## Analysis of amplitude fluctuation and timing jitter performance of spectrally periodic Talbot filters for optical pulse rate multiplication |

Optics Express, Vol. 19, Issue 16, pp. 15339-15347 (2011)

http://dx.doi.org/10.1364/OE.19.015339

Acrobat PDF (1410 KB)

### 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.

© 2011 OSA

## 1. Introduction

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]

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]

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]

*stable*pulse sources is extremely important in all these applications, particularly considering that pulse trains produced through conventional techniques, such as actively, passively or hybrid mode-locking, typically suffer from different noise contributions. To be more concrete, pulse-to-pulse amplitude fluctuations and timing jitter are two key factors that limit the performance of high-repetition-rate optical pulse trains in any application relying on the precise regularity and periodicity of these pulse trains.

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]

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]

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]

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]

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]

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]

*amplitude fluctuations*and

*timing jitter*of an optical pulse train [15

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]

**14**(10), 4270–4279 (2006). [CrossRef] [PubMed]

**14**(10), 4270–4279 (2006). [CrossRef] [PubMed]

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]

**14**(10), 4270–4279 (2006). [CrossRef] [PubMed]

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]

*simultaneous*amplitude fluctuation and timing jitter to recreate more realistic, thus more interesting, cases. Broadly speaking, we show that all the Talbot filtering configurations for PRRM can provide a mitigation of both the amplitude fluctuations and the timing jitter of the input pulse train; however, different filtering configurations provide a different level of mitigation and general noise performance. At last, performance of the PRRM filters concerning the pedestal of the output pulse train is also evaluated here.

**14**(10), 4270–4279 (2006). [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]

## 2. Filters design

**14**(10), 4270–4279 (2006). [CrossRef] [PubMed]

*f*and supposing a desired PRRM process by a factor

_{in}*m*, this PRRM operation can be achieved by filtering the original pulse train through either a single dispersive medium (e.g. a spool of fiber or a LC-FBG) or a spectrally periodic phase-only filtering device with a spectral period fixed by the output repetition rate, i.e.

*f*, where

_{out}=p(mf_{in})*p*can be any positive integer. Considering the first case, i.e. linear propagation of an input pulse train through a single first-order dispersive medium, fractional temporal Talbot effect is implemented when the medium’s dispersion coefficient satisfies the following condition:where

*T*is the input pulse period,

_{in}= 1/f_{in}*q = 1, 2, 3,...*and

*m = 1, 2, 3,...*such that

*(q/m)*is a non-integer and irreducible rational number [6

**7**(4), 728–744 (2001). [CrossRef]

*H(f) ∝ e*with:where the dispersion coefficient

^{jΦ(f)}^{2}/rad].

*m*following linear propagation through a dispersion medium with the first-order chromatic dispersion in Eq. (1). Figure 1 reports the phase function calculated from Eq. (2) with a dashed red line, considering the case of a 10-to-40 GHz PRRM process, with

*q*= 1 and

*m*= 4,

**14**(10), 4270–4279 (2006). [CrossRef] [PubMed]

*pm·f*and

_{in}*p = 1, 2, 3,...*. Equation (3) basically implies that in each period

*f*∈ (-kpmf

_{in}/2; kpmf

_{in}/2) and

*k = 0, ±1, ±2, ±3,...*. Thus, for a given input pulse rate

*f*and a given multiplication factor

_{in}*m*, we may identify a family made up of an infinite number of phase-only filters, just by changing

*p*(i.e. changing the spectral period of the filter), for each valid value of

*q*. In Fig. 1 several examples of

*p*, i.e. for different spectral periodicity, are reported, considering the same 10-to-40GHz PRRM process (multiplication factor

*m*= 4) and the two cases

*q*= 1,

*q*= 3. All these filters formally implement the same PRRM process. Please note that a single dispersive medium (i.e. single Talbot filter, dashed and dotted red lines in Fig. 1) is only a particular case of the general family defined by Eq. (3) for the case

*p→∞*. We recall that in practice, the spectrally-periodic quadratic phase filters defined by Eq. (3) can be implemented using superimposed LC-FBGs. A higher value of either the parameter

*p*(spectral period) or the parameter

*q*translates into a larger group-delay excursion in the filter’s transfer function, thus requiring the use of a longer device (the single Talbot filter, based on a single dispersive medium, LC-FBG, is the longest device among all the equivalent filtering configurations).

