Abstract

We analyze simultaneous amplitude fluctuation and timing jitter performance of a set of commonly believed equivalent spectrally periodic phase-only filters for implementing pulse repetition rate multiplication. Whereas amplitude noise and time jitter mitigation is observed in all cases, our analysis reveals different noise performance to that obtained with the classical Talbot filter implementation based on a single dispersive medium. Moreover, different noise improvements are achieved depending on the filter’s spectral period and a mutual interaction between amplitude noise and timing jitter is also observed.

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  1. P. J. Delfyett, S. Gee, S. Ozharar, F. Quinlan, K. Kim, S. Lee, and W. Lee, “Ultrafast modelocked semiconductor laser - techniques and applications in networking, instrumentation and signal processing”, The 18th Annual Meeting of the IEEE Lasers and Electro-Optics Society, LEOS 2005, pp. 38- 39, (2005)
  2. J. Wells, “Faster than fiber: The future of multi-G/s wireless,” IEEE Microw. Mag. 10(3), 104–112 (2009).
    [CrossRef]
  3. H.-P. Chuang and C.-B. Huang, “Generation and delivery of 1-ps optical pulses with ultrahigh repetition-rates over 25-km single mode fiber by a spectral line-by-line pulse shaper,” Opt. Express 18(23), 24003–24011 (2010).
    [CrossRef] [PubMed]
  4. F.-M. Kuo, J.-W. Shi, H.-C. Chiang, H.-P. Chuang, H.-K. Chiou, C.-L. Pan, N.-W. Chen, H.-J. Tsai, and C.-B. Huang, “Spectral Power Enhancement in a 100 GHz Photonic Millimeter-Wave Generator Enabled by Spectral Line-by-Line Pulse Shaping,” IEEE Photon. J. 2(5), 719–727 (2010).
    [CrossRef]
  5. A. Hirata, M. Harada, and T. Nagatsuma, “120-GHz wireless link using photonic techniques for generation, modulation, and emission of millimeter-wave signals,” J. Lightwave Technol. 21(10), 2145–2153 (2003).
    [CrossRef]
  6. J. Azaña and M. A. Muriel, “Temporal self-imaging effects: theory and application for multiplying pulse repetition rates,” IEEE J. Sel. Top. Quantum Electron. 7(4), 728–744 (2001).
    [CrossRef]
  7. J. Azaña and S. Gupta, “Complete family of periodic Talbot filters for pulse repetition rate multiplication,” Opt. Express 14(10), 4270–4279 (2006).
    [CrossRef] [PubMed]
  8. K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, “Generation of subpicosecond solitonlike optical pulses at 0.3 THz repetition rate by induced modulational instability,” Appl. Phys. Lett. 49(5), 236–238 (1986).
    [CrossRef]
  9. J. Azaña and M. A. Muriel, “Technique for multiplying the repetition rates of periodic trains of pulses by means of a temporal self-imaging effect in chirped fiber gratings,” Opt. Lett. 24(23), 1672–1674 (1999).
    [CrossRef] [PubMed]
  10. S. Longhi, M. Marano, P. Laporta, O. Svelto, M. Belmonte, B. Agogliati, L. Arcangeli, V. Pruneri, M. N. Zervas, and M. Ibsen, “40-GHz pulse-train generation at 1.5 mum with a chirped fiber grating as a frequency multiplier,” Opt. Lett. 25(19), 1481–1483 (2000).
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    [CrossRef] [PubMed]
  12. J. Caraquitena, Z. Jiang, D. E. Leaird, and A. M. Weiner, “Tunable pulse repetition-rate multiplication using phase-only line-by-line pulse shaping,” Opt. Lett. 32(6), 716–718 (2007).
    [CrossRef] [PubMed]
  13. J. Azaña, P. Kockaert, R. Slavik, L. R. Chen, and S. LaRochelle, “Generation of a 100-GHz optical pulse train by pulse repetition-rate multiplication using superimposed fiber Bragg gratings,” IEEE Photon. Technol. Lett. 15(3), 413–415 (2003).
    [CrossRef]
  14. J. Magné, J. Bolger, M. Rochette, S. LaRochelle, L. R. Chen, B. J. Eggleton, and J. Azaña, “Generation of a 4 × 100 GHz pulse-train from a single-wavelength 10-GHz mode-locked laser using superimposed fiber Bragg gratings and nonlinear conversion,” J. Lightwave Technol. 24(5), 2091–2099 (2006).
    [CrossRef]
  15. D. Pudo and L. R. Chen, “Simple estimation of pulse amplitude noise and timing jitter evolution through the temporal Talbot effect,” Opt. Express 15(10), 6351–6357 (2007).
    [CrossRef] [PubMed]
  16. C. Fernández-Pousa, F. Mateos, L. Chantada, M. Flores-Arias, C. Bao, M. Pérez, and C. Gómez-Reino, “Timing jitter smoothing by Talbot effect. I. Variance,” J. Opt. Soc. Am. B 21(6), 1170–1177 (2004).
    [CrossRef]
  17. C. Fernández-Pousa, F. Mateos, L. Chantada, M. Flores-Arias, C. Bao, M. Pérez, and C. Gómez-Reino, “Timing jitter smoothing by Talbot effect. II. Intensity spectrum,” J. Opt. Soc. Am. B 22(4), 753–763 (2005).
    [CrossRef]
  18. M. Oiwa, J. Kim, K. Tsuji, N. Onodera, and M. Saruwatari, “Experimental demonstration of timing jitter reduction based on the temporal Talbot effect using LCFBGs,” Conference on Lasers and Electro-Optics and Conference on Quantum Electronics and Laser Science. CLEO/QELS 2008, paper CTuA3, 2008.

