Abstract

A spectral line-by-line pulse shaper is used to experimentally generate and deliver ~1 ps optical pulses of 31~124 GHz repetition-rates over 25.33 km single-mode fiber without dispersion-compensating fiber. The correlation of such delivery capability to temporal Talbot effect is experimentally demonstrated. Incorporating shaper periodic phase control, the repetition-rates of these ~1 ps optical pulses are further multiplied up to 496 GHz and delivered over 25.33 km single-mode fiber.

© 2010 OSA

1. Introduction

The generation of high repetition-rate optical pulses is playing an important role in high-speed optical fiber and microwave photonics systems. In particular, millimeter-wave (MMW) carriers in the W-band (75-110 GHz) or above are essential to meet the recent demand of gigabits wireless access applications [1]. Due to the relatively higher propagation loss of W-band signal than that of RF bands in free space, radio-over-fiber technology provides an efficient and cost-effective way to distribute synchronized photonic MMW waveforms from the central office to base stations. Such scheme has been recently adopted for photonic-assisted MMW carrier generations using optical pulse trains with 100 GHz repetition-rate or higher [2,3]. In these works, optical pulses with duration of a few picoseconds and below have been proven beneficial in providing enhanced MMW spectral power under a lower photocurrent. Short pulse excitations are thus capable of extending the lifetime and reliability of the delicate MMW photodetectors. However, highly stable ultrahigh-rate (> 100 GHz) short optical pulses may not be easily generated through conventional laser mode-locking or direct modulation techniques. On the other hand, the delivery of such short pulses over long optical fiber links also requires careful dispersion control. Therefore, a simple scheme capable of simultaneously generating and delivering ultrahigh-rate optical short pulses over arbitrary fiber link length is of extreme value.

Ultrahigh-rate optical pulses have been typically generated by performing repetition-rate multiplication (RRM) to an initially lower-rate pulse train, either by exploiting external amplitude [4,5] or spectral phase filtering [6]. Temporal Talbot effect, in which RRM can be obtained by self-imaging as the pulses propagate in a first-order dispersive medium, has been investigated extensively by Azaña and associates [7,8]. Various theoretical and experimental works have been carried out using fiber Bragg gratings [911] and planar lightwave circuits [12,13]. However, temporal Talbot effect is sensitive to the spectral phase and hinders its real application in a long-haul fiber communication system. In other demonstrations using optical fibers as quadratic phase filters [14,15], precise fiber lengths need to be carefully managed. For short optical pulses, the higher-order phase terms of the fiber link cannot be ignored due to the broad bandwidth, which also poses difficulty in achieving the RRM conditions.

The most widely adopted dispersion-compensation technique is to incorporate a segment of dispersion-compensating fiber (DCF) for a given single-mode fiber (SMF) length. Using this approach, most second-order and partial third-order dispersion of the SMF can be compensated. However, due to the broad optical bandwidth of ultrashort pulses, complete dispersion compensation is essential and remains a challenging task. Conventional optical pulse shapers [16,17] have been extremely useful in compensating the remaining higher-order dispersions of the SMF-DCF link [18,19].

By increasing the spectral resolution of a pulse shaper so that discrete frequency components are individually resolved, spectral line-by-line pulse shaping [20,21] integrates the functionality of a conventional optical pulse shaper and the fine attributes of an optical frequency comb [22]. With the ability to independently control the amplitude and phase of each frequency comb line, line-by-line pulse shaping enables highly stable pulse generation from a phase-modulated continuous-wave (PMCW) laser frequency comb [23,24], optical arbitrary waveform generations [21,2527], optical arbitrary pulse train generations [28], and RRM utilizing temporal Talbot effect [29,30]. Line-by-line pulse shaping with added time-multiplexing functionality has also been used to demonstrate rapid reprogrammable arbitrary microwave waveform generation [31] as well as the tailoring of microwave power spectra [32,33]. While these demonstrations focused on the waveform generation aspects, the delivery of the resulting shaped waveforms over long fiber links has not been fully addressed.

In this paper, 0.93 ps optical pulses are generated by applying spectral line-by-line pulse shaping on a 31 GHz spacing PMCW frequency comb. We first demonstrate experimentally the line-by-line pulse shaper is capable of delivering the 31 GHz pulses over arbitrary length of SMF without the need of DCF. Temporal self-imaging is clearly observed, and the correlation of such delivery capability to temporal Talbot effect is experimentally demonstrated. Secondly, the repetition-rate of the initial 31 GHz optical pulses is multiplied to 62, 93 and 124 GHz using shaper amplitude control and delivered over 25 km SMF using shaper phase control. Finally, with periodic Talbot phase values applied to the spacing converted PMCW combs, ~1 ps optical pulse trains with up to 496 GHz repetition-rate can be delivered over 25 km SMF using a single line-by-line shaper. Similar approach have been reported using a planar-lightwave circuits pulse shaper [34,35]. However, the utilization of Talbot RRM effects and the tight linkage of such delivery capability to temporal Talbot effect have not been addressed in these works. To the best of our knowledge, our result shows the highest repetition-rate short optical pulses delivered over long fiber links using a line-by-line pulse shaper, and the first application of Talbot effect aimed on remote MMW signal generations.

2. Experimental setup

Figure 1(a) shows the schematic of our experimental setup. The PMCW laser frequency comb is generated by injecting a 1 kHz-linewidth CW laser (NKT Adjustik) into a low-Vπ LiNbO3 phase modulator (EO Space, with Vπ ~2.8 V at 1 GHz). The phase modulator is driven by a sinusoidal signal with frequency frep, which determines the resulting optical frequency comb line spacing. The sinusoidal signal of 31 GHz is derived from an ultra-low phase noise RF signal generator (Agilent E8257D-UNX), amplified to + 33 dBm through a power amplifier to drive the phase modulator. The resulting 31 GHz PMCW frequency comb is sent to a reflective line-by-line optical pulse shaper. The details of our line-by-line shaper are as follows: A fiber-pigtailed collimator with 3.5 mm spot diameter is used to send the comb onto an 1100 grooves/mm gold-coated grating. Discrete comb lines are diffracted by the grating and focused by a lens with 400 mm focal length. A fiberized polarization controller is used to adjust for horizontal polarization on the grating. A computer controllable 2 × 640 pixel liquid crystal modulator (LCM, CRI SLM-640-D-NM) array is placed just before the focal plane of the lens to independently control both amplitude and phase of individual spectral lines. A retro-reflecting mirror placed on the Fourier plane of the lens leads to a double-pass geometry, with all the spectral lines recombined into a single fiber and separated from the input via an optical circulator. Combined with a polarizer placed between the collimator and the grating, gray level intensity control can be achieved with maximum extinction ratio up to ~27 dB limited by the LCM. The fiber-to-fiber insertion loss of the pulse shaper is 6.5 dB. A short pulse erbium-doped fiber amplifier (EDFA, Pritel LNHPFA-27) is placed after the pulse shaper. Optical spectra are measured through the ten-percent port of a 90/10 optical coupler using an optical spectrum analyzer (OSA, Advantest Q8384). The ninety-percent port of the coupler is either connected directly (back-to-back: b2b) or after a spool of SMF to a home-made non-collinear intensity autocorrelator.

 

Fig. 1 (a) Schematic of the experimental setup. PA: power amplifier; frep: comb frequency spacing; EDFA: erbium-doped fiber amplifier; SMF: single-mode fiber; b2b: back-to-back; OSA: optical spectrum analyzer. (b) 31 GHz comb optical power spectrum. The arrow indicates the CW laser wavelength. (c) Experimental (dot) and calculated (solid) intensity autocorrelation traces for the b2b case.

