Abstract

In this paper, we propose and experimentally demonstrate a novel wideband on-chip photonic modulation transformer for phase-modulated microwave photonic links. The proposed device is able to transform phase-modulated optical signals into intensity-modulated versions (or vice versa) with nearly zero conversion of laser phase noise to intensity noise. It is constructed using waveguide-based ring resonators, which features simple architecture, stable operation, and easy reconfigurability. Beyond the stand-alone functionality, the proposed device can also be integrated with other functional building blocks of photonic integrated circuits (PICs) to create on-chip complex microwave photonic signal processors. As an application example, a PIC consisting of two such modulation transformers and a notch filter has been designed and realized in TriPleXTM waveguide technology. The realized device uses a 2 × 2 splitting circuit and 3 ring resonators with a free spectral range of 25 GHz, which are all equipped with continuous tuning elements. The device can perform phase-to-intensity modulation transform and carrier suppression simultaneously, which enables high-performance phase-modulated microwave photonics links (PM-MPLs). Associated with the bias-free and low-complexity advantages of the phase modulators, a single-fiber-span PM-MPL with a RF bandwidth of 12 GHz (3 dB-suppression band 6 to 18 GHz) has been demonstrated comprising the proposed PIC, where the achieved spurious-free dynamic range performance is comparable to that of Class-AB MPLs using low-biased Mach-Zehnder modulators.

© 2013 Optical Society of America

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2013

2012

L. Zhuang, M. R. Khan, W. P. Beeker, A. Leinse, R. G. Heideman, and C. G. H. Roeloffzen, “Novel microwave photonic fractional Hilbert transformer using a ring resonator-based optical all-pass filter,” Opt. Express20(24), 26499–26510 (2012).
[CrossRef] [PubMed]

J. Sancho, J. Bourderionnet, J. Lloret, S. Combrié, I. Gasulla, S. Xavier, S. Sales, P. Colman, G. Lehoucq, D. Dolfi, J. Capmany, and A. De Rossi, “Integrable microwave filter based on a photonic crystal delay line,” Nat. Commun. 3, article 9 (2012).

F. Morichetti, C. Ferrari, A. Canciamilla, and A. Melloni, “The first decade of coupled resonator optical waveguide: bringing slow light to applications,” Laser Photon. Rev.6(1), 74–96 (2012).
[CrossRef]

W. Li, M. Li, and J. Yao, “A narrow-passband and frequency-tunable micro-wave photonic filter based on phase-modulation to intensity-modulation conversion using a phase shifted fiber bragg grating,” IEEE Trans. Microw. Theory Tech.60(5), 1287–1296 (2012).
[CrossRef]

2011

2010

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1, article 29 (2010).

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics4(2), 117–122 (2010).
[CrossRef]

L. Zhuang, C. G. H. Roeloffzen, A. Meijerink, M. Burla, D. A. I. Marpaung, A. Leinse, M. Hoekman, R. G. Heideman, and W. C. van Etten, “Novel ring resonator-based integrated photonic beamformer for broadband phased-array antennas-Part II: experimental prototype,” J. Lightwave Technol.28(1), 19–31 (2010).

A. Meijerink, C. G. H. Roeloffzen, R. Meijerink, L. Zhuang, D. A. I. Marpaung, M. J. Bentum, M. Burla, J. Verpoorte, P. Jorna, A. Hulzinga, and W. C. van Etten, “Novel ring resonator-based integrated photonic beamformer for broadband phased-array antennas-Part I: design and performance analysis,” J. Lightwave Technol.28(1), 3–18 (2010).
[CrossRef]

L. Liu, S. Zheng, X. Zhang, X. Jin, and H. Chi, “Performances improvement in radio over fiber link through carrier suppression using stimulated brillouin scattering,” Opt. Express18(11), 11827–11837 (2010).
[CrossRef] [PubMed]

N. N. Feng, P. Dong, D. Feng, W. Qian, H. Liang, D. C. Lee, J. B. Luff, A. Agarwal, T. Banwell, R. Menendez, P. Toliver, T. K. Woodward, and M. Asghari, “Thermally-efficient reconfigurable narrowband RF-photonic filter,” Opt. Express18(24), 24648–24653 (2010).
[CrossRef] [PubMed]

D. A. I. Marpaung, C. G. H. Roeloffzen, A. Leinse, and M. Hoekman, “A photonic chip based frequency discriminator for a high performance microwave photonic link,” Opt. Express18(26), 27359–27370 (2010).
[CrossRef] [PubMed]

2009

2008

2007

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

V. J. Urick, F. Bucholtz, P. S. Devgan, J. D. Mckinney, and K. J. Williams, “Phase modualtion with interferometric detection as an alternative to intensity modulation with direct detection for analog-photonic links,” IEEE trans. MTT55(9), 1978–1985 (2007).
[CrossRef]

2006

T. Darcie and P. Driessen, “Class-AB techniques for high-dynamic-range microwave-photonic links,” IEEE Photon. Technol. Lett.18(8), 929–931 (2006).
[CrossRef]

J. Bull, T. Darcie, J. Zhang, H. Kato, and N. Jaeger, “Broadband class-AB microwave-photonic link using polarization modulation,” IEEE Photon. Technol. Lett.18(9), 1073–1075 (2006).
[CrossRef]

1997

L. Nichols, K. Williams, and R. Estman, “Optimizing the ultrawide-band photonic link,” IEEE Trans. Microw. Theory Tech.45(8), 1384–1389 (1997).
[CrossRef]

M. J. LaGasse and S. Thaniyavarn, “Bias-free high-dynamic-range phase-modulated fiber-optic link,” IEEE Photon. Technol. Lett.9(5), 681–683 (1997).
[CrossRef]

Ackerman, E.

E. Ackerman, S. Wanuga, J. MacDonald, and J. Prince, “Balanced receiver external modulation fiber-optic link architecture with reduced noise figure,” in Proc. IEEE MTT-S Int. Microwave Symp.2, 723–726 (1993).
[CrossRef]

Agarwal, A.

Asghari, M.

Azaña, J.

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1, article 29 (2010).

Banwell, T.

Beeker, W. P.

Bentum, M. J.

Bourderionnet, J.

J. Sancho, J. Bourderionnet, J. Lloret, S. Combrié, I. Gasulla, S. Xavier, S. Sales, P. Colman, G. Lehoucq, D. Dolfi, J. Capmany, and A. De Rossi, “Integrable microwave filter based on a photonic crystal delay line,” Nat. Commun. 3, article 9 (2012).

Bucholtz, F.