2010 (2)

H.-P. Chuang and C.-B. Huang, “Generation and delivery of 1-ps optical pulses with ultrahigh repetition-rates over 25-km single mode fiber by a spectral line-by-line pulse shaper,” Opt. Express 18(23), 24003–24011 (2010).
[CrossRef] [PubMed]

F.-M. Kuo, J.-W. Shi, H.-C. Chiang, H.-P. Chuang, H.-K. Chiou, C.-L. Pan, N.-W. Chen, H.-J. Tsai, and C.-B. Huang, “Spectral Power Enhancement in a 100 GHz Photonic Millimeter-Wave Generator Enabled by Spectral Line-by-Line Pulse Shaping,” IEEE Photon. J. 2(5), 719–727 (2010).
[CrossRef]

2009 (1)

J. Wells, “Faster than fiber: The future of multi-G/s wireless,” IEEE Microw. Mag. 10(3), 104–112 (2009).
[CrossRef]

2007 (2)

2006 (2)

2005 (1)

2004 (2)

2003 (2)

J. Azaña, P. Kockaert, R. Slavik, L. R. Chen, and S. LaRochelle, “Generation of a 100-GHz optical pulse train by pulse repetition-rate multiplication using superimposed fiber Bragg gratings,” IEEE Photon. Technol. Lett. 15(3), 413–415 (2003).
[CrossRef]

A. Hirata, M. Harada, and T. Nagatsuma, “120-GHz wireless link using photonic techniques for generation, modulation, and emission of millimeter-wave signals,” J. Lightwave Technol. 21(10), 2145–2153 (2003).
[CrossRef]

2001 (1)

J. Azaña and M. A. Muriel, “Temporal self-imaging effects: theory and application for multiplying pulse repetition rates,” IEEE J. Sel. Top. Quantum Electron. 7(4), 728–744 (2001).
[CrossRef]

2000 (1)

1999 (1)

1986 (1)

K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, “Generation of subpicosecond solitonlike optical pulses at 0.3 THz repetition rate by induced modulational instability,” Appl. Phys. Lett. 49(5), 236–238 (1986).
[CrossRef]

Agogliati, B.

Arcangeli, L.

Azaña, J.

Bao, C.

Belmonte, M.

Bolger, J.

Caraquitena, J.

Chang, Y.

Chantada, L.

Chen, L. R.

Chen, N.-W.

F.-M. Kuo, J.-W. Shi, H.-C. Chiang, H.-P. Chuang, H.-K. Chiou, C.-L. Pan, N.-W. Chen, H.-J. Tsai, and C.-B. Huang, “Spectral Power Enhancement in a 100 GHz Photonic Millimeter-Wave Generator Enabled by Spectral Line-by-Line Pulse Shaping,” IEEE Photon. J. 2(5), 719–727 (2010).
[CrossRef]

Chiang, H.-C.