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Figure 1(b) shows the measured 31 GHz spacing PMCW frequency comb power spectrum, where the CW laser wavelength is indicated by the arrow. Figure 1(c) shows the experimental (dotted) and calculated (solid, assuming a flat phase condition) intensity autocorrelation (IA) traces in the b2b configuration after the line-by-line shaper applies a spectral phase correction setting Φ0(ω˜k)onto the comb lines through an automated process maximizing the second-harmonic generation (SHG) yield [2,21]. Here k is an integer (from −18 to 18 for our 37-line PMCW comb), ω˜kk(2πfrep) is the frequency offset of the k-th comb line as referenced to the CW laser frequency ω0. This procedure ensures the spectral phases of the PMCW comb, EDFA, and the optical coupler are all compensated. The resulting IA traces agree perfectly and give a 31 GHz pulse train with de-convoluted full-width half maximum (FWHM) duration of 0.93 ps. In all experiments, the average power of the 90-percent fiber coupler output port is fixed at 20 dBm. This power level prevents the formation of fundamental soliton in SMF link.

3. Result and discussion

3.1 Delivery of 31 GHz optical pulses over arbitrary fiber links

We first show that the same line-by-line pulse shaper generating transform-limited pulses from the 31 GHz PMCW comb is also capable of delivering these pulses over arbitrary SMF link without the need for DCF. This is made possible in unison with temporal Talbot effect. The accumulated spectral phase for a given fiber length L can be expressed as exp[jΦf(ω˜k)]=exp[jβ(ω˜k)L]. The nonlinear SMF spectral phases sampled by the discrete comb lines can be approximated using the Taylor series expansions as

Φf,NL(ω˜k)=(β2ω˜k2/2+β3ω˜k3/6)L,
where (β2, β3) denote the (second, third)-order derivatives of the propagation constant with respect to the center frequency, respectively. It is well known that the quadratic (β2) term broadens the pulse while the cubic (β3) term causes fast pulse oscillatory tails.

Figure 2 shows the pulse distortion and temporal self-imaging effects with spectral phase being provided solely by the fiber link. Figure 2(a) shows the IA traces (dot: experiment; solid, calculation) of the 31 GHz, 0.93 ps optical pulses after 20.46 km of SMF. The length of SMF is measured via an optical time-domain reflectometer. In the calculation, β2 = −20.3272 ps2/km and β3 = 0.1033 ps3/km are extracted and used for all calculations that follows. These values are in excellent agreement to the SMF specifications provided by the vendor (Sumitomo Electric). Interestingly, the IA traces exhibit pulses of doubled repetition-rate, however broadened and distorted. For ideal 2-times RRM, the even and odd comb lines effectively pick-up a nominal constant phase difference of π/2 as a result of accumulated quadratic (symmetric) phase [6,7]. While the 2-times RRM may be achieved using short optical fiber, in a long fiber link, the exact Talbot RRM phase condition cannot be satisfied unless extreme effort is devoted in balancing the second- and third-order phase terms [36,37].

 

Fig. 2 (a) Experimental (dotted) and calculated (solid) IA traces of the 31 GHz, 0.93 ps optical pulses after 20.46 km of SMF without dispersion pre-compensation. (b) Φrem of the 20.46 km SMF in units of 2π.

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To facilitate quantitative investigations, the spectral phase sampled by the comb lines in Eq. (1) is formulated as the sum of modulo of 2π and a remainder phase Φrem(ω˜k),

Φf,NL(ω˜k)=Nk2π+Φrem(ω˜k),
where Nk is the corresponding integer modulus for the k-th comb line, and Φrem(ω˜k) is between [0, 2π]. The remainder phase Φrem(ω˜k) of Eq. (2) in units of 2π for the 20.46 km SMF is shown in Fig. 2(b) as a function of comb line number. Indeed, a constant phase difference between the even and odd comb lines cannot be obtained due to the existence of the cubic spectral phase. These examples reveal that RRM via Talbot effect is extremely sensitive to the fiber parameters, precise length control and are difficult to implement in a long-haul transmission system. As we will show in section 3.2, a line-by-line shaper alleviates these encumbrances and is capable of delivering repetition-rate multiplied pulses over arbitrary fiber length.

Figure 3(a) shows the IA traces (dot: experiment; solid, calculation) of the 31 GHz, 0.93 ps distorted optical pulses after 25.33 km of SMF. In order to restore the initial pulse intensity waveform and periodicity, we now demonstrate only the remainder phase needs to be compensated. A dispersion pre-compensation phase setting of

Φpc,25km(ω˜k)=Φrem,25km(ω˜k)
is applied by the LCM deterministically. In this case, the total phase applied by the LCM is ΦLCM(ω˜k)=Φ0(ω˜k)+Φpc,25km(ω˜k). This procedure only requires the LCM being programmed to apply phases within a 2π range. Figure 3(b) shows the dispersion pre-compensation phase values applied by the LCM onto the comb lines in units of 2π. The dispersion pre-compensated IA traces are given in Fig. 3(c). Comparison between the experimental (dot) and calculated (solid) traces reveal that the optical pulses are restored perfectly. Dispersion pre-compensation for 20.46 km SMF is also performed using the same approach. The result is in excellent agreement to that shown in Fig. 3(c), and is thus not reproduced here.

 

Fig. 3 31 GHz, 0.93 ps optical pulses after 25.33 km of SMF: (a) Experimental (dotted) and calculated (solid) IA traces without dispersion pre-compensation. (b) Dispersion pre-compensation values in units of 2π applied by the LCM onto the comb lines. (c) Dispersion pre-compensated IA traces (dot: experiment; solid, calculation). (d) Remaining uncompensated spectral phase in units of 2π.

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We note here since the pulse shaper is not able to fully compensate the dispersion of a long fiber link, the capability of delivering undistorted optical pulse train using only a line-by-line shaper over such link is in strong unison with temporal Talbot effect. Figure 3(d) shows the remaining uncompensated phases in units of 2π, that is, Nk for each corresponding comb line. It is evident that the remaining uncompensated phases result in a large quadratic phase and thus leads to huge pulse broadening that leads to the temporal self-imaging. It is evident such approach is an excellent platform for remote delivery of ultrahigh-rate clock signals, but not for data transmission. Under the circumstance where the phase of each comb line is an integer multiple of 2π, the coherent re-distribution of the fields satisfies the integer Talbot condition [7], and the original optical pulse train is restored. We note here the IA measurement provides an examination of the initial comb characteristics: our intrinsic 1 kHz laser linewidth gives a coherence length of 200 km within fiber. This sets the idealized upper limit of the maximum allowed fiber delivery length of this approach since phase noise introduced by the fiber has not been taken into account. Beyond this link length, integer Talbot condition will corrupt since coherence is no longer preserved.

As SHG is sensitive to the optical pulse duration, in addition to comparing the IA traces, the maximum SHG yield due to fiber loss is now quantitatively compared. The loss of the 25.33 km SMF spool is ~5.8 dB, thus the SHG yield should drop by a factor of 14.6 as compared to the back-to-back case. This well taken, as the ratio of the peak SHG value of 56 mV (back-to-back, Fig. 1(c)) to 3.8 mV (after 25.33 km SMF, Fig. 3(c)) gives 14.7.

3.2 Delivery of ultrahigh-rate pulses over 25 km single-mode fiber

In this part, ultrahigh-rate optical pulse trains are generated and delivered over 25.33 km of SMF through two approaches: (1) Shaper spectral filtering followed by phase pre-compensation. (2) Additional periodic phases for (2, 4)-times RRM are impressed onto the spectrally filtered comb lines.

Figures 4(a-c) show the experimental spectrally filtered optical power spectra of the {62, 93, and 124}-GHz spacing combs. A nominal 27 dB extinction ratio is achieved in suppressing the comb lines. Although lacking an adequate electrical spectrum analyzer and photodetector for such a large frequency range (31 to 124 GHz) for quantitative analysis, the resulting RF signal purity limited by the shaper extinction ratio is studied numerically. For the three amplitude filtered pulse trains, there should still be residual 31 GHz electrical signals due to the unsuppressed comb lines. The 31 GHz electrical signal values of (−20.99, −20.81, and −20.65)-dBc as referenced to the {62, 93, and 124}-GHz beat tones are obtained for the results shown in Fig. 4(a-c), respectively. Methods to greatly improve the signal purity have been addressed within Ref [2]. The recovered pulse durations are slight broadened during spectral filtering due to slight reduced comb bandwidth. The FWHM pulse durations are labeled within Figs. 4(d-f), where experimental and calculated dispersion pre-compensated IA traces are compared. In all cases, dispersion pre-compensation value as described by Eq. (3) is applied on the spacing-converted combs by the LCM.

