Abstract

An optically-controlled phase-tunable microwave mixer based on a dual-drive dual-parallel Mach-Zehnder modulator (DDDP-MZM) is proposed, which supports wideband phase shift and immunity to power fading caused by chromatic dispersion. By using carrier-suppressed single side-band (CS-SSB) modulation for the local oscillator (LO) signal and carrier-suppressed double side-band (CS-DSB) modulation for the input signal, no vector superposition for the same output microwave frequency occurs, making the system immune from power fading caused by chromatic dispersion. Phase tuning is achieved by shifting the phase of the LO signal, and direct electrical tuning of the wideband microwave input signal is avoided, thus supporting large working bandwidth. A phase-shifted down-conversion experiment is carried out, where a phase shift with 0 ~390° and down-conversion are achieved with a phase variation of less than 5° and power variation less than 3.5 dBm when the input signal sweeps between 12 ~16 GHz. The mixer is simple and power-efficient since it uses a single compact modulator, and does not require any optical filters. No power notches are observed in the output microwave spectrum, proving that the dispersion-related frequency-selective fading is mitigated.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. C. K. Sun, R. J. Orazi, S. A. Pappert, and W. K. Burns, “A photonic-link millimeter-wave mixer using cascaded optical modulators and harmonic carrier generation,” IEEE Photonics Technol. Lett. 8(9), 1166–1168 (1996).
    [Crossref]
  2. J. F. Coward, T. K. Yee, 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(1), 2201–2205 (1993).
    [Crossref]
  3. J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
    [Crossref]
  4. T. Jiang, S. Yu, R. Wu, D. Wang, and W. Gu, “Photonic downconversion with tunable wideband phase shift,” Opt. Lett. 41(11), 2640–2643 (2016).
    [Crossref] [PubMed]
  5. V. R. Pagán and T. E. Murphy, “Electro-optic millimeter-wave harmonic downconversion and vector demodulation using cascaded phase modulation and optical filtering,” Opt. Lett. 40(11), 2481–2484 (2015).
    [Crossref] [PubMed]
  6. Y. Gao, A. Wen, Z. Tu, W. Zhang, and L. Lin, “Simultaneously photonic frequency downconversion, multichannel phase shifting, and IQ demodulation for wideband microwave signals,” Opt. Lett. 41(19), 4484–4487 (2016).
    [Crossref] [PubMed]
  7. V. R. Pagán, B. M. Haas, and T. E. Murphy, “Linearized electrooptic microwave downconversion using phase modulation and optical filtering,” Opt. Express 19(2), 883–895 (2011).
    [Crossref] [PubMed]
  8. E. H. W. Chan and R. Minasian, “Microwave Photonic Downconverter With High Conversion Efficiency,” J. Lightwave Technol. 30(23), 3580–3585 (2012).
    [Crossref]
  9. X. Wang, J. Zhang, E. H. W. Chan, X. Feng, and B. O. Guan, “Ultra-wide bandwidth photonic microwave phase shifter with amplitude control function,” Opt. Express 25(3), 2883 (2017).
    [Crossref]
  10. T. Jiang, R. Wu, S. Yu, D. Wang, and W. Gu, “Microwave photonic phase-tunable mixer,” Opt. Express 25(4), 4519–4527 (2017).
    [Crossref] [PubMed]
  11. U. Gliese, S. Norskov, and T. N. Nielsen, “Chromatic dispersion in fiber-optic microwave and millimeter-wave links,” IEEE Trans. Microw. Theory Tech. 44(10), 1716–1724 (1996).
    [Crossref]
  12. J. L. Corral, J. Marti, and J. M. Fuster, “General expressions for IM/DD dispersive analog optical links with external modulation or optical up-conversion in a Mach–Zehnder electrooptical modulator,” IEEE Trans. Microw. Theory Tech. 49(10), 1968–1976 (2001).
    [Crossref]
  13. L. Grüner-Nielsen, M. Wandel, P. Kristensen, C. Jorgensen, L. V. Jorgensen, B. T. Edvold, B. Pálsdóttir, and D. Jakobsen, “Dispersion-Compensating Fibers,” J. Lightwave Technol. 23(11), 3566–3579 (2005).
    [Crossref]
  14. L. Huang, P. Wang, P. Xiang, D. Chen, Y. Zhang, J. Tao, T. Pu, and X. Chen, “Broadband Compensation of Dispersion in APL Using OPC Based on DFB Semiconductor Lasers,” IEEE Photonics Technol. Lett. 27(23), 2496–2499 (2015).
    [Crossref]
  15. A. Sheikh, C. Fougstedt, A. G. I. Amat, P. Johannisson, P. Larsson-Edefors, and M. Karlsson, “Dispersion Compensation FIR Filter With Improved Robustness to Coefficient Quantization Errors,” J. Lightwave Technol. 34(22), 5110–5117 (2016).
    [Crossref]
  16. Y. Gao, A. Wen, Y. Chen, S. Xiang, H. Zhang, and L. Shang, “An Analog Photonic Link With Compensation of Dispersion-Induced Power Fading,” IEEE Photonics Technol. Lett. 27(12), 1301–1304 (2015).
    [Crossref]
  17. S. Li, X. Zheng, H. Zhang, and B. Zhou, “Compensation of dispersion-induced power fading for highly linear radio-over-fiber link using carrier phase-shifted double sideband modulation,” Opt. Lett. 36(4), 546–548 (2011).
    [Crossref] [PubMed]
  18. Z. Chen, L. Yan, H. Jiang, W. Pan, B. Luo, and X. Zou, “Dispersion Compensation in Analog Photonic Link Utilizing a Phase Modulator,” J. Lightwave Technol. 32(23), 4040–4045 (2014).
  19. H. Zhang, S. Pan, M. Huang, and X. Chen, “Polarization-modulated analog photonic link with compensation of the dispersion-induced power fading,” Opt. Lett. 37(5), 866–868 (2012).
    [Crossref] [PubMed]