V. J. Urick, F. Bucholtz, P. S. Devgan, J. D. Mckinney, and K. J. Williams, “Phase modualtion with interferometric detection as an alternative to intensity modulation with direct detection for analog-photonic links,” IEEE trans. MTT55(9), 1978–1985 (2007).
[CrossRef]

Bull, J.

J. Bull, T. Darcie, J. Zhang, H. Kato, and N. Jaeger, “Broadband class-AB microwave-photonic link using polarization modulation,” IEEE Photon. Technol. Lett.18(9), 1073–1075 (2006).
[CrossRef]

Burla, M.

M. Burla, D. A. I. Marpaung, L. Zhuang, C. G. H. Roeloffzen, M. R. Khan, A. Leinse, M. Hoekman, and R. G. Heideman, “On-chip CMOS compatible reconfigurable optical delay line with separate carrier tuning for microwave photonic signal processing,” Opt. Express19(22), 21475–21484 (2011).
[CrossRef] [PubMed]

D. A. I. Marpaung, L. Chevalier, M. Burla, and C. G. H. Roeloffzen, “Impulse radio ultrawideband pulse shaper based on a programmable photonic chip frequency discriminator,” Opt. Express19(25), 24838–24848 (2011).
[CrossRef] [PubMed]

L. Zhuang, D. A. I. Marpaung, M. Burla, W. P. Beeker, A. Leinse, and C. G. H. Roeloffzen, “Low-loss, high-index-contrast Si₃N₄/SiO₂ optical waveguides for optical delay lines in microwave photonics signal processing,” Opt. Express19(23), 23162–23170 (2011).
[CrossRef] [PubMed]

A. Meijerink, C. G. H. Roeloffzen, R. Meijerink, L. Zhuang, D. A. I. Marpaung, M. J. Bentum, M. Burla, J. Verpoorte, P. Jorna, A. Hulzinga, and W. C. van Etten, “Novel ring resonator-based integrated photonic beamformer for broadband phased-array antennas-Part I: design and performance analysis,” J. Lightwave Technol.28(1), 3–18 (2010).
[CrossRef]

L. Zhuang, C. G. H. Roeloffzen, A. Meijerink, M. Burla, D. A. I. Marpaung, A. Leinse, M. Hoekman, R. G. Heideman, and W. C. van Etten, “Novel ring resonator-based integrated photonic beamformer for broadband phased-array antennas-Part II: experimental prototype,” J. Lightwave Technol.28(1), 19–31 (2010).

Canciamilla, A.

A. Perentos, F. Cuesta-Soto, A. Canciamilla, B. Vidal, L. Pierno, N. S. Losilla, F. Lopez-Royo, A. Melloni, and S. Iezekiel, “Using a Si3N4 ring resonator notch filter for optical carrier reduction and modulation depth enhancement in radio-over-fiber links,” IEEE Photon. J. 5(1), 5500110 (2013).

F. Morichetti, C. Ferrari, A. Canciamilla, and A. Melloni, “The first decade of coupled resonator optical waveguide: bringing slow light to applications,” Laser Photon. Rev.6(1), 74–96 (2012).
[CrossRef]

Capmany, J.

J. S. Fandiño, J. D. Doménech, P. Muñoz, and J. Capmany, “Integrated InP frequency discriminator for Phase-modulated microwave photonic links,” Opt. Express21(3), 3726–3736 (2013).
[CrossRef] [PubMed]

J. Sancho, J. Bourderionnet, J. Lloret, S. Combrié, I. Gasulla, S. Xavier, S. Sales, P. Colman, G. Lehoucq, D. Dolfi, J. Capmany, and A. De Rossi, “Integrable microwave filter based on a photonic crystal delay line,” Nat. Commun. 3, article 9 (2012).

J. Lloret, J. Sancho, M. Pu, I. Gasulla, K. Yvind, S. Sales, and J. Capmany, “Tunable complex-valued multi-tap microwave photonic filter based on single silicon-on-insulator microring resonator,” Opt. Express19(13), 12402–12407 (2011).
[CrossRef] [PubMed]

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

Chevalier, L.

Chi, H.

Choi, D. Y.

Chu, S. T.

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1, article 29 (2010).

Colman, P.

J. Sancho, J. Bourderionnet, J. Lloret, S. Combrié, I. Gasulla, S. Xavier, S. Sales, P. Colman, G. Lehoucq, D. Dolfi, J. Capmany, and A. De Rossi, “Integrable microwave filter based on a photonic crystal delay line,” Nat. Commun. 3, article 9 (2012).

Combrié, S.

J. Sancho, J. Bourderionnet, J. Lloret, S. Combrié, I. Gasulla, S. Xavier, S. Sales, P. Colman, G. Lehoucq, D. Dolfi, J. Capmany, and A. De Rossi, “Integrable microwave filter based on a photonic crystal delay line,” Nat. Commun. 3, article 9 (2012).

Cuesta-Soto, F.

A. Perentos, F. Cuesta-Soto, A. Canciamilla, B. Vidal, L. Pierno, N. S. Losilla, F. Lopez-Royo, A. Melloni, and S. Iezekiel, “Using a Si3N4 ring resonator notch filter for optical carrier reduction and modulation depth enhancement in radio-over-fiber links,” IEEE Photon. J. 5(1), 5500110 (2013).

Darcie, T.

T. Darcie and P. Driessen, “Class-AB techniques for high-dynamic-range microwave-photonic links,” IEEE Photon. Technol. Lett.18(8), 929–931 (2006).
[CrossRef]

J. Bull, T. Darcie, J. Zhang, H. Kato, and N. Jaeger, “Broadband class-AB microwave-photonic link using polarization modulation,” IEEE Photon. Technol. Lett.18(9), 1073–1075 (2006).
[CrossRef]

De Rossi, A.

J. Sancho, J. Bourderionnet, J. Lloret, S. Combrié, I. Gasulla, S. Xavier, S. Sales, P. Colman, G. Lehoucq, D. Dolfi, J. Capmany, and A. De Rossi, “Integrable microwave filter based on a photonic crystal delay line,” Nat. Commun. 3, article 9 (2012).

Devgan, P. S.

V. J. Urick, F. Bucholtz, P. S. Devgan, J. D. Mckinney, and K. J. Williams, “Phase modualtion with interferometric detection as an alternative to intensity modulation with direct detection for analog-photonic links,” IEEE trans. MTT55(9), 1978–1985 (2007).
[CrossRef]

Dolfi, D.

