Abstract

A novel approach to implementing a wideband microwave photonic phase shifter by a joint use of a polarization modulator (PolM) and a polarization-maintaining fiber Bragg grating (PM-FBG) is proposed and experimentally demonstrated. 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. Due to the birefringence of the polarization-maintaining (PM) fiber, the PM-FBG has two spectrally separated and orthogonally polarized reflection bands. By employing the PM-FBG to reflect one first-order sideband along one polarization direction and one optical carrier 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 polarizer and beating them at a photodetector, 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. A full 360° microwave photonic phase shifter over a frequency range of 30-40 GHz is experimentally demonstrated. The spurious free dynamic range (SFDR) of the phase shifter is also studied.

© 2012 OSA

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References

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  1. G. M. Yang, O. Obi, G. Wen, Y. Q. Jin, and N. X. Sun, “Novel compact and low-loss phase shifters with magnetodielectric disturber,” IEEE Microw. Wirel. Compon. Lett.21(5), 240–242 (2011).
    [CrossRef]
  2. M. Teshiba, R. Van Leeuwen, G. Sakamoto, and T. Cisco, “A SiGe MMIC 6-Bit PIN diode phase shifter,” IEEE Microw. Wirel. Compon. Lett.12(12), 500–501 (2002).
    [CrossRef]
  3. A. S. Nagra and R. A. York, “Distributed analog phase shifters with low insertion loss,” IEEE Trans. Microw. Theory Tech.47(9), 1705–1711 (1999).
    [CrossRef]
  4. B. Pillans, S. Eshelman, A. Malczewski, J. Ehmke, and C. Goldsmith, “Ka-band RF MEMS phase shifters,” IEEE Microwave Guid. Wave Lett.9(12), 520–522 (1999).
    [CrossRef]
  5. G. M. Rebeiz and N. S. Barker, “Optimization of distributed MEMS transmission-line phase shifters-U-band and W-band designs,” IEEE Trans. Microw. Theory Tech.48(11), 1957–1966 (2000).
    [CrossRef]
  6. J. P. Yao, “Microwave photonics,” J. Lightwave Technol.27(3), 314–335 (2009).
    [CrossRef]
  7. J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics1(6), 319–330 (2007).
    [CrossRef]
  8. A. Loayssa and F. J. Lahoz, “Broad-band RF photonic phase shifter based on stimulated Brillouin scattering and single-sideband modulation,” IEEE Photon. Technol. Lett.18(1), 208–210 (2006).
    [CrossRef]
  9. W. Xue, S. Sales, J. Capmany, and J. Mørk, “Wideband 360° microwave photonic phase shifter based on slow light in semiconductor optical amplifiers,” Opt. Express18(6), 6156–6163 (2010).
    [CrossRef] [PubMed]
  10. J. Sancho, J. Lloret, I. Gasulla, S. Sales, and J. Capmany, “Fully tunable 360° microwave photonic phase shifter based on a single semiconductor optical amplifier,” Opt. Express19(18), 17421–17426 (2011).
    [CrossRef] [PubMed]
  11. H. Shahoei and J. P. Yao, “Tunable microwave photonic phase shifter based on slow and fast light effects in a tilted fiber Bragg grating,” Opt. Express20(13), 14009–14014 (2012).
    [CrossRef] [PubMed]
  12. S. Pan and Y. Zhang, “Tunable and wideband microwave photonic phase shifter based on a single-sideband polarization modulator and a polarizer,” Opt. Lett.37(21), 4483–4485 (2012).
    [CrossRef] [PubMed]
  13. J. D. Bull, N. A. F. Jaeger, H. Kato, M. Fairburn, A. Reid, and P. Ghanipour, “40 GHz electro-optic polarization modulator for fiber optic communications systems,” Proc. SPIE5577, 133–143 (2004).
    [CrossRef]
  14. W. Li and J. P. Yao, “Microwave and terahertz generation based on photonically assisted microwave frequency twelvetupling with large tunability,” IEEE Photon. J.2(6), 954–959 (2010).
  15. Y. Liu, K. S. Chiang, and P. L. Chu, “Generation of dual-wavelength picosecond pulses from a self-seeded Fabry-Perot laser diode and a polarization-maintaining fiber Bragg grating,” IEEE Photon. Technol. Lett.16(7), 1742–1744 (2004).
    [CrossRef]
  16. Z. Li, M. Li, H. Chi, X. Zhang, and J. P. Yao, “Photonic generation of phase-coded millimeter-wave signal with large frequency tunability using a polarization-maintaining fiber Bragg grating,” IEEE Microw. Wirel Compon. Lett.21(12), 694–696 (2011).
    [CrossRef]
  17. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol.15(8), 1277–1294 (1997).
    [CrossRef]
  18. J. F. Coward, C. H. Chalfant, and P. H. Chang, “A photonic integrated-optic RF phase shifter for phased array antenna beam-forming applications,” J. Lightwave Technol.11(12), 2201–2205 (1993).
    [CrossRef]