2017 (2)

2016 (3)

2015 (3)

V. R. Pagán and T. E. Murphy, “Electro-optic millimeter-wave harmonic downconversion and vector demodulation using cascaded phase modulation and optical filtering,” Opt. Lett. 40(11), 2481–2484 (2015).
[Crossref] [PubMed]

Y. Gao, A. Wen, Y. Chen, S. Xiang, H. Zhang, and L. Shang, “An Analog Photonic Link With Compensation of Dispersion-Induced Power Fading,” IEEE Photonics Technol. Lett. 27(12), 1301–1304 (2015).
[Crossref]

L. Huang, P. Wang, P. Xiang, D. Chen, Y. Zhang, J. Tao, T. Pu, and X. Chen, “Broadband Compensation of Dispersion in APL Using OPC Based on DFB Semiconductor Lasers,” IEEE Photonics Technol. Lett. 27(23), 2496–2499 (2015).
[Crossref]

2014 (1)

2012 (2)

2011 (2)

2007 (1)

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
[Crossref]

2005 (1)

2001 (1)

J. L. Corral, J. Marti, and J. M. Fuster, “General expressions for IM/DD dispersive analog optical links with external modulation or optical up-conversion in a Mach–Zehnder electrooptical modulator,” IEEE Trans. Microw. Theory Tech. 49(10), 1968–1976 (2001).
[Crossref]

1996 (2)

U. Gliese, S. Norskov, and T. N. Nielsen, “Chromatic dispersion in fiber-optic microwave and millimeter-wave links,” IEEE Trans. Microw. Theory Tech. 44(10), 1716–1724 (1996).
[Crossref]

C. K. Sun, R. J. Orazi, S. A. Pappert, and W. K. Burns, “A photonic-link millimeter-wave mixer using cascaded optical modulators and harmonic carrier generation,” IEEE Photonics Technol. Lett. 8(9), 1166–1168 (1996).
[Crossref]

1993 (1)

J. F. Coward, T. K. Yee, 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(1), 2201–2205 (1993).
[Crossref]

Amat, A. G. I.