J. Sancho, J. Bourderionnet, J. Lloret, S. Combrié, I. Gasulla, S. Xavier, S. Sales, P. Colman, G. Lehoucq, D. Dolfi, J. Capmany, and A. De Rossi, “Integrable microwave filter based on a photonic crystal delay line,” Nat. Commun. 3, article 9 (2012).

Doménech, J. D.

Dong, P.

Driessen, P.

T. Darcie and P. Driessen, “Class-AB techniques for high-dynamic-range microwave-photonic links,” IEEE Photon. Technol. Lett.18(8), 929–931 (2006).
[CrossRef]

Eggleton, B. J.

Estman, R.

L. Nichols, K. Williams, and R. Estman, “Optimizing the ultrawide-band photonic link,” IEEE Trans. Microw. Theory Tech.45(8), 1384–1389 (1997).
[CrossRef]

Fandiño, J. S.

Feng, D.

Feng, N. N.

Ferrari, C.

F. Morichetti, C. Ferrari, A. Canciamilla, and A. Melloni, “The first decade of coupled resonator optical waveguide: bringing slow light to applications,” Laser Photon. Rev.6(1), 74–96 (2012).
[CrossRef]

Ferrera, M.

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1, article 29 (2010).

Gao, F.

Gasulla, I.

J. Sancho, J. Bourderionnet, J. Lloret, S. Combrié, I. Gasulla, S. Xavier, S. Sales, P. Colman, G. Lehoucq, D. Dolfi, J. Capmany, and A. De Rossi, “Integrable microwave filter based on a photonic crystal delay line,” Nat. Commun. 3, article 9 (2012).

J. Lloret, J. Sancho, M. Pu, I. Gasulla, K. Yvind, S. Sales, and J. Capmany, “Tunable complex-valued multi-tap microwave photonic filter based on single silicon-on-insulator microring resonator,” Opt. Express19(13), 12402–12407 (2011).
[CrossRef] [PubMed]

Heideman, R. G.

Hoekman, M.

Hulzinga, A.

Iezekiel, S.

A. Perentos, F. Cuesta-Soto, A. Canciamilla, B. Vidal, L. Pierno, N. S. Losilla, F. Lopez-Royo, A. Melloni, and S. Iezekiel, “Using a Si3N4 ring resonator notch filter for optical carrier reduction and modulation depth enhancement in radio-over-fiber links,” IEEE Photon. J. 5(1), 5500110 (2013).

Jaeger, N.

J. Bull, T. Darcie, J. Zhang, H. Kato, and N. Jaeger, “Broadband class-AB microwave-photonic link using polarization modulation,” IEEE Photon. Technol. Lett.18(9), 1073–1075 (2006).
[CrossRef]

Jin, X.

Jorna, P.

Kato, H.

J. Bull, T. Darcie, J. Zhang, H. Kato, and N. Jaeger, “Broadband class-AB microwave-photonic link using polarization modulation,” IEEE Photon. Technol. Lett.18(9), 1073–1075 (2006).
[CrossRef]

Khan, M. H.

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics4(2), 117–122 (2010).
[CrossRef]

Khan, M. R.

LaGasse, M. J.

M. J. LaGasse and S. Thaniyavarn, “Bias-free high-dynamic-range phase-modulated fiber-optic link,” IEEE Photon. Technol. Lett.9(5), 681–683 (1997).
[CrossRef]

Leaird, D. E.

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics4(2), 117–122 (2010).
[CrossRef]

Lee, D. C.

Lehoucq, G.

J. Sancho, J. Bourderionnet, J. Lloret, S. Combrié, I. Gasulla, S. Xavier, S. Sales, P. Colman, G. Lehoucq, D. Dolfi, J. Capmany, and A. De Rossi, “Integrable microwave filter based on a photonic crystal delay line,” Nat. Commun. 3, article 9 (2012).

Leinse, A.

L. Zhuang, W. P. Beeker, A. Leinse, R. G. Heideman, P. van Dijk, and C. Roeloffzen, “Novel wideband microwave polarization network using a fully-reconfigurable photonic waveguide interleaver with a two-ring resonator-assisted asymmetric Mach-Zehnder structure,” Opt. Express21(3), 3114–3124 (2013).
[CrossRef] [PubMed]

L. Zhuang, M. R. Khan, W. P. Beeker, A. Leinse, R. G. Heideman, and C. G. H. Roeloffzen, “Novel microwave photonic fractional Hilbert transformer using a ring resonator-based optical all-pass filter,” Opt. Express20(24), 26499–26510 (2012).
[CrossRef] [PubMed]

M. Burla, D. A. I. Marpaung, L. Zhuang, C. G. H. Roeloffzen, M. R. Khan, A. Leinse, M. Hoekman, and R. G. Heideman, “On-chip CMOS compatible reconfigurable optical delay line with separate carrier tuning for microwave photonic signal processing,” Opt. Express19(22), 21475–21484 (2011).
[CrossRef] [PubMed]

L. Zhuang, D. A. I. Marpaung, M. Burla, W. P. Beeker, A. Leinse, and C. G. H. Roeloffzen, “Low-loss, high-index-contrast Si₃N₄/SiO₂ optical waveguides for optical delay lines in microwave photonics signal processing,” Opt. Express19(23), 23162–23170 (2011).
[CrossRef] [PubMed]

D. A. I. Marpaung, C. G. H. Roeloffzen, A. Leinse, and M. Hoekman, “A photonic chip based frequency discriminator for a high performance microwave photonic link,” Opt. Express18(26), 27359–27370 (2010).
[CrossRef] [PubMed]

L. Zhuang, C. G. H. Roeloffzen, A. Meijerink, M. Burla, D. A. I. Marpaung, A. Leinse, M. Hoekman, R. G. Heideman, and W. C. van Etten, “Novel ring resonator-based integrated photonic beamformer for broadband phased-array antennas-Part II: experimental prototype,” J. Lightwave Technol.28(1), 19–31 (2010).

Li, E.

Li, M.

W. Li, M. Li, and J. Yao, “A narrow-passband and frequency-tunable micro-wave photonic filter based on phase-modulation to intensity-modulation conversion using a phase shifted fiber bragg grating,” IEEE Trans. Microw. Theory Tech.60(5), 1287–1296 (2012).
[CrossRef]

Li, W.

W. Li, M. Li, and J. Yao, “A narrow-passband and frequency-tunable micro-wave photonic filter based on phase-modulation to intensity-modulation conversion using a phase shifted fiber bragg grating,” IEEE Trans. Microw. Theory Tech.60(5), 1287–1296 (2012).
[CrossRef]

Liang, H.

Little, B. E.

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1, article 29 (2010).

Liu, F.

Liu, L.

Lloret, J.

