## Abstract

We demonstrate a photonic approach to simultaneously realize a frequency-multiplied and phase-shifted microwave signal based on the birefringence effects in the high nonlinear fiber. The phase shift caused by asymmetric variations in refractive indexes of fiber between two orthogonal polarization states is introduced into two coherent harmonic of the modulated signals. By beating the phase-modulated sidebands, a frequency-multiplied microwave signal is generated and its phase can be adjusted by simply controlling the pump power. A microwave signal at doubled- or quadrupled-frequency with a full 2π phase shift is obtained over a frequency range from 10 GHz to 30 GHz. The proposed approach has the potential applications in the system with larger-broadband, higher-frequency and -data-rate system, even to handle a multi-wavelength operation.

© 2014 Optical Society of America

## 1. Introduction

Using optical approach to generate, process, control and distribute microwave signals has attracted extensive research interest over the past few years. Compared with electronic technique, it has prominent advantages, such as large tunability, large bandwidth, high frequency and low loss [1–3]. Frequency multiplication is an effective solution to generate a high frequency microwave signal from a relatively low-frequency source [4]. When the frequency-multiplied microwave signal is combined with tunable broadband phase shifter, some specific functions can be achieved, such as generation of phase-coded microwave signal and beam-forming for phased array antenna [5, 6].

Numerous schemes for realizing the microwave frequency multiplication have been proposed. Using single or multiple modulators can obtain doubled- [7] or quadrupled- [8] frequency microwave signal. With special designed devices, the frequency multiplication factor can even reach higher [9]. Besides, frequency multiplier can also be implemented based on optical nonlinear effects [10, 11]. Microwave phase shifter (MPS) plays a key role in microwave systems. It can be accomplished based on slow light in a semiconductor optical amplifier (SOA) [12], stimulated Brillouin scattering [13] or cross-phase modulation [14, 15].

However, none of the above mentioned schemes can simultaneously accomplish frequency multiplication and phase control. It is quite promising to combine these two techniques. Some methods to achieve this goal are demonstrated. They are based on fiber Bragg grating and polarization modulator [16], filter [5], distributed feedback (DFB) laser [17] or SOA [18]. But the performance of these systems depends on the state of the polarization and wavelength seriously, which may cause instability and a narrow tuning range.

In this paper, we demonstrate a MPS with a full 2π tunable phase shift at doubled- and quadrupled-frequency based on birefringence effects in high nonlinear fiber (HNLF). Two optical sidebands are selected by a Mach-Zehnder modulator (MZM) and a delay line interferometer (DLI). They are fed into the HNLF after being combined as a single orthogonal polarization signal to receive different phase shift. In this way, a frequency-multiplied microwave signal is created in the photodetector (PD). Compared with the scheme in [14, 15, 19], the significant merits of the proposed system are the easy operation and the large tunable range in phase, frequency and wavelength. The phase of the microwave signal can be tuned by simply adjusting the pump power. Meanwhile, the frequency of generated microwave signal can switch between doubling and quadrupling by adjusting the free space range (FSR) of DLI. The system is independent of several parameters, such as the pump wavelength and the frequency of the input radio frequency (RF) signal, so it is quite flexible. Moreover, the wavelength of optical carrier is an irrelevant variable to the phase shift, indicating the system can support for multi-wavelength operation which is significant in wavelength division multiplexing (WDM) and radio-over-fiber (ROF) system.

## 2. Principle

Figure 1(a) schematically depicts the building blocks of the photonic MPS. The proposed MPS is based on two phase-locked orthogonal polarization carriers in the optical domain obtaining different phase shifts. Therefore, it demands a proper input signal. First, the RF signal drives a phase-locked signal generator (PLSG). Following the PLSG is an orthogonal modulation transmitter (OM Tx). The generated optical signals are modulated into a single orthogonal signal by OM Tx. After being processed based on optical nonlinear effect, the phase-shifted microwave signal can be detected at an optical receiver (Rx).

In our experiment, we use a single MZM to generate phase-locked carriers. By switching between the minimum and the maximum transmission points (MITP and MATP) of the MZM, odd-order or even-order sidebands are generated [20]. Figure 1(b) is the operation principle of OM Tx. It consists of a DLI, a polarization controller (PC) and a polarization beam combiner (PBC). In order to remove undesired frequency components, the FSR of DLI should be adjusted to quadruple or octuple frequency of the input RF signal according to the operation state of MZM. The frequency component at ${f}_{1}$ interferes constructively in output 1 and destructively in output 2. So it is filtered out in output 1. Because of the difference of phase shifts, the situation is contrary for the frequency component ${f}_{2}$. It is filtered out in output 2 [19, 21]. Under the approximation of small signal modulation, higher order sidebands are reasonably neglected so that the two phase locked carriers are demultiplexed. Assuming the optical carrier at the output of DLI polarizes linearly along the *x*- axis, the optical field can be expressed as

*m*= 1, 2, representing first- and second-order sidebands. ${A}_{+m}$ and ${A}_{-m}$ are the amplitudes of

*m*-order sidebands, respectively; ${f}_{C}$ and ${f}_{RF}$ are the frequencies of the optical carrier and the RF signal, respectively; and

*t*is the time. By adjusting the PC which is positioned between the DLI and the PBC, the separated sidebands are tuned into two orthogonal signals. Then the PBC combines them into one signal. The output field of PBC can be described by

*y*is the orthogonal polarization direction to

*x*.