2012 (2)

2011 (3)

J. Sancho, J. Lloret, I. Gasulla, S. Sales, and J. Capmany, “Fully tunable 360° microwave photonic phase shifter based on a single semiconductor optical amplifier,” Opt. Express19(18), 17421–17426 (2011).
[CrossRef] [PubMed]

Z. Li, M. Li, H. Chi, X. Zhang, and J. P. Yao, “Photonic generation of phase-coded millimeter-wave signal with large frequency tunability using a polarization-maintaining fiber Bragg grating,” IEEE Microw. Wirel Compon. Lett.21(12), 694–696 (2011).
[CrossRef]

G. M. Yang, O. Obi, G. Wen, Y. Q. Jin, and N. X. Sun, “Novel compact and low-loss phase shifters with magnetodielectric disturber,” IEEE Microw. Wirel. Compon. Lett.21(5), 240–242 (2011).
[CrossRef]

2010 (2)

W. Li and J. P. Yao, “Microwave and terahertz generation based on photonically assisted microwave frequency twelvetupling with large tunability,” IEEE Photon. J.2(6), 954–959 (2010).

W. Xue, S. Sales, J. Capmany, and J. Mørk, “Wideband 360° microwave photonic phase shifter based on slow light in semiconductor optical amplifiers,” Opt. Express18(6), 6156–6163 (2010).
[CrossRef] [PubMed]

2009 (1)

2007 (1)

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics1(6), 319–330 (2007).
[CrossRef]

2006 (1)

A. Loayssa and F. J. Lahoz, “Broad-band RF photonic phase shifter based on stimulated Brillouin scattering and single-sideband modulation,” IEEE Photon. Technol. Lett.18(1), 208–210 (2006).
[CrossRef]

2004 (2)

J. D. Bull, N. A. F. Jaeger, H. Kato, M. Fairburn, A. Reid, and P. Ghanipour, “40 GHz electro-optic polarization modulator for fiber optic communications systems,” Proc. SPIE5577, 133–143 (2004).
[CrossRef]

Y. Liu, K. S. Chiang, and P. L. Chu, “Generation of dual-wavelength picosecond pulses from a self-seeded Fabry-Perot laser diode and a polarization-maintaining fiber Bragg grating,” IEEE Photon. Technol. Lett.16(7), 1742–1744 (2004).
[CrossRef]

2002 (1)

M. Teshiba, R. Van Leeuwen, G. Sakamoto, and T. Cisco, “A SiGe MMIC 6-Bit PIN diode phase shifter,” IEEE Microw. Wirel. Compon. Lett.12(12), 500–501 (2002).
[CrossRef]

2000 (1)

G. M. Rebeiz and N. S. Barker, “Optimization of distributed MEMS transmission-line phase shifters-U-band and W-band designs,” IEEE Trans. Microw. Theory Tech.48(11), 1957–1966 (2000).
[CrossRef]

1999 (2)

A. S. Nagra and R. A. York, “Distributed analog phase shifters with low insertion loss,” IEEE Trans. Microw. Theory Tech.47(9), 1705–1711 (1999).
[CrossRef]

B. Pillans, S. Eshelman, A. Malczewski, J. Ehmke, and C. Goldsmith, “Ka-band RF MEMS phase shifters,” IEEE Microwave Guid. Wave Lett.9(12), 520–522 (1999).
[CrossRef]

1997 (1)

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol.15(8), 1277–1294 (1997).
[CrossRef]

1993 (1)

J. F. Coward, C. H. Chalfant, and P. H. Chang, “A photonic integrated-optic RF phase shifter for phased array antenna beam-forming applications,” J. Lightwave Technol.11(12), 2201–2205 (1993).
[CrossRef]

Barker, N. S.

