## Abstract

A photonic approach for microwave frequency measurement is proposed. In this approach, an optical carrier is modulated by an unknown microwave signal through a phase modulator. The modulated optical signal is then split into two parts; one part passes through a spool of polarization maintaining fiber (PMF) and the other one, through a dispersion compensation fiber (DCF), to introduce different microwave power penalties. After the microwave powers of the two parts are measured by two photodetectors, a fixed frequency-to-power mapping is established by obtaining an amplitude comparison function (ACF). A proof-of-concept experiment demonstrates frequency measurement over a range of 10.5 GHz, with measurement error less than ±0.07 GHz.

© 2009 Optical Society of America

## 1. Introduction

With the advantages of inherent low-loss, high bandwidth, light weight and immunity to electromagnetic interference (EMI), photonics has attracted significant interest for the transmission and processing of microwave signals in radar systems and other electronic warfare (EW) systems [1, 2]. In many military applications, the traditional EW receiver may need to have the capability of scanning, identification, or analysis over a large frequency range with high possibility of interception (POI). Instead of a single receiver, a number of specialized receivers are combined to reduce the required processing load of a single receiver [3, 4]. So it is important to estimate the carrier frequency of an unknown input signal over a wide frequency range instantly with high resolution before assigning a matched receiver which performs the subsequent processing. Conventional electronic solutions have some disadvantages such as limited bandwidth, high power consumption, and vulnerability to EMI. To overcome these limitations, photonic approaches have been proposed [4–6]. The main idea is to obtain an amplitude comparison function (ACF) between two different transfer functions. In order to generate different transfer functions, multichannel chirped fiber Bragg grating and single mode fiber (SMF) have been used in [4] and [5], respectively. Both schemes use different optical carrier wavelengths with double side band modulation for inducing power fading. For high accuracy results, the ACF measurement range in [4] and [5] is normally limited to a few gigahertzs in the vicinity of the low frequency notch. Optical power monitoring based approach has also been proposed, using carrier suppressed modulation and a sinusoidal optical comb filter [6]; however, special care needs to be taken to ensure the suppression of the optical carriers and the alignment of the wavelengths of the optical carriers with the valley and peak of the sinusoidal optical filter. Moreover, the fiber based Sagnac-loop filter may have stability problem.

In this paper, we propose and demonstrate a novel photonic approach for microwave frequency measurement based on phase modulation. Different from the previous approaches, the ACF in our approach is constructed by low pass and bandpass frequency responses induced by the power fading caused by a polarization maintaining fiber (PMF) and a dispersion compensation fiber (DCF), respectively. Such a characteristic ensures a steep change in ACF with respect to frequency over a wider frequency range. So the resulting ACF function can be used to estimate the microwave frequency over a wider range with a high resolution. Since only one laser source is used in our experimental setup, the cost of the measurement system is reduced.

## 2. Principle of operation and experimental setup

The experimental setup for verifying and demonstrating the proposed scheme for photonic microwave frequency measurement is shown in Fig. 1. A distributed feedback (DFB) laser source (Yokogawa AQ2200-111) is used to generate continuous wave (CW) light at 1550 nm with a linewidth of 5 MHz. The linearly polarized output light is sent to a 12 GHz phase modulator (EOspace PM-0K5-12-PFU-UL) through a half-wave plate. The pigtails of the laser source and the phase modulator are made of PMF. By adjusting the axis of the half-wave plate to 45° with respect to the slow axis of the PMF pigtails, two orthogonally polarized CW light signals, polarized along the slow and fast axes of the PMF, are excited equally and introduced to the subsequent phase modulator. The modulator is driven by the unknown microwave signal. After phase modulation, two orthogonally polarized out-of-phase optical signals are generated [7, 8] which carry the frequency information of the unknown microwave signal. A polarization maintaining coupler splits these two optical signals into two parts with the same power and polarization. In the upper arm, a polarizer is placed with its polarization angle set at 135° with respect to the slow axis of the PMF. This optical signal passes through the PMF and is detected by the photodetector (PD). The detected signal exhibits a low-pass frequency response due to the power fading induced by the differential group delay (DGD) [9, 10]. This frequency response can be expressed as:

In (1), *f* is the modulating microwave frequency, and Δ*τ* is the DGD value of the PMF.

In the lower arm, the polarization axis of the polarizer is aligned with the slow axis of the PMF. So, only the optical signal along the slow axis can pass though the polarizer. This signal is transmitted through the DCF. The detected signal in this case exhibits band-pass frequency response due to typical power fading induced by chromatic dispersion (CD) [11]:

In (2), *D* represents the total dispersion of the DCF, *λ _{c}* and

*c*denote the optical carrier wavelength and its speed in vacuum, respectively.

The ACF between the detected microwave powers from the two arms is expressed as

The calculated individual power fading response of the two arms and the corresponding ACF are plotted in Fig. 2, under the conditions of *λ _{c}* =1550nm,

*D*= 292ps/nm, and Δ

*τ*= 41ps. We can see that the frequency measurement range starts at a relatively low frequency. The upper limit of the measurement range is determined by the notch position of the PMF induced low-pass response which is given by $\mathrm{BW}=\frac{1}{2\Delta \tau}$. To achieve a high resolution measurement,

*H*and

_{B}*H*need to monotonically increase and decrease, respectively, within the BW. Thus the maximum transmission frequency of

_{L}*H*which is given by ${H}_{B,max}=\sqrt{\frac{c}{2D{\lambda}_{c}^{2}}}$, needs to be larger than the BW. Finally, the microwave frequency can be calculated from the measured ACF once the lengths of the DCF and PMF are fixed. Since the two frequency responses have notches at high frequency and zero frequency, respectively, the ACF varies monotonically from negative infinity to positive infinity. This ensures a steep change in ACF with respect to frequency over a wider frequency range. By varying the lengths of the dispersion compensation fiber (DCF) and polarization maintaining fiber (PMF), the measurement range can easily be extended further.

_{B}## 3. Measured results and discussion

A proof-of-concept experiment has been performed using 32 m PMF and 4.1 km DCF, keeping in view the bandwidth constraints of the phase modulator and photodetector. The corresponding responses are measured by connecting the input and output ports of a vector network analyzer (VNA) (Anritsu 37369C) to the photodetector and phase modulator, respectively. The measured ACF agrees well with the one calculated theoretically, as shown in Fig. 3. Based on Eq. (3), a look-up table is set up and the microwave frequency is estimated using the measured ACF.

The measurement results in Figs. 4(a) and 4(b) show that the proposed approach yields high accuracy over a frequency range extending from 1.7 GHz to 12.2 GHz. Over this frequency range, the measurement error remains within ±0.07 GHz. Furthermore, the measurement range can be extended by reducing the DGD and CD values of the PMF and DCF.

## 4. Summary

A novel photonic microwave frequency measurement approach has been proposed and experimentally verified. The frequency measurement is performed by obtaining the amplitude comparison function which is the ratio between bandpass and low pass responses. This results in a measurement over a wide frequency range with high accuracy. A proof-of-concept experiment shows a 10.5 GHz measurement range with measurement error within ±0.07 GHz.

## Acknowledgment

This work is partially supported by the Agency for Science, Technology and Research (A*Star), Singapore.

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