A wideband 360° photonic-assisted microwave phase shifter using a polarization modulator and a polarization-maintaining fiber Bragg grating

Wangzhe Li; Weifeng Zhang; Jianping Yao

doi:10.1364/OE.20.029838

1. Introduction

Microwave phase shifters are important devices in microwave systems. Microwave phase shifters can be implemented based on ferrite materials [1], p-i-n diodes [2], monolithic microwave integrated circuits (MMICs) [3], and micro-electro-mechanical systems (MEMS) [4]. A ferrite-based phase shifter can provide a large phase shift with a low insertion loss, but it can operate over a limited bandwidth and at slow tuning speed; a p-i-n diode- or MMIC-based phase shifter has a high insertion loss at a high frequency, and also exhibits limited bandwidth. A MEMS-based phase shifter shows good performance in terms of bandwidth, insertion loss, and size [4, 5], but with limited power handling capability and relatively poor reliability. For many applications, a microwave phase shifter should have a small size, high response speed, and wide bandwidth. In the past few years, photonic techniques have been extensively studied for the processing and transmission of microwave signals. The key advantages of using photonics techniques are the high speed, broad bandwidth and small size [6, 7]. Microwave phase shifters implemented based on photonics techniques have been investigated and numerous solutions have been proposed [8–12]. Based on stimulated Brillouin scattering (SBS) in an optical fiber [8], a microwave phase shifter with a tunable phase shift of 360° realized by tuning the frequency of an external microwave signal around 10 GHz was demonstrated. Slow- and fast-light effects in either a semiconductor optical amplifier (SOA) [9, 10] or a tilted erbium-ytterbium (Er/Yb) co-doped fiber Bragg grating (FBG) [11] pumped by a 980-nm laser diode have also been studied for the implementation of a phase shifter with a very fast (<ns) phase shift over a large bandwidth of over tens of GHz. For an SOA-based phase shifter, to achieve a large phase shift, multiple SOAs should be used, which may make the system complicated [9]. To use a single SOA while maintaining a full 360° phase shift, a solution is to jointly control the SOA injection current, the incident optical power and the dispersion of a notch filter [10]. The major limitation of the techniques utilizing slow- and fast-light effects is the large power variation when the phase is tuned, thus a power-compensating mechanism must be incorporated, which again makes the system complicated. By jointly using a polarization modulator and an edge filter to realize single-sideband (SSB) modulation [12], a 360° phase shifter with a bandwidth of tens of GHz has been demonstrated. The phase shift is introduced by changing the polarization status of the SSB-modulated light wave. However, to achieving fast phase tuning, an additional high-speed polarization controller is required.

In this paper, we propose and demonstrate a wideband 360° photonic-assisted microwave phase shifter with a constant output power. The phase shifter is implemented by a joint use of a polarization modulator (PolM) and a polarization-maintaining FBG (PM-FBG). A microwave signal to be phase shifted is applied to the PolM. Two phase-modulated signals along the two principal axes of the PolM are generated and sent to the PM-FBG. The phase-modulated signals have a static but complementary phase shift introduced by the dc bias applied to the PolM. The PM-FBG has two spectrally separated and orthogonally polarized reflection bands. By employing the PM-FBG to reflect one first-order sideband from one phase-modulated signal along one polarization direction and one optical carrier from the other phase-modulated signal along the other polarization direction and send them back to the PolM, a second-time phase modulation is imposed to the sideband and the optical carrier. By sending the two signals to a polarization analyzer (PolA) and beating them at a photodetector (PD), a phase-shifted microwave signal is obtained. Since the PolM is used twice, a low dc bias voltage would lead to a large phase shift. The proposed microwave phase shifter is experimentally investigated. A full 360° microwave photonic phase shifter over a frequency range of 30-40 GHz is demonstrated. The spurious free dynamic range (SFDR) of the phase shifter is also studied. For a noise floor of −160 dBm/Hz, the SFDR is measured to be 88 dB·Hz^2/3.

