# Ripple Suppression in Broadband Microwave Photonic Phase Shifter Frequency Response

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Phase Shifter Amplitude Variation and Phase Deviation

_{RF}is applied to the OFS, the electric field at the output of MZM

_{1}and MZM

_{2}are given by:

_{in}is the electric field amplitude at the MPPS input, t

_{ff}is the insertion loss of MZM

_{1}and MZM

_{2}, k

_{i}is the optical transmittance for light passing through the ith arm of the DPMZM, a

_{1}and a

_{2}are the modulation index of the top and bottom Mach Zehnder modulator (MZM), respectively, β

_{bi}is the optical phase shift induced by the bias voltage V

_{i}into MZM

_{i}, and θ is the phase deviation from 90° of the two RF signals into the DPMZM. MZM

_{1}and MZM

_{2}are biased at the null point, i.e., β

_{b}

_{1}= β

_{b}

_{2}= π/2, and the main MZM of the DPMZM is biased at the quadrature to realize SSB-SC modulation. Neglecting the second and higher order sidebands, the DPMZM output electric field can be written as:

_{ws}, i.e., the frequency shifted light, at an angular frequency ω

_{c}− ω

_{RF}, the unwanted sideband A

_{uns}at ω

_{c}+ ω

_{RF}, and the residual carrier A

_{rc}at ω

_{c}at the DPMZM-based OFS output can be obtained from Equation (3) and are given by:

_{OFS}is the OFS insertion loss. In the ideal case, k

_{1}= k

_{2}= k

_{3}= k

_{4}= 1 and the 90° hybrid coupler has no amplitude and phase imbalance, i.e., a

_{1}= a

_{2}and θ = 0°, thus the unwanted sideband and the residual carrier are cancelled at the OFS output.

_{c}+ ω

_{RF}is given by:

_{OPS}is the OPS insertion loss, γ = πV

_{DC}/V

_{π}is the optical phase shift introduced by the OPS, V

_{DC}is the DC voltage into the OPS, V

_{π}is the OPS switching voltage, and ϕ

_{uns}and ϕ

_{ws}are the unwanted and wanted sideband optical phases, respectively. The photocurrent at the RF signal angular frequency ω

_{RF}can be obtained from Equation (7) and is written as:

_{in}is the optical power into the MPPS, and φ is the output RF signal phase, which is given by:

_{ws}, A

_{uns}, ϕ

_{ws}, and ϕ

_{uns}. The presence of the unwanted sideband with amplitude A

_{uns}and phase ϕ

_{uns}is due to the amplitude and phase imbalance of the 90° hybrid coupler used in the MPPS. This shows that the 90° hybrid coupler amplitude and phase imbalance affects the MPPS output RF signal. Figure 4 shows the deviation from the desired phase shift and the amplitude variation of the MPPS as a function of the wanted to unwanted sideband power ratio. The figure shows that the amount of MPPS amplitude variation and phase deviation are different for different phase shifts. The ±90° phase shifts have the largest phase deviation, and the ±45° and ±135° phase shifts have the largest amplitude variation. The MPPS has a maximum amplitude variation of 3.8 dB and a maximum phase deviation of ±16° when the unwanted sideband is 15 dB below the wanted sideband. A 90° hybrid coupler with low amplitude and phase imbalance is required to minimize the unwanted sideband amplitude in order to reduce the MPPS amplitude variation and phase deviation. However, such couplers cannot operate in a wide frequency range, which limits the MPPS bandwidth.

^{2/3}when they have a shot noise limited performance with a noise floor of −161 dBm/Hz. However, in practice, an optical amplifier is required in the MPPS to compensate for the insertion loss of the integrated OFS and OPS structure, which is higher than the insertion loss of an MZM used in a fiber optic link. The use of an optical amplifier in the OFS and OPS-based MPPS introduces the signal-spontaneous beat noise, which is above the shot noise and is the dominant noise source in the system. This degrades the phase shifter dynamic range performance. A low insertion loss integrated OFS and OPS structures, and a low noise figure optical amplifier are required to minimize the degradation of the phase shifter dynamic range performance.

