Repetition rate multiplication of femtosecond
light pulses using a phase-locked all-pass fiber
resonator
Joohyung Lee,1,2 Seung-Woo Kim,1 and Young-Jin Kim1,3,*
1
Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon,
305-701, South Korea
2
Present address: Center for Space Optics, Korea Research Institute of Standards and Science (KRISS), Daejeon,
305-340, South Korea
3
Present address: School of Mechanical and Aerospace Engineering, Nanyang Technological University (NTU),
639798, Singapore
*
[email protected]
Abstract: We describe an all-pass fiber resonator with active phase-locking
capability for accurate multiplication of the repetition rate of femtosecond
light pulses. The cavity length of the resonator is precisely controlled using
the Pounder-Drever-Hall phase-locking technique so that the repetition rate
is multiplied in stabilization to the Rb atomic clock. Our test result proves
the proposed phase-locking scheme is an effective means of generating
higher repetition rate pulses with no significant power loss while providing
a high degree of long-term stability.
©2015 Optical Society of America
OCIS codes: (140.7090) Ultrafast lasers; (140.4050) Mode-locked lasers; (140.3425) Laser
stabilization; (120.3930) Metrological instrumentation.
References and links
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
R. Holzwarth, T. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Optical frequency
synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85(11), 2264–2267 (2000).
D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrierenvelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science
288(5466), 635–639 (2000).
J. Ye, H. J. Kimble, and H. Katori, “Quantum state engineering and precision metrology using state-insensitive
light traps,” Science 320(5884), 1734–1738 (2008).
J. J. McFerran, E. N. Ivanov, G. Wilpers, C. W. Oates, S. A. Diddams, and L. Hollberg, “Low noise synthesis of
microwave signals from an optical source,” Electron. Lett. 41(11), 36–37 (2005).
A. Bartels, S. A. Diddams, C. W. Oates, G. Wilpers, J. C. Bergquist, W. H. Oskay, and L. Hollberg,
“Femtosecond-laser-based synthesis of ultrastable microwave signals from optical frequency references,” Opt.
Lett. 30(6), 667–669 (2005).
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).
S. T. Cundiff and A. M. Weiner, “Optical arbitrary waveform generation,” Nat. Photonics 4(11), 760–766
(2010).
C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi,
and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1
cm-1,” Nature 452(7187), 610–612 (2008).
T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S.
D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical
observations,” Science 321(5894), 1335–1337 (2008).
G. C. Valley, “Photonic analog-to-digital converters,” Opt. Express 15(5), 1955–1982 (2007).
J. Kim, M. J. Park, M. H. Perrott, and F. X. Kärtner, “Photonic subsampling analog-to-digital conversion of
microwave signals at 40-GHz with higher than 7-ENOB resolution,” Opt. Express 16(21), 16509–16515 (2008).
T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y.
Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,”
Nat. Photonics 5(7), 425–429 (2011).
K. Minoshima and H. Matsumoto, “High-accuracy measurement of 240-m distance in an optical tunnel by use of
a compact femtosecond laser,” Appl. Opt. 39(30), 5512–5517 (2000).
J. Ye, “Absolute measurement of a long, arbitrary distance to less than an optical fringe,” Opt. Lett. 29(10),
1153–1155 (2004).
#235511 - $15.00 USD
© 2015 OSA
Received 3 Mar 2015; revised 7 Apr 2015; accepted 7 Apr 2015; published 10 Apr 2015
20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.010117 | OPTICS EXPRESS 10117
15. I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance
measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
16. J. Lee, Y.-J. Kim, K. Lee, S. Lee, and S.-W. Kim, “Time-of-flight measurement using femtosecond light pulses,”
Nat. Photonics 4(10), 716–720 (2010).