 

Fig. 4 (a-c) Optical power spectra of (62, 93, and 124)-GHz comb using shaper amplitude control, respectively. Experimental and calculated dispersion pre-compensated pulse train IA traces delivered over 25 km SMF for (d) 62, (e) 93, and (f) 124 GHz spacing combs. In (d-f), the de-convolved pulse duration and peak SHG readings are labeled.

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The power relation of the peak SHG yield due to different repetition-rate multiplication factor is examined. The peak SHG is expressed as P(t)P(t) [17], where P(t) denotes the waveform instantaneous power and <> denotes the time integration. For a fixed average power, the peak pulse power of the M-times repetition-rate multiplied train drops by a factor of M, but within the original pulse period, there are now M pulses. The resulting SHG peak value for repetition-rate multiplied pulse train is thus proportional to M/M 2, which drops linearly with M. For example, in the 31 to 62 GHz comb spacing conversion demonstration, the SHG peak is expected to drop by a factor of two. Referenced to the SHG peak of 3.8 mV in Fig. 3(c), all peak SHG values labeled in Figs. 4(d-f) are in good accord to this power relation, corroborating that the shortest optical pulses are delivered over 25.33 km optical fiber link.

Temporal Talbot effect is now applied through the shaper LCM so that pulse trains with even higher repetition-rates can be delivered over 25.33 km of SMF. A clear distinction as compared to that shown in Fig. 2(a) is that the pulse shaper allows flexible fine tuning of either excessive or deficient spectral phase provided solely by a given fiber link so ideal Talbot condition can be satisfied. Periodic spectral phases of Φ2x(ω) = {0, π/2} and Φ4x(ω) = {0, 0, π, 0} [6] are added onto the {31, 62, 93, and 124}-GHz comb lines for 2-times and 4-times RRM, respectively. For example, the phase applied by the LCM, within a range of 2π, for the 2-times RRM case is ΦLCM(ω˜k)=Φ0(ω˜k)+Φpc,25km(ω˜k)+Φ2x(ω˜k).

Figure 5(a) shows the (62, 124)-GHz optical pulse train originating from the 31 GHz spacing comb after 2-times (black) and 4-times (blue) RRM delivered over 25.33 km SMF. Experimental (solid) IA traces are compared along with calculated (symbols) IA traces. The 1/M peak SHG value dependence is corroborated by examining the SHG values in Fig. 5(a), where peak SHG values of (1.75, 0.83)-mV for the (2, 4)-times RRM are in good accord as compared to the 3.8 mV shown in Fig. 3(c).

 

Fig. 5 Experimental (symbol) and calculated (solid) IA traces of ultrahigh-rate optical pulse train generated and delivered over 25.33 km SMF using temporal Talbot phase control for 2- and 4-times RRM onto (a) 31 GHz, (b) 62 GHz, (c) 93 GHz, and (d) 124 GHz combs.

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Figures 5(b-d) show the 2- and 4-times RRM IA traces originating from the 62, 93, and 124 GHz spacing combs after 25.33 km of SMF, respectively. In Fig. 5(d), our result show that 1.04 ps pulses with 496 GHz repetition-rate can be generated and delivered over long optical fiber link using a single line-by-line pulse shaper. In all IA traces, excellent agreements in waveforms and SHG yields are obtained. Compared to Fig. 5(a), the non-uniform SHG peaks observed for amplitude filtered combs imply that the pulses within the repetition-rate multiplied train are of unequal height. This is due to two reasons: (1) the finite extinction ratio of the shaper amplitude control and (2) pulse overlapping in reaching a higher RRM factor [38]. The unsuppressed comb lines due to finite shaper extinction prevented us in performing further amplitude equalization to the remaining lines in order to achieve better pulse envelope uniformity. Our numerical study shows that the SHG peak variation for the 496 GHz pulse train can be reduced from the current 34% to 10% if ideal spectral filtering and the ensuing comb line amplitude equalization are performed. Broad combs with flat spectral envelope are highly desirable in this context, since a shorter pulse prevents temporal overlapping after RRM. Our numerical study shows if there can be 20 remaining 124 GHz comb lines, the SHG peak variation can be drastically reduced to 2.8%. An alternative approach to equalize the pulse amplitudes has been demonstrated by incorporating genetic algorithm into shaper phase tunings [29].

We note here the combination of PMCW comb and line-by-line shaper enables flexible repetition-rate tuning capability. This can be accomplished simply by changing the phase modulation frequency and the ensuing shaper design. Essentially one can obtain mostly any repetition-rate desired, as long as the individual pulses in the rate multiplied train remain well separated.

4. Conclusion and future work

In summary, 0.93 ps optical pulse train with 31 GHz repetition-rates are generated by applying spectral line-by-line pulse shaping on a 31 GHz spacing phase-modulated CW laser frequency comb. Working in unison with temporal Talbot effect, a line-by-line pulse shaper can deliver these short pulses over 25.33 km of single-mode fiber without the need of dispersion compensating fiber. The correlation of such delivery capability to temporal Talbot effect is experimentally demonstrated. Using shaper amplitude filtering, ~1 ps optical pulses with 62, 93, and 124 GHz repetition-rates are perfectly delivered over 25.33 km of single-mode fiber. By applying periodic temporal Talbot phases, the repetition-rate of these ~1 ps optical pulses are further multiplied up to 496 GHz and delivered over 25.33 km SMF using the line-by-line shaper. To the best of our knowledge, this is the highest repetition-rate short optical pulses are delivered over long fiber links using a line-by-line pulse shaper, and the first application of Talbot effect in this context.

Our results demonstrate a single line-by-line pulse shaper is capable of simultaneously generating and delivering short ultrahigh-rate optical pulses over arbitrary fiber link length. This unique optical source should find interesting applications such as remote MMW carrier generations with enhanced spectral power and the ensuing wireless data transmissions. Experiments in these directions are underway.

Acknowledgement

This work was supported by the National Science Council of Taiwan under contract NSC 97-2112-M-007-025-MY3. C.-B. Huang wishes to acknowledge Prof. S.-D. Yang for the support on intensity autocorrelator, Prof. K.-M. Feng for the support on optical fiber modules, and Allen P. Chang of Agilent Taiwan for the support on the 60 GHz signal generator.

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33. C.-B. Huang and A. M. Weiner, “Analysis of time-multiplexed optical line-by-line pulse shaping: application for radio-frequency and microwave photonics,” Opt. Express 18(9), 9366–9377 (2010). [CrossRef]   [PubMed]  

34. D. J. Geisler, N. K. Fontaine, R. P. Scott, K. Okamoto, J. P. Heritage, and S. J. Ben Yoo, “360 Gb/s optical transmitter with arbitrary modulation format and dispersion precompensation,” IEEE Photon. Technol. Lett. 21(7), 489–491 (2009). [CrossRef]  

35. D. J. Geisler, N. K. Fontaine, R. P. Scott, T. He, L. Paraschis, J. P. Heritage, and S. J. B. Yoo, “400-Gb/s Modulation-Format-Independent Single-Channel Transmission With Chromatic Dispersion Precompensation Based on OAWG,” IEEE Photon. Technol. Lett. 22(12), 905–907 (2010). [CrossRef]  

36. D. Duchesne, R. Morandotti, and J. Azaña, “Temporal Talbot phenomena in higher-order dispersive media,” J. Opt. Soc. Am. B 24(1), 113–125 (2007). [CrossRef]  

37. J. Fatome, S. Pitois, and G. Millot, “Influence of third-order dispersion on the temporal Talbot effect,” Opt. Commun. 234(1-6), 29–34 (2004). [CrossRef]  