G. M. Rebeiz and N. S. Barker, “Optimization of distributed MEMS transmission-line phase shifters-U-band and W-band designs,” IEEE Trans. Microw. Theory Tech.48(11), 1957–1966 (2000).
[CrossRef]

Bull, J. D.

J. D. Bull, N. A. F. Jaeger, H. Kato, M. Fairburn, A. Reid, and P. Ghanipour, “40 GHz electro-optic polarization modulator for fiber optic communications systems,” Proc. SPIE5577, 133–143 (2004).
[CrossRef]

Capmany, J.

Chalfant, C. H.

J. F. Coward, C. H. Chalfant, and P. H. Chang, “A photonic integrated-optic RF phase shifter for phased array antenna beam-forming applications,” J. Lightwave Technol.11(12), 2201–2205 (1993).
[CrossRef]

Chang, P. H.

J. F. Coward, C. H. Chalfant, and P. H. Chang, “A photonic integrated-optic RF phase shifter for phased array antenna beam-forming applications,” J. Lightwave Technol.11(12), 2201–2205 (1993).
[CrossRef]

Chi, H.

Z. Li, M. Li, H. Chi, X. Zhang, and J. P. Yao, “Photonic generation of phase-coded millimeter-wave signal with large frequency tunability using a polarization-maintaining fiber Bragg grating,” IEEE Microw. Wirel Compon. Lett.21(12), 694–696 (2011).
[CrossRef]

Chiang, K. S.

Y. Liu, K. S. Chiang, and P. L. Chu, “Generation of dual-wavelength picosecond pulses from a self-seeded Fabry-Perot laser diode and a polarization-maintaining fiber Bragg grating,” IEEE Photon. Technol. Lett.16(7), 1742–1744 (2004).
[CrossRef]

Chu, P. L.

Y. Liu, K. S. Chiang, and P. L. Chu, “Generation of dual-wavelength picosecond pulses from a self-seeded Fabry-Perot laser diode and a polarization-maintaining fiber Bragg grating,” IEEE Photon. Technol. Lett.16(7), 1742–1744 (2004).
[CrossRef]

Cisco, T.

M. Teshiba, R. Van Leeuwen, G. Sakamoto, and T. Cisco, “A SiGe MMIC 6-Bit PIN diode phase shifter,” IEEE Microw. Wirel. Compon. Lett.12(12), 500–501 (2002).
[CrossRef]

Coward, J. F.

J. F. Coward, C. H. Chalfant, and P. H. Chang, “A photonic integrated-optic RF phase shifter for phased array antenna beam-forming applications,” J. Lightwave Technol.11(12), 2201–2205 (1993).
[CrossRef]

Ehmke, J.

B. Pillans, S. Eshelman, A. Malczewski, J. Ehmke, and C. Goldsmith, “Ka-band RF MEMS phase shifters,” IEEE Microwave Guid. Wave Lett.9(12), 520–522 (1999).
[CrossRef]

Erdogan, T.

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol.15(8), 1277–1294 (1997).
[CrossRef]

Eshelman, S.

B. Pillans, S. Eshelman, A. Malczewski, J. Ehmke, and C. Goldsmith, “Ka-band RF MEMS phase shifters,” IEEE Microwave Guid. Wave Lett.9(12), 520–522 (1999).
[CrossRef]

Fairburn, M.

J. D. Bull, N. A. F. Jaeger, H. Kato, M. Fairburn, A. Reid, and P. Ghanipour, “40 GHz electro-optic polarization modulator for fiber optic communications systems,” Proc. SPIE5577, 133–143 (2004).
[CrossRef]

Gasulla, I.

Ghanipour, P.

J. D. Bull, N. A. F. Jaeger, H. Kato, M. Fairburn, A. Reid, and P. Ghanipour, “40 GHz electro-optic polarization modulator for fiber optic communications systems,” Proc. SPIE5577, 133–143 (2004).
[CrossRef]

Goldsmith, C.