17. S. A. Diddams, “The evolving optical frequency comb,” J. Opt. Soc. Am. B 27(11), B51–B62 (2010).
18. H. Byun, M. Y. Sander, A. Motamedi, H. Shen, G. S. Petrich, L. A. Kolodziejski, E. P. Ippen, and F. X. Kärtner,
“Compact, stable 1 GHz femtosecond Er-doped fiber lasers,” Appl. Opt. 49(29), 5577–5582 (2010).
19. A. Martinez and S. Yamashita, “Multi-gigahertz repetition rate passively modelocked fiber lasers using carbon
nanotubes,” Opt. Express 19(7), 6155–6163 (2011).
20. J. Chen, J. W. Sickler, P. Fendel, E. P. Ippen, F. X. Kärtner, T. Wilken, R. Holzwarth, and T. W. Hänsch,
“Generation of low-timing-jitter femtosecond pulse trains with 2 GHz repetition rate via external repetition rate
multiplication,” Opt. Lett. 33(9), 959–961 (2008).
21. 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).
22. A. Haboucha, W. Zhang, T. Li, M. Lours, A. N. Luiten, Y. Le Coq, and G. Santarelli, “Optical-fiber pulse rate
multiplier for ultralow phase-noise signal generation,” Opt. Lett. 36(18), 3654–3656 (2011).
23. H. Jiang, J. Taylor, F. Quinlan, T. Fortier, and S. A. Diddams, “Floor reduction of an Er:fiber laserbased photonic microwave generator,” IEEE Photon. J. 3(6), 1004–1012 (2011).
24. Y. Zhao, S. S. Min, H. C. Wang, and S. Fleming, “High-power figure-of-eight fiber laser with passive sub-ring
loops for repetition rate control,” Opt. Express 14(22), 10475–10480 (2006).
25. M. A. Preciado and M. A. Muriel, “Repetition-rate multiplication using a single all-pass optical cavity,” Opt.
Lett. 33(9), 962–964 (2008).
26. M. A. Preciado and M. A. Muriel, “All-pass optical structures for repetition rate multiplication,” Opt. Express
16(15), 11162–11168 (2008).
27. L. F. Stokes, M. Chodorow, and H. J. Shaw, “All-single-mode fiber resonator,” Opt. Lett. 7(6), 288–290 (1982).
28. R. W. P. Drever, J. L. Hall, F. V. Kovralski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and
frequency stabilization using an optical resonator,” Appl. Phys. B 31(2), 97–105 (1983).
29. E. D. Black, “An introduction to Pound-Drever-Hall laser frequency stabilization,” Am. J. Phys. 69(1), 79–87
(2001).
30. Y. Kim, Y.-J. Kim, S. Kim, and S.-W. Kim, “Er-doped fiber comb with enhanced fceo S/N ratio using Tm:Hodoped fiber,” Opt. Express 17(21), 18606–18611 (2009).
31. Y. Kim, S. Kim, Y.-J. Kim, H. Hussein, and S.-W. Kim, “Er-doped fiber frequency comb with mHz relative
linewidth,” Opt. Express 17(14), 11972–11977 (2009).
32. J. Kim, J. A. Cox, J. Chen, and F. X. Kärtner, “Drift-free femtosecond timing synchronization of remote optical
and microwave sources,” Nat. Photonics 2(12), 733–736 (2008).
33. Y. Song, C. Kim, K. Jung, H. Kim, and J. Kim, “Timing jitter optimization of mode-locked Yb-fiber lasers
toward the attosecond regime,” Opt. Express 19(15), 14518–14525 (2011).
34. C. Kim, K. Jung, K. Kieu, and J. Kim, “Low timing jitter and intensity noise from a soliton Er-fiber laser modelocked by a fiber taper carbon nanotube saturable absorber,” Opt. Express 20(28), 29524–29530 (2012).
35. J. Kim, J. Chen, Z. Zhang, F. N. C. Wong, F. X. Kärtner, F. Loehl, and H. Schlarb, “Long-term femtosecond
timing link stabilization using a single-crystal balanced cross correlator,” Opt. Lett. 32(9), 1044–1046 (2007).
