Abstract

A technique that can suppress the dominant phase-induced intensity noise in fibre optic delay line signal processors is presented. It is based on phase modulation of the optical carrier to distribute the phase noise at the information band into a high frequency band which can be filtered out. This technique is suitable for suppressing the phase noise in various delay line structures and for integrating in the conventional fibre optic links. It can also suppress the coherent interference effect at the same time. A model for predicting the amount of phase noise reduction in various delay line structures using the optical phase modulation technique is presented for the first time and is experimentally verified. Experimental results demonstrate the technique can achieve a large phase noise reduction in various fibre optic delay line signal processors.

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References

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  1. B. Moslehi and J. W. Goodman, “Novel amplified fiber-optic recirculating delay line processor,” J. Lightwave Technol. 10(8), 1142–1147 (1992).
    [CrossRef]
  2. J. Capmany and J. Cascon, “Discrete time fiber-optic signal processors using optical amplifiers,” J. Lightwave Technol. 12(1), 106–117 (1994).
    [CrossRef]
  3. D. B. Hunter and R. A. Minasian, “Photonic signal processing of microwave signals using an active-fiber Bragg-grating-pair structure,” IEEE Trans. Microw. Theory Tech. 45(8), 1463–1466 (1997).
    [CrossRef]
  4. E. H. W. Chan, K. E. Alameh, and R. A. Minasian, “Photonic bandpass filters with high skirt selectivity and stopband attenuation,” J. Lightwave Technol. 20(11), 1962–1967 (2002).
    [CrossRef]
  5. G. Yu, W. Zhang, and J. A. R. Williams, “High-performance microwave transversal filter using fiber Bragg grating arrays,” IEEE Photon. Technol. Lett. 12(9), 1183–1185 (2000).
    [CrossRef]
  6. D. B. Hunter and R. A. Minasian, “Tunable microwave fiber-optic bandpass filters,” IEEE Photon. Technol. Lett. 11(7), 874–876 (1999).
    [CrossRef]
  7. D. Pastor, S. Sales, J. Capmany, J. Marti, and J. Cascon, “Amplified double coupler fiber-optic delay line filter,” IEEE Photon. Technol. Lett. 7(1), 75–77 (1995).
    [CrossRef]
  8. E. H. W. Chan and R. A. Minasian, “Reflective amplified recirculating delay line bandpass filter,” J. Lightwave Technol. 25(6), 1441–1446 (2007).
    [CrossRef]
  9. J. Capmany, B. Ortega, D. Pastor, and S. Sales, “Discrete-time optical processing of microwave signals,” J. Lightwave Technol. 23(2), 702–723 (2005).
    [CrossRef]
  10. M. Y. Frankel and R. D. Esman, “Fiber-optic tunable microwave transversal filter,” IEEE Photon. Technol. Lett. 7(2), 191–193 (1995).
    [CrossRef]
  11. M. Tur and A. Arie, “Phase induced intensity noise in concatenated fiber-optic delay lines,” J. Lightwave Technol. 6(1), 120–130 (1988).
    [CrossRef]
  12. B. Moslehi, “Analysis of optical phase noise in fiber-optic systems employing a laser source with arbitrary coherence time,” J. Lightwave Technol. 4(9), 1334–1351 (1986).
    [CrossRef]
  13. J. T. Kringlebotn and K. Blotekjaer, “Noise analysis of an amplified fiber-optic recirculating delay line,” J. Lightwave Technol. 12(3), 573–582 (1994).
    [CrossRef]
  14. E. H. W. Chan and R. A. Minasian, “Suppression of phase induced intensity noise in optical delay line signal processors using a differential detection technique,” IEEE Trans. Microw. Theory Tech. 54(2), 873–879 (2006).
    [CrossRef]
  15. A. Yariv, H. Blauvelt, D. Huff, and H. Zarem, “An experimental and theoretical study of the suppression of interferometric noise and distortion in AM optical links by phase dither,” J. Lightwave Technol. 15(3), 437–443 (1997).
    [CrossRef]
  16. P. K. Pepeljugoski and K. Y. Lau, “Interferometric noise reduction in fiber-optic links by superposition of high frequency modulation,” J. Lightwave Technol. 10(7), 957–963 (1992).
    [CrossRef]
  17. A. H. Quoc and S. Tedjini, “Experimental investigation on the optical unbalanced Mach-Zehnder interferometers as microwave filters,” IEEE Microwave Guided Wave Lett. 4(6), 183–185 (1994).
    [CrossRef]
  18. E. H. W. Chan and R. A. Minasian, “Optical source coherence controller for fibre optic delay line RF/microwave signal processors,” Opt. Commun. 254(1-3), 104–111 (2005).
    [CrossRef]
  19. M. Nazarathy, W. V. Sorin, D. M. Baney, and S. A. Newton, “Spectral analysis of optical mixing measurements,” J. Lightwave Technol. 7(7), 1083–1096 (1989).
    [CrossRef]