## 3. Experimental Results

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Minasian, R.A.; Chan, E.H.W.; Yi, X. Microwave photonic signal processing. Opt. Express
**2013**, 21, 22918–22936. [Google Scholar] [CrossRef] [PubMed] - Li, W.; Sun, W.H.; Wang, W.T.; Zhu, N.H. Optically controlled microwave phase shifter based on nonlinear polarization rotation in a highly nonlinear fiber. Opt. Lett.
**2014**, 39, 3290–3293. [Google Scholar] [CrossRef] [PubMed] - Li, T.; Chan, E.H.W.; Wang, X.; Feng, X.; Guan, B. All-optical photonic microwave phase shifter requiring only a single DC voltage control. IEEE Photon. J.
**2016**, 8, 5501008. [Google Scholar] [CrossRef] - Shen, J.; Wu, G.; Zou, W.; Chen, J. A photonic RF phase shifter based on a dual-parallel Mach-Zehnder modulator and an optical filter. App. Phys. Express
**2012**, 5, 072502. [Google Scholar] [CrossRef] - Matsumoto, K.; Izutsu, M.; Sueta, T. Microwave phase shifter using optical waveguide structure. J. Lightwave Technol.
**1991**, 9, 1523–1527. [Google Scholar] [CrossRef] - Wang, X.; Chan, E.H.W.; Minasian, R.A. Optical-to-RF phase shift conversion based microwave photonic phase shifter using a fiber Bragg grating. Opt. Lett.
**2014**, 39, 142–145. [Google Scholar] [CrossRef] [PubMed] - Zhai, W.; Gao, X.; Xu, W.; Zhao, M.; Xie, M.; Huang, S.; Gu, W. Microwave photonic phase shifter with spectral separation processing using a linear chirped fiber Bragg grating. Chin. Opt. Lett.
**2016**, 14, 16–19. [Google Scholar] - Shimotsu, S.; Oikawa, S.; Saitou, T.; Mitsugi, N.; Kubodera, K.; Kawanishi, T.; Izutsu, M. Single side-band modulation performance of a LiNbO
_{3}integrated modulator consisting of four-phase modulator waveguides. IEEE Photon. Technol. Lett.**2001**, 13, 364–366. [Google Scholar] [CrossRef] - Madsen, C.K.; Zhao, J.H. Postfabrication optimization of an autoregressive planar waveguide lattice filter. Appl. Opt.
**1997**, 36, 642–647. [Google Scholar] [CrossRef] [PubMed] - Erdogan, T. Fiber grating spectra. J. Lightwave Technol.
**1997**, 15, 1277–1294. [Google Scholar] [CrossRef] - Marki Microwave. QH-0440 Datasheet. Available online: www.markimicrowave.com (accessed on 28 November 2018).
- PlugTech. MBC-DPIQ-01 Datasheet. Available online: www.plugtech.hk (accessed on 27 November 2018).

**Figure 1.**Schematic of a conventional microwave photonic phase shifter (MPPS) that involves a 90° hybrid coupler [5]. ω

_{c}is the angular carrier frequency and ω

_{RF}is the angular RF signal frequency.

**Figure 2.**(

**a**) Amplitude and (

**b**) phase responses of three Marki Microwave 4 to 40 GHz bandwidth 90° hybrid couplers measured at the coupler 90° output port with reference to the coupler 0° output port.

**Figure 3.**Ratio of the frequency shifted light power to the residual carrier power (

**dotted lines**) and the ratio of the frequency shifted light power to the unwanted sideband power (

**solid lines**) versus the two RF signal phase difference from 90°. The two RF signals into the dual-parallel Mach Zehnder modulator (DPMZM) have 1.5 dB (

**red**), 2.5 dB (

**blue**), and 3.5 dB (

**black**) power differences. The modulation index is 0.2.

**Figure 4.**(

**a**) Maximum phase deviation and (

**b**) maximum amplitude variation of the phase shifter output RF signal versus the wanted to unwanted sideband power ratio for different phase shifts.

**Figure 6.**Optical spectrum at the output of the dual-polarization DPMZM with (red dotted line) and without (blue solid line) the optical carrier from the lower DPMZM. The upper DPMZM was driven by a 32 GHz RF signal. The optical spectrum analyzer (OSA) resolution bandwidth was 0.02 nm.

**Figure 8.**Optical spectrum at the output of the dual-polarization DPMZM followed by an optical filter with (

**red dotted line**) and without (

**blue solid line**) the optical carrier from the lower DPMZM. The response of the optical filter used in the experiment (

**black dashed line**). The OSA resolution bandwidth was 0.02 nm.

**Figure 9.**(

**a**) Amplitude and (

**b**) phase response of the MPPS with an optical filter inserted after the polarizer to suppress the unwanted sideband.

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Xia, W.; Zheng, R.; Chen, B.; Chan, E.H.W.; Wang, X.; Feng, X.; Guan, B.-O. Ripple Suppression in Broadband Microwave Photonic Phase Shifter Frequency Response. *Appl. Sci.* **2018**, *8*, 2433.
https://doi.org/10.3390/app8122433

**AMA Style**

Xia W, Zheng R, Chen B, Chan EHW, Wang X, Feng X, Guan B-O. Ripple Suppression in Broadband Microwave Photonic Phase Shifter Frequency Response. *Applied Sciences*. 2018; 8(12):2433.
https://doi.org/10.3390/app8122433

**Chicago/Turabian Style**

Xia, Weicheng, Ruiqi Zheng, Bijuan Chen, Erwin H. W. Chan, Xudong Wang, Xinhuan Feng, and Bai-Ou Guan. 2018. "Ripple Suppression in Broadband Microwave Photonic Phase Shifter Frequency Response" *Applied Sciences* 8, no. 12: 2433.
https://doi.org/10.3390/app8122433