2. Principle

Figure 1(a) shows the schematic of the proposed wideband microwave phase shifter. A continuous-wave (CW) light wave from a tunable laser source (TLS) is sent to a PolM via a polarization controller (PC1) and an optical circulator (OC), which is modulated by a microwave signal to be phase shifted from a vector network analyzer (VNA). The PolM is a special phase modulator that supports phase modulation with complementary modulation indices along the two principal axes, $\hat{x}$ and $\hat{y}$ [13]. By adjusting PC1 to make the polarization direction of the incident light wave at an angle of 45° relative to one principal axis of the PolM, the light wave is projected equally to the two principal axes. At the output of the PolM, two phase-modulated light waves with identical amplitude but complementary phase modulation that are orthogonally polarized are generated.

Fig. 1 (a) Schematic of the proposed ultra-wideband 360° microwave phase shifter. (b) The spectral evolution of the light waves along the forward and backword directions of the PolM. The two dashed lines in the lower right corner refers to the reflection bands of the PM-FBG.

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Mathematically, the complementarily phase-modulated signals at the output of the PolM can be expressed as [14]

\begin{array}{l} E_{1} (t) = e^{j ω_{o} t} (\hat{x} E_{x}, \hat{y} E_{y}) (\begin{array}{l} e^{j β \cos (ω_{e} t) + j ϕ} \\ e^{- j β \cos (ω_{e} t) - j ϕ} \end{array}) = e^{j ω_{o} t} (\hat{x} E_{x} e^{j ϕ}, \hat{y} E_{y} e^{- j ϕ}) (\begin{array}{l} \sum_{n = - \infty}^{\infty} i^{n} J_{n} (β) e^{j n ω_{e} t} \\ \sum_{n = - \infty}^{\infty} i^{n} J_{n} (- β) e^{j n ω_{e} t} \end{array}) \\ \approx e^{j ω_{o} t} (\hat{x} E_{x} e^{j ϕ}, \hat{y} E_{y} e^{- j ϕ}) (\begin{array}{l} J_{0} (β) + J_{1} (β) i e^{j ω_{e} t} + J_{- 1} (β) i^{- 1} e^{- j ω_{e} t} \\ J_{0} (- β) + J_{1} (- β) i e^{j ω_{e} t} + J_{- 1} (- β) i^{- 1} e^{- j ω_{e} t} \end{array}) \end{array}

where

\hat{x}

and

\hat{y}

denote the two orthogonal principal axes of the PolM, E_x and E_y are the amplitudes of the incident light waves along the

\hat{x}

and the

\hat{y}

axes, ω_o and ω_e are the angular frequencies of the optical carrier and the microwave signal, J_n is the n^th-order Bessel function of the first kind, β is the phase modulation index, given by πV/V_{π_m}, where V is the amplitude of the microwave signal and V_{π_m} is the half-wave voltage of the PolM for a modulation signal applied via the microwave port and ϕ is the phase shift introduced by the dc bias applied to the PolM, given by πV_bias/V_{π_b}, where V_bias is the bias voltage, and V_{π_b} is the half-wave voltage of the PolM for a modulation signal applied via the bias port. Note that in Eq. (1) due to small signal modulation, the higher order sidebands are small and are ignored.

Then, the phase-modulated light waves along the $\hat{x}$ and the $\hat{y}$ axes are sent to a PM-FBG through a second PC (PC2). The PM-FBG is a uniform FBG fabricated in a polarization-maintaining (PM) fiber. Due to the birefringence of the PM fiber, the PM-FBG has two spectrally separated reflection bands along, respectively, the fast and slow axes of the PM fiber [15, 16]. By adjusting PC2, the polarization directions of the two light waves along the $\hat{x}$ and the $\hat{y}$ axes are aligned with the fast and slow axes of the PM fiber, respectively, so that the phase-modulated signals along the $\hat{x}$ and the $\hat{y}$ axes are reflected, respectively, by the reflection bands along the fast and the slow axes of the PM-FBG. By properly choosing the wavelength of the optical carrier, only the optical carrier along the $\hat{x}$ axis and one of the two first-order sidebands (say, the upper sideband) along the $\hat{y}$ axis will be reflected, as shown in Fig. 1(b). The reflected light waves then go through the PolM a second time in a reverse direction, and is then routed to a PolA via the OC and a third PC (PC3). Due to the fact that the PolM is a traveling wave modulator, when it is used in a reverse direction, the velocity mismatch between a forward microwave signal and a backward light wave would make the modulation have an extremely low efficiency and thus the microwave modulation can be ignored, and only the dc bias applied to the PolM would introduce an additional static phase shift. The reflected optical carrier and the sideband after passing through the PolM the second time are given by