2007 (1)

2006 (1)

E. H. W. Chan and R. A. Minasian, “Suppression of phase induced intensity noise in optical delay line signal processors using a differential detection technique,” IEEE Trans. Microw. Theory Tech. 54(2), 873–879 (2006).
[CrossRef]

2005 (2)

E. H. W. Chan and R. A. Minasian, “Optical source coherence controller for fibre optic delay line RF/microwave signal processors,” Opt. Commun. 254(1-3), 104–111 (2005).
[CrossRef]

J. Capmany, B. Ortega, D. Pastor, and S. Sales, “Discrete-time optical processing of microwave signals,” J. Lightwave Technol. 23(2), 702–723 (2005).
[CrossRef]

2002 (1)

2000 (1)

G. Yu, W. Zhang, and J. A. R. Williams, “High-performance microwave transversal filter using fiber Bragg grating arrays,” IEEE Photon. Technol. Lett. 12(9), 1183–1185 (2000).
[CrossRef]

1999 (1)

D. B. Hunter and R. A. Minasian, “Tunable microwave fiber-optic bandpass filters,” IEEE Photon. Technol. Lett. 11(7), 874–876 (1999).
[CrossRef]

1997 (2)

D. B. Hunter and R. A. Minasian, “Photonic signal processing of microwave signals using an active-fiber Bragg-grating-pair structure,” IEEE Trans. Microw. Theory Tech. 45(8), 1463–1466 (1997).
[CrossRef]

A. Yariv, H. Blauvelt, D. Huff, and H. Zarem, “An experimental and theoretical study of the suppression of interferometric noise and distortion in AM optical links by phase dither,” J. Lightwave Technol. 15(3), 437–443 (1997).
[CrossRef]

1995 (2)

D. Pastor, S. Sales, J. Capmany, J. Marti, and J. Cascon, “Amplified double coupler fiber-optic delay line filter,” IEEE Photon. Technol. Lett. 7(1), 75–77 (1995).
[CrossRef]

M. Y. Frankel and R. D. Esman, “Fiber-optic tunable microwave transversal filter,” IEEE Photon. Technol. Lett. 7(2), 191–193 (1995).
[CrossRef]

1994 (3)

J. T. Kringlebotn and K. Blotekjaer, “Noise analysis of an amplified fiber-optic recirculating delay line,” J. Lightwave Technol. 12(3), 573–582 (1994).
[CrossRef]

J. Capmany and J. Cascon, “Discrete time fiber-optic signal processors using optical amplifiers,” J. Lightwave Technol. 12(1), 106–117 (1994).
[CrossRef]

A. H. Quoc and S. Tedjini, “Experimental investigation on the optical unbalanced Mach-Zehnder interferometers as microwave filters,” IEEE Microwave Guided Wave Lett. 4(6), 183–185 (1994).
[CrossRef]

1992 (2)

P. K. Pepeljugoski and K. Y. Lau, “Interferometric noise reduction in fiber-optic links by superposition of high frequency modulation,” J. Lightwave Technol. 10(7), 957–963 (1992).
[CrossRef]