38. L. Chantada, C. R. Fernández-Pousa, and C. Gómez-Reino, “Spectral analysis of the temporal self-imaging phenomenon in fiber dispersive lines,” J. Lightwave Technol. 24(5), 2015–2025 (2006). [CrossRef]  

References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  27. V. R. Supradeepa, C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Femtosecond pulse shaping in two dimensions: towards higher complexity optical waveforms,” Opt. Express 16(16), 11878–11887 (2008).
    [Crossref] [PubMed]
  28. Z. Jiang, C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Spectral line-by-line pulse shaping for optical arbitrary pulse train generation,” J. Opt. Soc. Am. B 24(9), 2124–2128 (2007).
    [Crossref]
  29. 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]
  30. J. Caraquitena, Z. Jiang, D. E. Leaird, and A. M. Weiner, “Simultaneous repetition-rate multiplication and envelope control based on periodic phase-only and phase-mostly line-by-line pulse shaping,” J. Opt. Soc. Am. B 24(12), 3034–3039 (2007).
    [Crossref]
  31. C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Time-multiplexed photonically enabled radio-frequency arbitrary waveform generation with 100 ps transitions,” Opt. Lett. 32(22), 3242–3244 (2007).
    [Crossref] [PubMed]
  32. C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Synthesis of millimeter-wave power spectra using time-multiplexed optical pulse shaping,” IEEE Photon. Technol. Lett. 21(18), 1287–1289 (2009).
    [Crossref]
  33. C.-B. Huang and A. M. Weiner, “Analysis of time-multiplexed optical line-by-line pulse shaping: application for radio-frequency and microwave photonics,” Opt. Express 18(9), 9366–9377 (2010).
    [Crossref] [PubMed]
  34. D. J. Geisler, N. K. Fontaine, R. P. Scott, K. Okamoto, J. P. Heritage, and S. J. Ben Yoo, “360 Gb/s optical transmitter with arbitrary modulation format and dispersion precompensation,” IEEE Photon. Technol. Lett. 21(7), 489–491 (2009).
    [Crossref]
  35. D. J. Geisler, N. K. Fontaine, R. P. Scott, T. He, L. Paraschis, J. P. Heritage, and S. J. B. Yoo, “400-Gb/s Modulation-Format-Independent Single-Channel Transmission With Chromatic Dispersion Precompensation Based on OAWG,” IEEE Photon. Technol. Lett. 22(12), 905–907 (2010).
    [Crossref]
  36. D. Duchesne, R. Morandotti, and J. Azaña, “Temporal Talbot phenomena in higher-order dispersive media,” J. Opt. Soc. Am. B 24(1), 113–125 (2007).
    [Crossref]
  37. J. Fatome, S. Pitois, and G. Millot, “Influence of third-order dispersion on the temporal Talbot effect,” Opt. Commun. 234(1-6), 29–34 (2004).
    [Crossref]
  38. L. Chantada, C. R. Fernández-Pousa, and C. Gómez-Reino, “Spectral analysis of the temporal self-imaging phenomenon in fiber dispersive lines,” J. Lightwave Technol. 24(5), 2015–2025 (2006).
    [Crossref]

2010 (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]

P. Samadi, L. R. Chen, I. A. Kostko, P. Dumais, C. L. Callender, S. Jacob, and B. Shia, “Generating 4x20 and 4x40 GHz pulse trains from a single 10-GHz mode-locked laser using a tunable planar lightwave circuit,” IEEE Photon. Technol. Lett. 22(5), 281–282 (2010).
[Crossref]

C.-B. Huang and A. M. Weiner, “Analysis of time-multiplexed optical line-by-line pulse shaping: application for radio-frequency and microwave photonics,” Opt. Express 18(9), 9366–9377 (2010).
[Crossref] [PubMed]

D. J. Geisler, N. K. Fontaine, R. P. Scott, T. He, L. Paraschis, J. P. Heritage, and S. J. B. Yoo, “400-Gb/s Modulation-Format-Independent Single-Channel Transmission With Chromatic Dispersion Precompensation Based on OAWG,” IEEE Photon. Technol. Lett. 22(12), 905–907 (2010).
[Crossref]

2009 (4)

C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Synthesis of millimeter-wave power spectra using time-multiplexed optical pulse shaping,” IEEE Photon. Technol. Lett. 21(18), 1287–1289 (2009).
[Crossref]

D. J. Geisler, N. K. Fontaine, R. P. Scott, K. Okamoto, J. P. Heritage, and S. J. Ben Yoo, “360 Gb/s optical transmitter with arbitrary modulation format and dispersion precompensation,” IEEE Photon. Technol. Lett. 21(7), 489–491 (2009).
[Crossref]

M. S. Kirchner, D. A. Braje, T. M. Fortier, A. M. Weiner, L. Hollberg, and S. A. Diddams, “Generation of 20 GHz, sub-40 fs pulses at 960 nm via repetition-rate multiplication,” Opt. Lett. 34(7), 872–874 (2009).
[Crossref] [PubMed]

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

2008 (2)

2007 (8)

Z. Jiang, C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Spectral line-by-line pulse shaping for optical arbitrary pulse train generation,” J. Opt. Soc. Am. B 24(9), 2124–2128 (2007).
[Crossref]

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. Caraquitena, Z. Jiang, D. E. Leaird, and A. M. Weiner, “Simultaneous repetition-rate multiplication and envelope control based on periodic phase-only and phase-mostly line-by-line pulse shaping,” J. Opt. Soc. Am. B 24(12), 3034–3039 (2007).
[Crossref]

C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Time-multiplexed photonically enabled radio-frequency arbitrary waveform generation with 100 ps transitions,” Opt. Lett. 32(22), 3242–3244 (2007).
[Crossref] [PubMed]

Z. Jiang, C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Optical arbitrary waveform processing of more than 100 spectral comb lines,” Nat. Photonics 1(8), 463–467 (2007).
[Crossref]

N. K. Fontaine, R. P. Scott, J. Cao, A. Karalar, W. Jiang, K. Okamoto, J. P. Heritage, B. H. Kolner, and S. J. B. Yoo, “32 Phase X 32 amplitude optical arbitrary waveform generation,” Opt. Lett. 32(7), 865–867 (2007).
[Crossref] [PubMed]

D. Duchesne, R. Morandotti, and J. Azaña, “Temporal Talbot phenomena in higher-order dispersive media,” J. Opt. Soc. Am. B 24(1), 113–125 (2007).
[Crossref]

M. A. Preciado and M. A. Muriel, “Ultrafast all-optical Nth-order differentiator and simultaneous repetition-rate multiplier of periodic pulse train,” Opt. Express 15(19), 12102–12107 (2007).
[Crossref] [PubMed]

2006 (4)

2005 (5)

2004 (1)

J. Fatome, S. Pitois, and G. Millot, “Influence of third-order dispersion on the temporal Talbot effect,” Opt. Commun. 234(1-6), 29–34 (2004).
[Crossref]

2003 (1)

2001 (2)

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]

D. E. Leaird, S. Shen, A. M. Weiner, A. Sugita, S. Kamei, M. Ishii, and K. Okamoto, “Generation of high repetition rate WDM pulse trains from an arrayed-waveguide grating,” IEEE Photon. Lett. 13(3), 221–223 (2001).
[Crossref]

2000 (2)

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71(5), 1929–1960 (2000).
[Crossref]

C.-B. Huang and Y. C. Lai, “Loss-less pulse intensity repetition-rate multiplication using optical all-pass filtering,” IEEE Photon. Technol. Lett. 12(2), 167–169 (2000).
[Crossref]

1998 (2)

1989 (1)

T. Sizer, “Increase in laser repetition rate by spectral selection,” IEEE J. Quantum Electron. 25(1), 97–103 (1989).
[Crossref]

Arahira, S.

Azaña, J.

Ben Yoo, S. J.

D. J. Geisler, N. K. Fontaine, R. P. Scott, K. Okamoto, J. P. Heritage, and S. J. Ben Yoo, “360 Gb/s optical transmitter with arbitrary modulation format and dispersion precompensation,” IEEE Photon. Technol. Lett. 21(7), 489–491 (2009).
[Crossref]

Berrettini, G.