B. Pillans, S. Eshelman, A. Malczewski, J. Ehmke, and C. Goldsmith, “Ka-band RF MEMS phase shifters,” IEEE Microwave Guid. Wave Lett.9(12), 520–522 (1999).
[CrossRef]

Jaeger, N. A. F.

J. D. Bull, N. A. F. Jaeger, H. Kato, M. Fairburn, A. Reid, and P. Ghanipour, “40 GHz electro-optic polarization modulator for fiber optic communications systems,” Proc. SPIE5577, 133–143 (2004).
[CrossRef]

Jin, Y. Q.

G. M. Yang, O. Obi, G. Wen, Y. Q. Jin, and N. X. Sun, “Novel compact and low-loss phase shifters with magnetodielectric disturber,” IEEE Microw. Wirel. Compon. Lett.21(5), 240–242 (2011).
[CrossRef]

Kato, H.

J. D. Bull, N. A. F. Jaeger, H. Kato, M. Fairburn, A. Reid, and P. Ghanipour, “40 GHz electro-optic polarization modulator for fiber optic communications systems,” Proc. SPIE5577, 133–143 (2004).
[CrossRef]

Lahoz, F. J.

A. Loayssa and F. J. Lahoz, “Broad-band RF photonic phase shifter based on stimulated Brillouin scattering and single-sideband modulation,” IEEE Photon. Technol. Lett.18(1), 208–210 (2006).
[CrossRef]

Li, M.

Z. Li, M. Li, H. Chi, X. Zhang, and J. P. Yao, “Photonic generation of phase-coded millimeter-wave signal with large frequency tunability using a polarization-maintaining fiber Bragg grating,” IEEE Microw. Wirel Compon. Lett.21(12), 694–696 (2011).
[CrossRef]

Li, W.

W. Li and J. P. Yao, “Microwave and terahertz generation based on photonically assisted microwave frequency twelvetupling with large tunability,” IEEE Photon. J.2(6), 954–959 (2010).

Li, Z.

Z. Li, M. Li, H. Chi, X. Zhang, and J. P. Yao, “Photonic generation of phase-coded millimeter-wave signal with large frequency tunability using a polarization-maintaining fiber Bragg grating,” IEEE Microw. Wirel Compon. Lett.21(12), 694–696 (2011).
[CrossRef]

Liu, Y.

Y. Liu, K. S. Chiang, and P. L. Chu, “Generation of dual-wavelength picosecond pulses from a self-seeded Fabry-Perot laser diode and a polarization-maintaining fiber Bragg grating,” IEEE Photon. Technol. Lett.16(7), 1742–1744 (2004).
[CrossRef]

Lloret, J.

Loayssa, A.

A. Loayssa and F. J. Lahoz, “Broad-band RF photonic phase shifter based on stimulated Brillouin scattering and single-sideband modulation,” IEEE Photon. Technol. Lett.18(1), 208–210 (2006).
[CrossRef]

Malczewski, A.

B. Pillans, S. Eshelman, A. Malczewski, J. Ehmke, and C. Goldsmith, “Ka-band RF MEMS phase shifters,” IEEE Microwave Guid. Wave Lett.9(12), 520–522 (1999).
[CrossRef]

Mørk, J.

Nagra, A. S.

A. S. Nagra and R. A. York, “Distributed analog phase shifters with low insertion loss,” IEEE Trans. Microw. Theory Tech.47(9), 1705–1711 (1999).
[CrossRef]

Novak, D.

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics1(6), 319–330 (2007).
[CrossRef]

Obi, O.

G. M. Yang, O. Obi, G. Wen, Y. Q. Jin, and N. X. Sun, “Novel compact and low-loss phase shifters with magnetodielectric disturber,” IEEE Microw. Wirel. Compon. Lett.21(5), 240–242 (2011).
[CrossRef]

Pan, S.

Pillans, B.

B. Pillans, S. Eshelman, A. Malczewski, J. Ehmke, and C. Goldsmith, “Ka-band RF MEMS phase shifters,” IEEE Microwave Guid. Wave Lett.9(12), 520–522 (1999).
[CrossRef]

Rebeiz, G. M.