B. Moslehi and J. W. Goodman, “Novel amplified fiber-optic recirculating delay line processor,” J. Lightwave Technol. 10(8), 1142–1147 (1992).
[CrossRef]

1989 (1)

M. Nazarathy, W. V. Sorin, D. M. Baney, and S. A. Newton, “Spectral analysis of optical mixing measurements,” J. Lightwave Technol. 7(7), 1083–1096 (1989).
[CrossRef]

1988 (1)

M. Tur and A. Arie, “Phase induced intensity noise in concatenated fiber-optic delay lines,” J. Lightwave Technol. 6(1), 120–130 (1988).
[CrossRef]

1986 (1)

B. Moslehi, “Analysis of optical phase noise in fiber-optic systems employing a laser source with arbitrary coherence time,” J. Lightwave Technol. 4(9), 1334–1351 (1986).
[CrossRef]

Alameh, K. E.

Arie, A.

M. Tur and A. Arie, “Phase induced intensity noise in concatenated fiber-optic delay lines,” J. Lightwave Technol. 6(1), 120–130 (1988).
[CrossRef]

Baney, D. M.

M. Nazarathy, W. V. Sorin, D. M. Baney, and S. A. Newton, “Spectral analysis of optical mixing measurements,” J. Lightwave Technol. 7(7), 1083–1096 (1989).
[CrossRef]

Blauvelt, H.

A. Yariv, H. Blauvelt, D. Huff, and H. Zarem, “An experimental and theoretical study of the suppression of interferometric noise and distortion in AM optical links by phase dither,” J. Lightwave Technol. 15(3), 437–443 (1997).
[CrossRef]

Blotekjaer, K.

J. T. Kringlebotn and K. Blotekjaer, “Noise analysis of an amplified fiber-optic recirculating delay line,” J. Lightwave Technol. 12(3), 573–582 (1994).
[CrossRef]

Capmany, J.

J. Capmany, B. Ortega, D. Pastor, and S. Sales, “Discrete-time optical processing of microwave signals,” J. Lightwave Technol. 23(2), 702–723 (2005).
[CrossRef]

D. Pastor, S. Sales, J. Capmany, J. Marti, and J. Cascon, “Amplified double coupler fiber-optic delay line filter,” IEEE Photon. Technol. Lett. 7(1), 75–77 (1995).
[CrossRef]

J. Capmany and J. Cascon, “Discrete time fiber-optic signal processors using optical amplifiers,” J. Lightwave Technol. 12(1), 106–117 (1994).
[CrossRef]

Cascon, J.

D. Pastor, S. Sales, J. Capmany, J. Marti, and J. Cascon, “Amplified double coupler fiber-optic delay line filter,” IEEE Photon. Technol. Lett. 7(1), 75–77 (1995).
[CrossRef]

J. Capmany and J. Cascon, “Discrete time fiber-optic signal processors using optical amplifiers,” J. Lightwave Technol. 12(1), 106–117 (1994).
[CrossRef]

Chan, E. H. W.

E. H. W. Chan and R. A. Minasian, “Reflective amplified recirculating delay line bandpass filter,” J. Lightwave Technol. 25(6), 1441–1446 (2007).
[CrossRef]

E. H. W. Chan and R. A. Minasian, “Suppression of phase induced intensity noise in optical delay line signal processors using a differential detection technique,” IEEE Trans. Microw. Theory Tech. 54(2), 873–879 (2006).
[CrossRef]

E. H. W. Chan and R. A. Minasian, “Optical source coherence controller for fibre optic delay line RF/microwave signal processors,” Opt. Commun. 254(1-3), 104–111 (2005).
[CrossRef]

E. H. W. Chan, K. E. Alameh, and R. A. Minasian, “Photonic bandpass filters with high skirt selectivity and stopband attenuation,” J. Lightwave Technol. 20(11), 1962–1967 (2002).
[CrossRef]

Esman, R. D.