F.-M. Kuo, J.-W. Shi, H.-C. Chiang, H.-P. Chuang, H.-K. Chiou, C.-L. Pan, N.-W. Chen, H.-J. Tsai, and C.-B. Huang, “Spectral Power Enhancement in a 100 GHz Photonic Millimeter-Wave Generator Enabled by Spectral Line-by-Line Pulse Shaping,” IEEE Photon. J. 2(5), 719–727 (2010).
[CrossRef]

Chiou, H.-K.

F.-M. Kuo, J.-W. Shi, H.-C. Chiang, H.-P. Chuang, H.-K. Chiou, C.-L. Pan, N.-W. Chen, H.-J. Tsai, and C.-B. Huang, “Spectral Power Enhancement in a 100 GHz Photonic Millimeter-Wave Generator Enabled by Spectral Line-by-Line Pulse Shaping,” IEEE Photon. J. 2(5), 719–727 (2010).
[CrossRef]

Chuang, H.-P.

F.-M. Kuo, J.-W. Shi, H.-C. Chiang, H.-P. Chuang, H.-K. Chiou, C.-L. Pan, N.-W. Chen, H.-J. Tsai, and C.-B. Huang, “Spectral Power Enhancement in a 100 GHz Photonic Millimeter-Wave Generator Enabled by Spectral Line-by-Line Pulse Shaping,” IEEE Photon. J. 2(5), 719–727 (2010).
[CrossRef]

H.-P. Chuang and C.-B. Huang, “Generation and delivery of 1-ps optical pulses with ultrahigh repetition-rates over 25-km single mode fiber by a spectral line-by-line pulse shaper,” Opt. Express 18(23), 24003–24011 (2010).
[CrossRef] [PubMed]

Eggleton, B. J.

Fernández-Pousa, C.

Flores-Arias, M.

Gómez-Reino, C.

Gupta, S.

Han, Y. G.

Harada, M.

Hasegawa, A.

K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, “Generation of subpicosecond solitonlike optical pulses at 0.3 THz repetition rate by induced modulational instability,” Appl. Phys. Lett. 49(5), 236–238 (1986).
[CrossRef]

Hirata, A.

Huang, C.-B.

F.-M. Kuo, J.-W. Shi, H.-C. Chiang, H.-P. Chuang, H.-K. Chiou, C.-L. Pan, N.-W. Chen, H.-J. Tsai, and C.-B. Huang, “Spectral Power Enhancement in a 100 GHz Photonic Millimeter-Wave Generator Enabled by Spectral Line-by-Line Pulse Shaping,” IEEE Photon. J. 2(5), 719–727 (2010).
[CrossRef]

H.-P. Chuang and C.-B. Huang, “Generation and delivery of 1-ps optical pulses with ultrahigh repetition-rates over 25-km single mode fiber by a spectral line-by-line pulse shaper,” Opt. Express 18(23), 24003–24011 (2010).
[CrossRef] [PubMed]

Ibsen, M.

Jewell, J. L.

K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, “Generation of subpicosecond solitonlike optical pulses at 0.3 THz repetition rate by induced modulational instability,” Appl. Phys. Lett. 49(5), 236–238 (1986).
[CrossRef]

Jiang, Z.

Kim, S.

Kockaert, P.

J. Azaña, P. Kockaert, R. Slavik, L. R. Chen, and S. LaRochelle, “Generation of a 100-GHz optical pulse train by pulse repetition-rate multiplication using superimposed fiber Bragg gratings,” IEEE Photon. Technol. Lett. 15(3), 413–415 (2003).
[CrossRef]

Kuo, F.-M.

F.-M. Kuo, J.-W. Shi, H.-C. Chiang, H.-P. Chuang, H.-K. Chiou, C.-L. Pan, N.-W. Chen, H.-J. Tsai, and C.-B. Huang, “Spectral Power Enhancement in a 100 GHz Photonic Millimeter-Wave Generator Enabled by Spectral Line-by-Line Pulse Shaping,” IEEE Photon. J. 2(5), 719–727 (2010).
[CrossRef]

Laporta, P.

LaRochelle, S.

