1. Introduction

Photonic techniques for time, amplitude and phase manipulation of RF signals offer low electromagnetic interference, wide bandwidths, larger true time delays, and easy signal duplication to applications such as beam forming in phased array antennas, microwave filtering and range/Doppler deception in electronic warfare (EW) [1,2]. The benefits of optical techniques are maximized if all signal processing functions are carried out in the optical domain after electro-optic conversion. RF phase manipulation in photonics domain has been a difficult task and a number of solutions with varying complexity have been proposed. These include vector sum and homodyne mixing techniques [2–5], stimulated Brillouin scattering [6], slow- and fast-light effects [7], and use of liquid crystal on silicon devices [8]. Notch or band edge optical filters that utilize nonlinear phase response regions based on microring resonators and fiber Bragg grating (FBG) have also been used to achieve RF phase shifting [9,10] and microwave pulse compression [11].

In this paper, we propose a simple linear photonic technique for achieving fixed or time varying phase shifts of RF signals using an FBG which has a step group delay (GD) profile within the reflection band and a fixed or wavelength tunable RF modulated optical carrier. This approach is more practical and stable than the alternative techniques as it does not require splitting of optical signals, multiple or costly optical components, nonlinear phenomena or band edge or notch optical filters [2–10]. Optical single sideband with carrier (OSSB + C) modulation through the FBG optical filtering process is an intrinsic feature of the technique and this allows systematic phase shifts to be obtained which can be used in EW applications.

2. Principle of operation

The concept for achieving phase-shifted RF signals is based on introducing an optical path difference between two coherent optical signals such as the carrier and a sideband of an RF modulated optical signal using the FBG device. The phase difference $\Delta \phi ={\phi }_c-{\phi }_s$ between the carrier (C) and the sideband (S) is a function of the carrier wavelength and path difference, and can be controlled in real time to achieve variable phase shifts:

where ${\lambda }_c$ is the carrier wavelength, $n_{eff}$ is the effective refractive index of the fiber core mode and $2L$ is the physical path difference between the carrier and the sideband, the latter being achieved in a simple FBG device schematically shown in Fig. 1 (left). The FBG forms a Michelson interferometer for the two optical signals, and OSSB + C modulation is simultaneously achieved by virtue of the optical filtering process.

 

Fig. 1 Schematic representation of manipulating RF phase using an FBG with step group delay, with illustration showing reflection (a) group delay (b) and phase (c) spectra of the grating response.

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The optical path difference can be viewed as a delay between the carrier and sideband in the time domain which in turn results in a linear phase change with frequency in the optical frequency domain. Therefore, Eq. (1) can be re-written as a function of the group delay difference and the frequency detuning of the optical carrier from a reference:

where $f=c/\lambda$ and $\tau$ is the group delay. Figure 1 (right) schematically shows the reflection, group delay and phase spectra of the FBG device response. The carrier and a sideband are tuned to overlap with respective spectral regions of the FBG device and experience different group delay across a defined bandwidth. The other sideband is filtered out leading to an OSSB + C signal. The FBG phase spectrum in Fig. 1(c) is calculated by integrating the group delay spectrum over the FBG bandwidth

where $A=2\left|C\right|\left|S\right|$ and $\theta =\angle S-\angle C$ is an offset phase shift which is an artifact of the OSSB + C generation through optical filtering and is a constant for an FBG device.

3. Grating designs

We use the inverse scattering technique based on the layer-peeling algorithm [12] to calculate the FBG design profiles. The target reflection and group delay spectra shown in Fig. 2(a) to 2(c) (left) can be achieved in FBG devices with grating coupling coefficients $q\left(z\right)=-j\left(\pi /\lambda \right)\Delta n\left(z\right)\exp \left[-j\alpha \left(z\right)\right]$ shown in Fig. 2(a) to 2(c) (right) respectively, where $\lambda$ is the centre wavelength of the FBG, $\Delta n\left(z\right)$ is the local refractive index variation, $\alpha \left(z\right)$ is the local phase variation, $z$ is the distance along the grating. The FBG devices differ in the magnitude of the group delay difference at the carrier and sideband frequencies, being 100, 200 and 400 ps respectively. For sufficiently large group delay difference, the FBG device evolves into separate in-series gratings, covering ‘carrier’ and ’sideband’ regions respectively (see Fig. 2(c) right).

 

Fig. 2 Reflection and group delay spectra (left), and grating coupling coefficient (right) of FBG designs with (a) 100ps, (b) 200 ps, (c) 400 ps group delay step.

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The FBG devices are designed to operate with RF signals at or above X band (8 – 12 GHz), thus their reflection bandwidths are chosen to be ~20 GHz, with the ‘carrier’ region spanning ~9 GHz to the left from the dotted line in Fig. 1(a). Tuning the carrier wavelength in the range 1 – 8 GHz within the ‘carrier’ region is sufficient for achieving up to 1100° phase shifts (see section IV). A 1 GHz offset for the optical carrier from the edge of the FBG band is chosen to address typical wavelength drift of ± 10 pm in commercial lasers.