M. Y. Frankel and R. D. Esman, “Fiber-optic tunable microwave transversal filter,” IEEE Photon. Technol. Lett. 7(2), 191–193 (1995).
[CrossRef]

Frankel, M. Y.

M. Y. Frankel and R. D. Esman, “Fiber-optic tunable microwave transversal filter,” IEEE Photon. Technol. Lett. 7(2), 191–193 (1995).
[CrossRef]

Goodman, J. W.

B. Moslehi and J. W. Goodman, “Novel amplified fiber-optic recirculating delay line processor,” J. Lightwave Technol. 10(8), 1142–1147 (1992).
[CrossRef]

Huff, D.

A. Yariv, H. Blauvelt, D. Huff, and H. Zarem, “An experimental and theoretical study of the suppression of interferometric noise and distortion in AM optical links by phase dither,” J. Lightwave Technol. 15(3), 437–443 (1997).
[CrossRef]

Hunter, D. B.

D. B. Hunter and R. A. Minasian, “Tunable microwave fiber-optic bandpass filters,” IEEE Photon. Technol. Lett. 11(7), 874–876 (1999).
[CrossRef]

D. B. Hunter and R. A. Minasian, “Photonic signal processing of microwave signals using an active-fiber Bragg-grating-pair structure,” IEEE Trans. Microw. Theory Tech. 45(8), 1463–1466 (1997).
[CrossRef]

Kringlebotn, J. T.

J. T. Kringlebotn and K. Blotekjaer, “Noise analysis of an amplified fiber-optic recirculating delay line,” J. Lightwave Technol. 12(3), 573–582 (1994).
[CrossRef]

Lau, K. Y.

P. K. Pepeljugoski and K. Y. Lau, “Interferometric noise reduction in fiber-optic links by superposition of high frequency modulation,” J. Lightwave Technol. 10(7), 957–963 (1992).
[CrossRef]

Marti, J.

D. Pastor, S. Sales, J. Capmany, J. Marti, and J. Cascon, “Amplified double coupler fiber-optic delay line filter,” IEEE Photon. Technol. Lett. 7(1), 75–77 (1995).
[CrossRef]

Minasian, R. A.

E. H. W. Chan and R. A. Minasian, “Reflective amplified recirculating delay line bandpass filter,” J. Lightwave Technol. 25(6), 1441–1446 (2007).
[CrossRef]

E. H. W. Chan and R. A. Minasian, “Suppression of phase induced intensity noise in optical delay line signal processors using a differential detection technique,” IEEE Trans. Microw. Theory Tech. 54(2), 873–879 (2006).
[CrossRef]

E. H. W. Chan and R. A. Minasian, “Optical source coherence controller for fibre optic delay line RF/microwave signal processors,” Opt. Commun. 254(1-3), 104–111 (2005).
[CrossRef]

E. H. W. Chan, K. E. Alameh, and R. A. Minasian, “Photonic bandpass filters with high skirt selectivity and stopband attenuation,” J. Lightwave Technol. 20(11), 1962–1967 (2002).
[CrossRef]

D. B. Hunter and R. A. Minasian, “Tunable microwave fiber-optic bandpass filters,” IEEE Photon. Technol. Lett. 11(7), 874–876 (1999).
[CrossRef]

D. B. Hunter and R. A. Minasian, “Photonic signal processing of microwave signals using an active-fiber Bragg-grating-pair structure,” IEEE Trans. Microw. Theory Tech. 45(8), 1463–1466 (1997).
[CrossRef]

Moslehi, B.

B. Moslehi and J. W. Goodman, “Novel amplified fiber-optic recirculating delay line processor,” J. Lightwave Technol. 10(8), 1142–1147 (1992).
[CrossRef]

B. Moslehi, “Analysis of optical phase noise in fiber-optic systems employing a laser source with arbitrary coherence time,” J. Lightwave Technol. 4(9), 1334–1351 (1986).
[CrossRef]

Nazarathy, M.