Burns, W. K.

C. K. Sun, R. J. Orazi, S. A. Pappert, and W. K. Burns, “A photonic-link millimeter-wave mixer using cascaded optical modulators and harmonic carrier generation,” IEEE Photonics Technol. Lett. 8(9), 1166–1168 (1996).
[Crossref]

Capmany, J.

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
[Crossref]

Chalfant, C. H.

J. F. Coward, T. K. Yee, 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(1), 2201–2205 (1993).
[Crossref]

Chan, E. H. W.

Chang, P. H.

J. F. Coward, T. K. Yee, 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(1), 2201–2205 (1993).
[Crossref]

Chen, D.

L. Huang, P. Wang, P. Xiang, D. Chen, Y. Zhang, J. Tao, T. Pu, and X. Chen, “Broadband Compensation of Dispersion in APL Using OPC Based on DFB Semiconductor Lasers,” IEEE Photonics Technol. Lett. 27(23), 2496–2499 (2015).
[Crossref]

Chen, X.

L. Huang, P. Wang, P. Xiang, D. Chen, Y. Zhang, J. Tao, T. Pu, and X. Chen, “Broadband Compensation of Dispersion in APL Using OPC Based on DFB Semiconductor Lasers,” IEEE Photonics Technol. Lett. 27(23), 2496–2499 (2015).
[Crossref]

H. Zhang, S. Pan, M. Huang, and X. Chen, “Polarization-modulated analog photonic link with compensation of the dispersion-induced power fading,” Opt. Lett. 37(5), 866–868 (2012).
[Crossref] [PubMed]

Chen, Y.

Y. Gao, A. Wen, Y. Chen, S. Xiang, H. Zhang, and L. Shang, “An Analog Photonic Link With Compensation of Dispersion-Induced Power Fading,” IEEE Photonics Technol. Lett. 27(12), 1301–1304 (2015).
[Crossref]

Chen, Z.

Corral, J. L.

J. L. Corral, J. Marti, and J. M. Fuster, “General expressions for IM/DD dispersive analog optical links with external modulation or optical up-conversion in a Mach–Zehnder electrooptical modulator,” IEEE Trans. Microw. Theory Tech. 49(10), 1968–1976 (2001).
[Crossref]

Coward, J. F.

J. F. Coward, T. K. Yee, 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(1), 2201–2205 (1993).
[Crossref]

Edvold, B. T.

Feng, X.

Fougstedt, C.

Fuster, J. M.

J. L. Corral, J. Marti, and J. M. Fuster, “General expressions for IM/DD dispersive analog optical links with external modulation or optical up-conversion in a Mach–Zehnder electrooptical modulator,” IEEE Trans. Microw. Theory Tech. 49(10), 1968–1976 (2001).
[Crossref]

Gao, Y.

Y. Gao, A. Wen, Z. Tu, W. Zhang, and L. Lin, “Simultaneously photonic frequency downconversion, multichannel phase shifting, and IQ demodulation for wideband microwave signals,” Opt. Lett. 41(19), 4484–4487 (2016).
[Crossref] [PubMed]

Y. Gao, A. Wen, Y. Chen, S. Xiang, H. Zhang, and L. Shang, “An Analog Photonic Link With Compensation of Dispersion-Induced Power Fading,” IEEE Photonics Technol. Lett. 27(12), 1301–1304 (2015).
[Crossref]

Gliese, U.

U. Gliese, S. Norskov, and T. N. Nielsen, “Chromatic dispersion in fiber-optic microwave and millimeter-wave links,” IEEE Trans. Microw. Theory Tech. 44(10), 1716–1724 (1996).
[Crossref]

Grüner-Nielsen, L.