J. Sancho, J. Bourderionnet, J. Lloret, S. Combrié, I. Gasulla, S. Xavier, S. Sales, P. Colman, G. Lehoucq, D. Dolfi, J. Capmany, and A. De Rossi, “Integrable microwave filter based on a photonic crystal delay line,” Nat. Commun. 3, article 9 (2012).

J. Lloret, J. Sancho, M. Pu, I. Gasulla, K. Yvind, S. Sales, and J. Capmany, “Tunable complex-valued multi-tap microwave photonic filter based on single silicon-on-insulator microring resonator,” Opt. Express19(13), 12402–12407 (2011).
[CrossRef] [PubMed]

Lopez-Royo, F.

A. Perentos, F. Cuesta-Soto, A. Canciamilla, B. Vidal, L. Pierno, N. S. Losilla, F. Lopez-Royo, A. Melloni, and S. Iezekiel, “Using a Si3N4 ring resonator notch filter for optical carrier reduction and modulation depth enhancement in radio-over-fiber links,” IEEE Photon. J. 5(1), 5500110 (2013).

Losilla, N. S.

A. Perentos, F. Cuesta-Soto, A. Canciamilla, B. Vidal, L. Pierno, N. S. Losilla, F. Lopez-Royo, A. Melloni, and S. Iezekiel, “Using a Si3N4 ring resonator notch filter for optical carrier reduction and modulation depth enhancement in radio-over-fiber links,” IEEE Photon. J. 5(1), 5500110 (2013).

Luff, J. B.

Luther-Davies, B.

MacDonald, J.

E. Ackerman, S. Wanuga, J. MacDonald, and J. Prince, “Balanced receiver external modulation fiber-optic link architecture with reduced noise figure,” in Proc. IEEE MTT-S Int. Microwave Symp.2, 723–726 (1993).
[CrossRef]

Madden, S.

Marpaung, D. A. I.

K. Tan, D. A. I. Marpaung, R. Pant, F. Gao, E. Li, J. Wang, D. Y. Choi, S. Madden, B. Luther-Davies, J. Sun, and B. J. Eggleton, “Photonic-chip-based all-optical ultra-wideband pulse generation via XPM and birefringence in a chalcogenide waveguide,” Opt. Express21(2), 2003–2011 (2013).
[CrossRef] [PubMed]

M. Burla, D. A. I. Marpaung, L. Zhuang, C. G. H. Roeloffzen, M. R. Khan, A. Leinse, M. Hoekman, and R. G. Heideman, “On-chip CMOS compatible reconfigurable optical delay line with separate carrier tuning for microwave photonic signal processing,” Opt. Express19(22), 21475–21484 (2011).
[CrossRef] [PubMed]

D. A. I. Marpaung, L. Chevalier, M. Burla, and C. G. H. Roeloffzen, “Impulse radio ultrawideband pulse shaper based on a programmable photonic chip frequency discriminator,” Opt. Express19(25), 24838–24848 (2011).
[CrossRef] [PubMed]

L. Zhuang, D. A. I. Marpaung, M. Burla, W. P. Beeker, A. Leinse, and C. G. H. Roeloffzen, “Low-loss, high-index-contrast Si₃N₄/SiO₂ optical waveguides for optical delay lines in microwave photonics signal processing,” Opt. Express19(23), 23162–23170 (2011).
[CrossRef] [PubMed]

A. Meijerink, C. G. H. Roeloffzen, R. Meijerink, L. Zhuang, D. A. I. Marpaung, M. J. Bentum, M. Burla, J. Verpoorte, P. Jorna, A. Hulzinga, and W. C. van Etten, “Novel ring resonator-based integrated photonic beamformer for broadband phased-array antennas-Part I: design and performance analysis,” J. Lightwave Technol.28(1), 3–18 (2010).
[CrossRef]

D. A. I. Marpaung, C. G. H. Roeloffzen, A. Leinse, and M. Hoekman, “A photonic chip based frequency discriminator for a high performance microwave photonic link,” Opt. Express18(26), 27359–27370 (2010).
[CrossRef] [PubMed]

L. Zhuang, C. G. H. Roeloffzen, A. Meijerink, M. Burla, D. A. I. Marpaung, A. Leinse, M. Hoekman, R. G. Heideman, and W. C. van Etten, “Novel ring resonator-based integrated photonic beamformer for broadband phased-array antennas-Part II: experimental prototype,” J. Lightwave Technol.28(1), 19–31 (2010).

Mckinney, J. D.

V. J. Urick, F. Bucholtz, P. S. Devgan, J. D. Mckinney, and K. J. Williams, “Phase modualtion with interferometric detection as an alternative to intensity modulation with direct detection for analog-photonic links,” IEEE trans. MTT55(9), 1978–1985 (2007).
[CrossRef]

Meijerink, A.

Meijerink, R.

Melloni, A.

A. Perentos, F. Cuesta-Soto, A. Canciamilla, B. Vidal, L. Pierno, N. S. Losilla, F. Lopez-Royo, A. Melloni, and S. Iezekiel, “Using a Si3N4 ring resonator notch filter for optical carrier reduction and modulation depth enhancement in radio-over-fiber links,” IEEE Photon. J. 5(1), 5500110 (2013).

F. Morichetti, C. Ferrari, A. Canciamilla, and A. Melloni, “The first decade of coupled resonator optical waveguide: bringing slow light to applications,” Laser Photon. Rev.6(1), 74–96 (2012).
[CrossRef]

Menendez, R.

Morandotti, R.

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1, article 29 (2010).

Morichetti, F.

F. Morichetti, C. Ferrari, A. Canciamilla, and A. Melloni, “The first decade of coupled resonator optical waveguide: bringing slow light to applications,” Laser Photon. Rev.6(1), 74–96 (2012).
[CrossRef]

Moss, D. J.

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1, article 29 (2010).

Muñoz, P.

Nichols, L.

L. Nichols, K. Williams, and R. Estman, “Optimizing the ultrawide-band photonic link,” IEEE Trans. Microw. Theory Tech.45(8), 1384–1389 (1997).
[CrossRef]

Novak, D.

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

Pant, R.

Park, Y.

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1, article 29 (2010).

Perentos, A.

A. Perentos, F. Cuesta-Soto, A. Canciamilla, B. Vidal, L. Pierno, N. S. Losilla, F. Lopez-Royo, A. Melloni, and S. Iezekiel, “Using a Si3N4 ring resonator notch filter for optical carrier reduction and modulation depth enhancement in radio-over-fiber links,” IEEE Photon. J. 5(1), 5500110 (2013).

Pierno, L.