M. Nazarathy, W. V. Sorin, D. M. Baney, and S. A. Newton, “Spectral analysis of optical mixing measurements,” J. Lightwave Technol. 7(7), 1083–1096 (1989).
[CrossRef]

Newton, S. A.

M. Nazarathy, W. V. Sorin, D. M. Baney, and S. A. Newton, “Spectral analysis of optical mixing measurements,” J. Lightwave Technol. 7(7), 1083–1096 (1989).
[CrossRef]

Ortega, B.

Pastor, D.

J. Capmany, B. Ortega, D. Pastor, and S. Sales, “Discrete-time optical processing of microwave signals,” J. Lightwave Technol. 23(2), 702–723 (2005).
[CrossRef]

D. Pastor, S. Sales, J. Capmany, J. Marti, and J. Cascon, “Amplified double coupler fiber-optic delay line filter,” IEEE Photon. Technol. Lett. 7(1), 75–77 (1995).
[CrossRef]

Pepeljugoski, P. K.

P. K. Pepeljugoski and K. Y. Lau, “Interferometric noise reduction in fiber-optic links by superposition of high frequency modulation,” J. Lightwave Technol. 10(7), 957–963 (1992).
[CrossRef]

Quoc, A. H.

A. H. Quoc and S. Tedjini, “Experimental investigation on the optical unbalanced Mach-Zehnder interferometers as microwave filters,” IEEE Microwave Guided Wave Lett. 4(6), 183–185 (1994).
[CrossRef]

Sales, S.

J. Capmany, B. Ortega, D. Pastor, and S. Sales, “Discrete-time optical processing of microwave signals,” J. Lightwave Technol. 23(2), 702–723 (2005).
[CrossRef]

D. Pastor, S. Sales, J. Capmany, J. Marti, and J. Cascon, “Amplified double coupler fiber-optic delay line filter,” IEEE Photon. Technol. Lett. 7(1), 75–77 (1995).
[CrossRef]

Sorin, W. V.

M. Nazarathy, W. V. Sorin, D. M. Baney, and S. A. Newton, “Spectral analysis of optical mixing measurements,” J. Lightwave Technol. 7(7), 1083–1096 (1989).
[CrossRef]

Tedjini, S.

A. H. Quoc and S. Tedjini, “Experimental investigation on the optical unbalanced Mach-Zehnder interferometers as microwave filters,” IEEE Microwave Guided Wave Lett. 4(6), 183–185 (1994).
[CrossRef]

Tur, M.

M. Tur and A. Arie, “Phase induced intensity noise in concatenated fiber-optic delay lines,” J. Lightwave Technol. 6(1), 120–130 (1988).
[CrossRef]

Williams, J. A. R.

G. Yu, W. Zhang, and J. A. R. Williams, “High-performance microwave transversal filter using fiber Bragg grating arrays,” IEEE Photon. Technol. Lett. 12(9), 1183–1185 (2000).
[CrossRef]

Yariv, A.

A. Yariv, H. Blauvelt, D. Huff, and H. Zarem, “An experimental and theoretical study of the suppression of interferometric noise and distortion in AM optical links by phase dither,” J. Lightwave Technol. 15(3), 437–443 (1997).
[CrossRef]

Yu, G.

G. Yu, W. Zhang, and J. A. R. Williams, “High-performance microwave transversal filter using fiber Bragg grating arrays,” IEEE Photon. Technol. Lett. 12(9), 1183–1185 (2000).
[CrossRef]

Zarem, H.

A. Yariv, H. Blauvelt, D. Huff, and H. Zarem, “An experimental and theoretical study of the suppression of interferometric noise and distortion in AM optical links by phase dither,” J. Lightwave Technol. 15(3), 437–443 (1997).
[CrossRef]

Zhang, W.