## 3. Simulation results and discussion

*N*= 1000 Gaussian pulses with a period

_{in}*T*= 100 ps (

_{in}*f*= 10GHz) and an individual pulse width (FWHM)

_{in}*τ*=5 ps is considered. To emulate a realistic case, we assume that each of the input pulses is affected by both amplitude and timing jitter. Thus, the input pulse train may be expressed by:where

_{FWHM}*p(t)*represents the individual short Gaussian pulse with a normalized peak amplitude,

*A*is the

_{n}*n*-th extraction of a normal random variable with mean 1 and standard deviation

*σ*= 0.06 (6% of ideal amplitude), governing the random independent amplitude fluctuation, and

_{A}*τ*is the

_{n}*n*-th extraction of a normal random variable with mean 0 and standard deviation

*σ*= 0.3 ps (6% of the FWHM), governing the random independent timing jitter.

_{τ}*H*where

_{p}(f) = e^{jΦp(f)}*S(f)*is the Fourier transform of

*s(t)*and

*F*stands for the inverse Fourier transform.

^{−1}*q*= 1), Fig. 2(a) shows the overlapped temporal amplitude traces of the

*N*input periods and Fig. 2(b)-(d) show the output (temporal amplitude traces) of the periodic filter for the two cases p = 3 and

_{in}*p*= 15 and the output of the single Talbot filter (single dispersive medium). A few comments are pretty evident from the figure. Consistently with previous works [15

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]

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]

*p*= 3 to

*p*= 15. At last, we can also anticipate a practically identical performance for the single Talbot filter and the periodic one with

*p*= 15 (Fig. 2(c) and 2(d) look essentially the same). This last statement can be easily understood by considering the behavior of the periodic parabolic phase variation as the parameter

*p*is increased in Fig. 1: for

*p→∞*the periodic filter tends to be identical to the single Talbot filter along the frequency range corresponding to the entire support of the input pulse spectrum.

*p*) presents a different, specific noise performance and is not equivalent to the single Talbot filter case, unless the factor

*p*is sufficiently high. In the case

*q*= 1, the amplitude fluctuation and time jitter improvements are both more significant as the spectral period (

*p*parameter) is increased, regardless of whether the two noise contributions are considered separately or simultaneously; as a result, the best performance is always achieved for the single Talbot filter case. Focusing on the case where both noises are present (Fig. 3(c) and Fig. 4(c)), another interesting observation is the highly different behavior of the amplitude fluctuation between the two cases

*q*= 1 and

*q*= 3, revealing a sort of mutual interaction between the two kinds of noise for

*q*= 3. For higher values of

*q*(

*q*= 5, 7, 9...) we have observed that the amplitude fluctuation exhibits a similar trend to that reported in Fig. 4(c) for

*q*= 3. To be more concrete, in the case

*q*= 3 (simultaneous presence of amplitude and time jitters, Fig. 4(c)), for several specific values of

*p*, the amplitude fluctuation improvement is more pronounced than that of the single Talbot filter and in particular, for

*p*= 4, 5 this improvement is even slightly better than that of the single Talbot filter for

*q*= 1 (Fig. 3(c)).

*τ*and

_{ratio}*A*) thresholds for the single Talbot filter decrease as the input pulse duty cycle (or the multiplication factor

_{ratio}*m*[15

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]

*q*from 1 to 3, the timing jitter ratio is improved whereas the amplitude fluctuation ratio gets worse (Fig. 5(a)); then, for higher values of

*q*, i.e. 5, 7, 9..., the results in terms of amplitude fluctuation and time jitter performances are essentially the same as those obtained for

*q*= 3.

*q*= 3) looks so different from Fig. 3(c) (

*q*= 1), we believe that the key point is that amplitude fluctuation and timing jitter are not completely independent with respect to each other for the cases where q>1. From additional simulations (not included in the present manuscript), it comes out that the filtering process itself leading to a mitigation of either timing jitter or amplitude fluctuation (through any of the alternative Talbot filtering configurations) induces additional amplitude fluctuation or timing jitter component (which increases with

*p*) at the filter output, respectively. Furthermore, the amount of such induced amplitude fluctuation/timing jitter increases by increasing the input timing jitter/amplitude fluctuation to be mitigated. Thus, the induced amplitude fluctuation/timing jitter can degrade the filter performance, especially for the single Talbot filter or for the periodic phase filters with high values of

*p*. As an example, we show in Fig. 5 that considering a timing jitter with

*σ*= 2% and an amplitude jitter with

_{t}*σ*= 12%, a result with opposite behavior to the one reported in Fig. 4(c) has been obtained.