A. Perentos, F. Cuesta-Soto, A. Canciamilla, B. Vidal, L. Pierno, N. S. Losilla, F. Lopez-Royo, A. Melloni, and S. Iezekiel, “Using a Si3N4 ring resonator notch filter for optical carrier reduction and modulation depth enhancement in radio-over-fiber links,” IEEE Photon. J. 5(1), 5500110 (2013).

Prince, J.

E. Ackerman, S. Wanuga, J. MacDonald, and J. Prince, “Balanced receiver external modulation fiber-optic link architecture with reduced noise figure,” in Proc. IEEE MTT-S Int. Microwave Symp.2, 723–726 (1993).
[CrossRef]

Pu, M.

Qi, M.

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics4(2), 117–122 (2010).
[CrossRef]

Qian, W.

Qiang, L.

Qiu, M.

Razzari, L.

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1, article 29 (2010).

Roeloffzen, C.

Roeloffzen, C. G. H.

L. Zhuang, M. R. Khan, W. P. Beeker, A. Leinse, R. G. Heideman, and C. G. H. Roeloffzen, “Novel microwave photonic fractional Hilbert transformer using a ring resonator-based optical all-pass filter,” Opt. Express20(24), 26499–26510 (2012).
[CrossRef] [PubMed]

M. Burla, D. A. I. Marpaung, L. Zhuang, C. G. H. Roeloffzen, M. R. Khan, A. Leinse, M. Hoekman, and R. G. Heideman, “On-chip CMOS compatible reconfigurable optical delay line with separate carrier tuning for microwave photonic signal processing,” Opt. Express19(22), 21475–21484 (2011).
[CrossRef] [PubMed]

D. A. I. Marpaung, L. Chevalier, M. Burla, and C. G. H. Roeloffzen, “Impulse radio ultrawideband pulse shaper based on a programmable photonic chip frequency discriminator,” Opt. Express19(25), 24838–24848 (2011).
[CrossRef] [PubMed]

L. Zhuang, D. A. I. Marpaung, M. Burla, W. P. Beeker, A. Leinse, and C. G. H. Roeloffzen, “Low-loss, high-index-contrast Si₃N₄/SiO₂ optical waveguides for optical delay lines in microwave photonics signal processing,” Opt. Express19(23), 23162–23170 (2011).
[CrossRef] [PubMed]

A. Meijerink, C. G. H. Roeloffzen, R. Meijerink, L. Zhuang, D. A. I. Marpaung, M. J. Bentum, M. Burla, J. Verpoorte, P. Jorna, A. Hulzinga, and W. C. van Etten, “Novel ring resonator-based integrated photonic beamformer for broadband phased-array antennas-Part I: design and performance analysis,” J. Lightwave Technol.28(1), 3–18 (2010).
[CrossRef]

D. A. I. Marpaung, C. G. H. Roeloffzen, A. Leinse, and M. Hoekman, “A photonic chip based frequency discriminator for a high performance microwave photonic link,” Opt. Express18(26), 27359–27370 (2010).
[CrossRef] [PubMed]

L. Zhuang, C. G. H. Roeloffzen, A. Meijerink, M. Burla, D. A. I. Marpaung, A. Leinse, M. Hoekman, R. G. Heideman, and W. C. van Etten, “Novel ring resonator-based integrated photonic beamformer for broadband phased-array antennas-Part II: experimental prototype,” J. Lightwave Technol.28(1), 19–31 (2010).

Sales, S.

J. Sancho, J. Bourderionnet, J. Lloret, S. Combrié, I. Gasulla, S. Xavier, S. Sales, P. Colman, G. Lehoucq, D. Dolfi, J. Capmany, and A. De Rossi, “Integrable microwave filter based on a photonic crystal delay line,” Nat. Commun. 3, article 9 (2012).

J. Lloret, J. Sancho, M. Pu, I. Gasulla, K. Yvind, S. Sales, and J. Capmany, “Tunable complex-valued multi-tap microwave photonic filter based on single silicon-on-insulator microring resonator,” Opt. Express19(13), 12402–12407 (2011).
[CrossRef] [PubMed]

Sancho, J.

J. Sancho, J. Bourderionnet, J. Lloret, S. Combrié, I. Gasulla, S. Xavier, S. Sales, P. Colman, G. Lehoucq, D. Dolfi, J. Capmany, and A. De Rossi, “Integrable microwave filter based on a photonic crystal delay line,” Nat. Commun. 3, article 9 (2012).

J. Lloret, J. Sancho, M. Pu, I. Gasulla, K. Yvind, S. Sales, and J. Capmany, “Tunable complex-valued multi-tap microwave photonic filter based on single silicon-on-insulator microring resonator,” Opt. Express19(13), 12402–12407 (2011).
[CrossRef] [PubMed]

Shen, H.

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics4(2), 117–122 (2010).
[CrossRef]

Su, Y.

Sun, J.

Tan, K.

Thaniyavarn, S.

M. J. LaGasse and S. Thaniyavarn, “Bias-free high-dynamic-range phase-modulated fiber-optic link,” IEEE Photon. Technol. Lett.9(5), 681–683 (1997).
[CrossRef]

Toliver, P.

Urick, V. J.

V. J. Urick, F. Bucholtz, P. S. Devgan, J. D. Mckinney, and K. J. Williams, “Phase modualtion with interferometric detection as an alternative to intensity modulation with direct detection for analog-photonic links,” IEEE trans. MTT55(9), 1978–1985 (2007).
[CrossRef]

van Dijk, P.

van Etten, W. C.

Verpoorte, J.

Vidal, B.

A. Perentos, F. Cuesta-Soto, A. Canciamilla, B. Vidal, L. Pierno, N. S. Losilla, F. Lopez-Royo, A. Melloni, and S. Iezekiel, “Using a Si3N4 ring resonator notch filter for optical carrier reduction and modulation depth enhancement in radio-over-fiber links,” IEEE Photon. J. 5(1), 5500110 (2013).

Wang, J.

Wang, T.

Wanuga, S.

E. Ackerman, S. Wanuga, J. MacDonald, and J. Prince, “Balanced receiver external modulation fiber-optic link architecture with reduced noise figure,” in Proc. IEEE MTT-S Int. Microwave Symp.2, 723–726 (1993).
[CrossRef]

Weiner, A. M.

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics4(2), 117–122 (2010).
[CrossRef]

Williams, K.

L. Nichols, K. Williams, and R. Estman, “Optimizing the ultrawide-band photonic link,” IEEE Trans. Microw. Theory Tech.45(8), 1384–1389 (1997).
[CrossRef]

Williams, K. J.