G. M. Rebeiz and N. S. Barker, “Optimization of distributed MEMS transmission-line phase shifters-U-band and W-band designs,” IEEE Trans. Microw. Theory Tech.48(11), 1957–1966 (2000).
[CrossRef]

Reid, A.

J. D. Bull, N. A. F. Jaeger, H. Kato, M. Fairburn, A. Reid, and P. Ghanipour, “40 GHz electro-optic polarization modulator for fiber optic communications systems,” Proc. SPIE5577, 133–143 (2004).
[CrossRef]

Sakamoto, G.

M. Teshiba, R. Van Leeuwen, G. Sakamoto, and T. Cisco, “A SiGe MMIC 6-Bit PIN diode phase shifter,” IEEE Microw. Wirel. Compon. Lett.12(12), 500–501 (2002).
[CrossRef]

Sales, S.

Sancho, J.

Shahoei, H.

Sun, N. X.

G. M. Yang, O. Obi, G. Wen, Y. Q. Jin, and N. X. Sun, “Novel compact and low-loss phase shifters with magnetodielectric disturber,” IEEE Microw. Wirel. Compon. Lett.21(5), 240–242 (2011).
[CrossRef]

Teshiba, M.

M. Teshiba, R. Van Leeuwen, G. Sakamoto, and T. Cisco, “A SiGe MMIC 6-Bit PIN diode phase shifter,” IEEE Microw. Wirel. Compon. Lett.12(12), 500–501 (2002).
[CrossRef]

Van Leeuwen, R.

M. Teshiba, R. Van Leeuwen, G. Sakamoto, and T. Cisco, “A SiGe MMIC 6-Bit PIN diode phase shifter,” IEEE Microw. Wirel. Compon. Lett.12(12), 500–501 (2002).
[CrossRef]

Wen, G.

G. M. Yang, O. Obi, G. Wen, Y. Q. Jin, and N. X. Sun, “Novel compact and low-loss phase shifters with magnetodielectric disturber,” IEEE Microw. Wirel. Compon. Lett.21(5), 240–242 (2011).
[CrossRef]

Xue, W.

Yang, G. M.

G. M. Yang, O. Obi, G. Wen, Y. Q. Jin, and N. X. Sun, “Novel compact and low-loss phase shifters with magnetodielectric disturber,” IEEE Microw. Wirel. Compon. Lett.21(5), 240–242 (2011).
[CrossRef]

Yao, J. P.

H. Shahoei and J. P. Yao, “Tunable microwave photonic phase shifter based on slow and fast light effects in a tilted fiber Bragg grating,” Opt. Express20(13), 14009–14014 (2012).
[CrossRef] [PubMed]

Z. Li, M. Li, H. Chi, X. Zhang, and J. P. Yao, “Photonic generation of phase-coded millimeter-wave signal with large frequency tunability using a polarization-maintaining fiber Bragg grating,” IEEE Microw. Wirel Compon. Lett.21(12), 694–696 (2011).
[CrossRef]

W. Li and J. P. Yao, “Microwave and terahertz generation based on photonically assisted microwave frequency twelvetupling with large tunability,” IEEE Photon. J.2(6), 954–959 (2010).

J. P. Yao, “Microwave photonics,” J. Lightwave Technol.27(3), 314–335 (2009).
[CrossRef]

York, R. A.

A. S. Nagra and R. A. York, “Distributed analog phase shifters with low insertion loss,” IEEE Trans. Microw. Theory Tech.47(9), 1705–1711 (1999).
[CrossRef]

Zhang, X.

Z. Li, M. Li, H. Chi, X. Zhang, and J. P. Yao, “Photonic generation of phase-coded millimeter-wave signal with large frequency tunability using a polarization-maintaining fiber Bragg grating,” IEEE Microw. Wirel Compon. Lett.21(12), 694–696 (2011).
[CrossRef]

Zhang, Y.