G. Yu, W. Zhang, and J. A. R. Williams, “High-performance microwave transversal filter using fiber Bragg grating arrays,” IEEE Photon. Technol. Lett. 12(9), 1183–1185 (2000).
[CrossRef]

IEEE Microwave Guided Wave Lett. (1)

A. H. Quoc and S. Tedjini, “Experimental investigation on the optical unbalanced Mach-Zehnder interferometers as microwave filters,” IEEE Microwave Guided Wave Lett. 4(6), 183–185 (1994).
[CrossRef]

IEEE Photon. Technol. Lett. (4)

G. Yu, W. Zhang, and J. A. R. Williams, “High-performance microwave transversal filter using fiber Bragg grating arrays,” IEEE Photon. Technol. Lett. 12(9), 1183–1185 (2000).
[CrossRef]

D. B. Hunter and R. A. Minasian, “Tunable microwave fiber-optic bandpass filters,” IEEE Photon. Technol. Lett. 11(7), 874–876 (1999).
[CrossRef]

D. Pastor, S. Sales, J. Capmany, J. Marti, and J. Cascon, “Amplified double coupler fiber-optic delay line filter,” IEEE Photon. Technol. Lett. 7(1), 75–77 (1995).
[CrossRef]

M. Y. Frankel and R. D. Esman, “Fiber-optic tunable microwave transversal filter,” IEEE Photon. Technol. Lett. 7(2), 191–193 (1995).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (2)

E. H. W. Chan and R. A. Minasian, “Suppression of phase induced intensity noise in optical delay line signal processors using a differential detection technique,” IEEE Trans. Microw. Theory Tech. 54(2), 873–879 (2006).
[CrossRef]

D. B. Hunter and R. A. Minasian, “Photonic signal processing of microwave signals using an active-fiber Bragg-grating-pair structure,” IEEE Trans. Microw. Theory Tech. 45(8), 1463–1466 (1997).
[CrossRef]

J. Lightwave Technol. (11)

M. Nazarathy, W. V. Sorin, D. M. Baney, and S. A. Newton, “Spectral analysis of optical mixing measurements,” J. Lightwave Technol. 7(7), 1083–1096 (1989).
[CrossRef]

E. H. W. Chan, K. E. Alameh, and R. A. Minasian, “Photonic bandpass filters with high skirt selectivity and stopband attenuation,” J. Lightwave Technol. 20(11), 1962–1967 (2002).
[CrossRef]

J. Capmany, B. Ortega, D. Pastor, and S. Sales, “Discrete-time optical processing of microwave signals,” J. Lightwave Technol. 23(2), 702–723 (2005).
[CrossRef]

E. H. W. Chan and R. A. Minasian, “Reflective amplified recirculating delay line bandpass filter,” J. Lightwave Technol. 25(6), 1441–1446 (2007).
[CrossRef]

A. Yariv, H. Blauvelt, D. Huff, and H. Zarem, “An experimental and theoretical study of the suppression of interferometric noise and distortion in AM optical links by phase dither,” J. Lightwave Technol. 15(3), 437–443 (1997).
[CrossRef]

P. K. Pepeljugoski and K. Y. Lau, “Interferometric noise reduction in fiber-optic links by superposition of high frequency modulation,” J. Lightwave Technol. 10(7), 957–963 (1992).
[CrossRef]

B. Moslehi and J. W. Goodman, “Novel amplified fiber-optic recirculating delay line processor,” J. Lightwave Technol. 10(8), 1142–1147 (1992).
[CrossRef]

J. Capmany and J. Cascon, “Discrete time fiber-optic signal processors using optical amplifiers,” J. Lightwave Technol. 12(1), 106–117 (1994).
[CrossRef]

M. Tur and A. Arie, “Phase induced intensity noise in concatenated fiber-optic delay lines,” J. Lightwave Technol. 6(1), 120–130 (1988).
[CrossRef]

B. Moslehi, “Analysis of optical phase noise in fiber-optic systems employing a laser source with arbitrary coherence time,” J. Lightwave Technol. 4(9), 1334–1351 (1986).
[CrossRef]

J. T. Kringlebotn and K. Blotekjaer, “Noise analysis of an amplified fiber-optic recirculating delay line,” J. Lightwave Technol. 12(3), 573–582 (1994).
[CrossRef]

Opt. Commun. (1)

E. H. W. Chan and R. A. Minasian, “Optical source coherence controller for fibre optic delay line RF/microwave signal processors,” Opt. Commun. 254(1-3), 104–111 (2005).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Fibre optic link with a phase noise reduction unit inserted before the fibre optic delay line signal processor.