36. Y.-J. Kim, I. Coddington, W. C. Swann, N. R. Newbury, J. Lee, S. Kim, and S.-W. Kim, “Time-domain
stabilization of carrier-envelope phase in femtosecond light pulses,” Opt. Express 22(10), 11788–11796 (2014).
1. Introduction
Efforts are being made to bring the repetition rate of femtosecond light pulses upward,
preferably to the upper GHz regime, in response to the need in diverse applications; optical
frequency metrology [1–3], optical communications [4,5], arbitrary waveform generation
[6,7], calibration of astronomical spectrographs [8,9], photonic analog-to-digital converters
[10,11], microwave generation [12], and absolute distance measurements [13–16]. The pulse
repetition rate produced by an oscillator may be increased simply by shortening the cavity
length of the oscillator. However, this approach has limitations as it reduces the pulse peak
power which should be kept above a certain threshold to maintain the nonlinear mode locking
to produce normal short pulses [17]. The problem becomes more apparent for rare-earthdoped fiber lasers in which the gain medium has to be embedded along a lengthy fiber. The
state-of-the-art repetition rate of rare-earth-doped fiber lasers demonstrates above 1 GHz,
even though it is being limited by the rare-earth doping density of available gain fibers and its
physical length [18,19].
Pulse-interleaving performed by incorporating extra devices at the exit of the oscillator
permits producing higher repetition rate pulses. This approach of so-called repetition rate
multiplication has been demonstrated so far using Fabry-Perot etalons [20,21], Mach-Zehnder
interferometers [22,23] and sub-ring fiber resonators [24–26]. These methods have their own
#235511 - $15.00 USD
© 2015 OSA
Received 3 Mar 2015; revised 7 Apr 2015; accepted 7 Apr 2015; published 10 Apr 2015
20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.010117 | OPTICS EXPRESS 10118
merits and disadvantages particularly in terms of the hardware complexity and pulse energy
loss. For example, a single Fabry-Perot cavity is enough to sort out of the optical modes of the
frequency comb up to several tens of GHz spacing using the Hänsch–Couillaud locking
technique [20], but the pulse energy is weakened in proportion to the filter spacing. In the
case of unequal-arm Mach-Zehnder interferometers (MZIs), a single MZI leads to only
doubling of the repetition rate, requiring multiple MZIs cascaded in series to achieve a high
multiplication. Nonetheless, a 50% of the pulse energy is lost at every 2x2 coupler exit
junction of each MZI. On the other hand, the fiber sub-ring resonator is most effective in
conserving the pulse energy since it acts as an all-pass type resonator which transmits all the
input pulse energy through the exit junction without significant loss [25].
In this investigation, we demonstrate a phase-locked sub-ring fiber resonator devised for
stable multiplication of the repetition rate of an Er-doped fiber oscillator. The cavity length of
the sub-ring resonator is controlled using the Pound-Drever-Hall (PDH) locking technique so
that the temporal interval of pulse-interleaving is stabilized to the original pulses of the main
Er-doped oscillator [27–29]. Then the stability of multiplied pulses are tested to validate the
proposed resonator with phase-locking capability as an effective means of generating higher
repetition rate pulses with no significant power loss while providing a high degree of longterm stability.
2. All-pass fiber resonator for repetition rate multiplication
The fiber resonator intended to multiply the repetition rate in the time domain can be treated
as a periodic spectral filter in the frequency domain, which suppresses the frequency modes of
the frequency comb with an interval of the free spectral range (FSR) of the fiber resonator
(Fig. 1(a)). In this study an all-pass fiber resonator was devised by combining a single-mode
fiber with a fiber coupler of variable coupling ratio (Fig. 1(b)).