The frequency tuning required for one radian phase change $\Delta f_{1\text{rad}}=\Delta f/\Delta \phi =1/2\pi \Delta \tau$ (Hz/rad) is independent of the modulation frequency $\Omega$. The maximum achievable phase change $\Delta \phi <2\pi \Delta f\Delta \tau$ can be increased by increasing the group delay differential $\Delta \tau$. Operation at higher modulation frequencies (> 20 GHz) can be achieved if the grating design in Fig. 2 is modified to expand one of the group delay regions, e.g. the ‘sideband’ region as shown in Fig. 1.

4. Simulation results

We account for potential grating fabrication errors by adding amplitude and phase noise to the calculated FBG design profiles and use them in a realistic computer simulation of manipulating the phase of a pulsed CW signal at 10 GHz with 1.6 ns pulse-width. The simulation takes into account the effects of nonlinear optical modulation and both optical and RF component noise. The linewidth of the laser is assumed to be 1 MHz with an output power of 100 mW. The initial optical carrier wavelength is set to 1552.52 nm and is modulated with a microwave signal using a Mach-Zehnder modulator (MZM) biased at quadrature with V_π of 4 V, insertion loss of 3 dB and extinction ratio of 25 dB. The laser RIN is set at −160 dBc/Hz. The input power of the 10 GHz CW signal before pulse modulation is 1 mW. Figure 3(a) shows the simulated phase shift of the RF signal as a function of the carrier frequency offset from 1552.52 nm for the FBG designs with 100, 200 and 400 ps group delay step respectively.

 

Fig. 3 (a) Phase shift versus carrier wavelength tuning given as frequency offset (GHz) for FBGs with 100, 200 and 400 ps group delay step. (b) Pulse evolution with carrier frequency offset for the FBG with 200 ps group delay step.

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The phase shift follows the expected linear change up to ~7 GHz frequency offset. The phase change rates for the 100, 200 and 400 ps gratings are 36, 72 and 144 deg/GHz respectively. The linear relationship is broken when either the lower sideband is within the grating passband or the carrier is within the higher group delay region. We have also observed the predicted initial offset phase shift due to the optical filtering process, and this depends on the magnitude of the FBG group delay step. Figure 3(b) presents a simulation of the temporal profile of the RF pulses optically processed by the FBG with 200 ps group delay step (see Fig. 2(b)) for a variety of frequency offsets. The change in the phase of the carrier is not accompanied by any time shift in the pulse profile, with some amplitude modulation originating from the optical filtering process. If the amplitude change is detrimental for the application in concern, the OSSB + C signal can be generated before reflection by the FBG.

4.1 Doppler generation

A VPI TransmissionMaker and Matlab co-simulation were used to evaluate the generation of a range and Doppler shift of a pulsed CW signal return at 10 GHz. The simulated setup for the phase shifter is shown in Fig. 4 . The pulse repetition period was set to 3.28 μs with 5% duty cycle to reduce the simulation time, and a half-period time delay was used to obtain a range offset. The wavelength was swept at a rate of 0.8 nm/ms that gave 360° phase shift every 50 μs. This corresponds to Doppler frequency of −20 kHz according to $d\varphi /dt=-2\pi f_D$, which is equivalent to 300 m/s relative target velocity $v=-c{f}_D/2f_{RF}$, where $f{}_{RF}=\Omega /2\pi$. We used the 99% reflectivity FBG with 200 ps group delay step, ± 5 ps peak ripple and 40 dB sideband suppression (see Fig. 2(b)). Figure 4(a) shows the optical spectrum with 5.24 GHz frequency sweep over a 52.5 μs interval (16 pulses) and Fig. 4(b) shows the generated range-Doppler map for this scenario. It depicts a Doppler frequency of ~-20 kHz.

 

Fig. 4 Photonic variable phase shifter for Doppler generation. Insets: (a) simulated optical spectrum showing the wavelength tuning of the generated OSSB + C signal after FBG and (b) the range-Doppler map generated for this scenario.

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4. 2 Discussion

Wavelength tuning speeds of 0.8 nm/ms can be readily achieved with commercial tunable lasers that have wavelength sweep speeds of up to 2000 nm/s. For continuous operation over longer time periods, the wavelength should be swept using a serrodyne system where the wavelength is changed in a sawtooth pattern [2]. This can be achieved with custom programming of a commercial tunable laser with the use of built in wavelength meter for active wavelength control. The technique requires a change in the wavelength of the modulated carrier to achieve a linear change in the phase of the RF signal, and can be used for both fixed and time varying phase shift generation. Fixed phase changes can be achieved by stepping the wavelength of the carrier to specified wavelengths along the grating in a calibrated system. Therefore, phase modulation schemes that require discrete phase shifts in the RF signal is achievable limited by the wavelength switching speed of the laser. It will be possible to utilize the scheme in other radar applications such as phase-coding and pulse compression [13,14], however further analysis is required to quantify the effects of OSSB + C optical filtering and differential delay on the signal quality.

5. Conclusion

A simple linear photonic technique has been presented capable of achieving fixed or time varying phase shifts of microwave radar signals using a specially designed FBG and a tunable RF modulated optical carrier. The step group delay profile of the FBG results in relative phase shifts between the carrier and the sideband in the generated OSSB + C signal. Tuning the optical carrier wavelength in a controlled manner enables systematic phase changes in the RF signal over time, attractive for applications such as radar signal manipulation.