Fig. 2
Fig. 2

UMZI notch filter PIIN spectrums with (dash) and without (solid) a 5.05 GHz frequency single tone phase modulation. The phase modulation index is 1.2. The signal time delay is 10 ns.

Fig. 3
Fig. 3

Passive RDL notch filter impulse response.

Fig. 4
Fig. 4

The amount of phase noise reduction and the broadened laser linewidth as a function of the phase modulation index when a 200 MHz linewidth laser undergoes a 1 GHz bandwidth Lorentzian shape Gaussian noise phase modulation.

Fig. 5
Fig. 5

Measured (solid) and predicted (dots) PIIN spectrum of a two-tap delay line structure with and without single tone phase modulation. The phase modulation index is 1.45. The laser linewidth is 3 MHz. The signal time delay is 0.5 μs.

Fig. 6
Fig. 6

(a) Measured and predicted amount of UMZI notch filter PIIN reduction after different frequency single tone phase modulation. The phase modulation index is 2.92. (b) Measured and predicted amount of UMZI notch filter PIIN reduction for different phase modulation indexes. The input single tone frequency is 3 GHz.

Fig. 7
Fig. 7

(a) Measured and predicted amount of passive RDL notch filter PIIN reduction after different frequency single tone phase modulation. The phase modulation index is 2.84. (b) Measured and predicted amount of passive RDL notch filter PIIN reduction for different phase modulation indexes. The input single tone frequency is 2.9996 GHz.

Fig. 8
Fig. 8

(a) Measured and predicted amount of amplified RDL bandpass filter PIIN reduction after different frequency single tone phase modulation. The phase modulation index is 3.02. (b) Measured and predicted amount of amplified RDL bandpass filter PIIN reduction for different phase modulation indexes. The input single tone frequency is 3.002 GHz.

Fig. 9
Fig. 9

Measured and predicted amount of UMZI notch filter PIIN reduction versus the laser linewidth.

Fig. 10
Fig. 10

RF signal and PIIN at the output of the passive RDL notch filter for the laser linewidth of 50 MHz (solid) and 920 MHz (dots). The FSR of the passive RDL notch filter response is 30 MHz.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

S N , P M ( f ) = { J 0 2 ( A ) S N ( f ) + n = 1 J n 2 ( A ) [ S N ( f n f 0 ) + S N ( f + n f 0 ) ] } S δ ( f )
S N ( f ) = 1 / ( π Δ ν ) 1 + ( f / Δ ν ) 2
A = 2 a sin ( Ω 0 τ / 2 )
a = 1.2025 sin ( Ω 0 τ / 2 )
X 3 , 0 = [ 2 J 0 2 ( A 1 ) + J 0 2 ( A 2 ) ] / 3
X m , 0 = x = 1 m 1 ( m x ) J 0 2 ( A x ) / x = 1 m 1 ( m x )
A x = 2 a sin ( Ω 0 x τ / 2 )
S N , P M ( f ) = { X m , 0 S N ( f ) + n = 1 X m , n [ S N ( f n f 0 ) + S N ( f + n f 0 ) ] } S δ ( f )
R N , P M ( δ τ ) = 2 P o 2 R ( δ τ ) exp { 2 a 2 [ R n ( 0 ) R n ( δ τ ) cos ( Ψ 0 δ τ ) ] }
R ( δ τ ) = exp [ 1 2 τ c ( 2 | τ | | τ δ τ | | τ + δ τ | + 2 | δ τ | ) ]
S N , P M ( f ) = S δ ( f ) F T [ R N , P M ( δ τ ) ]

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