Fig. 1. Multiplication of the pulse repetition rate fr by an optical fiber resonator. (a) Conceptual
diagram of fr multiplication in the frequency domain. (b) Schematic of all-pass fiber resonator
structure for fr multiplication. (c) Selective filtering of optical modes by the transmittance of
the fiber resonator (solid black line). Red solid lines and red dotted line refer to the survived
and filtered optical modes, respectively.
The spectral transmittance Tcavity of the fiber resonator is expressed as [27]
Tcavity (ω ) =
#235511 - $15.00 USD
© 2015 OSA
I
out
I
in

= (1 − γ 0 ) 1 −



2
sin ( β L / 2 − π / 4) 

(1 − k r )
2
(1 + k r ) − 4 k r
2
(1)
Received 3 Mar 2015; revised 7 Apr 2015; accepted 7 Apr 2015; published 10 Apr 2015
20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.010117 | OPTICS EXPRESS 10119
where Iin and Iout are the input and output intensity of the all-pass fiber resonator. The other
variables are; γ0 the insertion loss, kr the resonant coupling ratio of the variable coupler, β the
propagation constant and L the optical path length of the fiber resonator. As shown in Fig.
1(c), the spectral transmittance of the fiber resonator provides resonant peaks repeatedly at the
positions where the condition of sin2(βL/2-π/4) = 1 is precisely met. For effective filtering, the
transmittance at the resonant peaks is made null by tuning the coupling ratio so as to satisfy kr
= (1-γ0)·exp(-2α0L) with α0 being the net attenuation within the fiber resonator. Consequently,
when the spectral modes of the main oscillator are overlapped with the transmittance of the
resonator, the frequency modes located at zero-transmittance positions are eliminated.
Figure 2 illustrates the optical layout of the phase-locked repetition rate multiplication
system configured in this study. It is comprised of an Er-doped fiber oscillator, an all-pass
fiber resonator and a Pound-Drever-Hall (PDH) phase-locking control unit. The Er-doped
fiber femtosecond laser (Menlosystems, C-Fiber) was used as the main oscillator which is set
to provide a pulse train of 100-fs duration at a 100-MHz repetition rate being stabilized to the
Rb clock with a 10−12 stability (10-s averaging) using the PLL technique [30,31]. The output
frequency of the main oscillator are then modulated using an electro-optic modulator (EOM,
Newfocus, 4004) for subsequent PDH phase-locking control of the cavity length of the fiber
resonator.
fr
2fr
Fig. 2. System configuration for phase-locked fr multiplication, LO: local oscillator, EOM:
electro-optic modulator, fr: pulse repetition rate, LPF: low-pass filter, CL: collimating lens, PD:
photodetector.
The fiber resonator is comprised of a single-mode fiber (Corning, SMF-28) and a
directional coupler with its coupling ratio being manually adjustable (Newport, F-CPL-1550).
The coupling ratio of the resonator is first coarsely tuned so that the relative intensity
fluctuation between the original and interleaved pulses is minimized by monitoring the
multiplied pulses using an oscilloscope together with an RF spectrum analyzer. The middle
point of the fiber resonator is separated and light-coupled via free space using two collimating
lenses. One of the lenses is mounted on a translational stage coupled with a PZT actuator for
fine motion control in order to precisely adjust the cavity length. The total optical path length
(OPL) of the fiber resonator including the single-mode fiber and also the free space is
controlled to be accurately half of the OPL of the main oscillator using the PDH technique,
enabling the resonating modes of the resonator to overlap exactly with the original modes of
the main oscillator. For the PDH locking, the EOM is set to modulate the optical phase of the
main oscillator at 1 kHz with a 100 Hz modulation depth. The PDH error signal is then
captured using a photo-detector and demodulated through a lock-in amplifier (Stanford
#235511 - $15.00 USD
© 2015 OSA
Received 3 Mar 2015; revised 7 Apr 2015; accepted 7 Apr 2015; published 10 Apr 2015
20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.010117 | OPTICS EXPRESS 10120
Research Systems, SR510). The PDH error signal is loop-filtered and fed-back to a
proportional-integral (PI) servo (Newport, LB1005) with a 1 kHz control bandwidth which
controls the PZT actuator to lock the cavity length of the resonator to precisely half of the
original oscillator cavity length.