G. Meloni, G. Berrettini, M. Scaffardi, A. Bogoni, L. Poti, and M. Guglielmucci, “250-times repetition frequency multiplication for 2.5 THz clock signal generation,” Electron. Lett. 41(23), 1294 (2005).
[Crossref]

Bogoni, A.

G. Meloni, G. Berrettini, M. Scaffardi, A. Bogoni, L. Poti, and M. Guglielmucci, “250-times repetition frequency multiplication for 2.5 THz clock signal generation,” Electron. Lett. 41(23), 1294 (2005).
[Crossref]

Bolger, J.

Braje, D. A.

Callender, C. L.

P. Samadi, L. R. Chen, I. A. Kostko, P. Dumais, C. L. Callender, S. Jacob, and B. Shia, “Generating 4x20 and 4x40 GHz pulse trains from a single 10-GHz mode-locked laser using a tunable planar lightwave circuit,” IEEE Photon. Technol. Lett. 22(5), 281–282 (2010).
[Crossref]

Cao, J.

Caraquitena, J.

Chang, C.-C.

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]

Diddams, S. A.

Duchesne, D.

Dumais, P.

P. Samadi, L. R. Chen, I. A. Kostko, P. Dumais, C. L. Callender, S. Jacob, and B. Shia, “Generating 4x20 and 4x40 GHz pulse trains from a single 10-GHz mode-locked laser using a tunable planar lightwave circuit,” IEEE Photon. Technol. Lett. 22(5), 281–282 (2010).
[Crossref]

Eggleton, B. J.

Fatome, J.

J. Fatome, S. Pitois, and G. Millot, “Influence of third-order dispersion on the temporal Talbot effect,” Opt. Commun. 234(1-6), 29–34 (2004).
[Crossref]

Fernández-Pousa, C. R.

Fontaine, N. K.

D. J. Geisler, N. K. Fontaine, R. P. Scott, T. He, L. Paraschis, J. P. Heritage, and S. J. B. Yoo, “400-Gb/s Modulation-Format-Independent Single-Channel Transmission With Chromatic Dispersion Precompensation Based on OAWG,” IEEE Photon. Technol. Lett. 22(12), 905–907 (2010).
[Crossref]

D. J. Geisler, N. K. Fontaine, R. P. Scott, K. Okamoto, J. P. Heritage, and S. J. Ben Yoo, “360 Gb/s optical transmitter with arbitrary modulation format and dispersion precompensation,” IEEE Photon. Technol. Lett. 21(7), 489–491 (2009).
[Crossref]

N. K. Fontaine, R. P. Scott, J. Cao, A. Karalar, W. Jiang, K. Okamoto, J. P. Heritage, B. H. Kolner, and S. J. B. Yoo, “32 Phase X 32 amplitude optical arbitrary waveform generation,” Opt. Lett. 32(7), 865–867 (2007).
[Crossref] [PubMed]

Fortier, T. M.

Geisler, D. J.

D. J. Geisler, N. K. Fontaine, R. P. Scott, T. He, L. Paraschis, J. P. Heritage, and S. J. B. Yoo, “400-Gb/s Modulation-Format-Independent Single-Channel Transmission With Chromatic Dispersion Precompensation Based on OAWG,” IEEE Photon. Technol. Lett. 22(12), 905–907 (2010).
[Crossref]

D. J. Geisler, N. K. Fontaine, R. P. Scott, K. Okamoto, J. P. Heritage, and S. J. Ben Yoo, “360 Gb/s optical transmitter with arbitrary modulation format and dispersion precompensation,” IEEE Photon. Technol. Lett. 21(7), 489–491 (2009).
[Crossref]

Gómez-Reino, C.

Guglielmucci, M.

G. Meloni, G. Berrettini, M. Scaffardi, A. Bogoni, L. Poti, and M. Guglielmucci, “250-times repetition frequency multiplication for 2.5 THz clock signal generation,” Electron. Lett. 41(23), 1294 (2005).
[Crossref]

Gupta, S.

Harada, M.

He, T.

D. J. Geisler, N. K. Fontaine, R. P. Scott, T. He, L. Paraschis, J. P. Heritage, and S. J. B. Yoo, “400-Gb/s Modulation-Format-Independent Single-Channel Transmission With Chromatic Dispersion Precompensation Based on OAWG,” IEEE Photon. Technol. Lett. 22(12), 905–907 (2010).
[Crossref]

Heritage, J. P.

D. J. Geisler, N. K. Fontaine, R. P. Scott, T. He, L. Paraschis, J. P. Heritage, and S. J. B. Yoo, “400-Gb/s Modulation-Format-Independent Single-Channel Transmission With Chromatic Dispersion Precompensation Based on OAWG,” IEEE Photon. Technol. Lett. 22(12), 905–907 (2010).
[Crossref]

D. J. Geisler, N. K. Fontaine, R. P. Scott, K. Okamoto, J. P. Heritage, and S. J. Ben Yoo, “360 Gb/s optical transmitter with arbitrary modulation format and dispersion precompensation,” IEEE Photon. Technol. Lett. 21(7), 489–491 (2009).
[Crossref]

N. K. Fontaine, R. P. Scott, J. Cao, A. Karalar, W. Jiang, K. Okamoto, J. P. Heritage, B. H. Kolner, and S. J. B. Yoo, “32 Phase X 32 amplitude optical arbitrary waveform generation,” Opt. Lett. 32(7), 865–867 (2007).
[Crossref] [PubMed]

Hirata, A.

Hollberg, L.

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]

C.-B. Huang and A. M. Weiner, “Analysis of time-multiplexed optical line-by-line pulse shaping: application for radio-frequency and microwave photonics,” Opt. Express 18(9), 9366–9377 (2010).
[Crossref] [PubMed]

C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Synthesis of millimeter-wave power spectra using time-multiplexed optical pulse shaping,” IEEE Photon. Technol. Lett. 21(18), 1287–1289 (2009).
[Crossref]

V. R. Supradeepa, C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Femtosecond pulse shaping in two dimensions: towards higher complexity optical waveforms,” Opt. Express 16(16), 11878–11887 (2008).
[Crossref] [PubMed]

C.-B. Huang, S.-G. Park, D. E. Leaird, and A. M. Weiner, “Nonlinearly broadened phase-modulated continuous-wave laser frequency combs characterized using DPSK decoding,” Opt. Express 16(4), 2520–2527 (2008).
[Crossref] [PubMed]

Z. Jiang, C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Optical arbitrary waveform processing of more than 100 spectral comb lines,” Nat. Photonics 1(8), 463–467 (2007).
[Crossref]

Z. Jiang, C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Spectral line-by-line pulse shaping for optical arbitrary pulse train generation,” J. Opt. Soc. Am. B 24(9), 2124–2128 (2007).
[Crossref]

C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Time-multiplexed photonically enabled radio-frequency arbitrary waveform generation with 100 ps transitions,” Opt. Lett. 32(22), 3242–3244 (2007).
[Crossref] [PubMed]

C.-B. Huang, Z. Jiang, D. E. Leaird, and A. M. Weiner, “High-rate femtosecond pulse generation via line-by-line processing of a phase-modulated CW laser frequency comb,” Electron. Lett. 42(19), 1114–1115 (2006).
[Crossref]

C.-B. Huang and Y. C. Lai, “Loss-less pulse intensity repetition-rate multiplication using optical all-pass filtering,” IEEE Photon. Technol. Lett. 12(2), 167–169 (2000).
[Crossref]

Ishii, M.

D. E. Leaird, S. Shen, A. M. Weiner, A. Sugita, S. Kamei, M. Ishii, and K. Okamoto, “Generation of high repetition rate WDM pulse trains from an arrayed-waveguide grating,” IEEE Photon. Lett. 13(3), 221–223 (2001).
[Crossref]

Jacob, S.