\begin{array}{l} E_{2} (t) \approx e^{j ω_{o} t} (\hat{x} E_{x} e^{j 2 ϕ}, \hat{y} E_{y} e^{- j 2 ϕ}) (\begin{array}{l} J_{0} (β) \\ J_{1} (- β) i e^{j ω_{e} t} \end{array}) \\ = \hat{x} E_{x} J_{0} (β) e^{j (ω_{o} t + 2 ϕ)} - \hat{y} E_{y} J_{1} (β) e^{j (ω_{o} t + ω_{e} t - 2 ϕ + π / 2)} \end{array}

The spectral evolution of the phase-modulated light waves when traveling along the forward and the backward directions of the PolM is shown in Fig. 1(b). The optical carrier and the upper first-order sideband are then applied to the PolA via PC3, and then applied to the PD. By beating the optical carrier and the upper first-order sideband at the PD, a microwave signal is generated which is given by

\begin{array}{l} V (t) \propto {| E_{x} J_{0} (β) e^{j (ω_{o} t + 2 ϕ)} - E_{y} J_{1} (β) e^{j (ω_{o} t + ω_{e} t - 2 ϕ + π / 2)} |}^{2} \\ = E_{x}^{2} J_{0}^{2} (β) + E_{y}^{2} J_{1}^{2} (β) - 2 E_{x} E_{y} J_{0} (β) J_{1} (β) \sin (ω_{e} t - 4 π V_{b i a s} / V_{π_b}) \end{array}

The first and the second terms in Eq. (3) are two dc components, and the third term is a microwave signal with a phase shift given by $4 π V_{b i a s} / V_{π_b}$ . The phase shifted microwave signal is then sent back to the VNA where the phase response of the microwave phase shifter is measured.

Based on Eq. (3), we can see: 1) the phase response of the microwave phase shifter can be easily tuned by tuning the bias voltage. To achieve a full 360° phase shift, the bias voltage should be tuned from 0 to $V_{π_b}$ /2. For the the PolM used in the experiment, $V_{π_b}$ is 30 V, a bias voltage for a full 360° phase shift is 0 to 15 V; 2) the amplitude of the phase-shifted microwave is independent of the phase shift. Therefore, when the phase is tuned, the amplitude of the phase-shifted microwave signal is maintained constant; 3) due to the fact that the PolM is used twice, a large phase shift with a relatively low dc bias voltage can be realized.

3. Experimental results and discussion

An experiment based on the setup shown in Fig. 1(a) is performed. The key component in the system is the PM-FBG, which is fabricated in a hydrogen-loaded PM fiber using a uniform phase mask with UV illumination. Figure 2(a) shows the measured spectral response of the PM-FBG. By controlling the polarization direction of the incident light wave at an angle of 0°, 45° or 90° to the fast axis of the PM-FBG, we obtain three different spectral responses, as shown in Fig. 2(a). It is clearly seen that the spectral response of the PM-FBG is polarization dependent. The bandwidth of the microwave phase shifter is determined by the reflection bandwidths of the PM-FBG (the frequency difference between points A and B, and C and D, expressed as AB and CD, similarly hereinafter), the frequency spacing between the two reflection bands, namely BC, and the wavelength of the optical carrier, which is located at point W in Fig. 2(a). For a PS-FBG, its reflection bandwidth, AB or CD, is determined by the length of the FBG and the fringe visibility of the refractive index modulation [17]. The shorter the FBG, or the larger the fringe visibility, and the larger AB or CD. The distance between the two reflection bands are determined by the birefringence of the PM-FBG. The larger the birefringence, the greater the distance.

Fig. 2 (a) Measured reflection spectral responses of the PM-FBG for the polarization direction of the incident light wave at an angle of 0°, 45° or 90° relative to the fast axis of the PM-FBG. (Resolution: 0.01 nm). (b) Measured optical spectrum of the reflected light wave at port 3 of the OC (the frequency of the microwave signal is 30 GHz). (Resolution: 0.01 nm).