V. J. Urick, F. Bucholtz, P. S. Devgan, J. D. Mckinney, and K. J. Williams, “Phase modualtion with interferometric detection as an alternative to intensity modulation with direct detection for analog-photonic links,” IEEE trans. MTT55(9), 1978–1985 (2007).
[CrossRef]

Woodward, T. K.

Xavier, S.

J. Sancho, J. Bourderionnet, J. Lloret, S. Combrié, I. Gasulla, S. Xavier, S. Sales, P. Colman, G. Lehoucq, D. Dolfi, J. Capmany, and A. De Rossi, “Integrable microwave filter based on a photonic crystal delay line,” Nat. Commun. 3, article 9 (2012).

Xiao, S.

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics4(2), 117–122 (2010).
[CrossRef]

Xuan, Y.

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics4(2), 117–122 (2010).
[CrossRef]

Yao, J.

W. Li, M. Li, and J. Yao, “A narrow-passband and frequency-tunable micro-wave photonic filter based on phase-modulation to intensity-modulation conversion using a phase shifted fiber bragg grating,” IEEE Trans. Microw. Theory Tech.60(5), 1287–1296 (2012).
[CrossRef]

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

H. Chi, X. Zou, and J. Yao, “Analytical models for phase-modulation-based microwave photonic systems with phase modualtion to intensity modulation conversion using a dispersive device,” J. Lightwave Technol.27(5), 511–521 (2009).
[CrossRef]

Ye, T.

Yvind, K.

Zhang, J.

J. Bull, T. Darcie, J. Zhang, H. Kato, and N. Jaeger, “Broadband class-AB microwave-photonic link using polarization modulation,” IEEE Photon. Technol. Lett.18(9), 1073–1075 (2006).
[CrossRef]

Zhang, X.

Zhang, Z.

Zhao, L.

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics4(2), 117–122 (2010).
[CrossRef]

Zheng, S.

Zhuang, L.

L. Zhuang, W. P. Beeker, A. Leinse, R. G. Heideman, P. van Dijk, and C. Roeloffzen, “Novel wideband microwave polarization network using a fully-reconfigurable photonic waveguide interleaver with a two-ring resonator-assisted asymmetric Mach-Zehnder structure,” Opt. Express21(3), 3114–3124 (2013).
[CrossRef] [PubMed]

L. Zhuang, M. R. Khan, W. P. Beeker, A. Leinse, R. G. Heideman, and C. G. H. Roeloffzen, “Novel microwave photonic fractional Hilbert transformer using a ring resonator-based optical all-pass filter,” Opt. Express20(24), 26499–26510 (2012).
[CrossRef] [PubMed]

M. Burla, D. A. I. Marpaung, L. Zhuang, C. G. H. Roeloffzen, M. R. Khan, A. Leinse, M. Hoekman, and R. G. Heideman, “On-chip CMOS compatible reconfigurable optical delay line with separate carrier tuning for microwave photonic signal processing,” Opt. Express19(22), 21475–21484 (2011).
[CrossRef] [PubMed]

L. Zhuang, D. A. I. Marpaung, M. Burla, W. P. Beeker, A. Leinse, and C. G. H. Roeloffzen, “Low-loss, high-index-contrast Si₃N₄/SiO₂ optical waveguides for optical delay lines in microwave photonics signal processing,” Opt. Express19(23), 23162–23170 (2011).
[CrossRef] [PubMed]

A. Meijerink, C. G. H. Roeloffzen, R. Meijerink, L. Zhuang, D. A. I. Marpaung, M. J. Bentum, M. Burla, J. Verpoorte, P. Jorna, A. Hulzinga, and W. C. van Etten, “Novel ring resonator-based integrated photonic beamformer for broadband phased-array antennas-Part I: design and performance analysis,” J. Lightwave Technol.28(1), 3–18 (2010).
[CrossRef]

L. Zhuang, C. G. H. Roeloffzen, A. Meijerink, M. Burla, D. A. I. Marpaung, A. Leinse, M. Hoekman, R. G. Heideman, and W. C. van Etten, “Novel ring resonator-based integrated photonic beamformer for broadband phased-array antennas-Part II: experimental prototype,” J. Lightwave Technol.28(1), 19–31 (2010).

Zou, X.

IEEE Photon. Technol. Lett.

M. J. LaGasse and S. Thaniyavarn, “Bias-free high-dynamic-range phase-modulated fiber-optic link,” IEEE Photon. Technol. Lett.9(5), 681–683 (1997).
[CrossRef]

T. Darcie and P. Driessen, “Class-AB techniques for high-dynamic-range microwave-photonic links,” IEEE Photon. Technol. Lett.18(8), 929–931 (2006).
[CrossRef]

J. Bull, T. Darcie, J. Zhang, H. Kato, and N. Jaeger, “Broadband class-AB microwave-photonic link using polarization modulation,” IEEE Photon. Technol. Lett.18(9), 1073–1075 (2006).
[CrossRef]

IEEE Trans. Microw. Theory Tech.

L. Nichols, K. Williams, and R. Estman, “Optimizing the ultrawide-band photonic link,” IEEE Trans. Microw. Theory Tech.45(8), 1384–1389 (1997).
[CrossRef]

W. Li, M. Li, and J. Yao, “A narrow-passband and frequency-tunable micro-wave photonic filter based on phase-modulation to intensity-modulation conversion using a phase shifted fiber bragg grating,” IEEE Trans. Microw. Theory Tech.60(5), 1287–1296 (2012).
[CrossRef]

IEEE trans. MTT

V. J. Urick, F. Bucholtz, P. S. Devgan, J. D. Mckinney, and K. J. Williams, “Phase modualtion with interferometric detection as an alternative to intensity modulation with direct detection for analog-photonic links,” IEEE trans. MTT55(9), 1978–1985 (2007).
[CrossRef]

Integrable microwave filter based on a photonic crystal delay line

J. Sancho, J. Bourderionnet, J. Lloret, S. Combrié, I. Gasulla, S. Xavier, S. Sales, P. Colman, G. Lehoucq, D. Dolfi, J. Capmany, and A. De Rossi, “Integrable microwave filter based on a photonic crystal delay line,” Nat. Commun. 3, article 9 (2012).

J. Lightwave Technol.

Laser Photon. Rev.

F. Morichetti, C. Ferrari, A. Canciamilla, and A. Melloni, “The first decade of coupled resonator optical waveguide: bringing slow light to applications,” Laser Photon. Rev.6(1), 74–96 (2012).
[CrossRef]

Nat. Photonics

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

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics4(2), 117–122 (2010).
[CrossRef]

On-chip CMOS-compatible all-optical integrator

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1, article 29 (2010).