As a nonlinear medium, different refractive index variation in *x*- and *y*- axes of the HNLF can be introduced to generate additional birefringence by a linearly polarized pump. The refractive index of the HNLF can be expressed as [22]

*x-*and

*y-*axes of the HNLF, ${n}_{x,l}$ and ${n}_{y,l}$ are linear parts of the refractive indexes caused by modal birefringence, $\Delta {n}_{x}$ and $\Delta {n}_{y}$ are the nonlinear parts caused by pump-induced birefringence. In the case of that the pump polarizes parallel to

*x*-axis and the self-phase modulation is neglected, the corresponding index change $\Delta {n}_{x}$ and $\Delta {n}_{y}$ has the following expression

^{3}is purely electronic,

*b*= 1/3 [22]. It can be written aswhere ${P}_{P}(t)$ is the optical pump power, ${A}_{eff}$ is the effective area of the HNLF. We assume that Therefore, the relative phase shift in orthogonal polarization induced by pump light is given by

*x-*and

*y-*axes to produce different phase shifts, the optical field signal at the output of HNLF is given by

Then, these two phase-shifted orthogonal polarization components are sent to a π/4 polarizer (POL) to interfere. The optical field signal at the output of POL can be written as

Finally, the output signal from POL is detected by a PD, and the alternating current (AC) part of the output current from the PD is described by

*m*. Furthermore, the difference in phase

*∆φ*is directly translated to the phase of the generated microwave signal, simultaneously. The value is directly proportional to the pump power and independent of wavelength and frequency. Thus, the phase can be continuously tuned by adjusting the pump power.

## 3. Experimental results

We carried out an experiment to verify the scheme based on the setup shown in Fig. 2. The system contains four modules including (a) the PLSG, which is composed of a DFB laser, a PC and a MZM. (b) the OM Tx, which consists of a DLI, a PC and a PBC. (c) the Phase processing, which incorporates a HNLF and an external optical signal as the pump. (d) the Rx, which has a POL and a PD.

In module (a), the output of a 1558 nm DFB laser is modulated by a 10 GHz RF signal. The DLI in module (b) has a tunable FSR from 10 GHz to infinite. To filter out two phase-locked carriers, the FSR of DLI is adjusted to 40 GHz at MITP and 80 GHz at MATP. The HNLF in module (c) has a length of 135m, an attenuation coefficient of 0.51 dB/km, a zero dispersion wavelength of 1552 nm, an effective surface area of 11 μm^{2} and a nonlinear coefficient of 100 /(W∙km). Figure 3 illustrates the optical spectra. Curve ‘@A’ is measured at the output of MZM, curves ‘@B’ and ‘@C’ stand for two separate sidebands measured at the point B and C, respectively.

Figure 4 plots the temporal waveforms of the microwave signal measured using a digital oscilloscope. As can be seen, frequency multiplication is realized in Fig. 4(a). A frequency-doubled (20 GHz) and -quadrupled (40 GHz) microwave signals are generated. And Fig. 4(b) illustrates the situations of π/2 and π phase shifts of a generated 20 GHz microwave signal induced by the MPS. It is clearly shown that the waveforms are almost identical except the phase. Thus, our proposed configuration can achieve not only phase shift tuning but also frequency multiplication.

In order to study its phase tunability, we investigate the variations of phase by controlling the pump power. Figure 5 shows the measured and fitted phase shifts. The R^{2} coefficient of determination is 0.9219, indicating the regression line fits the data well. It can be found that a near linear phase shift from 0 to 2π is achieved with the change of the pump power from 0 to 380 mW.

For an ideal phase shifter, it is expected that the phase shifts are independent of the input microwave signal frequency. To explore the wideband phase tuning property of the proposed MPS, the frequency of the microwave signal is swept from 5 to 15 GHz with a span of 1GHz. The pump power is from 0 to 380 mW. At a fixed pump power, we adjust the FSR of DLI by tuning the micrometer on the DLI manually according the frequency of input RF signal. The phase response is shown in Fig. 6(a). Almost a flat phase response can be obtained over a frequency range from 10 to 30 GHz, corresponding to the RF signal tuned from 5 to 15 GHz. The phase shift is independent of the microwave frequency, so the operation range of frequency is limited by the bandwidth of the MZM and the PD. The RF power fluctuation is a key index to judge the performance of MPS. Figure 6(b) illustrates the microwave power when different phase shifts are introduced for different frequencies. The output power variation for the entire 2π phase shift range is within 2 dB.

Finally, in order to evaluate the potential application in WDM-compatible ROF system, which means the output phase is wavelength-independent over the operation waveband, we also measured the performance of the MPS with different input wavelength of DFB laser. The result of the phase response is illustrated in Fig. 7(a). MZM is biased at MITP and the RF frequency is 10 GHz. Each curve in Fig. 7(a) is measured when the pump power is fixed. With the increase of the wavelength from 1525 nm to 1565 nm, the phase response fluctuates in a narrow range (less than π/24 over the entire range), indicating the phase shift is insensitive to the carrier wavelength. Figure 7(b) shows the RF power variations for different carrier wavelengths. The output power variation for the entire 2π phase shift range is within 2 dB.

## 4. Conclusion

We have demonstrated a novel photonic assisted MPS with frequency multiplication based on birefringence effects in HNLF. Tunable phase shift of full 2π with flat response at a microwave frequency from 10 GHz to 30 GHz is realized. The key merit of this technique is the use of nonlinear effects in HNLF to introduce a near linear phase shift to any linear polarized signal independent of wavelength and frequency. The phase shift is realized by simply tuning the pump power. Biasing the MZM, the frequency can switch between doubling and quadrupling. Due to the ultra-fast phase response and independence of the input wavelength of DBF Laser, the proposed scheme has the potential to overcome the electrical bottleneck in phased array beam forming, WDM ROF system and so on.

## Acknowledgments

This work is supported by the National Natural Science Foundation of China under Grant 61178002 and Research Fund for the Doctoral Program of High Education of China under Grant 20120142130004.

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