## Abstract

A new photonic RF instantaneous frequency measurement system is proposed and experimentally demonstrated. A frequency measurement independent of the optical input power and microwave modulation index is achieved by using the constructive and destructive ports of a polarization-domain interferometer. Experimental tests yield a peak-to-peak frequency error lower than 200 MHz for a frequency range of 1–18 GHz.

©2009 Optical Society of America

## 1. Introduction

Modern electronic warfare such as RADAR warning receivers rely on instantaneous frequency measurement (IFM) systems with broad bandwidth and high resolution. Traditional implementations of IFM systems require electrical delay lines and mixers, thus being limited by distortion and unwanted radiation [1].

Microwave signal processing on the optical domain offers many advantages, such as low losses, high time bandwidth products, light weight and immunity to electromagnetic interference [2]. These unique properties have recently brought an increasing interest in photonic IFM systems [3–7]. In [3], two optical carriers are modulated by a RF signal. Each carrier then experiences a different amount of chromatic dispersion, leading to distinct dispersion-induced power fading after direct detection. The difference between the detected optical powers allows measuring the RF frequency. This technique has the downside of needing high-bandwidth photodetectors. An approach based on this idea with adjustable measurement range and resolution was presented in [4]. The chromatic dispersion experienced by each optical carrier is tuned by using tunable laser sources and taking advantage of the dispersion slope of a dispersive fiber. Photonic implementations of traditional electrical IFM systems were proposed in [5] and [6]. The system presented in [6] allows measuring the RF frequency and power simultaneously and independently, by taking advantage of two orthogonal DC measurements; however, it uses a higher complexity setup in comparison to [5]. Although both systems require low-bandwidth photodiodes, two electrooptic modulators (EOMs) are needed, and their mathematical modeling is complex. A simple approach was presented in [7], in which two optical carriers modulated by the RF signal are filtered by a sinusoidal filter. One of the carriers is centered at a maximum of the filter’s response, whereas the other is centered at a minimum. The relation between the optical powers of both modulated carriers is used to measure the RF frequency, independently of the RF input power and microwave modulation index. Although this technique uses low-bandwidth photodiodes and a single EOM, it requires two optical carriers along with a multiplexer and a demultiplexer. Moreover, different wavelength drifts arise from both optical sources, leading to measurement errors.

In this paper, we propose and experimentally demonstrate a simple, cost-effective photonic IFM system based on an interferometer that operates on the polarization domain. The system uses a single optical source, avoiding the need of multiplexers/demultiplexers and different wavelength drifts. A Mach-Zehnder modulator (MZM) up-converts the signal to the optical domain with suppressed optical carrier. The modulated optical signal is fed to a polarization-based interferometer, composed by a polarization maintaining fiber (PMF), a polarization beam splitter (PBS) and two polarization controllers (PCs). The relation between the average optical powers measured at the constructive and destructive output ports of the interferometer yields the RF frequency independently of the input optical power and microwave modulation index.

## 2. Operation principle

Figure 1 illustrates the proposed IFM system concept. A laser diode (LD) is used to generate a continuous wave (CW) probe with linear polarization. PC1 adjusts the state of polarization (SOP) of the CW probe with the transmission axis of the MZM. The MZM bias is set at the minimum transmission point, so that optical carrier suppressed modulation is achieved.

The polarization-domain interferometer consists on the PC2, PMF, PC3 and PBS. The optical carrier suppressed signal at the output of the MZM can be written as

where *E*
_{CW} is the amplitude of the CW probe, *ω*
_{CW} is the angular frequency of the optical carrier, *z* is the microwave modulation index and *v*
_{RF}(*t*) is the RF signal voltage, assumed to have a null average value. Considering all PCs as ideal polarization rotators and the polarization axes *x* and *y* aligned with the fast and slow axes of the PMF, respectively, one can express the signal at the output of the PMF as

where *x*̂ and *ŷ* are the unit vectors along the *x* and *y* directions, *θ*
_{1} is the polarization rotation angle imposed by PC2 and *τ* represents the differential group delay (DGD) of the PMF. *S*(*f*) is the Fourier transform of *s*(*t*), where *f* is the RF frequency. The PC3 applies another polarization rotation according to an angle of *θ*
_{2}. The signal at its output is given by

Using equation (2), (3) can be written as

The optical signals at the outputs of the PBS are given by

Hence, the *x* output port of the PBS consists on the destructive port of the interferometer, whereas the *y* output port is the constructive port. The optical signals at the outputs of the PBS depend on *S*(*f*), that in turn depends on the CW probe power and microwave modulation index. To achieve a measurement independent on these parameters, an amplitude comparison function (ACF) defined as |*S*
_{PBS,x}(*f*)/*S*
_{PBS,y}(*f*)| is used to get the RF frequency.

Figure 2 shows that unambiguous RF frequency measurement can be achieved for RF frequencies up to 1/2*τ*. The highest sensitivity is achieved for cos(*θ*
_{1})cos(*θ*
_{2}) = sin(*θ*
_{1})sin(*θ*
_{2}) and cos(*θ*
_{1})sin(*θ*
_{2}) = sin(*θ*
_{1})cos(*θ*
_{2}), which yields *θ*
_{1} = *θ*
_{2} = (2*k* + 1)*π*/4, *k* ∈ ℤ. In this case, the ACF power variation is theoretically infinite. In practice, the sensitivity is reduced by the limited accuracy in setting *θ*
_{1} and *θ*
_{2}. Moreover, the extinction ratio of the output ports of the PBS and loss difference between both ports must be taken into account. Therefore, the ACF can be defined as

where ER_{x} and ER_{y} are the extinction ratios of the *x* and *y* ports of the PBS, respectively. *α* is the loss difference between both ports. The RF frequency is extracted from the measured ACF value, through *f* = ACF^{-1}(*f*).