IEEE Microw. Wirel Compon. Lett. (1)

Z. Li, M. Li, H. Chi, X. Zhang, and J. P. Yao, “Photonic generation of phase-coded millimeter-wave signal with large frequency tunability using a polarization-maintaining fiber Bragg grating,” IEEE Microw. Wirel Compon. Lett.21(12), 694–696 (2011).
[CrossRef]

IEEE Microw. Wirel. Compon. Lett. (2)

G. M. Yang, O. Obi, G. Wen, Y. Q. Jin, and N. X. Sun, “Novel compact and low-loss phase shifters with magnetodielectric disturber,” IEEE Microw. Wirel. Compon. Lett.21(5), 240–242 (2011).
[CrossRef]

M. Teshiba, R. Van Leeuwen, G. Sakamoto, and T. Cisco, “A SiGe MMIC 6-Bit PIN diode phase shifter,” IEEE Microw. Wirel. Compon. Lett.12(12), 500–501 (2002).
[CrossRef]

IEEE Microwave Guid. Wave Lett. (1)

B. Pillans, S. Eshelman, A. Malczewski, J. Ehmke, and C. Goldsmith, “Ka-band RF MEMS phase shifters,” IEEE Microwave Guid. Wave Lett.9(12), 520–522 (1999).
[CrossRef]

IEEE Photon. J. (1)

W. Li and J. P. Yao, “Microwave and terahertz generation based on photonically assisted microwave frequency twelvetupling with large tunability,” IEEE Photon. J.2(6), 954–959 (2010).

IEEE Photon. Technol. Lett. (2)

Y. Liu, K. S. Chiang, and P. L. Chu, “Generation of dual-wavelength picosecond pulses from a self-seeded Fabry-Perot laser diode and a polarization-maintaining fiber Bragg grating,” IEEE Photon. Technol. Lett.16(7), 1742–1744 (2004).
[CrossRef]

A. Loayssa and F. J. Lahoz, “Broad-band RF photonic phase shifter based on stimulated Brillouin scattering and single-sideband modulation,” IEEE Photon. Technol. Lett.18(1), 208–210 (2006).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (2)

G. M. Rebeiz and N. S. Barker, “Optimization of distributed MEMS transmission-line phase shifters-U-band and W-band designs,” IEEE Trans. Microw. Theory Tech.48(11), 1957–1966 (2000).
[CrossRef]

A. S. Nagra and R. A. York, “Distributed analog phase shifters with low insertion loss,” IEEE Trans. Microw. Theory Tech.47(9), 1705–1711 (1999).
[CrossRef]

J. Lightwave Technol. (3)

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol.15(8), 1277–1294 (1997).
[CrossRef]

J. F. Coward, C. H. Chalfant, and P. H. Chang, “A photonic integrated-optic RF phase shifter for phased array antenna beam-forming applications,” J. Lightwave Technol.11(12), 2201–2205 (1993).
[CrossRef]

J. P. Yao, “Microwave photonics,” J. Lightwave Technol.27(3), 314–335 (2009).
[CrossRef]

Nat. Photonics (1)

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics1(6), 319–330 (2007).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Proc. SPIE (1)

J. D. Bull, N. A. F. Jaeger, H. Kato, M. Fairburn, A. Reid, and P. Ghanipour, “40 GHz electro-optic polarization modulator for fiber optic communications systems,” Proc. SPIE5577, 133–143 (2004).
[CrossRef]

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Figures (4)

Fig. 1
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.

Fig. 2
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).

Fig. 3
Fig. 3

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

Fig. 4
Fig. 4

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

Equations (3)

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E 1 ( t )= e j ω o t ( x ^ E x , y ^ E y )( e jβcos( ω e t )+jϕ e jβcos( ω e t )jϕ )= e j ω o t ( x ^ E x e jϕ , y ^ E y e jϕ )( n= i n J n ( β ) e jn ω e t n= i n J n ( β ) e jn ω e t ) e j ω o t ( x ^ E x e jϕ , y ^ E y e jϕ )( 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 )
E 2 ( t ) e j ω o t ( x ^ E x e j2ϕ , y ^ E y e j2ϕ )( J 0 ( β ) J 1 ( β )i e j ω e t ) = x ^ E x J 0 ( β ) e j( ω o t+2ϕ ) y ^ E y J 1 ( β ) e j( ω o t+ ω e t2ϕ+π/2 )
V( t ) | E x J 0 ( β ) e j( ω o t+2ϕ ) E y J 1 ( β ) e j( ω o t+ ω e t2ϕ+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 t4π V bias / V π_b )

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