J. Magné, J. Bolger, M. Rochette, S. LaRochelle, L. R. Chen, B. J. Eggleton, and J. Azaña, “Generation of a 4 × 100 GHz pulse-train from a single-wavelength 10-GHz mode-locked laser using superimposed fiber Bragg gratings and nonlinear conversion,” J. Lightwave Technol. 24(5), 2091–2099 (2006).
[CrossRef]

J. Azaña, P. Kockaert, R. Slavik, L. R. Chen, and S. LaRochelle, “Generation of a 100-GHz optical pulse train by pulse repetition-rate multiplication using superimposed fiber Bragg gratings,” IEEE Photon. Technol. Lett. 15(3), 413–415 (2003).
[CrossRef]

Leaird, D. E.

Lee, J. H.

Lee, S.

Longhi, S.

Magné, J.

Marano, M.

Mateos, F.

Muriel, M. A.

J. Azaña and M. A. Muriel, “Temporal self-imaging effects: theory and application for multiplying pulse repetition rates,” IEEE J. Sel. Top. Quantum Electron. 7(4), 728–744 (2001).
[CrossRef]

J. Azaña and M. A. Muriel, “Technique for multiplying the repetition rates of periodic trains of pulses by means of a temporal self-imaging effect in chirped fiber gratings,” Opt. Lett. 24(23), 1672–1674 (1999).
[CrossRef] [PubMed]

Nagatsuma, T.

Pan, C.-L.

F.-M. Kuo, J.-W. Shi, H.-C. Chiang, H.-P. Chuang, H.-K. Chiou, C.-L. Pan, N.-W. Chen, H.-J. Tsai, and C.-B. Huang, “Spectral Power Enhancement in a 100 GHz Photonic Millimeter-Wave Generator Enabled by Spectral Line-by-Line Pulse Shaping,” IEEE Photon. J. 2(5), 719–727 (2010).
[CrossRef]

Pérez, M.

Pruneri, V.

Pudo, D.

Rochette, M.

Shi, J.-W.

F.-M. Kuo, J.-W. Shi, H.-C. Chiang, H.-P. Chuang, H.-K. Chiou, C.-L. Pan, N.-W. Chen, H.-J. Tsai, and C.-B. Huang, “Spectral Power Enhancement in a 100 GHz Photonic Millimeter-Wave Generator Enabled by Spectral Line-by-Line Pulse Shaping,” IEEE Photon. J. 2(5), 719–727 (2010).
[CrossRef]

Slavik, R.

J. Azaña, P. Kockaert, R. Slavik, L. R. Chen, and S. LaRochelle, “Generation of a 100-GHz optical pulse train by pulse repetition-rate multiplication using superimposed fiber Bragg gratings,” IEEE Photon. Technol. Lett. 15(3), 413–415 (2003).
[CrossRef]

Svelto, O.

Tai, K.

K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, “Generation of subpicosecond solitonlike optical pulses at 0.3 THz repetition rate by induced modulational instability,” Appl. Phys. Lett. 49(5), 236–238 (1986).
[CrossRef]

Tomita, A.

K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, “Generation of subpicosecond solitonlike optical pulses at 0.3 THz repetition rate by induced modulational instability,” Appl. Phys. Lett. 49(5), 236–238 (1986).
[CrossRef]

Tsai, H.-J.

F.-M. Kuo, J.-W. Shi, H.-C. Chiang, H.-P. Chuang, H.-K. Chiou, C.-L. Pan, N.-W. Chen, H.-J. Tsai, and C.-B. Huang, “Spectral Power Enhancement in a 100 GHz Photonic Millimeter-Wave Generator Enabled by Spectral Line-by-Line Pulse Shaping,” IEEE Photon. J. 2(5), 719–727 (2010).
[CrossRef]

Weiner, A. M.

Wells, J.

J. Wells, “Faster than fiber: The future of multi-G/s wireless,” IEEE Microw. Mag. 10(3), 104–112 (2009).
[CrossRef]

Zervas, M. N.