Gu, W.

Guan, B. O.

Haas, B. M.

Huang, L.

L. Huang, P. Wang, P. Xiang, D. Chen, Y. Zhang, J. Tao, T. Pu, and X. Chen, “Broadband Compensation of Dispersion in APL Using OPC Based on DFB Semiconductor Lasers,” IEEE Photonics Technol. Lett. 27(23), 2496–2499 (2015).
[Crossref]

Huang, M.

Jakobsen, D.

Jiang, H.

Jiang, T.

Johannisson, P.

Jorgensen, C.

Jorgensen, L. V.

Karlsson, M.

Kristensen, P.

Larsson-Edefors, P.

Li, S.

Lin, L.

Luo, B.

Marti, J.

J. L. Corral, J. Marti, and J. M. Fuster, “General expressions for IM/DD dispersive analog optical links with external modulation or optical up-conversion in a Mach–Zehnder electrooptical modulator,” IEEE Trans. Microw. Theory Tech. 49(10), 1968–1976 (2001).
[Crossref]

Minasian, R.

Murphy, T. E.

Nielsen, T. N.

U. Gliese, S. Norskov, and T. N. Nielsen, “Chromatic dispersion in fiber-optic microwave and millimeter-wave links,” IEEE Trans. Microw. Theory Tech. 44(10), 1716–1724 (1996).
[Crossref]

Norskov, S.

U. Gliese, S. Norskov, and T. N. Nielsen, “Chromatic dispersion in fiber-optic microwave and millimeter-wave links,” IEEE Trans. Microw. Theory Tech. 44(10), 1716–1724 (1996).
[Crossref]

Novak, D.

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
[Crossref]

Orazi, R. J.

C. K. Sun, R. J. Orazi, S. A. Pappert, and W. K. Burns, “A photonic-link millimeter-wave mixer using cascaded optical modulators and harmonic carrier generation,” IEEE Photonics Technol. Lett. 8(9), 1166–1168 (1996).
[Crossref]

Pagán, V. R.

Pálsdóttir, B.

Pan, S.

Pan, W.

Pappert, S. A.

C. K. Sun, R. J. Orazi, S. A. Pappert, and W. K. Burns, “A photonic-link millimeter-wave mixer using cascaded optical modulators and harmonic carrier generation,” IEEE Photonics Technol. Lett. 8(9), 1166–1168 (1996).
[Crossref]

Pu, T.

L. Huang, P. Wang, P. Xiang, D. Chen, Y. Zhang, J. Tao, T. Pu, and X. Chen, “Broadband Compensation of Dispersion in APL Using OPC Based on DFB Semiconductor Lasers,” IEEE Photonics Technol. Lett. 27(23), 2496–2499 (2015).
[Crossref]

Shang, L.

Y. Gao, A. Wen, Y. Chen, S. Xiang, H. Zhang, and L. Shang, “An Analog Photonic Link With Compensation of Dispersion-Induced Power Fading,” IEEE Photonics Technol. Lett. 27(12), 1301–1304 (2015).
[Crossref]

Sheikh, A.

Sun, C. K.

C. K. Sun, R. J. Orazi, S. A. Pappert, and W. K. Burns, “A photonic-link millimeter-wave mixer using cascaded optical modulators and harmonic carrier generation,” IEEE Photonics Technol. Lett. 8(9), 1166–1168 (1996).
[Crossref]

Tao, J.

L. Huang, P. Wang, P. Xiang, D. Chen, Y. Zhang, J. Tao, T. Pu, and X. Chen, “Broadband Compensation of Dispersion in APL Using OPC Based on DFB Semiconductor Lasers,” IEEE Photonics Technol. Lett. 27(23), 2496–2499 (2015).
[Crossref]

Tu, Z.

Wandel, M.

Wang, D.

Wang, P.