P. Samadi, L. R. Chen, I. A. Kostko, P. Dumais, C. L. Callender, S. Jacob, and B. Shia, “Generating 4x20 and 4x40 GHz pulse trains from a single 10-GHz mode-locked laser using a tunable planar lightwave circuit,” IEEE Photon. Technol. Lett. 22(5), 281–282 (2010).
[Crossref]

Jiang, W.

Jiang, Z.

Z. Jiang, C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Spectral line-by-line pulse shaping for optical arbitrary pulse train generation,” J. Opt. Soc. Am. B 24(9), 2124–2128 (2007).
[Crossref]

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]

Z. Jiang, C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Optical arbitrary waveform processing of more than 100 spectral comb lines,” Nat. Photonics 1(8), 463–467 (2007).
[Crossref]

J. Caraquitena, Z. Jiang, D. E. Leaird, and A. M. Weiner, “Simultaneous repetition-rate multiplication and envelope control based on periodic phase-only and phase-mostly line-by-line pulse shaping,” J. Opt. Soc. Am. B 24(12), 3034–3039 (2007).
[Crossref]

C.-B. Huang, Z. Jiang, D. E. Leaird, and A. M. Weiner, “High-rate femtosecond pulse generation via line-by-line processing of a phase-modulated CW laser frequency comb,” Electron. Lett. 42(19), 1114–1115 (2006).
[Crossref]

Z. Jiang, D. E. Leaird, and A. M. Weiner, “Line-by-line pulse shaping control for optical arbitrary waveform generation,” Opt. Express 13(25), 10431–10439 (2005).
[Crossref] [PubMed]

Z. Jiang, S.-D. Yang, D. E. Leaird, and A. M. Weiner, “Fully dispersion-compensated 500 fs pulse transmission over 50 km single-mode fiber,” Opt. Lett. 30(12), 1449–1451 (2005).
[Crossref] [PubMed]

Z. Jiang, D. S. Seo, D. E. Leaird, and A. M. Weiner, “Spectral line-by-line pulse shaping,” Opt. Lett. 30(12), 1557–1559 (2005).
[Crossref] [PubMed]

Kamei, S.

D. E. Leaird, S. Shen, A. M. Weiner, A. Sugita, S. Kamei, M. Ishii, and K. Okamoto, “Generation of high repetition rate WDM pulse trains from an arrayed-waveguide grating,” IEEE Photon. Lett. 13(3), 221–223 (2001).
[Crossref]

Karalar, A.

Kirchner, M. S.

Kolner, B. H.

Kostko, I. A.

P. Samadi, L. R. Chen, I. A. Kostko, P. Dumais, C. L. Callender, S. Jacob, and B. Shia, “Generating 4x20 and 4x40 GHz pulse trains from a single 10-GHz mode-locked laser using a tunable planar lightwave circuit,” IEEE Photon. Technol. Lett. 22(5), 281–282 (2010).
[Crossref]

Kunimatsu, D.

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]

Kutsuzawa, S.

Lai, Y. C.

C.-B. Huang and Y. C. Lai, “Loss-less pulse intensity repetition-rate multiplication using optical all-pass filtering,” IEEE Photon. Technol. Lett. 12(2), 167–169 (2000).
[Crossref]

LaRochelle, S.

Leaird, D. E.

C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Synthesis of millimeter-wave power spectra using time-multiplexed optical pulse shaping,” IEEE Photon. Technol. Lett. 21(18), 1287–1289 (2009).
[Crossref]

V. R. Supradeepa, C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Femtosecond pulse shaping in two dimensions: towards higher complexity optical waveforms,” Opt. Express 16(16), 11878–11887 (2008).
[Crossref] [PubMed]

C.-B. Huang, S.-G. Park, D. E. Leaird, and A. M. Weiner, “Nonlinearly broadened phase-modulated continuous-wave laser frequency combs characterized using DPSK decoding,” Opt. Express 16(4), 2520–2527 (2008).
[Crossref] [PubMed]

Z. Jiang, C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Optical arbitrary waveform processing of more than 100 spectral comb lines,” Nat. Photonics 1(8), 463–467 (2007).
[Crossref]

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]

Z. Jiang, C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Spectral line-by-line pulse shaping for optical arbitrary pulse train generation,” J. Opt. Soc. Am. B 24(9), 2124–2128 (2007).
[Crossref]

C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Time-multiplexed photonically enabled radio-frequency arbitrary waveform generation with 100 ps transitions,” Opt. Lett. 32(22), 3242–3244 (2007).
[Crossref] [PubMed]

J. Caraquitena, Z. Jiang, D. E. Leaird, and A. M. Weiner, “Simultaneous repetition-rate multiplication and envelope control based on periodic phase-only and phase-mostly line-by-line pulse shaping,” J. Opt. Soc. Am. B 24(12), 3034–3039 (2007).
[Crossref]

C.-B. Huang, Z. Jiang, D. E. Leaird, and A. M. Weiner, “High-rate femtosecond pulse generation via line-by-line processing of a phase-modulated CW laser frequency comb,” Electron. Lett. 42(19), 1114–1115 (2006).
[Crossref]

Z. Jiang, D. E. Leaird, and A. M. Weiner, “Line-by-line pulse shaping control for optical arbitrary waveform generation,” Opt. Express 13(25), 10431–10439 (2005).
[Crossref] [PubMed]

Z. Jiang, D. S. Seo, D. E. Leaird, and A. M. Weiner, “Spectral line-by-line pulse shaping,” Opt. Lett. 30(12), 1557–1559 (2005).
[Crossref] [PubMed]

Z. Jiang, S.-D. Yang, D. E. Leaird, and A. M. Weiner, “Fully dispersion-compensated 500 fs pulse transmission over 50 km single-mode fiber,” Opt. Lett. 30(12), 1449–1451 (2005).
[Crossref] [PubMed]

D. E. Leaird, S. Shen, A. M. Weiner, A. Sugita, S. Kamei, M. Ishii, and K. Okamoto, “Generation of high repetition rate WDM pulse trains from an arrayed-waveguide grating,” IEEE Photon. Lett. 13(3), 221–223 (2001).
[Crossref]

Magné, J.

Matsui, Y.

Meloni, G.

G. Meloni, G. Berrettini, M. Scaffardi, A. Bogoni, L. Poti, and M. Guglielmucci, “250-times repetition frequency multiplication for 2.5 THz clock signal generation,” Electron. Lett. 41(23), 1294 (2005).
[Crossref]

Millot, G.

J. Fatome, S. Pitois, and G. Millot, “Influence of third-order dispersion on the temporal Talbot effect,” Opt. Commun. 234(1-6), 29–34 (2004).
[Crossref]

Morandotti, R.

Muriel, M. A.

M. A. Preciado and M. A. Muriel, “Ultrafast all-optical Nth-order differentiator and simultaneous repetition-rate multiplier of periodic pulse train,” Opt. Express 15(19), 12102–12107 (2007).
[Crossref] [PubMed]

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]

Nagatsuma, T.

Ogawa, Y.

Okamoto, K.

D. J. Geisler, N. K. Fontaine, R. P. Scott, K. Okamoto, J. P. Heritage, and S. J. Ben Yoo, “360 Gb/s optical transmitter with arbitrary modulation format and dispersion precompensation,” IEEE Photon. Technol. Lett. 21(7), 489–491 (2009).
[Crossref]

N. K. Fontaine, R. P. Scott, J. Cao, A. Karalar, W. Jiang, K. Okamoto, J. P. Heritage, B. H. Kolner, and S. J. B. Yoo, “32 Phase X 32 amplitude optical arbitrary waveform generation,” Opt. Lett. 32(7), 865–867 (2007).
[Crossref] [PubMed]

D. E. Leaird, S. Shen, A. M. Weiner, A. Sugita, S. Kamei, M. Ishii, and K. Okamoto, “Generation of high repetition rate WDM pulse trains from an arrayed-waveguide grating,” IEEE Photon. Lett. 13(3), 221–223 (2001).
[Crossref]

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]

Paraschis, L.