More specifically, for the PDH locking control, the frequency ω(t) of the main oscillator is
modulated by the EOM with a sinusoidal voltage input as [28,29]
ω (t ) =
d
(ωt + σ sin Ωt ) = ω + Ωσ cos Ωt
dt
(2)
where σ is the modulation depth and Ω is the EOM modulation frequency. Assuming both σ
and Ω are small, the time-varying output intensity of the fiber resonator is approximated as
dI out (ω )
Ωσ cos Ωt
dω
dTcavity
= I out (ω ) + I in
Ωσ cos Ωt
dω
I out (ω + Ωσ cos Ωt ) ≈ I out (ω ) +
(3)
The derivative of the transmittance, i.e., dTcavity/dω, is then extracted by demodulation of the
output intensity of Eq. (3) using the lock-in amplifier in synchronization with the modulation
frequency Ω, and finally locked to the zero-crossing point as illustrated in Fig. 3.
Fig. 3. Conceptual diagram of the PDH lock-in signal, (a) Variation of the output amplitude
(red) with respect to the frequency mismatch between the frequency modulated input (green)
and transmittance peak (black). The point ‘C‘ corresponds to the zero-crossing PDH signal of
the steepest slope, while ‘B’ and ’D’ refer to the maximum and minimum amplitudes. (b) Sshape curve for the PDH lock-in technique.
3. Experiments and performance evaluation
Figure 4(a) shows a set of transmittance curves of the all-pass fiber resonator used in this
study calculated with different values of the net attenuation and coupling-ratio so as to
provide zero-transmittance at the resonant peaks. The cavity finesse decreases significantly
from 60 to 3 while the net attenuation increases from −0.1 dB to −2.0 dB. Nevertheless, the
linewidth of the resonant peaks is maintained within tens of MHz, which is narrow enough to
spectrally filter 100 MHz-spaced spectral modes of the main oscillator to 200 MHz-spaced
modes. In our experiments, the net-attenuation of the fiber cavity was selected to be −1.2 dB
in consideration of the light-coupling loss occurring between the collimating lenses installed
#235511 - $15.00 USD
© 2015 OSA
Received 3 Mar 2015; revised 7 Apr 2015; accepted 7 Apr 2015; published 10 Apr 2015
20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.010117 | OPTICS EXPRESS 10121
in the free space of the fiber resonator. Besides, based on the simulation results, the coupling
ratio was set to ~55% in achieving the zero-transmittance at the resonant peaks.
Fig. 4. (a) (Simulation) Resonant transmittance curves of the fiber resonator with different
values of net cavity attenuation and coupling ratio. (b) (Experiment) Transmittance curve (red
circle) and corresponding PDH locking signal (blue square) measured by detuning the
wavelength of a monochromatic DFB laser. Black solid line refers to the transmittance curve
fitted with −1.2 dB attenuation and 55% coupling-ratio.
In order to characterize the transmittance curve of the fiber resonator and corresponding
PDH phase-locking signal, a wavelength-tunable monochromatic distributed feedback (DFB)
laser operating at a 1560 nm wavelength range was adopted as the input light source. While
the input wavelength was detuned by an amount of 120 MHz, the transmittance intensity and
also the PDH control signal were measured as shown in Fig. 4(b). The full-width-halfmaximum (FWHM) linewidth of the transmittance curve was measured ~35 MHz, which
corresponds to the cavity finesse value of around 6.0. The PDH control signal was found to
follow exactly the derivative of the transmittance curve with the slope around the zerocrossing point reaching 1.25 V/GHz at the center of the transmittance peak. The solid black
line in Fig. 4(b) which was calculated with the coupling ratio and attenuation inside the fiber
resonator using Eq. (1) showed a good agreement with the experimental transmittance curve
(red circles).