Appl. Phys. Lett. (1)

K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, “Generation of subpicosecond solitonlike optical pulses at 0.3 THz repetition rate by induced modulational instability,” Appl. Phys. Lett. 49(5), 236–238 (1986).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

J. Azaña and M. A. Muriel, “Temporal self-imaging effects: theory and application for multiplying pulse repetition rates,” IEEE J. Sel. Top. Quantum Electron. 7(4), 728–744 (2001).
[CrossRef]

IEEE Microw. Mag. (1)

J. Wells, “Faster than fiber: The future of multi-G/s wireless,” IEEE Microw. Mag. 10(3), 104–112 (2009).
[CrossRef]

IEEE Photon. J. (1)

F.-M. Kuo, J.-W. Shi, H.-C. Chiang, H.-P. Chuang, H.-K. Chiou, C.-L. Pan, N.-W. Chen, H.-J. Tsai, and C.-B. Huang, “Spectral Power Enhancement in a 100 GHz Photonic Millimeter-Wave Generator Enabled by Spectral Line-by-Line Pulse Shaping,” IEEE Photon. J. 2(5), 719–727 (2010).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

J. Azaña, P. Kockaert, R. Slavik, L. R. Chen, and S. LaRochelle, “Generation of a 100-GHz optical pulse train by pulse repetition-rate multiplication using superimposed fiber Bragg gratings,” IEEE Photon. Technol. Lett. 15(3), 413–415 (2003).
[CrossRef]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. B (2)

Opt. Express (4)

Opt. Lett. (3)

Other (2)

M. Oiwa, J. Kim, K. Tsuji, N. Onodera, and M. Saruwatari, “Experimental demonstration of timing jitter reduction based on the temporal Talbot effect using LCFBGs,” Conference on Lasers and Electro-Optics and Conference on Quantum Electronics and Laser Science. CLEO/QELS 2008, paper CTuA3, 2008.

P. J. Delfyett, S. Gee, S. Ozharar, F. Quinlan, K. Kim, S. Lee, and W. Lee, “Ultrafast modelocked semiconductor laser - techniques and applications in networking, instrumentation and signal processing”, The 18th Annual Meeting of the IEEE Lasers and Electro-Optics Society, LEOS 2005, pp. 38- 39, (2005)

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Figures (6)

Fig. 1
Fig. 1

Spectral phase profiles for the single Talbot filter (single dispersive medium) and several examples of periodic filters corresponding to the PRRM case with m = 4, q = 1 and Tin = 100 ps. Spectral phase profile for the single Talbot filter and for an example of periodic filter (p = 4) for the case m = 4, q = 3 and Tin = 100 ps. All these phase-only filters implement a 10-to-40 GHz PRRM process.

Fig. 2
Fig. 2

Overlap over each period (Tin ) of the temporal-domain amplitude of 1000 consecutive pulses for the input signal (a), the normalized output when applying a spectrally periodic phase-only filter with p = 3 (b) and p = 15 (c) and the normalized output for the single Talbot filter (d); all plots are for the case m = 4, q = 1 and Tin = 100 ps.

Fig. 3
Fig. 3

Timing jitter ratio assuming input timing jitter only (a), amplitude fluctuation ratio assuming input amplitude fluctuation only (b), both timing jitter and amplitude fluctuation ratios assuming simultaneous input timing jitter and amplitude fluctuation (c). All cases plotted versus factor p (changing the filter frequency period) for q=1, m=4, Tin =100ps.

Fig. 4
Fig. 4

Same captions as for Fig. 3 with q=3.

Fig. 5
Fig. 5

Timing jitter and amplitude fluctuation ratios assuming simultaneous input timing jitter with σt = 2% and amplitude fluctuation with σA = 12%, for q=3, m=4, Tin =100ps.

Fig. 6
Fig. 6

(a) Timing jitter and amplitude fluctuation ratios versus the input duty cycle for the cases q = 1, 3. (b) Average output extinction ratio (ER) versus the input duty cycle for different values of q. The two plots report results for the single Talbot filter for m = 4, σt = σA = 6%. (c) Average ER versus parameter p for periodic filters for several values of q.

Equations (5)

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| Φ ¨ 0 | = q m ( T i n 2 2 π )
Φ ( f ) = Φ ¨ 0 2 ( 2 π f ) 2
Φ p ( f ) = k = + Φ ( f k p m f i n ) r e c t ( f k p m f i n p m f i n )
s ( t ) = n = 1 N i n A n p ( t n T i n τ n )
o ( t ) = F 1 { S ( f ) H p ( f ) }

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