D. J. Geisler, N. K. Fontaine, R. P. Scott, T. He, L. Paraschis, J. P. Heritage, and S. J. B. Yoo, “400-Gb/s Modulation-Format-Independent Single-Channel Transmission With Chromatic Dispersion Precompensation Based on OAWG,” IEEE Photon. Technol. Lett. 22(12), 905–907 (2010).
[Crossref]

Park, S.-G.

Pitois, S.

J. Fatome, S. Pitois, and G. Millot, “Influence of third-order dispersion on the temporal Talbot effect,” Opt. Commun. 234(1-6), 29–34 (2004).
[Crossref]

Poti, L.

G. Meloni, G. Berrettini, M. Scaffardi, A. Bogoni, L. Poti, and M. Guglielmucci, “250-times repetition frequency multiplication for 2.5 THz clock signal generation,” Electron. Lett. 41(23), 1294 (2005).
[Crossref]

Preciado, M. A.

Pudo, D.

Rochette, M.

Samadi, P.

P. Samadi, L. R. Chen, I. A. Kostko, P. Dumais, C. L. Callender, S. Jacob, and B. Shia, “Generating 4x20 and 4x40 GHz pulse trains from a single 10-GHz mode-locked laser using a tunable planar lightwave circuit,” IEEE Photon. Technol. Lett. 22(5), 281–282 (2010).
[Crossref]

Sardesai, H. P.

Scaffardi, M.

G. Meloni, G. Berrettini, M. Scaffardi, A. Bogoni, L. Poti, and M. Guglielmucci, “250-times repetition frequency multiplication for 2.5 THz clock signal generation,” Electron. Lett. 41(23), 1294 (2005).
[Crossref]

Scott, R. P.

D. J. Geisler, N. K. Fontaine, R. P. Scott, T. He, L. Paraschis, J. P. Heritage, and S. J. B. Yoo, “400-Gb/s Modulation-Format-Independent Single-Channel Transmission With Chromatic Dispersion Precompensation Based on OAWG,” IEEE Photon. Technol. Lett. 22(12), 905–907 (2010).
[Crossref]

D. J. Geisler, N. K. Fontaine, R. P. Scott, K. Okamoto, J. P. Heritage, and S. J. Ben Yoo, “360 Gb/s optical transmitter with arbitrary modulation format and dispersion precompensation,” IEEE Photon. Technol. Lett. 21(7), 489–491 (2009).
[Crossref]

N. K. Fontaine, R. P. Scott, J. Cao, A. Karalar, W. Jiang, K. Okamoto, J. P. Heritage, B. H. Kolner, and S. J. B. Yoo, “32 Phase X 32 amplitude optical arbitrary waveform generation,” Opt. Lett. 32(7), 865–867 (2007).
[Crossref] [PubMed]

Seo, D. S.

Shen, S.

D. E. Leaird, S. Shen, A. M. Weiner, A. Sugita, S. Kamei, M. Ishii, and K. Okamoto, “Generation of high repetition rate WDM pulse trains from an arrayed-waveguide grating,” IEEE Photon. Lett. 13(3), 221–223 (2001).
[Crossref]

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]

Shia, B.

P. Samadi, L. R. Chen, I. A. Kostko, P. Dumais, C. L. Callender, S. Jacob, and B. Shia, “Generating 4x20 and 4x40 GHz pulse trains from a single 10-GHz mode-locked laser using a tunable planar lightwave circuit,” IEEE Photon. Technol. Lett. 22(5), 281–282 (2010).
[Crossref]

Sizer, T.

T. Sizer, “Increase in laser repetition rate by spectral selection,” IEEE J. Quantum Electron. 25(1), 97–103 (1989).
[Crossref]

Sugita, A.

D. E. Leaird, S. Shen, A. M. Weiner, A. Sugita, S. Kamei, M. Ishii, and K. Okamoto, “Generation of high repetition rate WDM pulse trains from an arrayed-waveguide grating,” IEEE Photon. Lett. 13(3), 221–223 (2001).
[Crossref]

Supradeepa, V. R.

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.

C.-B. Huang and A. M. Weiner, “Analysis of time-multiplexed optical line-by-line pulse shaping: application for radio-frequency and microwave photonics,” Opt. Express 18(9), 9366–9377 (2010).
[Crossref] [PubMed]

C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Synthesis of millimeter-wave power spectra using time-multiplexed optical pulse shaping,” IEEE Photon. Technol. Lett. 21(18), 1287–1289 (2009).
[Crossref]

M. S. Kirchner, D. A. Braje, T. M. Fortier, A. M. Weiner, L. Hollberg, and S. A. Diddams, “Generation of 20 GHz, sub-40 fs pulses at 960 nm via repetition-rate multiplication,” Opt. Lett. 34(7), 872–874 (2009).
[Crossref] [PubMed]

V. R. Supradeepa, C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Femtosecond pulse shaping in two dimensions: towards higher complexity optical waveforms,” Opt. Express 16(16), 11878–11887 (2008).
[Crossref] [PubMed]

C.-B. Huang, S.-G. Park, D. E. Leaird, and A. M. Weiner, “Nonlinearly broadened phase-modulated continuous-wave laser frequency combs characterized using DPSK decoding,” Opt. Express 16(4), 2520–2527 (2008).
[Crossref] [PubMed]

Z. Jiang, C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Optical arbitrary waveform processing of more than 100 spectral comb lines,” Nat. Photonics 1(8), 463–467 (2007).
[Crossref]

Z. Jiang, C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Spectral line-by-line pulse shaping for optical arbitrary pulse train generation,” J. Opt. Soc. Am. B 24(9), 2124–2128 (2007).
[Crossref]

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]

C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Time-multiplexed photonically enabled radio-frequency arbitrary waveform generation with 100 ps transitions,” Opt. Lett. 32(22), 3242–3244 (2007).
[Crossref] [PubMed]

J. Caraquitena, Z. Jiang, D. E. Leaird, and A. M. Weiner, “Simultaneous repetition-rate multiplication and envelope control based on periodic phase-only and phase-mostly line-by-line pulse shaping,” J. Opt. Soc. Am. B 24(12), 3034–3039 (2007).
[Crossref]

C.-B. Huang, Z. Jiang, D. E. Leaird, and A. M. Weiner, “High-rate femtosecond pulse generation via line-by-line processing of a phase-modulated CW laser frequency comb,” Electron. Lett. 42(19), 1114–1115 (2006).
[Crossref]

Z. Jiang, D. E. Leaird, and A. M. Weiner, “Line-by-line pulse shaping control for optical arbitrary waveform generation,” Opt. Express 13(25), 10431–10439 (2005).
[Crossref] [PubMed]

Z. Jiang, D. S. Seo, D. E. Leaird, and A. M. Weiner, “Spectral line-by-line pulse shaping,” Opt. Lett. 30(12), 1557–1559 (2005).
[Crossref] [PubMed]

Z. Jiang, S.-D. Yang, D. E. Leaird, and A. M. Weiner, “Fully dispersion-compensated 500 fs pulse transmission over 50 km single-mode fiber,” Opt. Lett. 30(12), 1449–1451 (2005).
[Crossref] [PubMed]

D. E. Leaird, S. Shen, A. M. Weiner, A. Sugita, S. Kamei, M. Ishii, and K. Okamoto, “Generation of high repetition rate WDM pulse trains from an arrayed-waveguide grating,” IEEE Photon. Lett. 13(3), 221–223 (2001).
[Crossref]

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71(5), 1929–1960 (2000).
[Crossref]

C.-C. Chang, H. P. Sardesai, and A. M. Weiner, “Dispersion-free fiber transmission for femtosecond pulses by use of a dispersion-compensating fiber and a programmable pulse shaper,” Opt. Lett. 23(4), 283–285 (1998).
[Crossref]

Wells, J.

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

Yang, S.-D.

Yoo, S. J. B.