Once the PDH phase-locking of the fiber resonator was done, the time and frequency
domain characteristics were verified. First, the pulse train of two-fold multiplied pulses
produced by the fiber resonator was monitored using an oscilloscope as shown in Fig. 5(a).
Intensity fluctuation of ~7% shown in Fig. 5(a) is thought to be attributed to the free-running
carrier-envelope offset frequency and also the frequency-jitter-to-intensity-noise conversion
[20,21]. The dispersion of the single-mode fiber inside the resonator plus other fiber sections
was managed by adding a dispersion compensating fiber (Thorlabs, DCF38). The multiplied
pulse duration was 267 fs when measured using a second-harmonic interferometric autocorrelator (Femtochrome, FR-103PD) as shown in Fig. 5(b), which was slightly broadened
from the original duration of 100 fs of the main oscillator The output power was measured to
2.9 mW when a 3.3 mW input power was incident to the fiber cavity, which corresponds to a
1.29 dB loss. This power loss was mainly attributed to the coupling efficiency of the freespace optical delay line inside the fiber cavity. The multiplication result was also monitored
using an RF-spectrum analyzer (RBW: 100 kHz, VBW: 100 kHz) as in Fig. 5(c) and 5(d),
#235511 - $15.00 USD
© 2015 OSA
Received 3 Mar 2015; revised 7 Apr 2015; accepted 7 Apr 2015; published 10 Apr 2015
20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.010117 | OPTICS EXPRESS 10122
which shows the repetition-rate-doubled harmonics with suppression of unwanted modes by
40 dB in the RF domain. The relative amplitude decrease in the 200-MHz pulses was
attributable to the limited detection bandwidth of the used photodetector (Menlosystems,
FPD510). The long-term stability of the phase-locked multiplied pulses was monitored using
a frequency counter (Pendulum, CNT91) synchronized to the Rb clock (SRS, FS727) over an
interval of 2400 s in comparison to the 2fr original pulses of the main oscillator as plotted in
Fig. 5(e), verifying no notable degradation of stability in the process of multiplication. The
long-term locking stability for both cases shows 10−12 at 10 s averaging, while the stability
was ~10−8 in the free-running state.
Fig. 5. Experimental results of fr multiplication. (a) Multiplied femtosecond pulses in the time
domain. (b) Temporal pulse duration of multiplied pulses. (c) Original RF spectrum of the
main oscillator with a 100 MHz pulse repetition rate, (d) RF spectrum of two-fold multiplied
pulses of a 200 MHz repetition rate. (e) Frequency stability of the second harmonic of the
original pulses (blue dots) locked to the Rb reference clock and two-fold multiplied pulses (red
dots).
With the aim of verifying the short-term characteristics of the repetition-rate-multiplied
pulse train, a balance cross-correlator (BCC) permitting sub-femtosecond timing
measurement was exploited [32–35]. We used a type-II phase-matched second harmonic
generation crystal which generates frequency doubled sub-pulses by providing two orthogonal
polarization pulses [35]. Balancing of the two sub-pulses’ intensities of both the forward and
backward propagation in the crystal which has polarization dependent GVD walk-off results
in a S-shape curve as shown in the inset diagram of Fig. 6. The S-shape curve quantifies the
temporal offset between the pulses under test and the reference pulses which enables precise
measuring of timing jitter. As shown in Fig. 6, the optical path difference (OPD) between the
two interferometer arms was set to 1.5 m, which corresponds to c/(2mfr) with m = 1 and fr =
200 MHz. This OPD allows for interference between two sets of pulse trains – one is the
original pulse train and the other the interleaved pulse train. The resulting BCC signal
consequently represents the relative timing jitter between the original and interleaved pulses.
