system is limited to 8 GHz, based on the measured ACF. Next, the estimated frequencies with respect to the real input frequencies are shown in Fig. 4 (b). It is worth noting that the measured results are in a good agreement with the real values over the frequency range of 0.5-8 GHz. Meanwhile, the measurement errors are within ± 0.15 GHz over the whole frequency measurement range, as shown in Fig. 5
.

## 5. Conclusion

A novel photonic-assisted approach for microwave frequency measurement has been proposed, theoretically investigated, and experimentally verified. Besides the benefits from the assistance of photonic technique, our approach possessed its own advantages such as low-cost by replacing commonly used photodetectors (PDs) with optical power meters, independent optimization of measurement range and measurement resolution, provided the bias drift of MZM and the power fluctuation of laser source is well solved. The proposed IFM system was experimentally verified with the measurement error less than ±0.15 GHz over a frequency range of 0.5-8 GHz. The approach is oriented for future EW systems but it can be extended to any applications which require fast microwave frequency measurements over a broad frequency range.

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