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If the frequency spacing between the two reflection bands is larger than the reflection bandwidth, namely, BC > AB (or CD), the operation band of the microwave phase shifter is from WC to WD. The bandwidth of the microwave phase shifter is CD, and the upper and the lower limits of the operation band is determined by W. If BC < AB (or CD), the upper limit of the operation band is WD, while the lower limit is the either AW or WC depending on which is greater, therefore, the operation band is from Max {AW, WC} to WD. For a given PM-FBG, the wavelength of the optial carrier will determine the upper and lower limits, and the operation frequency range.

As can be seen from Fig. 2(a), BC of the PM-FBG used in the experiment is greater than AB (or CD), thus the operation band is from WC to WD, giving an operation frequency range of CD, which is about 20 GHz. The wavelength of the optical carrier is tuned at 1551.55 nm, which is located at the reflection band of the PM-FBG along the fast axis, close to point B. Therefore, the operation band is from about 30 to 50 GHz. The microwave signal is generated by the VNA (Agilent, E8364A). The power of the microwave signal is amplified by a microwave amplifier (Agilent, 83050A) to about 18 dBm, and applied to the PolM (Versawave) with a bandwidth of 40 GHz and a half-wave voltage of about 7 V, giving a phase modulation index of about 1.12. The frequency of the microwave signal is large enough to make the upper first-order sideband of the modulated light wave along the $\hat{y}$ axis located at the reflection band of the PM-FBG along the slow axis. Therefore, after reflection by the PM-FBG, only the optical carrier and the upper first-order sideband along with the $\hat{x}$ and the $\hat{y}$ axes would be obtained. As shown in Fig. 2(b), the power of the lower first-order sideband is 20 dB smaller than those of the optical carrier and the upper first-order sideband; therefore, the lower first-order sideband is eliminated.

By applying the two orthogonally polarized backward-traveling light waves to the PolA through PC3 and then the PD (u²t, XPDV2150R), a microwave signal with a phase shift of 4ϕ is obtained. The phase-shifted microwave signal is then sent back to the VNA to measure the phase response. The tunable range of the phase shift is performed by adjusting the dc bias voltage. The results are shown in Fig. 3 . Due to the limited bandwidth of the PolM, the results only cover a frequency range from 30 to 40 GHz. As can be seen from Fig. 3, for a given bias voltage a constant phase shift over a frequency range from 30 to 40 GHz is achieved. For the proposed microwave phase shifter, a full 360° phase shift is achieved.

Fig. 3 Measured phase response at different dc bias voltages over a microwave frequency range from 30 to 40 GHz.

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For many applications, such as in a radar receiver, microwave phase shifters should have a large dynamic range [18]. To evaluate the dynamic range performance of the proposed microwave phase shifter, a two-tone RF signal at 10 GHz and 10.1 GHz is applied to the PolM, and the measurements of the output microwave powers of the fundamental signals and the third-order intermodulation distortion (IMD3) are performed and the results are shown in Fig. 4 . It can be seen that the SFDR of the microwave phase shifter is about 88 dB·Hz^2/3 given a noise floor of −160 dBm/Hz.

Fig. 4 Measured spurious-free dynamic range (SFDR) of the microwave phase shifter.

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4. Conclusion

A novel approach to implementing an ultra-wideband full 360° photonic-assisted microwave phase shifter based on a PolM and a PM-FBG was proposed and experimentally demonstrated. The key features of the microwave phase shifter includes: 1) the phase of a microwave signal could be tuned by simply tuning a dc bias; 2) thanks to the large reflection bands of the PM-FBG, the microwave phase shifter could operate over a large bandwidth; 3) when the phase was tuned, the amplitude of the microwave signal was maintained constant; 4) the PolM was used twice, which enables a large phase shift with a relatively low dc bias voltage. In the experiment, a tunable phase shift of 360° over a frequency range from 30 to 40 GHz was experimentally demonstrated. The dynamic range of the phase shifter was also evaluated. Given a noise floor of −160 dBm/Hz, the SFDR of the microwave phase shifter was measured to be 88 dB·Hz^2/3.

Acknowledgments

This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC).

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A wideband 360° photonic-assisted microwave phase shifter using a polarization modulator and a polarization-maintaining fiber Bragg grating

Abstract

1. Introduction

2. Principle

3. Experimental results and discussion

4. Conclusion

Acknowledgments

References and links

Cited By

Figures (4)

Equations (3)

Optics Express