In order to remove detritus timing jitters caused by other external noise sources, the BCC
signal was fed back to the cavity-length-controlling PZT inside the main oscillator. This
feedback loop locks the BCC signal to a zero voltage by controlling the pulse repetition rate
by adjusting the intra-cavity PZT. This locking control effectively compensates for the timing
jitter induced by the measurement itself not by the multiplication process. An alternative way
is controlling one of the interferometer arm length using PZT [36]. The inset diagram in Fig. 6
#235511 - $15.00 USD
© 2015 OSA
Received 3 Mar 2015; revised 7 Apr 2015; accepted 7 Apr 2015; published 10 Apr 2015
20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.010117 | OPTICS EXPRESS 10123
shows the s-shaped balanced cross-correlation signal at the given OPD of 1.5 m, indicating a
high linearity of 2.84 mV/fs around the zero-crossing point with respect to the time difference
between the reference and measurement pulses. In order to minimize the undesired timing
jitter originated from the BCC control, the locking bandwidth of the BCC control should be
set to be as low as possible [34]. Thereby, the BCC control works to compensate the
environmental change but generate insignificant level timing jitter. In our experiment, the
BCC control loop was set to have a 30 Hz-bandwidth by using a PI servo controller (Newport,
LB1005).
Fig. 6. Timing jitter measurement of interleaved pulses compared to original pulses. L: lens,
PBS: polarization beam splitter, HWP: half-wave plate, QWP: quarter- wave plate, M: mirror,
MREF (MMEA): reference (target) mirror, PD: photodetector, DM: dichroic mirror, PPKTP:
periodically poled KTiOPO4 crystal, fr: pulse repetition rate, m: multiple integer. (inset)
Balanced optical cross-correlation signal recorded by moving the reference mirror.
Fig. 7. Relative timing jitter evaluation. (a) Time trace of timing jitter recorded using a 4 kHz
sampling oscilloscope. (b) Timing jitter spectral density by Fourier transform of time trace
signal (red) and integrated timing jitter from 1 Hz to 2 kHz (black).
#235511 - $15.00 USD
© 2015 OSA
Received 3 Mar 2015; revised 7 Apr 2015; accepted 7 Apr 2015; published 10 Apr 2015
20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.010117 | OPTICS EXPRESS 10124
A time trace of the balanced cross-correlation signal under the locked status was recorded
with a 4 kHz update rate as shown in Fig. 7(a). The standard deviation of the timing jitter was
evaluated 1.65 fs. Furthermore, a frequency domain analysis was performed as shown in Fig.
7(b) by Fourier-transforming the time trace of the jitter signal. There was found no distinct
noise peaks including the EOM modulation from 1 Hz to 2 kHz due to the high PDH feedback
bandwidth. The integrated timing jitter over the bandwidth was 1.61 fs which implies that
there was no significant degradation in the timing jitter during the repetition rate
multiplication process.
4. Conclusions
We demonstrated a stable method of repetition-rate multiplication of femtosecond light pulses
by PDH phase-locking of an all-pass fiber resonator to the harmonics of the original pulses.
Long-term and also short-term stability tests performed on the doubled pulse repetition rate
revealed no significant degradation in not only the frequency stability and but also the timing
jitter. Our test result proves the proposed phase-locking scheme is an effective means of
generating higher repetition rate pulses with no significant power loss while providing a high
degree of stability. Higher-order repetition-rate multiplication to several GHz could be
realized by shortening the cavity length or using the cascaded cavity configuration.
Acknowledgments
This work was supported by the National Honor Scientist Program funded by the National
Research Foundation of Korea. Y.-J. Kim acknowledges support from the Singapore National
Research Foundation under its NRF Fellowship (NRF-NRFF2015-02).
#235511 - $15.00 USD
© 2015 OSA
Received 3 Mar 2015; revised 7 Apr 2015; accepted 7 Apr 2015; published 10 Apr 2015
20 Apr 2015 | Vol. 23, No. 8 | DOI:10.1364/OE.23.010117 | OPTICS EXPRESS 10125