## 3. Experiment

An experimental setup similar to the scheme shown in Fig. 1 is considered. A CW laser with a wavelength of 1554.13 nm, 13 dBm of optical power and linewidth lower than 20 MHz is used. A MZM with 30 GHz electrical bandwidth and half-wave voltage of 2 V yields an optical signal with suppressed optical carrier. Low RF input powers are considered since the MZM has a built-in electrical amplifier placed at its RF input. The electrical amplifier has an approximated small signal gain of 26 dB and an output power compression of 16 dBm. It is designed not to significantly overdrive the MZM if carrier suppressed modulation is employed. The PMF is 20 meter long and produces a DGD of τ = 22 ps. PC1 and PC2 are manually adjustable three-plate polarization controllers, whereas PC3 is a polarization locker that allows automatic adjustment. The extinction ratios of the PBS are ER_{x} = 26 dB and ER_{y} = 25 dB. An optical switch and a power meter are used instead of the two power meters of Fig. 1. The insertion losses of the MZM, PMF, PBS and optical switch are 6 dB, 1 dB, 0.5 dB and 1 dB, respectively. The RF cable that connects the signal generator to the electrical amplifier has a loss of 1 dB. The measured loss difference between both output ports of the PBS is of α = -0.6 dB. The system calibration process is done automatically through a LabVIEW© interface that controls the RF input frequency and power, PC3 adjustment, optical switch and power meter reading. The calibration process is completed in about 20 seconds (500 ms/GHz), limited mainly by the RF frequency generator settling time and power meter reading time. All the used devices are non polarization-maintaining, except the PMF and the PBS. Experimental results and theoretical curves derived from the mathematical model are presented in Fig. 3. All theoretical curves result from an optimization of θ_{1} and θ_{2} within a range of 40° to 50°, in order to achieve the lowest peak-to-peak frequency error. This optimization is done because it is impossible to experimentally set both angles at exactly 45°. Moreover, random temperature changes and mechanical vibrations affect PC2 and PC3, thus adding uncertainty to the real values of θ_{1} and θ_{2}. Figure 3(a) shows that experimental optical powers deviate significantly from the theoretical predictions. This deviation is expected since *S*(*f*) depends on the microwave modulation index, that in turn decreases with the increase of the RF frequency. Therefore, the measured optical powers decrease relatively to the theoretical predictions as the frequency increases. However, since the ACF does not depend on *S*(*f*), theoretical and experimental ACF values agree, as shown in Fig. 3(b).

The measured RF frequency and frequency errors for various RF input powers are displayed in Fig. 4. For each RF power, the peak-to-peak frequency error is lower than 200 MHz, considering a frequency range of 1 to 18 GHz. Errors increase for high RF frequencies close to 1/2τ = 22.7 GHz, since the residual power of the optical carrier interferes on the measurement taken at the constructive port. This situation is illustrated in Fig. 2. The lower peak-to-peak frequency error (50 MHz) is achieved for a RF input power of -9 dBm. For lower RF input powers, the optical carrier suppression ratio decreases. In this case, the power of the optical carrier cannot be neglected relatively to the power of the RF tones, causing a slight increase of the error. On the other hand, for RF input powers higher than -9 dBm, nonlinear distortion occurs in the modulation. The distortion arises mainly from gain saturation of the electrical amplifier and also from the nonlinear modulation transfer function of the MZM. As depicted in Fig. 2, this distortion results in increased power of the higher-order RF tones. This means that the optical signal has at least four spectral lines (±2f_{RF} and ±f_{RF}), where it should ideally have just two, ±f_{RF}. As such, the measurement accuracy is reduced for RF input powers higher than -9 dBm. RF signals with higher input powers can still be considered, at the cost of using an electrical attenuator.

The residual optical carrier derives from the bias drift and limited extinction ratio of the MZM. The MZM bias drift can be mitigated using an automatic bias control device. Another source of error that cannot be neglected is the instability of the signal’s SOP, that can be mathematically described as a random variation of θ_{1} and θ_{2}. The instability can be severely reduced using only PM devices and removing PC2 and PC3. Instead of using polarization controllers, a PMF with adjustable key connectors at both ends can be employed.

## 4. Conclusion

A new photonic RF instantaneous frequency measurement system based on a polarization-domain interferometer was presented and experimentally demonstrated. Since the system takes advantage of the constructive and destructive ports of the interferometer, only a single laser source is needed. This simplifies the system design and avoids different wavelength drifts from different sources. An experimental error lower than 200 MHz was achieved within a RF frequency range of 1–18 GHz. The range and resolution can be adjusted using a PMF with different DGD. The accuracy of the system can be further improved increasing the optical carrier suppression and using only PM devices.

## Acknowledgments

THRONE (PTDC/EEA-TEL/66840/2006) Fundação para a Ciência e a Tecnologia (FCT) project and BONE Network of Excellence funded by the European Commission through the 7th ICT-Framework Programme are acknowledged. M. V. Drummond was supported by FCT under the SFRH/BD/40250/2007 scholarship.

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