L. Huang, P. Wang, P. Xiang, D. Chen, Y. Zhang, J. Tao, T. Pu, and X. Chen, “Broadband Compensation of Dispersion in APL Using OPC Based on DFB Semiconductor Lasers,” IEEE Photonics Technol. Lett. 27(23), 2496–2499 (2015).
[Crossref]

Wang, X.

Wen, A.

Y. Gao, A. Wen, Z. Tu, W. Zhang, and L. Lin, “Simultaneously photonic frequency downconversion, multichannel phase shifting, and IQ demodulation for wideband microwave signals,” Opt. Lett. 41(19), 4484–4487 (2016).
[Crossref] [PubMed]

Y. Gao, A. Wen, Y. Chen, S. Xiang, H. Zhang, and L. Shang, “An Analog Photonic Link With Compensation of Dispersion-Induced Power Fading,” IEEE Photonics Technol. Lett. 27(12), 1301–1304 (2015).
[Crossref]

Wu, R.

Xiang, P.

L. Huang, P. Wang, P. Xiang, D. Chen, Y. Zhang, J. Tao, T. Pu, and X. Chen, “Broadband Compensation of Dispersion in APL Using OPC Based on DFB Semiconductor Lasers,” IEEE Photonics Technol. Lett. 27(23), 2496–2499 (2015).
[Crossref]

Xiang, S.

Y. Gao, A. Wen, Y. Chen, S. Xiang, H. Zhang, and L. Shang, “An Analog Photonic Link With Compensation of Dispersion-Induced Power Fading,” IEEE Photonics Technol. Lett. 27(12), 1301–1304 (2015).
[Crossref]

Yan, L.

Yee, T. K.

J. F. Coward, T. K. Yee, 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(1), 2201–2205 (1993).
[Crossref]

Yu, S.

Zhang, H.

Zhang, J.

Zhang, W.

Zhang, Y.

L. Huang, P. Wang, P. Xiang, D. Chen, Y. Zhang, J. Tao, T. Pu, and X. Chen, “Broadband Compensation of Dispersion in APL Using OPC Based on DFB Semiconductor Lasers,” IEEE Photonics Technol. Lett. 27(23), 2496–2499 (2015).
[Crossref]

Zheng, X.

Zhou, B.

Zou, X.

IEEE Photonics Technol. Lett. (3)

C. K. Sun, R. J. Orazi, S. A. Pappert, and W. K. Burns, “A photonic-link millimeter-wave mixer using cascaded optical modulators and harmonic carrier generation,” IEEE Photonics Technol. Lett. 8(9), 1166–1168 (1996).
[Crossref]

L. Huang, P. Wang, P. Xiang, D. Chen, Y. Zhang, J. Tao, T. Pu, and X. Chen, “Broadband Compensation of Dispersion in APL Using OPC Based on DFB Semiconductor Lasers,” IEEE Photonics Technol. Lett. 27(23), 2496–2499 (2015).
[Crossref]

Y. Gao, A. Wen, Y. Chen, S. Xiang, H. Zhang, and L. Shang, “An Analog Photonic Link With Compensation of Dispersion-Induced Power Fading,” IEEE Photonics Technol. Lett. 27(12), 1301–1304 (2015).
[Crossref]

IEEE Trans. Microw. Theory Tech. (2)

U. Gliese, S. Norskov, and T. N. Nielsen, “Chromatic dispersion in fiber-optic microwave and millimeter-wave links,” IEEE Trans. Microw. Theory Tech. 44(10), 1716–1724 (1996).
[Crossref]

J. L. Corral, J. Marti, and J. M. Fuster, “General expressions for IM/DD dispersive analog optical links with external modulation or optical up-conversion in a Mach–Zehnder electrooptical modulator,” IEEE Trans. Microw. Theory Tech. 49(10), 1968–1976 (2001).
[Crossref]

J. Lightwave Technol. (5)

Nat. Photonics (1)

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
[Crossref]

Opt. Express (3)

Opt. Lett. (5)