_{A}*ER*) of the output pulse train, generally defined as the ratio between the amplitude peak of each pulse and the pedestal level between pulses. Since in our simulations no pedestal is assumed at the input pulse train, the input ER is consequently assumed to approach infinity. Considering a signal affected by stochastic noises, as in our analysis, we can define here an average output

*ER*as the ratio between the average of the pulse peak amplitudes of all the

*m*·

*N*output pulses and the average of the output pedestal level over the entire pulse train. In particular, we define the pedestal of the

_{in}*n*-th output period to be the signal ranging from the “time position of the

*n*-th peak” + 2

*τ*to the “time position of the

_{FWHM}*(n+1)*-th peak” - 2

*τ*. The average

_{FWHM}*ER*for the single Talbot filter decreases as the input duty cycle is increased, as reported in Fig. 6(b) . Moreover, this result is almost independent on the value of

*q*. Finally, when analyzing the output average

*ER*behavior for different spectral periods (Fig. 6(c)), we observe that the

*ER*fluctuates over a range of less than 1 dB and there is not a particularly relevant dependence with respect to the parameter

*q*; this observation applies to all cases except for

*p*= 1, for which the

*ER*reaches ~60 dB for any value of

*q*.

## 4. Conclusion

*q*) for which the improvements in the amplitude fluctuation are better than in the equivalent single Talbot case. Furthermore we analyzed noise performance for different input pulse train duty cycles and at last, we also evaluated the effect of these filters on the pedestal level between output pulses.

## References and links

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”, |

2. | J. Wells, “Faster than fiber: The future of multi-G/s wireless,” IEEE Microw. Mag. |

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 |

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. |

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. |

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. | J. Azaña and S. Gupta, “Complete family of periodic Talbot filters for pulse repetition rate multiplication,” Opt. Express |

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. |

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. |

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. |

11. | J. H. Lee, Y. Chang, Y. G. Han, S. Kim, and S. Lee, “2 ~ 5 times tunable repetition-rate multiplication of a 10 GHz pulse source using a linearly tunable, chirped fiber Bragg grating,” Opt. Express |

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. |

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. |

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. |

15. | D. Pudo and L. R. Chen, “Simple estimation of pulse amplitude noise and timing jitter evolution through the temporal Talbot effect,” Opt. Express |

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 |

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 |

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,” |

**OCIS Codes**

(030.4280) Coherence and statistical optics : Noise in imaging systems

(070.6760) Fourier optics and signal processing : Talbot and self-imaging effects

(100.5090) Image processing : Phase-only filters

(320.5540) Ultrafast optics : Pulse shaping

(320.5550) Ultrafast optics : Pulses

**ToC Category:**

Ultrafast Optics

**History**

Original Manuscript: May 12, 2011

Revised Manuscript: July 14, 2011

Manuscript Accepted: July 18, 2011

Published: July 26, 2011

**Citation**

Antonio Malacarne and José Azaña, "Analysis of amplitude fluctuation and timing jitter performance of spectrally periodic Talbot filters for optical pulse rate multiplication," Opt. Express **19**, 15339-15347 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-16-15339

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### References

- 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)
- J. Wells, “Faster than fiber: The future of multi-G/s wireless,” IEEE Microw. Mag. 10(3), 104–112 (2009). [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]
- 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]
- 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]
- 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 S. Gupta, “Complete family of periodic Talbot filters for pulse repetition rate multiplication,” Opt. Express 14(10), 4270–4279 (2006). [CrossRef] [PubMed]
- 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]
- 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]
- 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). [CrossRef] [PubMed]
- J. H. Lee, Y. Chang, Y. G. Han, S. Kim, and S. Lee, “2 ~ 5 times tunable repetition-rate multiplication of a 10 GHz pulse source using a linearly tunable, chirped fiber Bragg grating,” Opt. Express 12(17), 3900–3905 (2004). [CrossRef] [PubMed]
- 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]
- 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. 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]
- 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]
- 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]
- 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]
- 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.

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