Opt. Express

L. Liu, S. Zheng, X. Zhang, X. Jin, and H. Chi, “Performances improvement in radio over fiber link through carrier suppression using stimulated brillouin scattering,” Opt. Express18(11), 11827–11837 (2010).
[CrossRef] [PubMed]

N. N. Feng, P. Dong, D. Feng, W. Qian, H. Liang, D. C. Lee, J. B. Luff, A. Agarwal, T. Banwell, R. Menendez, P. Toliver, T. K. Woodward, and M. Asghari, “Thermally-efficient reconfigurable narrowband RF-photonic filter,” Opt. Express18(24), 24648–24653 (2010).
[CrossRef] [PubMed]

D. A. I. Marpaung, C. G. H. Roeloffzen, A. Leinse, and M. Hoekman, “A photonic chip based frequency discriminator for a high performance microwave photonic link,” Opt. Express18(26), 27359–27370 (2010).
[CrossRef] [PubMed]

J. Lloret, J. Sancho, M. Pu, I. Gasulla, K. Yvind, S. Sales, and J. Capmany, “Tunable complex-valued multi-tap microwave photonic filter based on single silicon-on-insulator microring resonator,” Opt. Express19(13), 12402–12407 (2011).
[CrossRef] [PubMed]

M. Burla, D. A. I. Marpaung, L. Zhuang, C. G. H. Roeloffzen, M. R. Khan, A. Leinse, M. Hoekman, and R. G. Heideman, “On-chip CMOS compatible reconfigurable optical delay line with separate carrier tuning for microwave photonic signal processing,” Opt. Express19(22), 21475–21484 (2011).
[CrossRef] [PubMed]

L. Zhuang, D. A. I. Marpaung, M. Burla, W. P. Beeker, A. Leinse, and C. G. H. Roeloffzen, “Low-loss, high-index-contrast Si₃N₄/SiO₂ optical waveguides for optical delay lines in microwave photonics signal processing,” Opt. Express19(23), 23162–23170 (2011).
[CrossRef] [PubMed]

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L. Zhuang, W. P. Beeker, A. Leinse, R. G. Heideman, P. van Dijk, and C. Roeloffzen, “Novel wideband microwave polarization network using a fully-reconfigurable photonic waveguide interleaver with a two-ring resonator-assisted asymmetric Mach-Zehnder structure,” Opt. Express21(3), 3114–3124 (2013).
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Using a Si3N4 ring resonator notch filter for optical carrier reduction and modulation depth enhancement in radio-over-fiber links

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Other

A. Leinse, R. G. Heideman, M. Hoekman, F. Schreuder, F. Falke, C. G. H. Roeloffzen, L. Zhuang, M. Burla, D. A. I. Marpaung, D. H. Geuzebroek, R. Dekker, E. J. Klein, P. W. L. van Dijk, and R. M. Oldenbeuving, “TriPleX waveguide platform: low-loss technology over a wide wavelength range,” In: Proceedings of SPIE Optics & Optoelectronics 8767, (Proceedings of Integrated Photonics: Materials, Devices, and Applications II), 1–13 (2013).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Phase-domain illustration of modulation transform between PM and IM by means of sideband phase manipulation.

Fig. 2
Fig. 2

(a) a schematic of a RR and the simulated power transmissions; (b) simulated phase responses of the RR and the corresponding phase-jump approximations; (c) a demonstration of frequency shift by varing θ; (d) an illustration of two phase response configurations to implement Case 1 and Case 2 of Fig. 1.

Fig. 3
Fig. 3

(a-c) system architectures and the phase-domain signal spectrum schematics of the proposed PM-MPL using RR-based modulation transformers and notch filter.

Fig. 4
Fig. 4

(a) simulated equivalent RF power transmissions of the RR-based modulation transformer for different values of Δν, where κ = 0.87 and r = 1 are considered, (b) the 3-dB RF bandwidth and maximum passband transmission versus Δν.

Fig. 5
Fig. 5

Calculated RIP3PM-RR as a function of the normalized RF frequency, where device parameters κ = 0.87, r = 0.96, and Δν = 0.4π are considered.

Fig. 6
Fig. 6

(a) schematic and (b) mask layout of the proposed modulation transformer PIC, which is part of a complex MWP signal processor chip realizaed in TriPleXTM waveguide technology; (c) a photo of the packaged chip with full optical and electrical connections.

Fig. 7
Fig. 7

(a) measurement setup for the characterizations of the PIC, (b) measurement setup for the characterization of link performance.

Fig. 8
Fig. 8

(a) frequency response of the RRs optimized for the modulation transformer functionality, (b) demonstration of the relative positions of the resonance frequencies (transmission dips or group delay peaks) of the three RRs in the PIC.

Fig. 9
Fig. 9

(a) detected RF signals at the output of the balanced photodetector; (b) demonstration of RF bandwidth dependency on Δf in comparison to the simulations; (c) demonstration of an extra RF gain achieved by performing carrier suppression technique.

Fig. 10
Fig. 10

Two-tone transmission measurements of the realized PM-PML with RF frequencies of 10 GHz ± 25 MHz for two different system parameter settings (black and blue), in comparison to a (red) theoretical calculation.

Fig. 11
Fig. 11

(a) measured RIP3PM-RR of the realized PM-MPL for different RF frequencies; (b) optical intensity noise measurements regarding a RR-based modulation transformer and an optical attenuator with equal insertion loss. In the setup, a laser with a RIN of −160 dB/Hz and a linewidth of 1 MHz was employed, and an EDFA was used to boost the input optical power at the detector.