D. J. Geisler, N. K. Fontaine, R. P. Scott, T. He, L. Paraschis, J. P. Heritage, and S. J. B. Yoo, “400-Gb/s Modulation-Format-Independent Single-Channel Transmission With Chromatic Dispersion Precompensation Based on OAWG,” IEEE Photon. Technol. Lett. 22(12), 905–907 (2010).
[Crossref]

N. K. Fontaine, R. P. Scott, J. Cao, A. Karalar, W. Jiang, K. Okamoto, J. P. Heritage, B. H. Kolner, and S. J. B. Yoo, “32 Phase X 32 amplitude optical arbitrary waveform generation,” Opt. Lett. 32(7), 865–867 (2007).
[Crossref] [PubMed]

Electron. Lett. (2)

G. Meloni, G. Berrettini, M. Scaffardi, A. Bogoni, L. Poti, and M. Guglielmucci, “250-times repetition frequency multiplication for 2.5 THz clock signal generation,” Electron. Lett. 41(23), 1294 (2005).
[Crossref]

C.-B. Huang, Z. Jiang, D. E. Leaird, and A. M. Weiner, “High-rate femtosecond pulse generation via line-by-line processing of a phase-modulated CW laser frequency comb,” Electron. Lett. 42(19), 1114–1115 (2006).
[Crossref]

IEEE J. Quantum Electron. (1)

T. Sizer, “Increase in laser repetition rate by spectral selection,” IEEE J. Quantum Electron. 25(1), 97–103 (1989).
[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-Gb/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. Lett. (1)

D. E. Leaird, S. Shen, A. M. Weiner, A. Sugita, S. Kamei, M. Ishii, and K. Okamoto, “Generation of high repetition rate WDM pulse trains from an arrayed-waveguide grating,” IEEE Photon. Lett. 13(3), 221–223 (2001).
[Crossref]

IEEE Photon. Technol. Lett. (5)

P. Samadi, L. R. Chen, I. A. Kostko, P. Dumais, C. L. Callender, S. Jacob, and B. Shia, “Generating 4x20 and 4x40 GHz pulse trains from a single 10-GHz mode-locked laser using a tunable planar lightwave circuit,” IEEE Photon. Technol. Lett. 22(5), 281–282 (2010).
[Crossref]

C.-B. Huang and Y. C. Lai, “Loss-less pulse intensity repetition-rate multiplication using optical all-pass filtering,” IEEE Photon. Technol. Lett. 12(2), 167–169 (2000).
[Crossref]

C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Synthesis of millimeter-wave power spectra using time-multiplexed optical pulse shaping,” IEEE Photon. Technol. Lett. 21(18), 1287–1289 (2009).
[Crossref]

D. J. Geisler, N. K. Fontaine, R. P. Scott, K. Okamoto, J. P. Heritage, and S. J. Ben Yoo, “360 Gb/s optical transmitter with arbitrary modulation format and dispersion precompensation,” IEEE Photon. Technol. Lett. 21(7), 489–491 (2009).
[Crossref]

D. J. Geisler, N. K. Fontaine, R. P. Scott, T. He, L. Paraschis, J. P. Heritage, and S. J. B. Yoo, “400-Gb/s Modulation-Format-Independent Single-Channel Transmission With Chromatic Dispersion Precompensation Based on OAWG,” IEEE Photon. Technol. Lett. 22(12), 905–907 (2010).
[Crossref]

J. Lightwave Technol. (5)

J. Opt. Soc. Am. B (3)

Nat. Photonics (1)

Z. Jiang, C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Optical arbitrary waveform processing of more than 100 spectral comb lines,” Nat. Photonics 1(8), 463–467 (2007).
[Crossref]

Opt. Commun. (1)

J. Fatome, S. Pitois, and G. Millot, “Influence of third-order dispersion on the temporal Talbot effect,” Opt. Commun. 234(1-6), 29–34 (2004).
[Crossref]

Opt. Express (6)

Opt. Lett. (7)

M. S. Kirchner, D. A. Braje, T. M. Fortier, A. M. Weiner, L. Hollberg, and S. A. Diddams, “Generation of 20 GHz, sub-40 fs pulses at 960 nm via repetition-rate multiplication,” Opt. Lett. 34(7), 872–874 (2009).
[Crossref] [PubMed]

C.-C. Chang, H. P. Sardesai, and A. M. Weiner, “Dispersion-free fiber transmission for femtosecond pulses by use of a dispersion-compensating fiber and a programmable pulse shaper,” Opt. Lett. 23(4), 283–285 (1998).
[Crossref]

Z. Jiang, S.-D. Yang, D. E. Leaird, and A. M. Weiner, “Fully dispersion-compensated 500 fs pulse transmission over 50 km single-mode fiber,” Opt. Lett. 30(12), 1449–1451 (2005).
[Crossref] [PubMed]

Z. Jiang, D. S. Seo, D. E. Leaird, and A. M. Weiner, “Spectral line-by-line pulse shaping,” Opt. Lett. 30(12), 1557–1559 (2005).
[Crossref] [PubMed]

N. K. Fontaine, R. P. Scott, J. Cao, A. Karalar, W. Jiang, K. Okamoto, J. P. Heritage, B. H. Kolner, and S. J. B. Yoo, “32 Phase X 32 amplitude optical arbitrary waveform generation,” Opt. Lett. 32(7), 865–867 (2007).
[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]

C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Time-multiplexed photonically enabled radio-frequency arbitrary waveform generation with 100 ps transitions,” Opt. Lett. 32(22), 3242–3244 (2007).
[Crossref] [PubMed]

Rev. Sci. Instrum. (1)

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71(5), 1929–1960 (2000).
[Crossref]

Other (2)

A. M. Weiner, Ultrafast Optics (Wiley, 2009).

J. Ye, and S. T. Cundiff, eds., Femtosecond Optical Frequency Comb: Principle, Operation, and Applications (Springer, 2005).

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Figures (5)

Fig. 1
Fig. 1

(a) Schematic of the experimental setup. PA: power amplifier; frep: comb frequency spacing; EDFA: erbium-doped fiber amplifier; SMF: single-mode fiber; b2b: back-to-back; OSA: optical spectrum analyzer. (b) 31 GHz comb optical power spectrum. The arrow indicates the CW laser wavelength. (c) Experimental (dot) and calculated (solid) intensity autocorrelation traces for the b2b case.

Fig. 2
Fig. 2

(a) Experimental (dotted) and calculated (solid) IA traces of the 31 GHz, 0.93 ps optical pulses after 20.46 km of SMF without dispersion pre-compensation. (b) Φrem of the 20.46 km SMF in units of 2π.

Fig. 3
Fig. 3

31 GHz, 0.93 ps optical pulses after 25.33 km of SMF: (a) Experimental (dotted) and calculated (solid) IA traces without dispersion pre-compensation. (b) Dispersion pre-compensation values in units of 2π applied by the LCM onto the comb lines. (c) Dispersion pre-compensated IA traces (dot: experiment; solid, calculation). (d) Remaining uncompensated spectral phase in units of 2π.

Fig. 4
Fig. 4

(a-c) Optical power spectra of (62, 93, and 124)-GHz comb using shaper amplitude control, respectively. Experimental and calculated dispersion pre-compensated pulse train IA traces delivered over 25 km SMF for (d) 62, (e) 93, and (f) 124 GHz spacing combs. In (d-f), the de-convolved pulse duration and peak SHG readings are labeled.

Fig. 5
Fig. 5

Experimental (symbol) and calculated (solid) IA traces of ultrahigh-rate optical pulse train generated and delivered over 25.33 km SMF using temporal Talbot phase control for 2- and 4-times RRM onto (a) 31 GHz, (b) 62 GHz, (c) 93 GHz, and (d) 124 GHz combs.

Equations (3)

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Φ f , N L ( ω ˜ k ) = ( β 2 ω ˜ k 2 / 2 + β 3 ω ˜ k 3 / 6 ) L ,
Φ f , N L ( ω ˜ k ) = N k 2 π + Φ r e m ( ω ˜ k ) ,
Φ p c , 25 k m ( ω ˜ k ) = Φ r e m , 25 k m ( ω ˜ k )

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