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Figures (7)

Fig. 1
Fig. 1 System structure of the anti-dispersion phase-tunable microwave mixer based on DDDP-MZM. (VSG: Vector signal generator. PS: Power splitter. MZ: Mach-Zehnder modulator. OC: Optical coupler. LD: Laser diode. VNA: Vector network analyzer. OSA: Optical spectrum analyzer. MSA: Microwave spectrum analyzer. SMF: Single mode fiber. EDFA: Erbium-doped fiber amplifier. PD: Photodiode. DDDP-MZM: Dual-drive dual-parallel Mach-Zehnder modulator.)
Fig. 2
Fig. 2 Experiment structure of the anti-dispersion phase-tunable microwave mixer based on DDDP-MZM to test the frequency mixing performance.
Fig. 3
Fig. 3 (a) The optical spectrum and (b) the beating output when input signal is 14 GHz and the LO is 18 GHz. (c) The optical spectrum and (d) the beating output when input signal is 4 GHz and the LO is 8 GHz.
Fig. 4
Fig. 4 (a) Experiment structure of the anti-dispersion phase-tunable microwave mixer based on DDDP-MZM with different transmission process, (b) to test the phase-shift performance and (c) to test the anti-dispersion performance.
Fig. 5
Fig. 5 The (a) phase and (b) power response at different initial phase φ when the input signal sweeps between 12 ~16 GHz. The LO signal is 18 GHz. The long-term (200 s) (c) phase stability and (d) power stability (compared to mean power) of the proposed scheme at 14 GHz.
Fig. 6
Fig. 6 Spur-free dynamic range performance of the proposed scheme at 14 GHz. (IMD3: third-order intermodulation distortion).
Fig. 7
Fig. 7 Measured output power as the function of the input frequency with different modulation schemes for the LO signal.

Equations (12)

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E M = P o 8 exp( j ω o t )[ 2 m in cos( ω in t )+2 m LO cos( ω LO t ) ]
E M = P o 8 exp( j ω 0 t ) [ 2 m in cos( ω in t )cos( β 2 L ω in 2 2 ) +2 m LO cos( ω LO t )cos( β 2 L ω LO 2 2 ) ]
I = 1 4 P o R A in A LO { cos[ ( ω LO ω in )t ]+cos[ ( ω LO + ω in )t ] }cos φ 2
E M = P o 8 exp( j ω 0 t ) [ 2 A in cos( ω in t )cos( β 2 L ω in 2 2 ) + A LO exp( ω LO t+φ )cos( β 2 L ω LO 2 2 ) ]
I = 1 8 P o R A in A LO { cos[ ( ω LO ω in )t+ β 2 L 2 ( ω LO 2 ω in 2 )+φ ] +cos[ ( ω LO + ω in )t+ β 2 L 2 ( ω LO 2 ω in 2 )+φ ] }
E out1 = P o 16 { j2 J 1 ( m LO )exp[ j( ω o ω LO )tjφ ]+( 1+j ) J 0 ( m LO )exp( j ω o t ) }
E out2 = P o 16 { j J 1 ( m in )exp[ j( ω 0 ω in )t ]+( j+ J 0 ( m in ) )exp( j ω o t ) +j J 1 ( m in )exp[ j( ω 0 + ω in )t ] }
E out =j P o 16 { J 1 ( m )exp[ j( ω o ω LO )tjφ ]+ A err exp( j ω o t ) J 1 ( m )exp[ j( ω 0 ω in )t ] J 1 ( m )exp[ j( ω 0 + ω in )t ] }
I out = I C1 + I C2 + I err
I C1 = P o 16 R J 1 2 ( m )cos[ ( ω LO ω in )t+φ ]
I C2 = P o 16 R J 1 2 ( m )cos[ ( ω LO + ω in )t+φ ]
I err = P o 16 R J 1 ( m ) A err [ cos( ω LO t+φ )2cos( ω in t ) ]

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