Tables (1)

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Table 1 Link performance metrics

Equations (14)

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E MZM-Q ( t ) = E in L cos ( π 4 + m MZM cos ( 2 π f RF t + ϕ RF ) ) = E in L / 2 [ cos ( m MZM cos ( 2 π f RF t + ϕ RF ) ) sin ( m MZM cos ( 2 π f RF t + ϕ RF ) ) ] = E in L / 2 [ k = exp ( j π 2 2 k ) J 2 k ( m MZM ) exp ( j 2 k ( 2 π f RF t + ϕ RF ) ) + j k = exp ( j π 2 ( 2 k + 1 ) ) J 2 k + 1 ( m MZM ) exp ( j( 2 k + 1 ) ( 2 π f RF t + ϕ RF ) ) ]
E PM ( t ) = E in L exp ( j m PM cos ( 2 π f R F t + ϕ RF ) ) = E in L k = j k J k ( m PM ) exp ( j k ( 2 π f R F t + ϕ RF ) )
E MZM-Q ( t ) = η MZM [ J 0 ( m MZM ) + J 1 ( m MZM ) exp ( j 2 π f RF t ) J 1 ( m MZM ) exp ( j 2 π f RF t ) J 2 ( m MZM ) exp ( j2π2 f RF t ) J 2 ( m MZM ) exp ( j2π2 f RF t ) ]
E PM ( t ) = η PM [ J 0 ( m PM ) J 1 ( m PM ) exp ( j 2 π f RF t ) J 1 ( m PM ) exp ( j 2 π f RF t ) + J 2 ( m PM ) exp ( j2π2 f RF t ) + J 2 ( m PM ) exp ( j2π2 f RF t ) ]
H RR ( ν ) = 1 κ r e j ( ν + θ ) 1 r ( 1 κ ) e j ( ν + θ )
| H RR ( ν ) | 2 = 1 κ + r 2 r ( 1 κ ) cos ( ν + θ ) 1 + r 1 κ 2 r ( 1 κ ) cos ( ν + θ )
Ψ RR ( ν ) = arc tan [ r sin ( ν + θ ) 1 κ r cos ( ν + θ ) ] arc tan [ r ( 1 κ ) sin ( ν + θ ) 1 r ( 1 κ ) cos ( ν + θ ) ]
H RF ( ν RF ) = Γ U + Γ L = 1 2 [ H RR MT ( Δ ν ) H RR MT ( ν RF Δ ν ) ] + 1 2 [ H RR MT ( ν RF Δ ν ) H RR MT ( Δ ν ) ]
E out ( t ) = E in 2 L 2 exp [ j m RF1 cos ( 2 π f RF1 t ) j m RF2 cos ( 2 π f RF2 t + φ ) ] h RR NOF ( t ) h RR MT ( t ) = E in 2 L 2 p = q = j p + q J p ( m RF1 ) J q ( m RF2 ) exp [ j 2 π( p f RF1 + q f RF2 ) t + j q φ ] H RR NOF ( ν p , q ) H RR MT ( ν p , q Δ ν ) = E in 2 L 2 p , q Γ p , q
I n 1 , n 2 ( t ) = r PD | E in | 2 L 2 Re { p , q Γ p + n 1 , q + n 2 Γ p , q } = A Re { p , q Γ p + n 1 , q + n 2 Γ p , q }
| I 1,0 Fund. | =| ARe{ Γ 1,1 Γ 0,1 + Γ 2,0 Γ 1,0 0,1 Γ 1,1 + Γ 1,0 Γ 0,0 + Γ 0,0 Γ 1,0 + Γ 1,1 Γ 0,1 + Γ 1,0 Γ 2,0 + Γ 0,1 Γ 1,1 } | =| A |{ J 0 (m) J 1 (m) 3 | H RR MT ( ν RF1 + v RF2 Δν) H RR MT* ( ν RF2 Δν) H RR NOF ( ν RF1 + v RF2 ) H RR NOF* ( ν RF2 ) | + J 0 2 (m) J 1 (m) J 2 (m)| H RR MT (2 ν RF1 Δν) H RR MT* ( ν RF1 Δν) H RR NOF (2 ν RF1 ) H RR NOF* ( ν RF1 ) | J 0 (m) J 1 3 (m)| H RR MT ( v RF2 Δν) H RR MT* ( v RF1 + ν RF2 Δν) H RR NOF ( v RF2 ) H RR NOF* ( ν RF1 + ν RF2 ) | + J 0 3 (m) J 1 (m)| H RR MT ( ν RF1 Δν) H RR MT* (Δν) H RR NOF ( ν RF1 ) H RR NOF* (0) | J 0 3 (m) J 1 (m)| H RR MT (Δν) H RR MT* ( ν RF1 Δν) H RR NOF (0) H RR NOF* ( ν RF1 ) | + J 0 (m) J 1 3 (m)| H RR MT ( ν RF1 v RF2 Δν) H RR MT* ( ν RF2 Δν) H RR NOF ( ν RF1 v RF2 ) H RR NOF* ( ν RF2 ) | J 0 2 (m) J 1 (m) J 2 (m)| H RR MT ( ν RF1 Δν) H RR MT* (2 ν RF1 Δν) H RR NOF ( ν RF1 ) H RR NOF* (2 ν RF1 ) | J 0 (m) J 1 3 (m)| H RR MT ( ν RF2 Δν) H RR MT* ( ν RF1 ν RF2 Δν) H RR NOF ( ν RF2 ) H RR NOF* ( ν RF1 ν RF2 ) |}
| I 2,-1 IMD3 | =| ARe{ Γ 2,0 Γ 0,2 2,1 Γ 0,0 + Γ 1,0 Γ 1,1 + Γ 1,1 Γ 1,0 + Γ 0,0 Γ 2,1 + Γ 0,1 Γ 2,0 } | =| A |{ J 0 2 (m) J 1 (m) J 2 (m)| H RR MT (2 ν RF1 Δν) H RR MT* ( ν RF2 Δν) H RR NOF (2 ν RF1 ) H RR NOF* ( ν RF2 ) | J 0 2 (m) J 1 (m) J 2 (m)| H RR MT (2 ν RF1 ν RF2 Δν) H RR MT* (Δν) H RR NOF (2 ν RF1 ν RF2 ) H RR NOF* (0) | J 0 (m) J 1 3 (m)| H RR MT ( v RF1 Δν) H RR MT* ( v RF1 + ν RF2 Δν) H RR NOF ( v RF1 ) H RR NOF* ( ν RF1 + ν RF2 ) | + J 0 (m) J 1 3 (m)| H RR MT ( ν RF1 ν RF2 Δν) H RR MT* ( v RF1 Δν) H RR NOF ( ν RF1 ν RF2 ) H RR NOF* ( v RF1 ) | + J 0 2 (m) J 1 (m) J 2 (m)| H RR MT (Δν) H RR MT* (2 ν RF1 + ν RF2 Δν) H RR NOF (0) H RR NOF* (2 ν RF1 + ν RF2 ) | J 0 2 (m) J 1 (m) J 2 (m)| H RR MT ( v RF2 Δν) H RR MT* (2 ν RF1 Δν) H RR NOF ( v RF2 ) H RR NOF* (2 ν RF1 ) |}
OIP3= R L 2 I 1,0 Fund. (m) 2 for | I 1,0 Fund. (m) |=| I 2,-1 IMD3 (m) |
SFDR = 2/3( OIP3 dBm S th 1/4( S shot + S RIN ))

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